ENERGY SECURITY 45057 Coping with Oil Price Volatility Robert Bacon Masami Kojima Energy Sector Management Assistance Program Copyright © 2008 The International Bank for Reconstruction and Development/The World Bank Group 1818 H Street, NW Washington, DC 20433, USA All rights reserved Produced in the United States First printing August 2008 ESMAP Reports are published to communicate the results of ESMAP's work to the development community with the least possible delay. Some sources cited in this paper may be informal documents that are not readily available. The findings, interpretations, and conclusions expressed in this paper are entirely those of the author(s) and should not be attributed in any manner to the World Bank or its affiliated organizations or to members of its Board of Executive Directors or the countries they represent. 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ENERGY SECURITY Special Report 005/08 Coping with Oil Price Volatility Robert Bacon Masami Kojima Energy Sector Management Assistance Program Contents Acknowledgments ix Abbreviations and Acronyms xi Executive Summary xiii 1 Context 1 Oil Price Trends 1 Effects of Oil Price Volatility 2 Report Structure 3 2 Measurement of Oil Price Volatility 5 Trends, Cycles, and Volatility: Measurement and Statistical Analysis 5 Statistical Analysis of Oil Prices 8 3 Statistical Analysis of U.S. Gulf Coast Prices 9 Are Crude Oil Prices Stationary? 9 Are Oil Product Prices Stationary? 10 Construction of Filtered Series 10 Volatility of Returns 11 4 Application to Prices in Developing Countries 19 Chile 19 Ghana 21 India 23 The Philippines 24 Thailand 25 Observations 27 5 Hedging 29 Role of Hedging 29 Hedging with Futures Contracts 31 Costs of Running a Hedging Program 33 Estimation of Hedge Ratios, the Efficiency of Hedging, and Returns from Hedging 35 Use of Options 39 Issues in Operating an Oil Hedging Program 41 6 Security Stocks and Price Hikes 47 Supply Disruptions 47 The Operation of a Two-Period Price-Smoothing Security Stock Scheme 50 Simulation of a Security Stock Scheme between 1986 and 2007 52 International Experience with Strategic Petroleum Reserves 56 iii iv Special Report Coping with Oil Price Volatility 7 Price-Smoothing Schemes 59 Setting a Target Price 59 Case Studies in Price Smoothing 65 Assessment 67 8 Tackling Oil Intensity and Diversification 69 Oil Share of GDP and Intensity 69 Relative Price Levels and Price Volatility 72 Energy Diversification Index and Oil Share of Primary Energy 76 Policies for Reducing Dependence on Oil 78 9 Conclusions 81 Statistical Analysis of Price Volatility 81 Hedging 83 Strategic Stocks 84 Price-Smoothing Schemes 84 Reducing the Importance of Oil Consumption 84 Annexes 1 Impact of Fiscal Parameters on Government Oil Revenue 87 2 Statistical Methods 93 3 Statistical Analysis of U.S. Gulf Coast Prices 97 4 Statistical Analysis of Developing Country Prices 115 5 Hedging Parameters 141 6 Price-Smoothing Formulae 145 Glossary 147 References 149 Boxes 5.1 Sasol's Hedging Experience 29 6.1 Experiences with Other Commodities 47 Figures 1.1 Monthly Average Spot Price of WTI Crude 1 3.1 Weekly Nominal Prices of WTI Crude and HP Filter 11 3.2 Weekly Real Prices of WTI Crude and HP Filter 11 3.3 Weekly Real Prices of Gasoline in the U.S. Gulf Coast and HP Filter 11 3.4 Returns on Weekly Real WTI Crude Prices 12 3.5 Returns on Weekly Real Gasoline Prices in theU.S. Gulf Coast 12 5.1 Spot and Futures Prices of WTI Crude 43 7.1 WTI Crude Monthly and Six-Month Moving Average Prices 61 7.2 Cumulative Cost of Regulating the Price of Crude Oil with Lagged Three- and Six-Month Moving Averages 62 7.3 Thai Oil Fund Financial Status 66 7.4 Actual and Hypothetical Diesel Prices in Thailand, January 2002­September 2007 66 8.1 Historical Oil Share of GDP for Select Countries 70 8.2 Historical Oil Intensity for Select Countries 71 8.3 Historical Oil, Gas, and Coal Prices 72 8.4 Volatility of Historical Oil and Coal Prices 74 8.5 Volatility of Historical Gas and Coal Prices 74 8.6 Historical HHDI for Select Countries 77 8.7 Historical Oil Share of Primary Energy for Select Countries 78 A1.1 Production Profile of Each Field 87 Contents v A1.2 Aggregate Production Profile of All Fields 87 A1.3 Oil Prices Used in the Calculations 88 A1.4 Production-Sharing Revenue Flow 88 A1.5 Government Revenue from First Field to Come on Stream 90 A1.6 Government Revenue from Sixth Field to Come on Stream 90 A1.7 Government Revenue from All Fields 90 A3.1 Forecast of Returns of Logarithms of WTI Crude Daily Spot Prices and Variance of Returns, April 4­November 14, 2007 104 Tables 1 Ratio of Price Increase in U.S. Dollars to Increase in Local Currency Units, January 2004­January 2008 xiv 2 Statistics on Monthly Spot Oil and Oil Product Prices xiv 3.1 ADF Test Results for WTI Crude Oil 9 3.2 ADF Test Statistics for Monthly U.S. Gulf Coast Oil Product Prices 10 3.3 Standard Deviation of Returns for Logarithms of Nominal WTI Crude and U.S. Gulf Coast Oil Product Prices 12 3.4 Variance Equality Tests for Returns for Nominal WTI Crude and U.S. Gulf Coast Oil Product Prices 14 3.5 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices 15 3.6 GARCH Analysis of Returns of Logarithms of Nominal Weekly Prices 16 3.7 GARCH of Returns of Logarithms of Nominal Monthly Prices 17 3.8 Runs on Cumulative Cycles of Nominal Prices, September 1995­March 2007 17 4.1 Difference between Percentage Price Increase in U.S. Dollars to That in Chilean Pesos 20 4.2 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Chilean Pesos 21 4.3 Cumulative Cycles of Nominal Monthly Chilean Prices, July 1999­March 2007 21 4.4 Difference between Percentage Price Increase in U.S. Dollars to That in Ghanaian Cedis 22 4.5 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Ghanaian Cedis 22 4.6 Cumulative Cycles of Nominal Monthly Ghanaian Prices, July 1999­March 2007 22 4.7 Difference between Percentage Price Increase in U.S. Dollars to That in Indian Rupees 23 4.8 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Indian Rupees 23 4.9 Cumulative Cycles of Nominal Monthly Indian Prices, July 1999­March 2007 24 4.10 Difference between Percentage Price Increase in U.S. Dollars to That in Philippine Pesos 24 4.11 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Philippine Pesos 25 4.12 Cumulative Cycles of Nominal Monthly Philippine Prices, July 1999­March 2007 25 4.13 Difference between Percentage Price Increase in U.S. Dollars to That in Thai Bahts 26 4.14 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Thai Bahts 26 4.15 Cumulative Cycles of Nominal Monthly Thai Prices, July 1999­March 2007 26 5.1 Margin Account for a Buy Hedge 34 5.2 Ex Post Risk-Minimizing Sell Hedging for WTI Crude for Various Periods Based on Monthly Prices, January 1987­March 2007 36 5.3 Optimal Three-Month Ex Post Sell Hedge for WTI Crude, January 2004­July 2005 38 5.4 Ex Post Risk-Minimizing Six-Month Sell Hedge Ratio and Hedging Efficiency for Various Crudes, February 1988­December 2006 39 5.5 Ex Post Risk-Minimizing Three-Month Sell Hedge Ratio and Hedging Efficiency for Gasoline and Heating Oil on NYMEX, January 1987­April 2007 40 5.6 European Call Options for WTI Crude on NYMEX, October 11, 2007 (US$) 41 6.1 Types of Oil Market Disruptions, 1950­2003 48 6.2 Costs of Security Stock Operations in Two-Period Case 51 6.3 Costs and Benefits of a Security Stock Scheme Operated January 1986­December 1999 53 6.4 Costs and Benefits of a Security Stock Scheme Operated January 2000­March 2007 54 7.1 Summary Volatility Statistics for Returns of Current Prices, Moving Average WTI Crude Prices, and Futures Prices, July 1986­October 2007 61 7.2 Fiscal Costs of Regulating WTI Prices through Three-Month Averaging for Different Price Bands, April 1986­October 2007 63 vi Special Report Coping with Oil Price Volatility 7.3 Standard Deviation of Returns for Oil Products Imported to Kenya Based on Various Moving Average Prices, July 1986­September 2007 64 7.4 Standard Deviation of Returns for Oil Products Imported to Ghana Based on Various Moving Average Prices, July 1986­September 2007 64 8.1 Distribution of Oil Share of GDP in 2006 70 8.2 Maximum and Minimum Oil Shares of GDP, Selected Years, 1980­2006 70 8.3 Distribution of Oil Intensity in 2006 Barrels per US$1,000 of GDP (2000 US$) 71 8.4 Maximum and Minimum Oil Intensity, Selected Years, 1980­2006 72 8.5 Fuel Price Correlation 73 8.6 Standard Deviation of Fuel Price Volatility 74 8.7 Fuel Price Volatility Correlation 75 8.8 Standard Deviation of Fuel Mix Price Volatility 75 8.9 Distribution of HHDI, 2005 76 8.10 Maximum and Minimum HHDI, 1980-2005 77 8.11 Distribution of Oil Share of Primary Energy, 2005 78 8.12 Maximum and Minimum Oil Share of Primary Energy, Selected Years, 1980-2005 79 A1.1 Description of Two Fiscal Regimes 89 A1.2 Sliding Scale Royalty and Production Sharing in Case 2 89 A1.3 Cumulative Government Revenue at Different Discount Rates (US$ million) 91 A3.1 First Month When Price Data Are Available 97 A3.2 ADF Test Statistics for WTI Crude Oil 98 A3.3 Cochrane Statistics for Nominal Crude Oil Prices 98 A3.4 ADF Test Statistics for Daily U.S. Gulf Coast Oil Product Prices 99 A3.5 ADF Test Statistics for Weekly U.S. Gulf Coast Oil Product Prices 99 A3.6 ADF Test Statistics for Monthly U.S. Gulf Coast Oil Product Prices 100 A3.7 Cochrane Statistics for Nominal Daily U.S. Gulf Coast Product Prices 101 A3.8 Cochrane Statistics for Nominal Weekly U.S. Gulf Coast Product Prices 101 A3.9 Cochrane Statistics for Nominal Monthly U.S. Gulf Coast Product Prices 101 A3.10 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices, Beginning­March 2007 102 A3.11 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices, Beginning­November 14, 2007 102 A3.12 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices, Beginning­December 1999 103 A3.13 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices, January 2000­December 2003 103 A3.14 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices, January 2004­March 2007 103 A3.15 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices, January 2004­November 14, 2007 104 A3.16 GARCH Analysis of Returns of Logarithms of Nominal Weekly Prices, Beginning­March 2007 105 A3.17 GARCH Analysis of Returns of Logarithms of Nominal Weekly Prices, Beginning­December 1999 105 A3.18 GARCH Analysis of Returns of Logarithms of Nominal Weekly Prices, January 2000­December 2003 106 A3.19 GARCH Analysis of Returns of Logarithms of Nominal Weekly Prices, January 2004­March 2007 106 A3.20 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices, Beginning­March 2007 107 A3.21 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices, Beginning­October 2007 107 A3.22 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices, June 1995­March 2007 107 A3.23 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices, Beginning­December 1999 108 Contents vii A3.24 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices, January 2000­December 2003 108 A3.25 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices, January 2000­end October 2007 108 A3.26 GARCH Analysis of Returns of Logarithms of Nominal Weekly Prices, January 1990­May 2005 109 A3.27 Runs Tests on Nominal Daily Prices, Beginning­March 2007 109 A3.28 Runs Tests on Real Daily Prices, Beginning­March 2007 109 A3.29 Runs Tests on Nominal Daily Prices, Beginning­December 1999 110 A3.30 Runs Tests on Real Daily Prices, Beginning­December 1999 110 A3.31 Runs Tests on Nominal Daily Prices, January 2000­December 2003 110 A3.32 Runs Tests on Nominal Daily Prices, January 2004­March 2007 111 A3.33 Runs Tests on Nominal Weekly Prices, Beginning­March 2007 111 A3.34 Runs Tests on Nominal Weekly Prices, Beginning­December 1999 112 A3.35 Runs Tests on Nominal Weekly Prices, January 2000­December 2003 112 A3.36 Runs Tests on Nominal Weekly Prices, January 2004­March 2007 112 A3.37 Runs Tests on Nominal Monthly Prices, Beginning­March 2007 113 A3.38 Runs Tests on Nominal Monthly Prices, Beginning­December 1999 113 A3.39 Runs Tests on Nominal Monthly Prices, January 2000­March 2007 113 A3.40 Runs Tests on Nominal Daily Prices, September 1995­March 2007 114 A3.41 Runs Tests on Nominal Weekly Prices, September 1995­March 2007 114 A3.42 Runs Tests on Nominal Monthly Prices, September 1995­March 2007 114 A4.1 First Month in the Price Data Series 115 A4.2 Period Average Prices in Chile 116 A4.3 Ratio of January 2008 Prices to January 2004 Prices in Chile 117 A4.4 Standard Deviation of Returns for Logarithms of Prices and Exchange Rate in Chile 117 A4.5 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Chilean Pesos, Beginning­March 2007 118 A4.6 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Chilean Pesos, Beginning­June 1999 118 A4.7 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Chilean Pesos, July 1999­March 2007 118 A4.8 Runs Tests on Nominal Monthly Prices in Chile, in U.S. Dollars, Beginning­March 2007 119 A4.9 Runs Tests on Nominal Monthly Prices in Chile, in Chilean Pesos, Beginning­March 2007 119 A4.10 Runs Tests on Nominal Monthly Prices in Chile, in U.S. Dollars, Beginning­June 1999 119 A4.11 Runs Tests on Nominal Monthly Prices in Chile, in Chilean Pesos, Beginning­June 1999 120 A4.12 Runs Tests on Nominal Monthly Prices in Chile, in U.S. Dollars, July 1999­March 2007 120 A4.13 Runs Tests on Nominal Monthly Prices in Chile, in Chilean Pesos, July 1999­March 2007 120 A4.14 Period Average Prices in Ghana 121 A4.15 Ratio of January 2008 Prices to January 2004 Prices in Ghana 122 A4.16 Standard Deviation of Returns for Logarithms of Prices and Exchange Rate in Ghana 122 A4.17 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Ghanaian Cedis, Beginning­March 2007 123 A4.18 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Ghanaian Cedis, Beginning­June 1999 123 A4.19 Runs Tests on Nominal Monthly Prices in Ghana, in U.S. Dollars, Beginning­March 2007 124 A4.20 Runs Tests on Nominal Monthly Prices in Ghana, in Ghanaian Cedis, Beginning­March 2007 124 A4.21 Runs Tests on Nominal Monthly Prices in Ghana, in U.S. Dollars, Beginning­June 1999 124 A4.22 Runs Tests on Nominal Monthly Prices in Ghana, in Ghanaian Cedis, Beginning­June 1999 125 A4.23 Runs Tests on Nominal Monthly Prices in Ghana, in U.S. Dollars, July 1999­March 2007 125 A4.24 Runs Tests on Nominal Monthly Prices in Ghana, in Ghanaian Cedis, July 1999­March 2007 125 A4.25 Period Average Prices in India 126 A4.26 Ratio of January 2008 Prices to January 2004 Prices in India 127 A4.27 Standard Deviation of Returns for Logarithms of Prices and Exchange Rate in India 127 A4.28 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Indian Rupees, Beginning­March 2007 128 viii Special Report Coping with Oil Price Volatility A4.29 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Indian Rupees, Beginning­June 1999 128 A4.30 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Indian Rupees, July 1999­March 2007 128 A4.31 Runs Tests on Nominal Monthly Prices in India, in U.S. Dollars, Beginning­March 2007 129 A4.32 Runs Tests on Nominal Monthly Prices in India, in Indian Rupees, Beginning­March 2007 129 A4.33 Runs Tests on Nominal Monthly Prices in India, in U.S. Dollars, Beginning­June 1999 129 A4.34 Runs Tests on Nominal Monthly Prices in India, in Indian Rupees, Beginning­June 1999 130 A4.35 Runs Tests on Nominal Monthly Prices in India, in U.S. Dollars, July 1999­March 2007 130 A4.36 Runs Tests on Nominal Monthly Prices in India, in Indian Rupees, July 1999­March 2007 130 A4.37 Period Average Prices in the Philippines 131 A4.38 Ratio of January 2008 Prices to January 2004 Prices in the Philippines 132 A4.39 Standard Deviation of Returns for Logarithms of Prices and Exchange Rate in the Philippines 132 A4.40 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Philippine Pesos, Beginning­March 2007 133 A4.41 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Philippine Pesos, Beginning­June 1999 133 A4.42 Runs Tests on Nominal Monthly Prices in Philippines, in U.S. Dollars, Beginning­March 2007 133 A4.43 Runs Tests on Nominal Monthly Prices in Philippines, in Philippine Pesos, Beginning­March 2007 134 A4.44 Runs Tests on Nominal Monthly Prices in Philippines, in U.S. Dollars, Beginning­June 1999 134 A4.45 Runs Tests on Nominal Monthly Prices in Philippines, in Philippine Pesos, Beginning­June 1999 134 A4.46 Runs Tests on Nominal Monthly Prices in Philippines, in U.S. Dollars, July 1999­March 2007 135 A4.47 Runs Tests on Nominal Monthly Prices in Philippines, in Philippine Pesos, July 1999­March 2007 135 A4.48 Period Average Prices in Thailand 136 A4.49 Ratio of January 2008 Prices to January 2004 Prices in Thailand 136 A4.50 Standard Deviation of Returns for Logarithms of Prices and Exchange Rate in Thailand 137 A4.51 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Thai Bahts, Beginning­March 2007 137 A4.52 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Thai Bahts, Beginning­June 1999 138 A4.53 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Thai Bahts, July 1999­March 2007 138 A4.54 Runs Tests on Nominal Monthly Prices in Thailand, in Thai Bahts, Beginning­March 2007 138 A4.55 Runs Tests on Nominal Monthly Prices in Thailand, in Thai Bahts, Beginning­June 1999 139 A4.56 Runs Tests on Nominal Monthly Prices in Thailand, in Thai Bahts, July 1999­March 2007 139 A5.1 Ex Post Risk-Minimizing Six-Month Hedged Return and Unhedged Return for Various Crudes, February 1988­December 2006 143 Acknowledgments This study was conducted with support from the Energy Sector Management Assistance Program (ESMAP) and the World Bank. The financial assistance provided by ESMAP's donors is gratefully acknowledged. The report was prepared by Robert Bacon and Masami Kojima of the Oil, Gas, and Mining Policy Division. The authors thank Delfin Sia Go (Office of the Chief Economist, Africa Region) and Donald Larson (Development Research Group) for providing comments as peer reviewers. Additional useful comments were provided by Silvana Tordo (Oil, Gas, and Mining Policy Division). The authors thank Nita Congress for editorial and graphics assistance and ESMAP staff for overseeing the production and dissemination of the report. ix Abbreviations and Acronyms ADF Augmented Dickey-Fuller ESMAP Energy Sector Management Assistance Program GARCH generalized autoregressive conditional heteroskedasticity GDP gross domestic product HHDI Herfindahl-Hirschman diversification index HP Hodrick-Prescott ICE Intercontinental Exchange IEA International Energy Agency IRR internal rate of return NYMEX New York Mercantile Exchange OPEC Organization of the Petroleum Exporting Countries PSA production-sharing agreement U.S. EIA U.S. Energy Information Administration WTI West Texas Intermediate Currency B Thai baht C/ Ghanaian cedi Ch$ Chilean peso K Sh Kenyan shilling = P Philippine peso R South African rand Rs Indian rupee US$ U.S. dollar xi Executive Summary Oil prices have been variable since the large price Gulf Coast between 1986 and 2007. The study period increases of the 1970s and 1980s. The wide price is divided into three subperiods, the first through fluctuations in 2007, when daily spot prices for marker end 1999, the second from 2000 to end 2003, and the crudesnearlydoubledbetweenJanuaryandNovember, third from 2004 to March 2007. In some cases, price and fluctuations by more than US$20 a barrel in early data were extended to February 2008. The analysis of 2008 reinforce the idea that oil prices are volatile. Oil is monthly prices also covers crude oil and oil products important in every economy; when its prices are high in five developing countries--Chile, Ghana, India, and volatile, governments feel compelled to intervene. the Philippines, and Thailand--converted to local Because there can be large costs associated with currency units to account for currency fluctuations in such interventions, reserve banks, central planning addition to oil price volatility. The statistical analysis institutions, and think tanks in industrial countries suggests the following: have been carrying out quantitative analyses of oil · With the exception of the first subperiod for some price volatility for a number of years. of the fuels, price levels are nonstationary--that is, This study is a sequel to Coping with Higher Oil the mean, the variance, or both were not constant Prices (Bacon and Kojima 2006) and is part of a broader over time. There are indications that shocks to assessmentofenergysecurityundertakenbytheWorld the prices have both permanent and temporary Bank. The previous report dealt with higher oil price (decaying) components. Some differences exist levels; this report focuses on fluctuations around trends between local currency and U.S. dollar prices, in oil prices. It examines measurements of oil price whereby one would be stationary but not the volatility and evaluates several different approaches to other. Somewhat surprisingly, in two cases, copingwithoilpricevolatility:hedging,securitystocks, gasoline prices in local currency were found to be price-smoothingschemes,andreducingdependenceon stationary (and hence mean-reverting) between oil including diversification. It does not deal with the 2000 and 2007, but not in U.S. dollars. impactofoilpricevolatilityoncountries'macroeconomic · The recent depreciation of the U.S. dollar relative performance or with macroeconomic policy responses; to other currencies means that the magnitude thesegenerallyhavemoretodowithcopingwithhigher of the price increase has been less severe in pricelevelsthanwithhighervolatilityperse.Thestudy many countries in which the exchange rate has examines oil price volatility largely from the point of strengthened against the dollar. An examination viewofconsumersanddoesnotcoverthemanagement of international prices converted to local currency of revenue volatility by large oil exporters. units in the five developing countries between 2004 and 2008 showed that nominal price Statistical Analysis of Crude Oil and increases were lower in local currency units Oil Product Prices in every country except Ghana. In real terms, price increases were lower in local currency in The report begins by examining daily, weekly, and all five countries (table 1). Ratios greater than monthly prices of crude oil and oil products in the U.S. unity represent the offsetting effects of nominal xiii xiv Special Report Coping with Oil Price Volatility Table 1 Europe and shows the mean of the monthly price levels, the standard deviation (the square root of Ratio of Price Increase in U.S. Dollars to Increase in the variance) of returns (the change in successive Local Currency Units, January 2004­January 2008 prices), and the standard deviation of returns Country Nominal price Real price based on logarithms of prices (which approximate fractional changes between successive prices Chile 1.19 1.23 when the changes are small, as in table 2). The Ghana 0.92 1.27a lowest volatility is observed for the period since India 1.15 1.24 2004 for crude oil and gasoil, and in the period up Philippines 1.36 1.50 to1999forgasoline(althoughthesedifferencesare not statistically significant with monthly prices). Thailand 1.18 1.21 · Tests were carried out to determine whether Source: Author calculations. historical price volatility was stationary, and, if a. Real prices only through November 2007. so, how long the reversion to the historic mean took. The volatility of daily prices tends to be and real exchange rate appreciation against the stationary, and the half-life for mean reversion dollar. ranges from 2 to about 100 days. The results with · When the variance of the volatility of daily weekly prices are less conclusive, but there are and weekly prices is compared across different two cases where price volatility is not stationary subperiods, the third subperiod is least volatile and grows without bound. Analysis of monthly for crude oil. For some oil products, the reverse prices is the least conclusive and does not yield holds: volatility is higher after 2000 than before, meaningful results for the most part, especially but it appears to decrease slightly in the third during the last subperiod. The price volatility subperiod without returning to the levels of the data are not "well behaved" for the purpose of first. Most monthly price series--arguably the statistical analysis, indicating the randomness of most important for policy consideration--do not their temporal movements. yield statistically significant results. Table 2 takes · The variance of price volatility in local currency the marker crude Brent, gasoline, and gasoil in units in the five developing countries showed Table 2 Statistics on Monthly Spot Oil and Oil Product Prices Brenta Gasoline Gasoil SD SD log SD SD log SD SD log Period Mean returns returns Mean returns returns Mean returns returns 1987­99 $18.06 $1.68 0.085 $21.94 $2.06 0.084 $22.24 $2.10 0.084 2000­03 $26.65 $2.54 0.096 $31.32 $3.27 0.107 $31.32 $2.87 0.087 2004­08b $59.01 $4.53 0.079 $66.62 $6.75 0.102 $70.83 $4.96 0.071 1987­08 $27.75 $2.68 0.086 $32.50 $3.70 0.092 $33.52 $3.06 0.083 Sources: Energy Intelligence 2008; author calculations. Note: SD = standard deviation. Prices are in U.S. dollars. a. Mean = monthly average spot prices of Brent crude; SD returns = standard deviation of differences in two consecutive monthly Brent crude prices; SD log returns = standard deviation of returns on logarithms of consecutive monthly average prices. b. January 2004 to February 2008. Executive Summary xv that currency appreciation against the dollar did A comparison of spot prices and 6-, 12-, and not reduce volatility except in Chile prior to 2000. 24-month futures contract prices for WTI crude In both nominal and real terms, local currency between 1986 and 2007 shows that futures prices were prices were the same as, or slightly more volatile lower than current spot prices more than half the than, prices denominated in U.S. dollars in all time and that the degree of underprediction of future other cases. prices on NYMEX increased with increasing contract duration. Since January 2004, futures contract prices underpredicted the actual prices three-quarters of the Hedging time or more, and 100 percent of the time in the case Hedging is a strategy intended to reduce the risk of of 24-month futures contracts. adverse price movements (future oil prices increasing These ex post findings, however, should not be for an oil purchaser, declining for an oil seller). A taken as an endorsement of the use of futures markets government of a major oil exporter may wish to hedge to mitigate the adverse effects of large price volatility. future oil revenues; a state-run transport company At any given time, futures prices are probably the may consider hedging the purchase of diesel for its best estimates of the spot price at the time of closing fleet. In the futures oil markets, a contract can be out the futures contract. Governments or their agents entered into at a known price to purchase oil in a given are unlikely to be able to make a systematically better number of months, enabling the purchaser to lock in estimate of prices in the coming months than the the future price of oil and eliminate price uncertainty. market itself. Hedging is designed to remove risk, If the price at the future date turns out to be higher not increase returns; and the ex post experience of than the futures contract price, the purchaser clearly a period of unhedged returns exceeding hedged benefits. If it is lower, the purchaser would have been returns is no gauge as to whether this will continue. better off not having entered into the contract. A seller There are several considerations to note before a of oil participates in the futures markets in the same government agency or state-run company embarks way, with the impact of the difference between actual on hedging. There are financial costs associated with and futures prices reversed. There are variants of this futures contracts and their variants--sometimes basic setup with varying degrees of sophistication requiring financing on a daily basis--even if most and cost. of these costs are eventually returned to the hedger. This study took WTI crude futures contract prices This financing requirement could lead to cash flow of varying duration on the New York Mercantile problems and could even prove to be unmanageable. Exchange (NYMEX) between 1987 and 2007, and There is a basis risk, which is the difference in price carried out an ex post analysis to calculate the between what is hedged and the crude oil or oil percentage of physical oil for sale that should be product as traded on the futures markets, arising hedged to minimize overall risk (risk-minimizing from the difference in quality and the location and hedge ratio) and the percentage reduction in the risk timing of delivery. The public typically holds the compared to not hedging (hedging efficiency), and government accountable for the success or failure of compared returns on a hedged portfolio with those a hedge program; when the hedging strategy results on an unhedged one. For a buyer, the risk-minimizing in financial losses, political support for the strategy hedge ratio and hedging efficiency tends to increase may evaporate rapidly. For some governments, the with the duration of the futures contract. Hedged lack of well-known and successful examples in and unhedged returns are closer for the short- other countries that could be studied and copied is a duration hedges; but for 24-month futures contracts, considerable drawback. Governments have hedged the unhedged return is much lower than the hedged sales or purchases at various times, but do not appear return, indicating a loss on the unhedged portfolio. to be doing so on a broad scale today. Such caution The hedging performance of gasoline and diesel on would suggest that hedging is not a simple solution NYMEX is similar. for dealing with oil price volatility. xvi Special Report Coping with Oil Price Volatility Security Stocks and Price Hikes maximumallowablemonthlysalesvolumeorthelower the ceiling trigger selling price, the greater the benefit Between 1950 and 2003, there were 24 major toconsumers.However,thecaseswiththetwogreatest disruptions to world oil supply, each lasting on benefitstoconsumersfoundstrategicstocksexhausted average about half a year and affecting about 4 percent of world supply. Security stocks can be used to help at the end of the simulation period, thereby leaving the reduce the magnitude of sharp price spikes due to country unprotected against subsequent price spikes. physical disruptions to supply. A virtual security Terminal net costs to the government were lower than stock scheme--by which no physical stocks are held during the first subperiod, in large measure because and cash is instead transferred to consumers in times the government was able to benefit from a generally of sharp price spikes--can protect consumers, but a increasing oil price by buying low and selling high. simulation in this study shows that a virtual stock will The simulation results suggest that using a fixed bemoreexpensivetothegovernmentintimesofrising set of rules for purchases and sales would limit the oil prices, which is when such a scheme is needed. effectiveness of the scheme. The trigger prices would Certain decisions need to be taken as inputs for need to be updated, as the mean price forecast changes the design of a security stock scheme to be used to significantly. The rules that were adequate during combat price spikes: (1) the nature of the price event to be ameliorated, (2) the maximum size of the stock, the first subperiod would have been inadequate after (3) the floor trigger price below which purchases 1999, because they would never have permitted any would be made if the stock is not full, (4) a ceiling purchase of stock, and the stock left over from the first trigger price above which sales from the security subperiodwouldhavebeenexhaustedbeforetheprice stock would be made, and (5) the maximum allowable increases of the second subperiod. The simulation sales volume per time period when the ceiling trigger of the second subperiod shows that it is possible to selling price is exceeded. One indicative guide for operate a security stock scheme at a relatively low the size of security stocks is the requirement by the net cost to the government even when prices follow International Energy Agency (IEA) that each member a generally rising path for much of the period. A hold stocks equivalent to at least 90 days use of net challenge is to determine beforehand when prices imports. Such stocks may be held by the government are likely to follow a rising pattern. One conventional directly,orcompaniescanbemandatedtoholdcertain amounts of stocks beyond their normal commercial tool for assessing market views of likely price trends levels, as in Japan and the Republic of Korea. is futures prices for crude oil and oil products. This study carried out a simulation of a security The simulation illustrates that, when prices stock scheme between 1986 and 2007. The years were fluctuate around a fairly constant mean, the period divided into two subperiods: the first from 1986 to end during which stocks have to be stored will be lengthy. 1999, and the second from January 2000 to March 2007. Moreover, if refilling takes place, the government will Different release criteria were applied to the two be holding stock throughout the period, except for a subperiods, with much lower floor trigger purchase few months when prices are abnormally high. Where and ceiling trigger selling prices in the first subperiod. variability around the mean is low, stocks would be Based on the release criteria, there would have been used only rarely, and the operation of security stocks just one release taking place from September to will be costly. For high-income countries, the costs November 2000 during the first subperiod. The net cost to the government would have been about three of filling and running security stocks that are rarely times the net benefit to consumers. In the second used will be affordable; for lower income countries, subperiod, several combinations of floor and ceiling the costs may be too high, and the number of days prices as well as different maximum allowable sales covered may need to be fewer than the 90 days of volumes were examined. As expected, the larger the imports mandated by the IEA. Executive Summary xvii Price-Smoothing Schemes gross domestic product (GDP) or total primary energy demand by lowering the demand for oil through Many governments have operated schemes designed energyefficiencyimprovement,demandrestraint,and to smooth the variation in domestic oil prices to diversification away from oil. The greater the amount consumers. The success of a price-smoothing scheme of oil a country consumes relative to its current GDP, can be judged on (1) the reduction in the volatility of the larger will be the consequences throughout the domestic prices; (2) the reduction, if any, in the overall economy. To that end, the study examined global level of domestic prices; and/or (3) the fiscal cost or historical trends in the following: revenue forgone. One commonly adopted approach of price-smoothing schemes is to set the domestic price · The percentage of GDP spent on oil consumption by averaging past, and possibly futures, prices over valued at the market price, both expressed in several months. An analysis of historical spot and current U.S. dollars (oil share of GDP) futures WTI crude prices shows that, as expected, · Barrels of oil consumed per unit of GDP in volatility declines with increasing averaging period. constant U.S. dollars (oil intensity) Additionally, the volatility of the target domestic · Oil consumption as a percentage of primary price based on averaging spot prices from the past energy demand, both measured in common three months is about the same as that based on energy units (oil share of primary energy) averaging spot prices during the past three months · An energy diversification index based on six and the futures contract prices during the next three energy sources (oil, gas, coal, nuclear power, months. Similar calculations in local currency in hydropower, and renewable energy) Kenya and Ghana (which experienced high levels of depreciation during the study period) show that Of the 163 countries in the sample, half spent volatility is somewhat higher than in U.S. dollars, but, more than 6 percent of their GDP on oil in 2006, and despite much larger depreciation in Ghana, there is 16 countries spent more than 15 percent of GDP. All essentially no difference between the two countries. countrieswithahighoilshareofGDPweredeveloping This study carried out a simulation of a price- countries. The oil share of GDP had generally been smoothing scheme between 1986 and 2007 using declining until the late 1990s, but has been rising this the target domestic price based on averaging WTI decade and almost universally in the last few years. crude prices over varying durations. The results About 40 percent of the countries experienced the show that, even between 1986 and 2000 when prices highest oil share of GDP in 2005 or 2006. For about were fluctuating around a reasonably constant mean, half the countries, oil intensity was at its highest in the the cumulative balance for the scheme would have early 1980s; in more than 30 percent of the countries, been negative most of the time and would have been oil intensity was at is lowest in 2006. Therefore, the consistently negative after 2000 when the negative high oil share of GDP in 2006 largely reflects high oil cumulative balance grew sharply. Allowing a band prices and not high oil intensity. around the target price--whereby the government Energy diversification could help mitigate does not adjust the domestic price as long as the the adverse effects of energy price increases and current price is within a certain percentage of the fluctuations if prices levels and price volatility of computed target price--would have reduced the different energy sources are not well correlated. The cumulative cost to the government markedly, albeit with some increases in price volatility. price gap between coal and hydrocarbons (oil and gas) has been widening since 2000, making switching to coal financially attractive. Among energy sources, Oil Intensity and Diversification spot natural gas prices in the United States have had the highest price volatility in the last two decades, and Another way of coping with oil price volatility is to the average of contract prices for natural gas imported reduce the importance of oil consumption relative to to Europe the lowest. The volatility of spot Australian xviii Special Report Coping with Oil Price Volatility coal prices was much lower than that of spot crude especially when monthly prices are tracked. Where oil prices until 2004. Since then, the volatility of these analysis suggests that oil price volatility appears two fuels has been almost the same. The correlation to grow without bound, attempts at stabilizing oil between oil price volatility and the volatility of other prices would not be successful, and even smoothing fuels has been weak. Diversification away from oil oil price fluctuations should be approached with to other fuels--even if their price volatility is not care. Under these circumstances, a policy that relies any lower--may be attractive. Weak correlation has on a systematic formula--such as formula-based interesting consequences. The price volatility of a mix price smoothing or strategic stock operation-- of 25 percent coal and 75 percent oil was lower than carries a large risk and could even become fiscally that of either oil or coal alone in 2004 to 2007. This unsustainable. illustrates that diversifying into a more volatile fuel (in Oil intensity peaked in this decade in close to this case, from 100 percent coal to 75 percent coal and one-fifth of the countries in the sample. In virtually 25 percent oil) could decrease, rather than increase, every country, the oil share of GDP has been the overall price volatility of the fuel mix. climbing in the last three years, making what was Small island nations, several small African a lesser problem a decade ago a much more serious countries, and a few other small countries are entirely concern today. The rapidly rising oil share of GDP dependent on oil for their energy. The oil share of would seem to suggest that countries apparently primary energy around the world has been generally have not been able to do enough to address what declining since the early 1980s. In 2005, a quarter now looks like a long-term issue. If oil price of countries had an oil share of energy less than volatility continues at the present level--which 25 percent. However, a third had a share larger than is a highly likely scenario--the economic effects 75 percent. More than half the countries had an energy could become substantial, unless governments are diversification index equivalent to dependence on two or fewer energy sources with equal shares. able to reduce oil use, especially in those countries with rising oil intensity. Given the difficulties Concluding Remarks of diversifying away from oil, the importance of fuel conservation through energy efficiency Statistical analysis of price volatility appears to show improvement and demand restraint measures that volatility does not follow any systematic path, cannot be overemphasized. 1 Context Oil prices have been variable since the large price Oil Price Trends increases of the 1970s and 1980s. The perception that oil prices are more volatile than those of most other Figure 1.1 provides a starting point to the analysis of commoditieshaspromptedgovernments--especially oil price behavior over the last 20 years. The graph in developing countries--to intervene in the oil shows that monthly prices of West Texas Intermediate market in various ways, including price-smoothing (WTI) crude--one of the marker crudes--have varied schemes for end users, fuel tax adjustments, price continuously, with a spike between August 1990 controls, and incentives for diversification away from and January 1991 related to the first Persian Gulf oil. While there are other commodities whose prices War, and a large run-up in prices starting at a low of are just as volatile, if not more so, oil price volatility US$19.39 a barrel in December 2001 and reaching a is considered especially deleterious because of oil's peak of US$95.39 in February 2008.2 Discounting the importance in every economy. In the transport exceptional circumstances of the first Persian Gulf sector in particular, there are no suitable substitutes War, prices had tended to fluctuate within a narrower for gasoline and diesel on a large scale. Oil price band for most of the 1990s. volatility affects the cost of freight transport, on Recent events, which have followed a period of which virtually all commodities depend, as well as relative stability, have renewed interest in oil price that of passenger transport. behavior as governments and individuals have had Quantitative studies have not necessarily to adjust their policies in an effort to cope with rapid supported the widely held belief that oil prices are more volatile than those of most other commodities. Figure 1.1 Clem (1985) found that agricultural commodity prices were the most volatile between 1975 and 1984, Monthly Average Spot Price of WTI Crude a period that included the second oil shock. More 100 WTI real recently, Regnier (2007) examined commodity prices l WTI nominal 80 between January 1945 and August 2005. The study re found that the prices of crude oil, refined oil products, 60 and natural gas were more volatile than those of arbrep 40 about 95 percent of products sold by U.S. producers. $SU20 Comparedtothepricesofotherprimarycommodities, 0 oil price volatility was found to be greater than that of `86 `88 `90 `92 `94 `96 `98 `00 `02 `04 `06 `08 60 percent of primary commodities (including farm Source: U.S. EIA 2008a. products, foods, and feeds) but less volatile than those Note: Real prices are in January 2007 U.S. dollars, adjusted using of 21 percent of primary commodities.1 the consumer price index. 1The reason these two percentages do not total 100 is that the difference in volatility for the two sets of commodities mentioned is statistically significant, which is not true for the remaining 19 percent of commodities. 2Throughout this report, real prices are defined in terms of the consumer price index in January 2007. 1 2 Special Report Coping with Oil Price Volatility changes. The history of price movements illustrates import demand, especially for oil, and this would that policy makers are faced with two separate but affect all segments of society. Volatility can exacerbate linked uncertainties. The first is the trend of prices this problem because temporary price increases above themselves; the second is the extent to which prices trend cannot be easily distinguished from the trend have varied around this trend. Even if prices had itself, especially when prices are not fluctuating moved with a smooth progression, policy makers around a nearly constant value. An increase in the would still have to take into account the change in oil import bill may force a government into action for price level and would have to adjust behavior to fear that it is permanent, while in fact it later turns substantially new circumstances and expected future out that the increase had been temporary. Thus, for price levels. The second uncertainty arises from the example, the institution of a subsidy program might large variation around the medium- to long-run be triggered by a very sharp rise in prices, but such trend in price level. Policy makers need to recognize a program cannot, from a political point of view, be that some price movements are temporary and may withdrawn easily if prices fall back to their trend. This be reversed--at least in part--but the economy is applies equally to price falls that turn out to be only affected by price movements (whether the country temporary; these can lull a government into a false is buying or selling oil or its products). The larger sense of security and cause it to take actions that it these variations, the more important it may become later regrets, such as slowing down on programs to to have a strategy to manage or cope with the price reduce energy and oil intensity. variations. Budget Surplus or Deficit Effects of Oil Price Volatility For those governments that are subsidizing domestic oil prices, the volatility of international prices is Volatile oil prices may have a number of adverse transmitted into volatility in the actual government effects on an economy. Some of these directly affect spending stream. This circumstance can lead to the economy as a whole, some affect the government difficulties in managing fiscal programs, which tend and hence the economy through the government's to be planned a year ahead and are based on estimates reactions, and some affect individual firms and of average oil price. Sudden but temporary increases consumers directly. that cannot be distinguished from permanent increases may lead a government to change its fiscal Balance of Payments policy for fear that the changes are permanent. In the face of rising oil prices, the balance of payments will worsen as the import bill rises. This effect will be Domestic Economic Output offset by any currency appreciation against the U.S. Volatile oil prices, as may be experienced in the dollar in which international oil sales are priced. At absence of price smoothing by the government, have the same time, there may be other reinforcing import been linked to lower output. There appear to be three cost increases (such as food prices) or offsetting reasons for this linkage. First, volatility tends to delay benefits from a simultaneous increase in the price of investment as firms wait to see where price levels export commodities (especially minerals) for those settle in order to justify their investment decision. countries that are net exporters. A worsening of the Second, as oil prices rise, sectors where oil use is more balance of payments may be accommodated in the intensive should see resources shift away to those short run through currency reserves or international sectors where it is less intensive, but lack of labor borrowing, but this would not be sustainable in the mobility may merely result in unemployment in the long run against persistent oil price increases, such as oil-intensive sectors as workers who are laid off do not thosethathaveoccurredsince2004.Governmentsmay readily move to other sectors. If real wages are sticky be forced to deflate the economy in order to reduce downwards (they do not fall even when demand for 1 The Context 3 labor is declining), this will also hamper intersectoral schemes, the costs of such a program will eventually adjustment. Third, constantly adjusting prices and also have to be borne by consumers. However, the outputs in response to changes in input costs leads incidence of changed expenditure (or tax) policies firms to incurs costs of adjustment, slowing short-run required to finance these budgetary costs may be responses to changing prices. This in turn leads to different from the incidence of price volatility on suboptimal output decisions, an effect that would be consumers, making a redistribution of welfare exacerbated by increasing oil price volatility. possible. This effect is most clearly seen where oil price smoothing results in large temporary subsidies Household Behavior that benefit consumers proportionately to their oil use, while the costs of the policy are borne by all Households facing volatile prices normally attempt to households through reduced fiscal spending. smooth real expenditures. Consumption smoothing is the welfare-maximizing response to fluctuations around expected income or price trajectories. However, at times of higher prices for oil (or other Report Structure important consumer goods), it may not be possible ThisstudyisasequeltotheEnergySectorManagement for households to maintain their consumption levels. Assistance Program (ESMAP) report Coping with If households need to borrow or run down savings Higher Oil Prices (Bacon and Kojima 2006) and is to maintain expenditure patterns at times of higher part of a broader assessment of energy security prices but are credit-constrained or lack assets that can undertaken by the World Bank. The previous report easily be drawn down, then they will need to reduce dealt with higher oil price levels; this report focuses consumption, which would result in a loss in welfare. on fluctuations around trends in oil price levels. It The lowest income groups may therefore be most hurt asks if the nature of oil price volatility has changed by price volatility. The share of direct and indirect in recent years and examines different policy options expenditures on oil may very well be larger for them governments may consider in response to oil price than for higher income groups, thus magnifying volatility. the adverse effects of any given swing in oil prices, The next three chapters employ statistical because their coping mechanisms are weakest. techniques to examine oil price volatility in an important reference market--the U.S. Gulf Coast--as Government Response well as in five developing countries in different Many governments have attempted to reduce the regions of the world--Chile, Ghana, India, the adverse effects of oil price volatility on the economy. Philippines, and Thailand. The report then discusses Where these policies are designed to shift risks to a several strategies designed to cope with oil price party outside the country, any costs of such a program volatility: hedging, strategic petroleum reserves, will still be borne through the budget and thus affect price-smoothing schemes, and energy conservation current or future generations of its citizens. The and diversification measures. trade-offs of such a program may be large, and the Two caveats are in order. To narrow the focus gains from reduced volatility may not be worthwhile. of the study, this report considers oil price volatility Moreover, since the total balance of payments or the primarily from the point of view of oil consumers government deficit is affected by volatility from a and oil importers. For a significant oil exporter that number of sources, focusing on reducing only the depends on oil sale receipts for much or even most of effects of volatile oil prices may provide just a partial its government revenue, oil price volatility is closely remedy. linked to revenue volatility and presents unique Where governments have attempted to shift the challenges related to government budget planning adverse effects of volatility from consumers to the and execution. This report touches upon revenue government itself through price-smoothing and other volatility in two places: 4 Special Report Coping with Oil Price Volatility · Inannex1,theimpactofvaryingfiscalparameters market. By symmetry, the case of an oil purchaser on smoothing revenue is examined. This is the reverse of that of an oil seller. examination concludes that adjusting fiscal parameters is not a good way of smoothing oil The second caveat is that the report does not revenue and that other means are likely to be consider the use of macro-level policies to cope with needed to manage revenue volatility. the impact of oil price volatility on the macroeconomy · Chapter 5 discusses hedging. Hedging can (which in any event have to do largely with coping provide greater certainty to prices received for with higher oil prices rather than higher oil price selling oil, which can help manage the budget volatility), nor the measurement of the impact of oil process for major oil exporters. For ease of price volatility on the macroeconomic performance of exposition, the analysis in chapter 5 focuses on oil countries. The report is focused primarily on sector- producers that sell crude oil on the international level issues. 2 Measurement of Oil Price Volatility In examining oil price volatility--the focus of this there is a large technical literature on various aspects and the next two chapters--this study extends the of the subject. This section does not aim to provide a analysis carried out by other researchers by including review of this literature, but rather to introduce the recent price data and applying widely used statistical particular approaches and statistical tools used in techniques to prices in local currency in developing this report. countries. The recent history of oil prices raises a number of questions that need to be answered before Prices and Time Interval of policies to cope with volatility can be analyzed: Measurement Oil price data are available as daily quotations and · Is there a trend or pattern in the development of weekly, monthly, and annual averages. The level and oil prices over time, or are they random? fluctuations of these different measures are relevant · How much variability is there around any trend to different agents for different purposes. Oil traders in prices that can be identified, and has the (which can include large exporting countries) will variability changed over time? need to follow daily movements; at the other extreme, · Is the variability similar for series measured over governments making annual budget plans will relate different time intervals (daily, weekly, monthly), these to annual prices or to price changes. In between, for prices expressed in nominal and real terms, smoothing schemes--by which the government and for prices of crude oil and different oil regulates prices to consumers--are usually updated products? monthly, or on occasion fortnightly, to ensure that · In non-U.S. markets, how does the variability of international price changes are tracked to some oil and oil product prices behave in local currency extent by domestic prices. The statistical analysis terms? of this report focuses primarily on fluctuations at monthly or shorter intervals because there are too Before moving to analysis of these issues, this few annual observations available to carry out any chapter presents a brief description of the standard robust statistical analysis. statistical methodology used to address questions of this nature. Only those concepts essential for Prices and Stationarity understanding the rest of the main report are given Statisticalanalysisofthebehaviorofpricesdependson below. Further details are provided in annex 2. whether they are stationary. If the mean and variance of a series remain constant as more data are added, Trends, Cycles, and Volatility: thentheseriesisstationaryand conventional statistical Measurement and Statistical Analysis models are appropriate. A series of prices that grow without bound in time is not stationary, and, in this The statistical behavior of oil prices has received a case, the mean is not constant. Even if a price series great deal of attention over the years as has that of has a constant mean, if fluctuations around that mean many other commodities and financial assets, and become increasingly larger with time, the series is 5 6 Special Report Coping with Oil Price Volatility again not stationary: in this case, because the variance, that prices always return toward the same value in which is a measure of volatility, is not constant. A price time--would be inadequate to describe the general series can be fitted by a trend, but, even having made behavior of oil prices since that date. A standard this adjustment, the variance may still not be constant technique for constructing a trend in prices without over time. An important example of nonstationarity using a formal model based on supply and demand occurs when a series follows a so-called random to explain the sequence of prices is to use a filter that walk. In this case, each successive price is equal to smooths price fluctuations. The Hodrick-Prescott the previous price--that is, multiplied by a coefficient (HP) filter creates a series whose period-by-period equal to one (unity)--plus a new random shock, so changes are fairly smooth, while staying close to that after a number of time periods k the price is equal the actual data. The differences between the filtered to the price k periods before plus the sum of k random series and the actual data--more specifically, actual variables. A price series exhibiting this behavior has data minus filtered series--are referred to as the cycle a variance that tends to grow over time. Series where component of the data, although they may not contain the current price is equal to the previous price plus any obvious regular cyclical pattern. other factors are said to exhibit a unit root. If the series does not have a unit root, the impact of the previous Establishing a Series for Volatility price on the current price is less than unity, and the Theanalysisofthevolatilityofapriceseriesisbasedon variance tends to a constant value. the returns of the data, which are the period-by-period The standard test for the presence of a unit root changes in the data. For example, returns on monthly is the Augmented Dickey-Fuller (ADF) test, which prices are the differences between prices in two can allow for a mean and a linear trend in the price consecutive months. In this study, as in many others, series, as well as a number of previous (lagged) values. the preferred measure of the return is the difference in This test was carried out on all the series used in this the logarithms of prices over two consecutive periods. report. As detailed in annex 2, standard ADF tests Such a calculation gives an approximate percentage can have very little power under certain conditions. change in price when the magnitude of variation To provide more evidence on whether variances are from one period to the next is small compared to the constant over time, variance ratio tests introduced by price levels themselves. Differences in logarithms Cochrane (1988) were also carried out. are conventionally preferred because they are dimensionless: thus, the statistical measures used to Establishing Series Trend Values summarize their behavior (such as the variance) can It is important to establish the value or trend to which be compared directly with those of other series where prices tend to revert. In the simplest case where there the price data may be given in different units. is no trend, the mean of the series is the value to which The historical volatility of a series is based on the prices tend to revert and can serve as the best forecast sequenceofsquaredreturns,whileasummarymeasure of future prices. As is evident from figure 1.1, it is of the volatility over a period is either the variance or unlikely that the mean price has stayed constant for thestandarddeviation(thesquarerootofthevariance) the whole of the last 20 years. Models with structural of the series of returns. This forms a measure of the change can allow for one or more changes in the mean degree of unpredictability of prices, which enters into at various specified dates relating to well-known and policies designed to cope with volatility. understood external events that explain why the When a trend can be fitted to the price level, general level of prices shifted at certain times. Tests some of the period-to-period changes are due to the of equality of means for subsamples (containing price increment in the trend. An alternative measure of data from different time periods) can be carried out volatility is based on cycle returns from the HP filter. A to check if the mean has shifted over time. cycle return is the change in the differences between The movement of the price level since 2000 actual and filtered values (which form a trend curve indicatesthatamean-reversionmodel--onepostulating for the price level). The nearer the change in filter 2 Measurement of Oil Price Volatility 7 values are to zero, the closer will be the cycle returns An equation with only the first term is denoted by to the returns in the foregoing paragraph. GARCH(1,0); that with both terms present is denoted by GARCH(1,1). A Wald test is used to check for Testing for Changes in Volatility nonstationarity of the conditional variances. If the process is stationary, an estimate of the half-life of the One of the study's central concerns was whether duration of a shock to the variance can be estimated volatilityhasincreasedorshowsanysystematicpattern from the GARCH equation. that would need to be taken into account in designing policies to cope with it. Several statistical tools can be used to investigate the question of whether volatility Testing for Sequential Patterns in Returns is itself random or exhibits some underlying pattern. The simplest technique is to split the returns data In designing policies to cope with the volatility of into subperiods and compare the variance for the oil prices, agents may also be concerned with the subperiods.Thestandardtestforcheckingifvariances temporal patterns of returns. A series of positive fromtwodifferentperiodsarenotstatisticallydifferent returns with a given variance (price levels going (that is, are essentially the same) is the F-test. steadily up) may be more difficult to accommodate A substantial body of literature is devoted to the than a series of positive and negative returns (price question of whether the variances of returns tend to be levels moving up and down) with the same variance. clustered. In such a case, a large squared return is likely Tests for sequential patterns can be used to check this to be followed by another large squared return (even characteristic of the prices. if the actual returns are of opposite signs) and a small Because there are periods when prices move value by another small value. If this occurs, a sudden mainly upward, returns based on prices themselves increase in volatility due to an external event will could well show a sequence of largely positive be followed by high volatility for several periods-- values. Distinguishing longer term sequences of shocks to the variance do not die out rapidly. The price increases from temporary sequences around model used to test this hypothesis is the generalized the trend thus becomes important. For this purpose, autoregressive conditional heteroskedasticity tests should be based on cycles, which have removed (GARCH) model, described in annex 2. The period-by- the filtered trend from the data. period variances themselves could be nonstationary, The Wald-Wolfowitz test focuses on the signs of showing no tendency to return to a constant value. successive returns; more specifically, on runs. A run If variances are nonstationary, measures of volatility is a consecutive sequence of values with the same based on the variances themselves would tend to sign (positive or negative). For example, the sequence [+ +---+] commences with a run of two positive exhibit increasing values over time, and the best signs, followed by a run of three negative signs, and predictor of future volatility (as measured by the concludes with a run of one positive sign. There variance)wouldbethemostrecentvalue.TheGARCH are three runs in the sample of six observations. formulation used in this study consists of up to two Because the mean cycle as fitted by the HP filter is, terms in the conditional variance equation (conditional by virtue of the calculation procedures used, zero, because the equation for the one-period-ahead the set of sequences of positive and negative runs forecast variance is based on past information): should be random. In a given sample, too large a · News about volatility from the previous period number of runs would indicate constant switching (previous day, week, or month, depending on the of sign, pointing to nonrandom behavior; a very low time aggregation for the price series) number of runs would point to long duration at the · The forecast variance from the previous period same sign, which would again suggest nonrandom behavior. The first term, called ARCH, is always present; A descriptive statistic that can be used in while the second, called GARCH, may be omitted. conjunction with investigating the patterns of runs is 8 Special Report Coping with Oil Price Volatility the distribution of sojourns of a series, which are useful time aggregates and time periods. All the tests were in evaluating price-smoothing schemes. Starting at carried out using data up to the end of March 2007. the beginning of the sample period, successive cycle GARCH analysis was repeated using data through values can be cumulated to give a new series. Since November 14, 2007, and equality of means tests the mean cycle is zero, the final value of the cumulated were repeated through the end of December 2007, cycle series will also be around zero. However, the to compare the results. In addition, out-of-sample cumulated series will have periods when it remains testing was performed using price data between positive before going back to a negative value, and April and November 2007. Extrapolation beyond other periods when it remains negative. The period March 2007 enables comparison of model predictions during which it remains the same sign is a sojourn. with actual price movements and assessment of the The distribution of the lengths of sojourns has a predictability of the statistical models. relation to the arc-sine law, as analyzed by Feller All statistical analysis in this study was carried (1950) and utilized by van Marrewijk and de Vries out in Eviews. In chapter 3, prices of crude and oil (1990). The arc-sine law indicates that reversions to products on the U.S. Gulf Coast are studied in detail. the origin of a cumulated series based on random, The price information is available on a daily, weekly, equally probable events are surprisingly infrequent. monthly, and annual basis from 1986 (later for oil This means that sojourns can be lengthy, which has products) to date. Annual prices were not examined implications for policy makers contemplating price- because there were too few annual observations in smoothing schemes (discussed in chapter 6). the period in question to be used for formal statistical analysis. In chapter 4, monthly prices in northwestern Statistical Analysis of Oil Prices Europe, the Persian Gulf, Singapore, the U.S. Gulf Coast, and Africa (for crude) are examined in U.S. The statistical testing documented in this report was dollars and in the local currencies of five developing carried out on a number of time series and on various countries. 3 Statistical Analysis of U.S. Gulf Coast Prices Statistical tests were carried out for the whole of reversion). Tests on the crude oil price series were the period as well as for three subperiods: (1) from followed by similar tests on the oil product prices. January 1986 (or later for oil products) to the end of The study then conducted GARCH analysis, runs 1999, (2) from the beginning of 2000 to the end of tests, and other statistical tests described in chapter 2 2003, and (3) from the beginning of 2004 to March to examine volatility. 2007. The first subperiod, which includes the first Persian Gulf War, covers a period of fairly stable Are Crude Oil Prices Stationary? price behavior barring the war. The second reflects a transition period in which prices were less stable but An ADF test was applied at a one-sided 5 percent did not exhibit a steadily increasing trend. The third confidence level to nominal and real crude oil prices. corresponds to the recent past during which, up to The results are shown in table 3.1 for WTI crude. July 2006, prices fluctuated around a rising trend, The null hypothesis was that the price series has a followed by a downward trend of a few months, and, unit root and is thus not stationary. If the ADF test since January 2007, another rising trend. These periods statistic is larger than the critical value (shown for are different from those identified by Lee and Zyren 5 percent), then the null hypothesis holds and prices (2007), who divided the data between 1990 and 2005 are not stationary--the mean, the variance, or both into four subperiods, the last one of which began in grow without bound over time. March 1999, when the Organization of Petroleum In all cases except the first subperiod, the nominal Exporting Countries (OPEC) changed its pricing prices are consistent with there being a unit root. Real strategy. The initial statistical tests investigated and nominal prices yielded similar results. During whether crude oil and oil product prices on the U.S. the first subperiod, with the exception of weekly Gulf Coast were stationary (thereby following mean nominal prices, prices appeared stationary. Data Table 3.1 ADF Test Results for WTI Crude Oil Jan. 1986­ Jan. 1986­ Jan. 2000­ Jan. 2004­ Averaging period Mar. 2007 Dec. 1999 Dec. 2003 Mar. 2007 Daily, nominal Not stationary Stationary Not stationary Not stationary Daily, real Not stationary Stationary Not stationary Not stationary Weekly, nominal Not stationary Not stationary Not stationary Not stationary Weekly, real Not stationary Stationary Not stationary Not stationary Monthly, nominal Not stationary Stationary Not stationary Not stationary Monthly, real Not stationary Stationary Not stationary Not stationary Source: Author calculations. 9 10 Special Report Coping with Oil Price Volatility are not presented for other time intervals since the component of liquefied petroleum gas) are consistent results for crude oil indicate that the degree of time with the price series being nonstationary, with the aggregation does not markedly change the picture on exception of nominal residual fuel oil prices. the presence of a unit root in the oil markets. Construction of Filtered Series Are Oil Product Prices Stationary? The data on crude oil prices indicate the presence of ADF tests were applied to nominal and real daily, a notable trend at the end of the period considered. weekly, and monthly oil product prices. The results Rather than create arbitrary subperiods, which still for monthly prices are shown in table 3.2; detailed would not produce trendless data in each, a Hodrick- results for monthly prices--as well as for daily and Prescott filter was used to produce a smoothly weekly prices--are given in annex 3. The results for evolving trend. Such a trend may correspond to a oil product prices are largely similar to those for crude forecast of the trend in prices made by an agent in oil prices. There is again little difference in behavior in the market (see Ash and others 2002). Filtered data nominal versus real terms. With the exception of the are shown in figure 3.1 using nominal weekly prices. first subperiod, oil product prices, whether nominal The general shapes of filters for daily and monthly or real, are mostly nonstationary. Time averaging was prices are similar. The filter method used requires foundtoaffecttheresultsforgasoline.Weeklygasoline that the data for the period of the first Persian Gulf prices are stationary in every subperiod, which is not War be included. The results reveal a fairly constant true for either daily or monthly average prices. In the price level during the late 1980s and the 1990s, with a first subperiod, both heating oil and jet kerosene are steady upward climb since 2002. stationary when weekly and monthly average prices Figure 3.2 shows the same results in real terms. are considered; for the entire period, the statistics for They show a fall in trend prices until the end of the diesel, residual fuel oil, and propane (an important 1990s, with a steep trend increase thereafter. The Table 3.2 ADF Test Statistics for Monthly U.S. Gulf Coast Oil Product Prices Beginning­ Beginning­ Jan. 2000­ Jan. 2004­ Fuel Mar. 2007 Dec. 1999 Dec. 2003 Mar. 2007 Gasoline, nominal Not stationary Not stationary Not stationary Not stationary Diesel, nominal Not stationary Not stationary Not stationary Not stationary Heating oil, nominal Not stationary Stationary Not stationary Not stationary Jet kerosene, nominal Not stationary Stationary Not stationary Not stationary Residual fuel oil, nominal Not stationary Not stationary Not stationary Not stationary Propane, nominal Not stationary Not stationary Not stationary Not stationarya Gasoline, real Not stationary Not stationary Not stationary Not stationary Diesel, real Not stationary Not stationary Not stationary Not stationary Heating oil, real Not stationary Stationary Not stationary Not stationary Jet kerosene, real Not stationary Stationary Not stationary Not stationary Residual fuel oil, real Not stationary Not stationary Not stationary Not stationary Propane, real Not stationary Not stationary Not stationary Not stationary Source: Author calculations. a. The null hypothesis narrowly escapes being rejected at 5 percent. 3 Statistical Analysis of U.S. Gulf Coast Prices 11 Figure 3.1 Figure 3.3 Weekly Nominal Prices of WTI Crude and HP Filter Weekly Real Prices of Gasoline in the U.S. Gulf Coast and HP Filter 120 WTI 120 100 Filter Gasoline l 100 Filter 80 arreb l 80 60 per arreb $ 60 40 US per 40 20 US$ 20 0 1986 1991 1996 2001 2006 0 1986 1991 1996 2001 2006 Sources: WTI crude prices from U.S. EIA 2008a; author calculations. Sources: Regular gasoline prices from U.S. EIA 2008a; author calculations. Figure 3.2 Weekly Real Prices of WTI Crude and HP Filter Volatility of Returns Returnsdata,whichformthebasisofthemeasurement 100 WTI Filter of volatility of a price series, are calculated in two 80 ways. barrel 60 · Basicreturnsarecalculatedasthefirstdifferencesof per 40 prices (price at period [N + 1] - price at period N). US$ · Cycle returns are the first differences of cycles 20 (actual series - filtered series). 0 1986 1991 1996 2001 2006 Returns on weekly WTI crude and gasoline Sources: WTI crude prices from U.S. EIA 2008a; author prices in real terms are shown in figures 3.4 and 3.5, calculations. respectively. For the most part, returns and cycle returns track each other closely: there are only four trend is steep, and its rise in both real and nominal datapointsforwhichthedifferencebetweenthereturn terms is similar. and the cycle return is more than US$0.40 per barrel. The filtered series for gasoline is shown in real All the graphs of returns show a few observations terms in figure 3.3. Other fuel prices and nominal where there were extremely large changes from prices show trends similar to those for crude and week to week. Changes of more than 20 percent have gasoline. occurred for all products and for crude; for gasoline, Examination of the actual data and the filtered residual fuel oil, and propane, there are weekly series reveals that there is a close correlation between changes of more than 30 percent. the different series, and that all exhibit similar trend The standard deviation of the returns series behavior. A feature of the product prices not existing serves as a measure of the average volatility of that in the crude prices was the exceedingly sharp spike series during the measurement period. Table 3.3 in product prices in the first week of September presents the standard deviations for returns (based 2005. In that week, gasoline reached US$110 a barrel, on logarithms of prices) on nominal crude and while crude reached a peak for that year of US$68 a product prices for the whole period and the three barrel. subperiods. As long as the standard deviations 12 Special Report Coping with Oil Price Volatility Figure 3.4 Figure 3.5 Returns on Weekly Real WTI Crude Prices Returns on Weekly Real Gasoline Prices in the U.S. Gulf Coast 10 8 35 6 30 4 25 20 2 15 barrel 0 10 5 per -2 barrel -4 0 per -5 US$ -6 -10 -8 US$-15 -10 -20 1986 1990 1994 1998 2002 2006 -25 -30 1986 1990 1994 1998 2002 2006 Sources: WTI crude prices from U.S. EIA 2008a; author calculations. Sources: Regular gasoline prices from U.S. EIA 2008a; author calculations. Table 3.3 Standard Deviation of Returns for Logarithms of Nominal WTI Crude and U.S. Gulf Coast Oil Product Prices Beginning­ Beginning­ Jan. 2000­ Jan. 2004­ Fuel Mar. 2007 Dec. 1999 Dec. 2003 Mar. 2007a WTI crude, daily 0.025 0.026 0.027 0.021 (0.021) Gasoline, daily 0.029 0.025 0.034 0.035 (0.033) Jet kerosene, daily 0.027 0.025 0.028 0.030 (0.028) Heating oil, daily 0.026 0.025 0.029 0.027 (0.026) Diesel, daily 0.027 0.023 0.028 0.031 (0.029) Residual fuel oil, daily 0.018 0.014 0.021 0.020 (0.019) Propane, daily 0.025 0.020 0.032 0.024 (0.022) WTI crude, weekly 0.043 0.044 0.046 0.036 (0.035) Gasoline, weekly 0.052 0.046 0.059 0.066 (0.063) Jet kerosene, weekly 0.047 0.043 0.050 0.052 (0.049) Heating oil, weekly 0.044 0.042 0.050 0.045 (0.043) Diesel, weekly 0.046 0.040 0.048 0.050 (0.047) Residual fuel oil, weekly 0.043 0.038 0.051 0.043 (0.041) Propane, weekly 0.048 0.037 0.064 0.047 (0.043) WTI crude, monthly 0.084 0.087 0.082 0.074 (0.071) Gasoline, monthly 0.106 0.095 0.124 0.125 (0.117) Jet kerosene, monthly 0.091 0.089 0.089 0.099 (0.091) Heating oil, monthly 0.085 0.083 0.090 0.086 (0.080) Diesel, monthly 0.086 0.078 0.089 0.094 (0.087) Residual fuel oil, monthly 0.094 0.093 0.098 0.093 (0.090) Propane, monthly 0.090 0.074 0.119 0.087 (0.079) Source: Author calculations. a. Standard deviations for January 2004 to December 2007 are shown in parentheses. 3 Statistical Analysis of U.S. Gulf Coast Prices 13 are small, multiplying them by 100 when taking The variance equality tests for daily and weekly logarithms of prices gives the percentage change prices indicate that volatility is higher after 2000 than from period to period. The standard deviations of before for all oil products, but volatility appears to returns based on real prices are almost identical to decrease slightly in the period from the beginning of those for nominal returns and are thus not shown. 2004, without returning to the levels before 2000. One The standard deviations are also calculated for the exception is crude oil, for which the price volatility period January 2004 to December 2007 (shown in before 2000 is greater than in the subsequent years. parentheses in the last column of table 3.3) as a check This change in the variance of the returns points to on whether volatility increased because of the large the possibility that the pattern of returns does not increase in prices during the latter half of 2007. The simply relate to a permanent structural change, as standard deviations were slightly smaller when the is implicit in the use of a variance ratio test, but is price series was extended to the end of 2007. more systematic. Several studies on oil price returns, Most oil products had an average volatility of including Wickham (1996) and Kuper (2002), have between 4 and 5 percent, with gasoline exhibiting found evidence that there is clustering of volatility. the greatest volatility and crude oil the least. The Large returns (whether positive or negative) tend to first subperiod shows the lowest volatility, with a be followed by large returns, and small values tend substantial increase in the second subperiod for all to be followed by small values. products. The most recent subperiod shows lower The foregoing suggests that shocks to the variance volatility in percentage terms than the second or the of returns persist rather than rapidly die down. A first for several products and for crude; this effect GARCH formulation was used to test whether the was more marked when the data set was extended variance of returns is stationary and if price levels until the end of 2007. Gasoline prices are the most eventually revert back to a mean and, if they do, over volatile, showing an average daily, weekly, and what time period. The GARCH formulation tests an monthly price variation of 3.5, 6.6, and 12.5 percent, equation specification for the mean of the return series respectively. (in logarithms) and an equation for the conditional Since an important consideration in analyzing the variance of the returns. The first equation for the volatility of oil prices is their degree of constancy over mean, called the conditional mean equation, relates time, a series of F-tests for constant variance across the return to a constant and several lagged values, subperiods was carried out. The results are shown while the conditional variance equation utilizes in table 3.4 for daily, weekly, and monthly prices. a GARCH(1,1) or GARCH(1,0) formulation. Price The tests on daily and weekly data indicate that the volatility is classified based on GARCH test results returns are more variable in the second subperiod as follows: than in the first for every oil product. However, crude variability is not significantly different between · Category A: The conditional variance, and hence the first and second subperiods. Daily prices show price volatility, is not stationary but grows over greater variance in the third subperiod than for the time without bound. first for every fuel, but this trend is not observed for · Category B: The conditional variance is stationary, heating and residual fuel oil when weekly prices are and the half-life for mean reversion can be examined. Comparing monthly prices in the third calculated. subperiod to those in the second or first reveals that · Category C: No statistically significant equations in no case are the recent returns significantly more can be found, suggesting that the conditional variable than in the first two periods; the returns for variance may be constant. gasoline and propane are more variable in the second · Category D: Statistically significant equations can subperiod than the first. Extending the price series to be found but fail to meet one or more criteria: one the end of 2007 did not change statistical significance or more coefficients in the conditional variance or conclusions. equation have the wrong (negative) sign, or 14 Special Report Coping with Oil Price Volatility Table 3.4 Variance Equality Tests for Returns for Nominal WTI Crude and U.S. Gulf Coast Oil Product Prices Averaging period Fuel type Subperiod 1/2 Subperiod 2/3 Subperiod 1/3 WTI crude 0.92 1.63 (1.72) 1.50 (1.59) Gasoline 0.56 0.95 (1.03) 0.54 (0.58) Jet kerosene 0.77 0.91 (1.03) 0.70 (0.80) Daily Heating oil 0.75 1.14 (1.26) 0.86 (0.95) Diesel 0.67 0.81 (0.90) 0.54 (0.60) Residual fuel oil 0.45 1.10 (1.19) 0.50 (0.54) Propane 0.40 1.77 (2.02) 0.70 (0.80) WTI crude 0.92 1.69 (1.76) 1.55 (1.61) Gasoline 0.59 0.81 (0.90) 0.48 (0.53) Jet kerosene 0.74 0.92 (1.07) 0.68 (0.79) Weekly Heating oil 0.71 1.21 (1.38) 0.86 (0.98) Diesel 0.67 0.92 (1.05) 0.61 (0.70) Residual fuel oil 0.54 1.43 (1.57) 0.78 (0.85) Propane 0.33 1.87 (2.18) 0.62 (0.72) WTI crude 1.13 1.23 (1.31) 1.40 (1.49) Gasoline 0.59 1.00 (1.13) 0.58 (0.66) Jet kerosene 1.01 0.81 (0.95) 0.82 (0.96) Monthly Heating oil 0.86 1.10 (1.25) 0.94 (1.07) Diesel 0.77 0.91 (1.06) 0.70 (0.81) Residual fuel oil 0.90 1.12 (1.21) 1.01 (1.08) Propane 0.38 1.84 (2.24) 0.71 (0.86) Sources: Prices from U.S. EIA 2008a; author calculations. Note: Subperiod 1 is from the beginning of the price data series to end of 1999, subperiod 2 is from the beginning of 2000 to end of 2003, and subperiod 3 is from the beginning of 2004 to end of March 2007. Subperiod 1/2 is the ratio of the variance of returns in subperiod 1 to that in subperiod 2, and so on. Ratios that are different from unity using a two-sided test at 2.5 percent are in bold. Results for January 2004 to December 2007 are shown in parentheses. there is serial correlation in the conditional mean for mean reversion, stabilizing or smoothing prices equation,typicallybecauseofomittedvariables.In could be costly, and alternative ways of mitigating oil this case, the conditional variance is unlikely to be price volatility may have to be found. constant, but it is not possible to determine how GARCH modeling was carried out using nominal the variance changes over time. daily, weekly, and monthly prices. The analysis enabled determination of whether historical oil price The above categories of results carry policy volatility has exhibited stationarity and, if so, how implications. If oil price volatility is found to grow long the reversion to the historic mean takes. The without bound, attempts at stabilizing oil prices results show that the explanatory power of GARCH would not be successful. Even smoothing oil price modeling is, on the whole, weak. Many data series are fluctuations should be approached with care. If oil not "well behaved," in that eliminating statistically price volatility is stationary but has a long half-life insignificant coefficients one by one sometimes 3 Statistical Analysis of U.S. Gulf Coast Prices 15 leads to the statistical significance of the remaining persistence of shocks to the variance is low for crude coefficients varying widely from one equation oil, gasoline, residual fuel oil, and propane in the specification to the next. This problem becomes second subperiod, suggesting little clustering of daily pronounced with decreasing sample size (for example, price volatility. In several cases, the sum of the ARCH with monthly data or data from a subperiod). The and GARCH terms is near unity, and even small systematic, predictable component of the variance changes in this sum from subperiod to subperiod (calculated from the conditional variance equation) produce large changes in the estimate of the half-life has a weak correlation with historical variance and of shocks. As annex 3 shows, these results remain makes only a small contribution to the overall price essentially the same when the data are extended to volatility at each point in time in every case. include prices to November 14, 2007. The results for daily prices are shown in table 3.5. Also shown in annex 3 is out-of-sample testing For the entire time period, the variance equation using the equations derived for WTI crude from includes a time-trend term with a positive coefficient, table 3.5. Model predictions are compared with which means that the constant term (the intercept) actual prices between the beginning of April and in the conditional variance equation increases with November 14, 2007. The model predicts that the time. The conditional variance is stationary and has conditional variance would nearly double during this a half-life of 101 days or shorter in all cases, except for period, but statistical analysis of the results shows WTI crude in the last subperiod, where it is found to that the greatest difference by far between predicted grow without bound. Annex 3 provides more detailed and actual returns is due to the difference between results, including several cases in which GARCH(1,0) the variances of the forecast and the actual price and GARCH(1,1) give seemingly valid results but with return series. GARCH(1,0) giving a markedly shorter half-life. The results for weekly prices are given in table 3.6. The results of the estimates suggest that there The correlation with the results based on daily prices is a substantial degree of persistence in shocks is not particularly strong, and there are several cases to the variance of returns when the entire period where an equation that is statistically significant is considered. This phenomenon is particularly and that met other criteria--that is, those falling marked for crude oil and gasoline; the results are under either category A or B--could be found with less pronounced for the subperiods. In particular, the daily prices but not with weekly average prices. Table 3.5 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices Parameter WTI Gasoline Diesel Heating oil Jet kerosene Residual fuel oil Propane Beginning­Mar. 2007 B B B B D Ba B Half-life (days) 87 101 18 21 n.a. 2 63 Beginning­Dec. 1999 D B B B D Ba D Half-life (days) n.a. 44 25 24 n.a. 0.9 n.a. Jan. 2000­Dec. 2003 B Ba B B B Ba B Half-life (days) 3 2 12 11 19 3 7 Jan. 2004­Mar. 2007 A B B B B Ba B Half-life (days) n.a. 15 10 12 16 2 5 Source: Author calculations. Note: n.a. = not applicable. Results are classified into the four categories defined on p. 13. a. The results using a GARCH(1,0) formulation giving a shorter half-life are given in annex 3. 16 Special Report Coping with Oil Price Volatility Table 3.6 GARCH Analysis of Returns of Logarithms of Nominal Weekly Prices Parameter WTI Gasoline Diesel Heating oil Jet kerosene Residual fuel oil Propane Beginning­Mar. 2007 B B B B B Ba Aa Half-life (weeks) 12 10 3 6 8 6 n.a. Beginning­Dec. 1999 B B C B B B Ba Half-life (weeks) 13 13 n.a. 7 9 0.6 1 Jan. 2000­Dec. 2003 D C B B B B Ba Half-life (weeks) n.a. n.a. 0.4 0.3 0.4 7 1 Jan. 2004­Mar. 2007 C B D C B Aa Ba Half-life (weeks) n.a. 1 n.a. n.a. 5 n.a. 4 Source: Author calculations. Note: n.a. = not applicable. Results are classified into the four categories defined on p. 13. a. Results using a GARCH(1,0) formulation--where the half-life was found to be finite (for category A) or shorter (for category B)--are given in annex 3. This difference is especially pronounced for the last equation. The authors attributed this to the new subperiod, where no satisfactory equation could be pricing policy introduced by OPEC in March 1999. found for weekly prices of WTI crude, diesel, and Inclusion of a variable for OPEC spare capacity heating oil, but equations that appear satisfactory did not yield statistically significant results. could be identified with daily prices. More detailed results (given in annex 3) show that there are several Most monthly price series fall under category D: cases where GARCH(1,0) and GARCH(1,1) give no statistically significant and valid equations could seemingly valid results, but with the GARCH(1,0) be found, which may suggest that averaging prices formulation giving a stationary conditional variance removes much of the systematic dynamics. If so, it and GARCH(1,1) giving a conditional variance that would be difficult to establish how variable price grows without bound. returns are and whether there is clustering--which The most extensive analysis was conducted on in turn would make it difficult for governments to monthly prices; this was in part for comparison with optimize policy responses. As with daily prices, the analysis of monthly oil and product prices in repeating the GARCH analysis using data through different regions of the world presented in chapter 4. October 2007 returned essentially the same results Results from a total of six time periods are given in (see annex 3). table 3.7. Two additional time periods are included: The results of runs tests are briefly summarized in table 3.8, with additional results given in annex 3. · June1995toMarch2007,asubperiodduringwhich For comparison with cycle returns, logarithms are not data are available for all the fuels. This subperiod taken in runs tests. The period from September 1995 was selected to see how much of the difference to March 2007 was selected, because continuous amongfuelsfortheentireperiodisduetodifferent price information is available for all fuels beginning durations of data availability. in September 1995. Table 3.8 gives the percentage of · April 1999 to March 2007, which was selected months cumulative cycles are negative as well as the based on findings by Lee and Zyren (2007), maximumsojourn,expressedinmonths,ofcumulative who, in testing weekly prices, found a dummy cycles. variable for the months after March 1999 to be Cumulative cycles provide an indication of the statistically significant in the conditional variance balance in an oil account for smoothing petroleum 3 Statistical Analysis of U.S. Gulf Coast Prices 17 Table 3.7 GARCH of Returns of Logarithms of Nominal Monthly Prices Parameter WTI Gasoline Diesel Heating oil Jet kerosene Residual fuel oil Propane Beginning­Mar. 2007 A D D B B D D Half-life (months) n.a. n.a. n.a. 0.4 4.8 n.a. n.a. June 1995­Mar. 2007 D D D D B D D Half-life (months) n.a. n.a. n.a. n.a. 0.6 n.a. n.a. Beginning­Dec. 1999 A D D B B D B Half-life (months) n.a. n.a. n.a. 0.8 3.7 n.a. 0.9 Jan. 2000­Dec. 2003 D D D D D D A Half-life (months) n.a. n.a. n.a. n.a. n.a. n.a. n.a. Jan. 2004­Mar. 2007 D D D D B D D Half-life (months) n.a. n.a. n.a. n.a. 0.6 n.a. n.a. Apr. 1999­Mar. 2007 A C B B D B D Half-life (months) n.a. n.a. 3.1 4.9 n.a. 4.4 n.a. Source: Author calculations. Note: n.a. = not applicable. Results are classified into the four categories defined on p. 13. Table 3.8 Runs on Cumulative Cycles of Nominal Prices, September 1995­March 2007 Averaging Jet Residual period Parameter WTI Gasoline kerosene Heating oil Diesel fuel oil Propane Percent negativea 66 79 52 58 65 53 55 Daily Maximum sojournb 5.3 6.5 4.6 8.0 6.5 4.7 5.6 Percent negativea 58 63 45 46 51 51 56 Weekly Maximum sojournb 24 23 28 27 26 21 25 Percent negativea 34 36 32 32 39 39 42 Monthly Maximum sojournb 40 39 40 40 38 32 27 Source: Author calculations. a. Percentage of months when the cumulative returns are negative. b. Maximum sojourn in months. pricesbasedonalong-termpricetrend.Theoilaccount depends on when the oil account is put into operation will receive the difference between the trend price (or the beginning of summation of cycles). The results and the actual price when the latter is lower, and, show that cumulative cycles become increasingly conversely, will pay for the difference if the actual positive with the increasing length over which prices price is higher. At any time when the cumulative areaveraged:cumulativecyclesarenegativemorethan cycle is negative, the balance in the oil account would half the time for all fuels when daily prices are used, be positive; when the cumulative cycle is positive, the butlessthanhalfthetimewhenmonthlyaverageprices oil account balance would be negative. This balance areconsidered.Thus,aprice-smoothingschemebased 18 Special Report Coping with Oil Price Volatility on the long-term trend of monthly prices--whereby sojourns for monthly average prices are nearly all for prices are adjusted and transfers in or out of the oil positive cumulative cycles, which would correspond account are made on a monthly basis--would have to months when the balance of this hypothetical a negative account balance more than half the time. oil account for smoothing prices is negative. More The maximum sojourn for a given fuel also increases information on price smoothing can be found in with increasing averaging period. The maximum chapter 7. 4 Application to Prices in Developing Countries The tests run on U.S. Gulf prices presented in chapter 3 examined. In the case of real prices in Ghana, the price were applied to monthly prices in Chile, Ghana, India, series had to be terminated in November 2007 because thePhilippines,andThailandtocapturethecombined the consumer price index was not available after that impact of foreign exchange and oil price fluctuations. month at the time of completing this report. For this purpose, international crude and oil product This chapter describes the price level and price prices in U.S. dollars and local currency units in the volatility differences between the U.S. and local U.S. Gulf Coast (for Chile), northwestern Europe currencies, the results of ADF tests, GARCH analysis (Ghana), the Persian Gulf (India), and Singapore of nominal prices in local currency, and calculations (the Philippines and Thailand) were examined. For of cumulative cycles during the second subperiod. crude, prices for Nigerian Bonny Light were used for Additional results are given in annex 4. As discussed Ghana, those for Indonesian Minas for the Philippines in chapter 3, one interpretation of cumulative cycles is and Thailand, and Dubai Fateh for India. Additional to consider a fund for smoothing oil prices (referred information on these price data are presented in to here as the oil account) based on a long-term annex 4. price trend constructed using an HP filter. When Price information is available beginning in cumulative cycles are positive, the balance of the oil January 1987 for all fuels except those from the U.S. account is negative. In this chapter, the maximum Gulf Coast, where the crude price series is available sojourn (the number of continuous months when from January 1986 but the prices of oil products appear cumulative cycles have one sign) corresponds to the for the first time between June 1986 and as late as May months when cumulative cycles are positive in every 1995. In analyzing the prices in the five developing case. Thus, the maximum sojourns presented here countries, three time periods were examined: the tell how many months the oil account balance would entire time period from the beginning to March 2007, have remained negative, imposing a fiscal burden on a first subperiod from the beginning to June 1999, and the government managing such an account. Note that a second subperiod from July 1999 to March 2007. the account balance is a function of when the fund is The cut-off point of June 1999 was chosen because started. Computing cumulative cycles for the second prices in local currency generally began to rise in subperiod is equivalent to setting up the oil account the middle of 1999. The results from runs tests are in July 1999. reported only for the second subperiod and only for cumulative cycles in this chapter. Additional results Chile can be found in annex 4. For reporting price level and price volatility Price increases in U.S. dollars and Chilean pesos differences (presented in the first three tables for were compared for the three subperiods (table 4.1). each country), three subperiods--from the beginning The increases in the mean local currency prices to June 1999, July 1999 to December 2003, and (averaged over each subperiod) were higher than January 2004 to January 2008--as well as the entire those corresponding to prices in U.S. dollars in both period from the beginning to January 2008 were nominal and real terms except when going from the 19 20 Special Report Coping with Oil Price Volatility Table 4.1 Difference between Percentage Price Increase in U.S. Dollars to That in Chilean Pesos Jet Residual Price Subperiods compared Crude Gasoline Diesel kerosene Gasoil fuel oil 2 to 1 118 84 67 114 116 134 Nominal 3 to 2 -28 -28 -31 -30 -30 -28 3 to 1 179 118 90 188 186 185 2 to 1 18 28 48 17 17 20 Real 3 to 2 -24 -23 -26 -25 -25 -23 3 to 1 3 19 53 2 2 1 Sources: U.S. EIA 2008a; author calculations. Note: Subperiod 1 beginning in the month shown in table A4.1 to June 1999; subperiod 2 is July 1999­December 2003; subperiod 3 is January 2004­January 2008. The increase in the mean price from subperiod 1 to subperiod 2 (percentage increase in subperiod 2 over subperiod 1) computed in U.S. dollars is subtracted from the percentage increase in the mean price between the same two subperiods in Chilean pesos. second to the third subperiod. In real terms, price real prices when expressed in U.S. dollars. When increases from the first subperiod to the third for WTI the prices are converted to Chilean pesos, gasoline crude, diesel, jet kerosene, and residual fuel oil were and kerosene prices are nonstationary in nominal the same regardless of whether fuels were priced in terms and gasoline prices are nonstationary in real U.S. dollars or Chilean pesos. See annex 4 for more terms; other prices are stationary. During the second information. subperiod, all U.S. prices are nonstationary but local A comparison of standard deviations of returns of gasoline prices, nominal and real, are stationary. logarithms of nominal and real prices in U.S. dollars The results of GARCH tests performed on local and Chilean pesos shows that nominal Chilean peso nominal prices are summarized in table 4.2. WTI prices were less volatile during the first subperiod for crude, jet kerosene, and residual fuel oil have a gasoline,diesel,andjetkeroseneandrealChileanpeso conditional variance that is stationary for the entire prices were less volatile for all six fuels. For all other period and during the first subperiod. Gasoline and fuels and periods, volatility was the same or higher gasoil have a nonstationary conditional variance for Chilean peso prices. Exchange rate fluctuations even during the first subperiod. During the second were largest during the second subperiod, which subperiod, only residual fuel oil has a stationary also saw higher price volatility in local currency. conditional variance; meaningful equations could During the third subperiod, the Chilean peso was not be found for the other fuels. appreciating against the U.S. dollar, but fluctuations Examination of cumulative cycles is given in served to amplify, rather than reduce, local currency table 4.3. The percentage of months when cumulative price volatility. cycles is negative is lower for local prices, illustrating ADF tests show some differences between U.S. the impact of exchange rate fluctuations. This finding and local currency prices. For the entire period, the implies that the oil account balance would have been results are the same and all prices are nonstationary negative over a longer period than if prices were in except for residual fuel oil (in both nominal and real U.S. dollars. The maximum sojourn during which the prices). In the first subperiod, prices for all fuels oil account balance remains negative continuously is except gasoline are nonstationary in nominal and 5.5 years for residual fuel oil. 4 Application to Prices in Developing Countries 21 Table 4.2 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Chilean Pesos Parameter Crude Gasoline Diesel Jet kerosene Gasoil Residual fuel oil Beginning­Mar. 2007 B D D B Aa B Half-life (months) 0.6 n.a. n.a. 0.4 n.a. 0.6 Beginning­June 1999 B Aa C B Aa B Half-life (months) 1 n.a. n.a. 0.5 n.a. 0.5 July 1999­Mar. 2007 D D D D D B Half-life (months) n.a. n.a. n.a. n.a. n.a. 0.8 Source: Author calculations. Note: n.a. = not applicable. Results are classified into the four categories defined on p. 13. a. The results from not retaining the GARCH term, whereby a finite half-life was found, are presented in annex 4. Table 4.3 Cumulative Cycles of Nominal Monthly Chilean Prices, July 1999­March 2007 Currency Parameter Crude Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Percent negativea 28 26 30 31 32 22 US$ Maximum sojournb 49 50 47 46 48 59 Averagec 32 34 33 32 29 26 Percent negativea 5 6 24 23 26 4 Ch$ Maximum sojournb 56 62 50 50 50 66 Averagec 24,875 27,558 26,953 26,016 21,098 20,107 Source: Author calculations. a. Percentage of months when the cumulative returns are negative. b. Maximum sojourn in months. c. Average cumulative cycles over the period. Ghana ADF tests show that both U.S. and local prices, nominal and real, are nonstationary for the full period Price increases were compared in U.S. dollars and and the second subperiod. For the first subperiod, Ghanaian cedis. As shown in table 4.4, the local all prices are stationary except nominal local prices; currencypriceincreaseswerehigherinnominalterms these are nonstationary for every fuel, underscoring for all subperiod comparisons. In real terms, however, the magnitude of local inflation. local currency price increases in the third subperiod over the second subperiod were lower than U.S. dollar As shown in table 4.5, GARCH analysis of returns price increases, and the magnitude of the difference found meaningful equations for all fuels except gasoil between the two sets of prices is the largest among during both the full period and the first subperiod. the five countries examined here. No satisfactory equations could be found for any fuel Comparison of standard deviations of returns of during the second subperiod, logarithms of nominal and real prices in U.S. dollars Cumulative cycles during the second subperiod and Ghanaian cedis shows that volatility was higher are negative less than a third of the time in U.S. dollars, forallperiodsinnominalandrealterms.Exchangerate but more frequently in local currency (table 4.6). This fluctuations amplified local currency price volatility. is the reverse of the Chilean case. Maximum sojourns 22 Special Report Coping with Oil Price Volatility are shorter in local currency than in U.S. dollars. The in the local currency than in U.S. dollars, it would still average cycle return is positive for every fuel. Thus, have posed a fiscal challenge, with the account balance whilemanagingtheoilaccountmighthavebeeneasier being negative continuously for three years or longer. Table 4.4 Difference between Percentage Price Increase in U.S. Dollars to That in Ghanaian Cedis Price Subperiods compared Crude Gasoline Jet kerosene Gasoil Residual fuel oil 2 to 1 974 957 938 934 1,005 Nominal 3 to 2 75 72 75 75 65 3 to 1 3,044 2,846 2,941 2,937 2,727 2 to 1 94 92 90 90 99 Real 3 to 2 -44 -41 -44 -44 -37 3 to 1 93 89 91 91 84 Sources: Energy Intelligence 2008; author calculations. Note: For definitions and calculation procedures, see the notes to table 4.1. Real prices only through November 2007. Table 4.5 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Ghanaian Cedis Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Beginning­Mar. 2007 B B A D Aa Half-life (months) 0.6 0.5 n.a. n.a. n.a. Beginning­June 1999 B Aa A D B Half-life (months) 0.9 n.a. n.a. n.a. 0.7 July 1999­Mar. 2007 D D D D D Half-life (months) n.a. n.a. n.a. n.a. n.a. Source: Author calculations. Note: n.a. = not applicable. Results are classified into the four categories defined on p. 13. a. The results from not retaining the GARCH term, whereby a finite half-life was found, are presented in annex 4. Table 4.6 Cumulative Cycles of Nominal Monthly Ghanaian Prices, July 1999­March 2007 Currency Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Percent negativea 28 26 31 31 20 US$ Maximum sojournb 52 50 46 46 60 Averagec 34 42 37 30 31 Percent negativea 47 42 45 46 35 C/ Maximum sojournb 37 35 35 35 47 Averagec 45,237 90,771 52,540 31,425 97,924 Source: Author calculations. a. Percentage of months when the cumulative returns are negative. b. Maximum sojourn in months. c. Average cumulative cycles over the period. 4 Application to Prices in Developing Countries 23 India subperiod are considered. In the first subperiod, all prices are stationary except nominal local gasoil Price increases are compared for U.S. dollars and prices. Indian rupees (table 4.7). The local currency price As in other countries, GARCH analysis of returns increases in the third subperiod over the second in local currency found meaningful equations for the were lower in nominal and real terms; the difference entire period as well as for the first subperiod, with between the two currencies is greater when prices are the exception of gasoil (table 4.8). During the second measured in real terms. A comparison of standard deviations of returns of subperiod, no meaningful equations could be found logarithms of nominal and real prices in U.S. dollars except for residual fuel oil, the conditional variance and Indian rupees shows that there is virtually no of which seems to grow without bound. difference in volatility between the two currencies. Cumulative cycles are negative slightly less Where they differ slightly, local currency prices have frequently in local currency than in U.S. dollars higher volatility. (table 4.9). The maximum sojourns are longer in local ADF tests show that all prices are nonstationary currency and range from one month shy of four years when the entire period as well as the second to longer than five years. Table 4.7 Difference between Percentage Price Increase in U.S. Dollars to That in Indian Rupees Price Subperiods compared Crude Gasoline Jet kerosene Gasoil Residual fuel oil 2 to 1 112 99 96 97 127 Nominal 3 to 2 -14 -13 -15 -16 -13 3 to 1 211 174 199 208 211 2 to 1 29 25 24 24 33 Real 3 to 2 -24 -23 -26 -28 -22 3 to 1 20 16 19 19 21 Sources: Energy Intelligence 2008; author calculations. Note: For definitions and calculation procedures, see the notes to table 4.1. Table 4.8 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Indian Rupees Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Beginning­Mar. 2007 Aa B B D B Half-life (months) n.a. 2 2 n.a. 0.7 Beginning­June 1999 A A B Aa B Half-life (months) n.a. n.a. 1 n.a. 0.7 July 1999­Mar. 2007 D D D D A Half-life (months) n.a. n.a. n.a. n.a. n.a. Source: Author calculations. Note: n.a. = not applicable. Results are classified into the four categories defined on p. 13. a. The results from not retaining the GARCH term, whereby a finite half-life was found, are presented in annex 4. 24 Special Report Coping with Oil Price Volatility Table 4.9 Cumulative Cycles of Nominal Monthly Indian Prices, July 1999­March 2007 Currency Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Percent negativea 30 34 34 38 18 US$ Maximum sojournb 53 49 48 46 61 Averagec 29 22 25 16 36 Percent negativea 27 30 33 37 15 Rs Maximum sojournb 56 53 50 47 63 Averagec 1,598 1,388 1,429 1,019 1,852 Source: Author calculations. a. Percentage of months when the cumulative returns are negative. b. Maximum sojourn in months. c. Average cumulative cycles over the period. The Philippines stationary except nominal and real U.S. gasoline prices, nominal and real local crude oil prices, and real The results of the price increase comparison are U.S. gasoline prices. During the second subperiod, as shown in table 4.10. As in Ghana, the local currency in Chile, all prices are nonstationary except nominal price increases are higher in nominal terms for all and real local gasoline prices. subperiod comparisons. In real terms, prices in The GARCH analysis results follow the trend Philippine pesos increased less in the third subperiod observed in other countries, with no meaningful over the second subperiod. equations identified during the second subperiod A comparison of standard deviations of returns of (table 4.11). During the first subperiod, the conditional logarithms of nominal and real prices in U.S. dollars variance is bounded for crude oil, gasoline, and and Philippine pesos shows that local prices were residual fuel oil. consistently more volatile than U.S. dollar prices for Thepercentageofmonthswhencumulativecycles all the periods examined. are negative is 40 percent or less in all cases and ADF tests for the entire period show that all prices comparable between the two currencies (table 4.12). are nonstationary. For the first subperiod, prices are The maximum sojourns are also comparable. Table 4.10 Difference between Percentage Price Increase in U.S. Dollars to That in Philippine Pesos Price Subperiods compared Crude Gasoline Jet kerosene Gasoil Residual fuel oil 2 to 1 128 110 109 110 142 Nominal 3 to 2 7 8 9 8 6 3 to 1 300 266 277 278 293 2 to 1 34 29 29 30 39 Real 3 to 2 -13 -12 -13 -13 -11 3 to 1 48 42 44 45 47 Sources: Energy Intelligence 2008; author calculations. Note: For definitions and calculation procedures, see the notes to table 4.1. 4 Application to Prices in Developing Countries 25 Table 4.11 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Philippine Pesos Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Beginning­Mar. 2007 D B Aa A D Half-life (months) n.a. 0.7 n.a. n.a. n.a. Beginning­June 1999 B B A D B Half-life (months) 1.5 1.6 n.a. n.a. 0.6 July 1999­Mar. 2007 D D D D D Half-life (months) n.a. n.a. n.a. n.a. n.a. Source: Author calculations. Note: n.a. = not applicable. Results are classified into the four categories defined on p. 13. a. The results from not retaining the GARCH term, whereby a finite half-life was found, are presented in annex 4. Table 4.12 Cumulative Cycles of Nominal Monthly Philippine Prices, July 1999­March 2007 Currency Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Percent negativea 28 32 34 40 17 US$ Maximum sojournb 52 46 47 44 60 Averagec 35 26 27 21 39 Percent negativea 29 33 33 37 18 = P Maximum sojournb 47 43 43 40 57 Averagec 1,323 868 967 731 1,625 Source: Author calculations. a. Percentage of months when the cumulative returns are negative. b. Maximum sojourn in months. c. Average cumulative cycles over the period. Thailand For the first subperiod, all prices are stationary except nominal U.S gasoline prices and real U.S. and local Theresultsofthepriceincreasecomparisonareshown gasoline prices. in table 4.13. As in Chile and the Philippines, the local It was difficult to identify meaningful equations currency price increases in the third subperiod over through GARCH analysis except for gasoline in the second were smaller in nominal and real terms. the first subperiod and residual fuel oil in both A comparison of standard deviations of returns of subperiods (table 4.14). For data from the full period, logarithms of nominal and real prices in U.S. dollars the conditional variance is bounded for gasoline and and Thai baht shows that Thai baht prices were the kerosene, and unbounded for gasoil and residual same or more volatile than U.S. dollar prices for all fuel oil. the periods examined except for residual fuel oil in There is no marked difference in the cumulative the first subperiod in nominal terms. cycles between local and U.S. dollar prices during the ADF tests show that all prices--nominal or real, second subperiod (table 4.15). Cumulative cycles are in U.S. or local currency--are nonstationary for the negative less than a third of the time, and as little as entire period as well as during the second subperiod. 12 percent for local residual fuel oil prices. 26 Special Report Coping with Oil Price Volatility Table 4.13 Difference between Percentage Price Increase in U.S. Dollars to That in Thai Bahts Price Subperiods compared Crude Gasoline Jet kerosene Gasoil Residual fuel oil 2 to 1 80 69 69 70 88 Nominal 3 to 2 -22 -22 -23 -24 -20 3 to 1 125 111 117 117 121 2 to 1 47 40 40 41 52 Real 3 to 2 -20 -19 -21 -21 -17 3 to 1 59 52 55 55 58 Sources: Energy Intelligence 2008; author calculations. Note: For definitions and calculation procedures, see the notes to table 4.1. Table 4.14 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Thai Bahts Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Beginning­Mar. 2007 D B B A A Half-life (months) n.a. 0.5 6 n.a. n.a. Beginning­Dec. 1999 D B D D B Half-life (months) n.a. 2 n.a. n.a. 0.8 Jan. 2000­Mar. 2007 D D D D A Half-life (months) n.a. n.a. n.a. n.a. n.a. Source: Author calculations. Note: n.a. = not applicable. Results are classified into the four categories defined on p. 13. Table 4.15 Cumulative Cycles of Nominal Monthly Thai Prices, July 1999­March 2007 Currency Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Percent negativea 28 26 31 31 20 US$ Maximum sojournb 54 49 48 45 63 Averagec 34 42 37 30 31 Percent negativea 24 27 27 31 12 B Maximum sojournb 52 49 49 45 63 Averagec 1,715 1,366 1,505 1,247 1,874 Source: Author calculations. a. Percentage of months when the cumulative returns are negative. b. Maximum sojourn in months. c. Average cumulative cycles over the period. 4 Application to Prices in Developing Countries 27 Observations rates in most of the countries examined in this study, price returns have varied slightly more since 2004 in Nominal prices in some countries show large local currency units than in U.S. dollars. This finding effects of exchange rate fluctuations, with marked would suggest that, from the point of view of tackling differences from the behavior of prices in U.S. dollars. price volatility, the problem faced by the governments Because government interventions target local price in these countries was not much different from movements, local prices are more useful in assessing those dealing in U.S. dollars. While some correlation policy options. In Chile, local prices have tended to be between local inflation (relative to that in the United more stable, potentially making policy interventions States) and exchange rate variation over time is easier than if the government were dealing with expected, the correlation is not necessarily systematic; world oil prices in U.S. dollars. At the opposite end these two factors thus may have separate effects. of spectrum is Ghana where, in the first subperiod, As shown in annex 4, average nominal cumulative nominallocalpriceswerenonstationarybutrealprices cycles in the first subperiod are positive even in local were stationary, suggesting high local inflation. currency for all the fuels. This finding, combined with There was no marked difference in the variance of the results reported here, would suggest that price price returns between U.S. dollar and local currency smoothing based on long-term trends would have prices.Ifanything,despiteappreciatinglocalexchange imposed a considerable fiscal drain. 5 Hedging Role of Hedging Box 5.1 In response to the variability and unpredictability Sasol's Hedging Experience of the prices of oil and other commodities, futures markets have become widespread. In these markets, The South African synfuel producer Sasol has been a contract can be entered into at a known price to hedging a portion of its production since 2004 to protect the firm from downside risks so that it could purchase or sell a given quantity of the commodity fund its capital spending program. In its most recent in a given number of months. In this sense, they hedge, effective for a year from May 2007 and perform a similar function for agents as the long- 45,000 barrels a day of oil, Sasol would receive an term contracts that were in common use before the average floor price of US$62.40 a barrel and, in first oil price shock of 1973­74. The futures price return, would forgo the upside if the price of Brent crude essentially removes the risk associated with unknown oil exceeded US$76.80 barrel. This hedging strategy is spot prices, but does not eliminate the possibility of reported to have cost Sasol R 3 billion (US$375 million regret--for a seller, if spot prices rise (box 5.1), and at the exchange rate prevailing in March 2008) since inception. The amount includes projected losses from for a purchaser, if they fall. hedging for the second half of fiscal 2008 (April to For example, on the last trading day of January March). These losses were previously estimated at 2007, the price of a futures contract for WTI crude R 854 million (US$110 million), but, with oil prices for delivery in April 2007 was US$58.85 a barrel, for surpassing US$100 a barrel, some analysts believe delivery in July 2007 was US$60.67, and for delivery the second half hedging loss could double (Business in January 2008 was US$62.92. At that point (January Report 2008). 2007), the monthly average spot price for the same oil was US$54.51 a barrel. A company or government agency wishing to purchase (or sell) oil in July 2007 obligation, to purchase a specific futures contract for might have been concerned that if it waited until that a prespecified price (the exercise or strike price). The date to purchase (or sell), the spot price then might be holder of the option has to pay a premium (the option considerably higher (or lower) than the futures price price) to the writer of the option. A put option gives for that month. It would thus be less risky to purchase the owner the right, but not the obligation, to sell the (or sell) the futures contract so as to lock in a certain specific futures contract at a prespecified price. The price. In July, the purchaser (or seller) would receive holder of the put option also has to pay a premium (or deliver) the oil paid for in the futures contract. If to the writer of the option. Options, which are traded the spot price had actually fallen below the futures on the same exchanges as oil futures, can be used to price by July, there would have been an opportunity hedge physical sales or purchases while avoiding cost of making the purchase on the futures market. the risk of not being able to benefit from rising spot To provide insurance against the possibility of prices (for a physical seller) or falling spot prices (for a regrets, options on futures contracts can be used. physical purchaser). Options are distinct from futures A call option gives the holder the right, but not the contracts in that they involve upfront costs (for the 29 30 Special Report Coping with Oil Price Volatility holders of the option), which are incurred regardless between these and world market prices. The of whether the option is actually exercised. unexpected fluctuations in oil prices make the costs In practice, futures markets are not normally used of such a policy highly variable and lead to budget to buy or sell oil for delivery. Instead futures (paper) planning difficulties for the government. Oil- contracts are combined with a physical sale of the importing companies can face the same difficulty, commodity to provide a hedge against the uncertainty but if they are free to pass on the full price increase of prices in the future. Hedging crude oil and oil to consumers, they bear relatively little of the risk products is a well-established practice. Every day on attached to price volatility. In this case, consumers face the New York Mercantile Exchange (NYMEX) and the full oil price risk, but, with the exception of large on the Intercontinental Exchange (ICE), oil futures industrial consumers (such as power stations), their and options contracts are traded at a volume many consumption levels will be too small relative to the times that of world oil daily consumption. Although fixed costs of entering the futures market to consider a substantial volume of this trading is by buyers and hedging as a risk-reduction instrument. However, sellers that neither produce crude oil and oil products the government of an oil-importing country that norconsumethemintheirinstitutionalcapacity,much subsidizes fuel prices may use the futures market to is nevertheless traded by those directly concerned hedge the cost of the subsidy. with the oil industry. The primary purpose of futures The attractiveness of the futures market in markets is to allow one party to transfer some risk reducing the risks attached to oil price volatility associated with future price changes to another party depends on several factors: more willing to bear the risk. Actual producers and consumers of oil may wish to use this instrument in · The extent of the risks currently being faced in order to lower their exposure to the risks inherent in the oil market, which depends primarily on the oil price volatility over time. volatility of oil prices but also on the correlation Because the volatility of oil prices--even when between the price of the oil product actually prices are averaged over intervals as long as a exported or imported and the price of the month--is considerable, producers face a substantial instrument traded on the futures market degree of risk in assessing their future revenues. · The extent to which risks can be reduced through The actual price received six months from now may futures trading be very different from the price received for current · The costs of futures trading sales. When a government derives a sizable fraction · The benefits of risk reduction relative to the costs of its budget revenues from the oil sector, or when of futures trading the seller of oil is the government (for example, through its ownership of the national oil company), Many writers have described the mechanics oil price volatility can have large effects on budget of hedging (see, for example, Bailey 2005), and revenue forecasts and expenditure planning. Under its possible use by governments in the oil market these circumstances, reducing the risk of revenue has been discussed in several studies, including fluctuations through hedging may be an attractive Claessens and Varangis (1991, 1994), Satyanarayan policy. And even if a government is not involved in and Somensatto (1997), Daniel (2001), the Alaska the direct sale of oil (which is usually the case), it may Department of Revenue (2002), Devlin and Titman nevertheless treat its oil revenue flow as if it were (2004), and the United Nations Conference on Trade receipts from direct sale of oil by the government. and Development (2005). Until recently, however, Similarly, purchasers of oil face substantial only a few governments have acknowledged hedging uncertainty about the future costs of such purchases. oil exports or imports. Some national oil companies In several oil-importing countries, governments possibly had hedged as part of their daily business subsidize the price of oil by instituting fixed or without the direct involvement of the government. formula-based prices and financing the difference Chile hedged oil imports in 1991 during the First Gulf 5 Hedging 31 War, while Ecuador and Mexico have hedged crude against which a discussion of the attractiveness of oil sales at various times. the strategy can be evaluated. The use of options In the last couple of years, the steep rise and high strategies are briefly outlined; for other, more complex, variability of crude oil and oil product prices have instruments such as swaps, see such sources as led several governments in oil-consuming countries Bailey (2005). An evaluation of the attractions of to consider the possibility of hedging. A previous hedging in current market conditions follows, and ESMAP report (Bacon and Kojima 2006) noted that an assessment of the difficulties in instituting such a Pakistan had recently considered whether to hedge oil policy is outlined. imports; there have been reports in other countries as For ease of exposition, much of the analysis well that this option has been under discussion. For focuses on oil producers that need to sell crude oil, example, in response to continuing high oil prices but, as explained in the chapter at various points, the and concerns about swelling fuel price subsidies case of oil consumers that need to purchase crude in Sri Lanka, the Ceylon Petroleum Corporation in oil or oil products is symmetric: in a situation where February 2007 announced that it was pursuing a the former would make a gain through a hedging hedging proposal made by several banks (Financial strategy the latter would make an equivalent loss, Times 2007) and concluded its first hedging deal for and vice versa. diesel in April 2007 (Daily Mirror 2007). Recent oil price behavior and the evolving nature of oil futures markets make consideration of hedges Hedging with Futures Contracts particularly timely. As chapter 3 indicates, oil prices Consider a single sale six months ahead by a producer have exhibited considerable volatility over the last of oil that regularly sells a known amount each month. few years, and it is possible that the correlations A possible hedging strategy would be to sell now a between futures prices of standard traded crude futures contract, covering the same volume as the oil and oil products with those of actual imports or planned physical sales, that matures in six months. exports have also changed. This possibility has been At the end of the six months, the producer would analyzed by Switzer and El-Khoury (2007). These buy a futures contract for immediate delivery and changes could affect the amount of risk being carried sell the actual crude oil then available. The purchase by importers and exporters, as well as the reduction of the immediate delivery contract would cancel out in in risk that hedging might make possible. With regard volumethecontractforsaletakenoutearlierandwould to changes in futures markets, not only has the total involve no net commitment to deliver or purchase any volume of transactions increased, but the number of physical oil on the futures market. This strategy is transactions that relate to future prices with longer designed to exploit two features of the prices: horizons (durations) has increased markedly. These developments may now provide risk reduction · The sale price of the six-month futures contract that previously was not available for oil-producing is known at the time of purchase and provides and -consuming countries that are concerned with certainty on this part of the transaction. volatility over periods of many months, in part · The futures price for immediate delivery should because of the link to the budget process. be identical to the actual market (spot) price then This chapter begins with a description of a simple in effect for the commodity defined in the futures hedging strategy. The analysis opens with the case of contract. a short hedger--that is, an entity committed to make a physical sale at a future date. It then reviews the case of The second feature ensures that, for example, if a long hedger, an entity committed to make a physical the spot price falls during the six months, the futures purchase in the future.1 This provides a background price for immediate delivery at that time will also have 1"Short" and "long" here do not refer to time duration. A short hedger is a seller of the physical commodity; a long hedger is a buyer of the physical commodity. 32 Special Report Coping with Oil Price Volatility fallen, so that the price received for actual oil sales is Although the futures price converges toward the balanced by the price paid for immediate delivery on spot price as the closing date approaches, this the futures market. As a result, the producer receives restriction gives rise to a risk that the two will net the amount of the futures contract taken out at the be different. beginning of the six months and has avoided the risks · The location in which the physical product is to of the unknown price at the time of sale. be sold may not be the same as the one where This simple strategy, the so-called perfect hedge, the futures contract is exercised. NYMEX crude would remove all risk from the sale of the crude but oil futures contracts are based on the underlying would commit the seller to the price currently set in restriction that any delivery of a physical that the futures contract. If spot prices were to increase takes place because contracts have not been during the six months, the seller would not be able to closed out will be at Cushing, Oklahoma. Due benefit from that increase. If spot prices fell, however, to differences in transportation costs, the price the seller would not be adversely affected by that set for this location would not necessarily be the fall. same as the price for an identical product at the The case of a long hedger that intends to purchase same time in a different location. This is another oil at some future date is symmetric. Consider a reason why the futures price and the spot price hedger buying a futures contract now with a six- received by the seller could differ. month duration. Just before the hedge expires, an · The futures contract is specified for a particular equivalent amount is sold through a futures contract type of crude oil (or oil product). The major for immediate delivery. At the closing date, the crude traded on NYMEX is WTI, while Brent hedger purchases physical oil on the spot market at blend is traded on the ICE. If the physical sale a price that will ideally equal the price at which the is of a different quality, this introduces another futures sell contract is liquidated. The overall cost of risk that the prices will diverge. Crude oil the purchase is the initial futures buy contract price, can vary in quality across different types; the thus removing risk from the transaction. Again, if prices of the different crudes are highly, but not spot prices rose, the hedger would not be exposed perfectly, correlated (see Bacon and Tordo 2005 for to these (the sell hedge cancels out this effect); but if quantitative correlations). The greater the quality spot prices fell, the hedger would not be able to benefit difference from the standard futures crude, the from them since the price on the sell hedge would more room for the margin between the futures also have fallen. contract and the spot price to change over time A perfect hedge can rarely be implemented in and to introduce another source of risk. Moreover, practice, and the spot price received or paid is different the quality of oil can change over the lifetime of from the price of the buy or sell hedge taken to close a field, leading to variations in the basis risk that the futures market position. This difference, termed may not be entirely foreseeable. the basis, is not constant and introduces a source of risk to the hedging strategy. The reasons for the existence Therefore, the use of a hedge reduces the risks of basis risk, and why these two prices can differ, are from the sale price of oil itself, but introduces another given below. risk from the existence of the basis. Because of this risk, it is generally not optimal to execute the so-called · The futures contract for immediate delivery may naďve hedge in which all the oil for sale (or purchase) notcoincideexactlywiththetimingofthephysical is hedged. Instead, only a fraction of this physical total spot sale. The last trading day for a contract on should be hedged on the futures market. NYMEX is the third business day before the 25th Hedging theory provides a model that determines on the month preceding the delivery month. Thus, the risk-minimizing hedge ratio--the proportion of to close out a sell hedge due to expire in July, a buy physical oil for sale that should be hedged to provide hedge to expire in July must be executed in June. the minimum overall risk. In this chapter, return is 5 Hedging 33 used in the conventional sense to mean a change in the In analyzing the period January 2000 to December value of an investment or portfolio over a given period 2003, for example, the risk-minimizing hedge ratio of time. As explained in annex 5, the risk-minimizing and expected return can be estimated from the price hedge ratio is given by the coefficient obtained when behavior during that period. These values (which in regressing historical data for the change in spot prices practice would not be known by the hedger until the on the change in the futures contract price over the end of the period) yield the ex post hedging ratio. hedge duration. The efficiency (effectiveness) of Using a value of the risk-minimizing hedge ratio the hedging strategy--the percentage reduction in and expected return derived from data generated the risk compared to not hedging--is given by the prior to January 2000 would generate an ex ante squared correlation from this regression. Although hedging strategy. If the risk-minimizing hedge ratio a risk-minimizing hedging strategy does not take and expected changes in spot and futures prices over into account the expected return from the portfolio a given duration remain fairly constant over long of hedged and unhedged sales, the expected return periods of time, the ex ante and ex post hedge ratios can be estimated by examining the past price history would be similar. However, changes in the oil market and taking the mean of the actual change in the value suggest that this may not be the case, and that it would of the portfolio over the same historic period for not be possible to obtain as good a performance which the risk-minimizing hedge ratio is estimated. as suggested by the ex post hedge calculations. In This estimate can be compared to the mean of the particular, forming expectations of the changes in actual return from the change in spot prices over the spot and futures prices over the duration of the hedge same period, which gives the return on an unhedged is difficult. It is reasonable to assume that the futures strategy. Annex 5 provides more details. price of oil for a particular date is the best estimate Hedging theory also considers the case where the that can be made of the spot price that will be in effect expected return on the hedged portfolio is taken into at that time. account, and an optimal combination of return and risk is calculated. The choice of risk versus return is influenced by the hedger's preferences, as expressed Costs of Running a Hedging Program through a risk parameter. Large values of the risk Several costs will be incurred beyond any profits parameter lead the hedger to choose a strategy that or losses that may be made directly from a hedging reduces risk slightly relative to the benefits of a higher program. Some of these are proportional to the size of return. In the extreme case where the risk parameter the program; others have a large upfront component becomes very large, the optimum hedge is identical relating to program establishment which may deter to the risk-minimizing hedge. The optimal hedging governments from starting such a program. strategy generally leads to a different hedge ratio, On both NYMEX and the ICE, a single futures hedging efficiency, and expected return on the hedged contract is for 1,000 barrels of crude oil. A producer portfolio from the risk-minimizing hedge. wishing to hedge 50 percent of a production of 100,000 Forboththerisk-minimizinghedgeandtheoptimal barrels a day would thus have to sell 1,500 separate hedge,animportantdistinctionmustbemadebetween contracts each month. Although revenues will be anexposthedgeandanexantehedge.Anexposthedge proportional to the production volume--as will most is a hypothetical hedge set up after the fact and asks costs--the operation of the futures contract can entail whatdecisionwouldhavebeenoptimalbasedonwhat large short-term financing requirements, as explained actually came to pass. An ex ante hedge is how hedges below. aremadeinpractice,beforecompleteinformationabout prices becomes available. In an ex post hedge, the risk- minimizing hedge ratio and return on the hedge are Exchange Fees and Brokerage Fees calculated from the actual data covering the period for Exchanges charge a number of small fees, including which the hedge is to be evaluated. a trading fee, a clearing fee, and--within the United 34 Special Report Coping with Oil Price Volatility States, for example--the National Futures Association call for US$30. On day 4, a further fall in price drops fee. Brokers acting as agents to make purchases or the margin account (after replenishment to bring it sales on the futures markets also charge fees. These up to US$250) down to US$210, so there is a further fees are small on a per barrel basis when compared to margin call. By the end of day 7, when the contract the risk and returns per barrel that can be achieved. expires, there is a profit of US$10 on the hedge itself (the difference between the final price and the initial Margin Requirements price). This profit is equal to the value of the final margin account, which is returned to the hedger less To cover the risks of default, an initial margin is the initial margin and the sum of the margin calls. deposited with a broker (when used) upon entering In practice, the margin account is credited with the into a futures contract. This amount is determined interest earned on the balance during the period, so by the rules of the exchange and is presently about there is no financial cost to the hedger in making US$3,300 per contract of 1,000 barrels. Each day the these payments. price of the futures contract for the month in question Although the operation of the margin account changes, and the hedger has to "tail the hedge." has no long-term financial implications, it could Specifically, if the price of a buy contract falls below present a government with a substantial short-term the initial price, the hedger has incurred a temporary financing requirement. A series of price falls during loss in terms of what the contract could be sold for. the period could result in a substantial maximum This notional loss is debited against the margin temporary outflow. Similarly, for a sell hedger, a account. The hedger will then face a "margin call" series of price increases could result in a substantial and have to deposit a sufficient amount to bring the short-term financing requirement considerably margin up to its original level. Alternatively, if the larger than the initial margin payment. Even if prices price rises, the margin account will be credited with eventually revert to a historic mean level, oil prices the increment. This procedure continues each day are characterized by runs of successive increases, as until the contract is closed out. Over the life of the shown in chapter 2. hedge, the change in the futures price will exactly equal the difference in the value of the margin account between the opening and closing amounts less any margin calls. Table 5.1 A simplified example derived from Bailey (2005) illustrates the process. Assume that one buy contract Margin Account for a Buy Hedge for seven days into the future is purchased on day 1 Price Daily Margin Margin at US$1,000. The margin requirement to be held by Day (US$) gain/loss account call the broker is US$250, so the initial margin account 1 1,000 n.a. 250 0 has this value. Each day, the futures price for delivery 2 1,020 +20 270 0 on day 7 is assessed and the margin account is 3 970 -50 220 30 credited or debited with the day's change in value of 4 930 -40 210 40 the hedge. If the margin account is reduced in value below the initial amount, the margin call restores 5 950 +20 270 0 its value.2 Table 5.1 simulates the daily prices, daily 6 980 +30 300 0 gains or losses, the margin account, and the margin 7 1,010 +30 330 0 calls. On day 3, the fall in price by US$50 takes the Source: Author calculations. margin account below the initial margin, so there is a Note: n.a. = not applicable. 2In practice, a separate maintenance margin, which is lower than the initial margin, is used, and only when the account drops below this value is it replenished. 5 Hedging 35 External Management Costs average end-of-day price for all days in the month for Governments or national oil companies considering the specified month ahead. The latter represents the whether to initiate a hedging program are unlikely average cost of purchase during the month but does to have the expertise to design and implement not necessarily represent the price available on any an effective hedging strategy over a sustained particular day, whereas the former represents a well- period. Actual hedging strategies are usually much defined opportunity in futures markets. Spot prices more complicated than a series of straight futures were taken as the average for the months in question. transactions as described above. Either an all-service Contract durations of 3, 6, 12, and 24 months broker or specialist adviser can be entrusted with were examined. Because the longer horizon contracts designing a strategy to obtain the best execution, but set in a particular month mature at later dates, the this will add to the costs of the program. last date for taking the initial contract for which It is recommended that governments new to the closing contract price was available at the time hedging follow the market for a substantial period of this analysis, was July 2005. To ensure exact through a set of simulated hedges. Such simulations comparability for the third subperiod estimations, help governments track potential costs and benefits the risk-minimizing hedge ratios were all estimated and learn the mechanics of hedging and the various for contracts beginning on January 2004 through July strategies available. Only when a government is fully 2005. Three- and six-month futures contracts were aware of the potential costs and benefits of hedging quoted for the entire period studied, but 12-month should an actual program be initiated. contracts became common after January 1989 and 24-month contracts after January 1996. Therefore, Internal Management Costs for the whole period and for the first subperiod, the number of data points varies by hedge duration. For In order to manage a hedging program and to instruct the second and third subperiods, the same number and cooperate with the adviser or brokerage firm, of data points were used for all hedges. the government or national oil company will likely The risk-minimizing hedge ratios used in the have to establish a specialist division responsible calculations over the period are based on data from for checking transactions, authorizing payments on each period, meaning the values given are for ex margin calls, and instigating changes of hedging post hedges. Table 5.2 presents the risk-minimizing strategy. This action involves both the fixed costs of hedge ratios (h* as discussed in annex 5), the hedging establishing such a division, and possibly extra costs efficiency (R2), and the mean return for the period of hiring specialist staff to run the operation. considered (y*) for the hedged portfolio for these various parameters. The mean unhedged return ( p) Estimation of Hedge Ratios, the is also given for comparison, although it is not taken Efficiency of Hedging, and Returns into account in determining the risk-minimizing hedge ratio. Returns are measured in U.S. dollars from Hedging per barrel hedged. The equations from which these The risk-minimizing hedge ratio for the sale of parameters are derived are shown in annex 5. WTI crude was estimated for a number of different The analysis of hedging strategies over the period hedging durations for the period January 1987 from 1987 to 2007 yields the following findings: to March 2007 (using monthly data), and for the three subperiods--January 1987 to December 1999, · The regressions for the maximum data span January 2000 to December 2003, and January 2004 to for each hedging horizon show that the risk- March 2007--identified in chapter 3. Futures prices minimizing hedge ratio tends to increase with the were used in two different forms. The first form used length of the horizon. The minimum risk strategy prices quoted on the last trading day of the month for a two-year contract requires 92 percent of the for a specified month ahead; the second used the crude available to be hedged. 36 Special Report Coping with Oil Price Volatility Table 5.2 Ex Post Risk-Minimizing Sell Hedging for WTI Crude for Various Periods Based on Monthly Prices, January 1987­March 2007 3 months 6 months 12 months 24 months 3 months Subperiod Parameter (month end) (month end) (month end) (month end) (month avg.) Hedge ratio 0.76 0.83 0.80 0.92 0.99 Jan. 1987­ Hedging return 0.32 0.08 -0.28 -1.79 -0.02 Mar. 2007 Unhedged return 0.59 1.18 2.54 9.13 0.59 Hedging efficiency 0.50 0.66 0.70 0.85 0.61 Hedge ratio 1.04 0.97 0.90 1.16 1.15 Jan. 1987­ Hedging return -0.06 -0.36 -0.60 -1.91 -0.20 Dec. 1999 Unhedged return 0.20 0.38 0.97 3.38 0.20 Hedging efficiency 0.71 0.79 0.72 0.89 0.65 Hedge ratio 0.78 0.89 0.90 0.97 0.96 Jan. 2000­ Hedging return -0.47 -1.54 -2.83 -4.21 -0.59 Dec. 2003 Unhedged return 0.46 1.16 3.05 10.80 0.40 Hedging efficiency 0.53 0.68 0.73 0.89 0.58 Hedge ratio 0.49 0.24 0.17 0.65 0.75 Jan. 2004­ Hedging return 2.92 6.47 12.47 5.29 1.81 July 2005 Unhedged return 4.58 8.17 15.19 19.51 4.60 Hedging efficiency 0.28 0.08 0.06 0.69 0.40 Sources: Month-end futures prices from Bloomberg.com and average month futures prices from U.S. EIA 2008a; author calculations. Note: The month-end futures price is the closing price on the last trading day of the month in which the hedge is taken out. The average month futures price is based on the average of closing prices for every trading day in the month in which the hedge is taken out. · The hedging efficiency estimated over the whole · The first subperiod confirms the results for data period also increases with the length of the whole period, but at each horizon the risk- the hedging horizon. A 3-month hedge removes minimizing hedge ratio and hedging efficiency 50 percent of the risk, while a 24-month hedge were greater than for the entire period. The removes 85 percent of the risk. estimated risk-minimizing hedge ratio is greater · Hedged and unhedged returns are closer for the than unity in some cases, indicating that a risk- short-duration hedges; at the longest duration, minimizing strategy would have hedged the the unhedged return is much greater than the whole portfolio.3 Hedging efficiency increases hedged return, which shows a loss on the hedged with contract duration, while the gap between portfolio. This disparity is due to the rise in spot the hedged and unhedged returns is substantial prices through the latter part of the period--any especially for the longest duration hedge. amount of hedging reduces the gains that could · The results for the second subperiod indicate that have been made by waiting and selling only spot boththerisk-minimizinghedgeratioandhedging on the delivery date. efficiency increase with contract duration. The 3A risk-minimizing hedge ratio of greater than unity indicates that a risk-minimizing strategy would have hedged more than the seller had crude available to sell. It is assumed that the oil producer would not wish to take such an action. 5 Hedging 37 gap between the hedged and unhedged returns than the cost of remaining unhedged. This effect increasesmarkedlywiththedurationofthehedge. is particularly strong for the longest duration The increase in spot prices during this period is hedge in all periods. particularly large for the two-year hedge. · The returns from hedging at all contract lengths · For the most recent subperiod, hedging efficiency indicate that, over the duration of the hedge, the is low for all but the longest hedge, and the futures contract underestimated the rise in spot risk-minimizing hedge ratio shows no pattern prices that actually took place. This effect is most with respect to duration. The unhedged return noticeable during the most recent subperiod is extremely large for long duration hedges, where all durations show a substantial gap so sell hedgers would have experienced large between hedged and unhedged returns. opportunity losses. · The three-month hedge calculated from average These results from a risk-minimizing hedging futures prices produces a higher risk-minimizing strategy indicate that taking expected returns into hedge ratio and a lower hedging return than the account might go far in making the case for hedging. three-month hedge based on month-end prices. The risk-minimizing hedge is in effect identical to an Hedging efficiency and unhedged return are optimal hedge when the risk parameter is so great similar to those for the end-month prices. that a large trade-off in return would be accepted for · Although the risk-minimizing hedging strategy a small reduction in risk. The impacts of different does not take return on portfolio into account, relative preferences for risk are explored through it can be seen that ex post hedges in all cases the use of an optimal hedge, calculated for different have lower returns than an unhedged portfolio. values of the risk parameter. Because futures prices rose during the length As an example, the three-month sell hedge based of the hedge, the strategy of selling and then onend-of-monthpricesforWTIcrudeisestimatedand buying back the hedge to close out the position simulated over the period January 2004 to July 2005. reduces the return of the portfolio. In all cases, This again is an ex post hedge using the estimated the difference between unhedged and hedged values of the optimal hedge ratio and mean change returns increases with the length of the hedge. in futures prices derived from the same subperiod. During the second subperiod, when oil prices The results of this hedging strategy are shown in were beginning their steep climb, futures prices table 5.3 for a range of risk parameters. Values of the rose rapidly during the period of the hedge: for optimal hedge ratio, the variance of the portfolio, long hedgers, the failure to see the future's higher and the return for the optimal hedge are shown. prices would have resulted in a large opportunity Values for the risk-minimizing hedge (where the risk loss relative to an unhedged portfolio. parameter is set equal to infinity) and the return from · For long hedgers, the negative of the returns of the unhedged position are also included. the hedged and unhedged positions shown in The calculation shows that the impacts of varying table 5.2 are interpreted as the direct costs of the risk parameter--unless it is very low--on the the hedge. For example, a buyer of crude during choice of optimal hedge ratio, return, and risk as the period from January 2004 to July 2005 using measured by variance are small. However, the ability a 24-month hedge would have experienced a to forecast the average spot price return over the cost per barrel of US$5.29 through hedging; an period and build this into the hedging strategy does unhedged buy would have resulted in a cost of allow a considerable reduction in risk to be achieved US$19.51. These costs, like the returns of a sell if risk is seen as highly important relative to return. hedger, are measured relative to the current spot Thus far, the hedges considered have all been prices prevailing each month at the time of taking calculated for a seller of WTI crude, allowing out the hedge. For every subperiod and duration, removal of the basis risk element due to quality the cost of the risk-minimizing buy hedge is lower differentials. For sellers of other crudes, whose spot 38 Special Report Coping with Oil Price Volatility Table 5.3 crudes for which the differences are more marked in the second and third subperiods. For Kole and Optimal Three-Month Ex Post Sell Hedge for WTI Mandji, the efficiency falls to about 30 percent in Crude, January 2004­July 2005 the second subperiod. Risk Optimal Optimal Optimal · The risk-minimizing hedge ratio is near unity in parameter hedge ratio return variance both the first and third subperiods, suggesting that virtually all physical sales should have been 0.4 0.36 3.38 23.07 hedgedtominimizerisk.Inthesecondsubperiod, 0.5 0.39 3.29 22.44 the risk-minimizing hedge ratio is substantially 1 0.44 3.10 21.05 lower for most crudes. The variations in hedging 3 0.48 2.98 20.03 efficiency and the risk-minimizing hedge ratio suggest that a dynamic hedging strategy and 5 0.48 2.96 19.81 alteration of the risk-minimizing hedge ratio as 10 0.49 2.94 19.65 markets changed over time would have been 20 0.49 2.93 19.56 useful. · The unhedged and hedged returns (shown in 40 0.49 2.93 19.52 annex 5) are similar to those for WTI crude for 60 0.49 2.93 19.51 a six-month duration hedge. In the second and, 0.49 2.92 19.48 especially, the third subperiod, unhedged returns are greater than hedged for sellers of crude. Unhedged n.a. 4.58 27.07 Source: Author calculations. Buyers or sellers of oil products can hedge certain Note: n.a. = not applicable. products on NYMEX, which could enable importing governments to reduce the risk of future purchase prices may not move as closely to crude futures costs. Because only certain specifications of these as does WTI crude spot, the greater basis risk can products are quoted on the exchange, there will be a tarnish the attractiveness of a hedging strategy. Data basis risk element relating to the difference between were available for a number of monthly average the quoted quality and the imported quality. For spot crude prices starting in February 1988, and example, for motor gasoline, the NYMEX contract is the risk-minimizing ex post hedge was estimated for reformulated regular gasoline; for heating oil, it for these 16 crudes for the whole period and the is the "number 2" heating oil used in domestic and subperiods. The risk-minimizing hedge ratio and medium-capacity industrial burners. Contracts for hedging efficiency are shown in table 5.4. The results reformulated gasoline ended in mid-2006 and were of additional calculations for hedged and unhedged replaced by those for the gasoline blendstock for returns are given in annex 5. blending with ethanol. The risk-minimizing three- Thehedgingperformanceofvariouscrudesbased month hedge for these two products was calculated on a six-month ex post hedging ratio reveals some for the whole period for which data were available important characteristics: and for the subperiods identified above. The results are shown in table 5.5. · The efficiency of hedging for all crudes is lower The performance of hedging oil products on than that for WTI crude; the basis risk increases NYMEX would have been similar to that of hedging for crudes for which no futures contracts exist. WTI crude. In the earlier subperiods, the risk- This effect is particularly pronounced in the most minimizing hedge ratio is near unity, suggesting that recent subperiod. hedging virtually all products for sale or purchase · Hedging efficiency does not vary greatly among would have minimized risk. Hedging efficiency falls crudes in the first subperiod, but there are certain inthemostrecentsubperiodandislowestforgasoline, 5 Hedging 39 Table 5.4 Ex Post Risk-Minimizing Six-Month Sell Hedge Ratio and Hedging Efficiency for Various Crudes, February 1988­December 2006 Feb. `88­Dec. `06 Feb. `88­Dec. `99 Jan. `00­Dec. `03 Jan. `04­Dec. `06 Hedge Hedging Hedge Hedging Hedge Hedging Hedge Hedging Crude, country ratio efficiency ratio efficiency ratio efficiency ratio efficiency Brega, Libya 0.96 0.61 1.04 0.73 0.82 0.64 0.98 0.56 Cabinda, Angola 0.90 0.58 1.00 0.71 0.75 0.55 0.91 0.52 Cossack, Australia 0.97 0.61 1.00 0.74 0.90 0.59 1.00 0.56 Dukhan, Qatar 0.91 0.59 0.96 0.72 0.75 0.65 0.94 0.53 Es Sider, Libya 0.95 0.60 1.04 0.72 0.80 0.62 0.96 0.55 Forcados, Nigeria 0.99 0.60 1.07 0.73 0.80 0.62 1.02 0.55 Iran Heavy, Iran, Islamic Rep. of 0.85 0.57 0.95 0.71 0.66 0.51 0.86 0.52 Iran Light, Iran, Islamic Rep. of 0.89 0.58 1.00 0.71 0.69 0.53 0.90 0.54 Kole, Cameroon 0.99 0.59 1.06 0.74 0.68 0.30 1.06 0.60 Mandji, Gabon 0.97 0.58 1.03 0.71 0.65 0.32 1.05 0.60 Marine, Qatar 0.87 0.57 0.96 0.72 0.72 0.62 0.88 0.50 Murban, Abu Dhabi, UAE 0.91 0.59 0.97 0.72 0.77 0.66 0.94 0.52 Oriente, Ecuador 0.89 0.54 1.00 0.72 0.80 0.52 0.88 0.47 Saharan, Algeria 0.97 0.60 1.07 0.72 0.83 0.64 0.98 0.54 Urals, Russian Federation 0.90 0.58 1.04 0.69 0.69 0.54 0.90 0.54 Widuri, Indonesia 0.94 0.62 1.00 0.75 0.88 0.66 0.96 0.56 WTI crude, U.S. 0.82 0.67 0.99 0.79 0.89 0.68 0.71 0.67 Sources: Spot prices from Energy Intelligence 2008; author calculations. Note: UAE = United Arab Emirates. at only 33 percent. A sell hedger would generally have imports or exports have begun making much greater found that the return from an unhedged position was use of this financial instrument. Nevertheless, an greater than that for a hedged position, while a buy instrument that avoids large regrets could become hedger would have found the reverse. One exception increasingly attractive. is crude oil in the third subperiod, which shows On any day in the market, call and put options for that the unhedged return was lower at 2.29 than the future months can be obtained. Although these can hedged return at 2.44. extend six years ahead, few deals are concluded on any day for more than one year ahead. The options Use of Options contract offers a potential option-holder a menu of choices. For a wide variety of strike prices (the prices The use of options on futures contracts has become at which the holder will have the right to purchase or better established in recent years, but, although sell at the time of contract expiry4) the premiums to be there is regular activity on the markets, there is little paid forthis rightwill vary accordingto marketbeliefs evidence that governments wishing to hedge oil about future prices. Table 5.6 shows call options prices 4A European option gives the right to exercise the option only at its expiration, while an American option gives the right to exercise the option at any time until the expiration date. 40 Special Report Coping with Oil Price Volatility Table 5.5 Ex Post Risk-Minimizing Three-Month Sell Hedge Ratio and Hedging Efficiency for Gasoline and Heating Oil on NYMEX, January 1987­April 2007 Fuel and dates Hedge ratio Hedging efficiency Hedged return Unhedged return Gasoline (US˘/U.S. gallon) Jan. 1995­Mar. 2007 0.98 0.60 0.95 1.92 Jan. 1995­Dec. 1999 1.05 0.54 -0.36 1.37 Jan. 2001­Dec. 2003 1.03 0.58 -2.71 1.34 Jan. 2004­Mar. 2007 0.84 0.33 5.80 12.09 Heating oil (US˘/U.S. gallon) Jan. 1986­Apr. 2007 0.98 0.60 0.95 1.92 Jan. 1986­Dec. 1999 1.16 0.59 0.65 0.92 Jan. 2000­Dec. 2003 1.14 0.54 -2.54 0.38 Jan. 2004­Apr. 2007 0.84 0.65 5.99 7.85 WTI crude (US$/barrel) Jan. 1987­Mar. 2007 0.76 0.50 0.32 0.59 Jan. 1987­Dec. 1999 1.04 0.71 -0.06 0.20 Jan. 2000­Dec. 2003 0.78 0.53 -0.47 0.46 Jan. 2004­Mar. 2007 0.61 0.44 2.44 2.29 Source: Author calculations. quoted on the NYMEX on October 11, 2007, when the of US$77 a barrel, paying US$5.34 as the option price. spot price for WTI crude was about US$84 a barrel. As the expiry date approaches, the decision will The table indicates that a call option giving the right have to be made as to whether the option should be to buy WTI crude in December at a price of US$69 a exercised. Affecting the decision are two potential barrel would have required a premium of US$11.71 to situations, as follows: be paid, while an option with the right to purchase at US$79 in December would have required a premium · The spot price in effect at the time the agent is of US$3.45. The very high premium attached to a considering whether to exercise the option is above the strike price of US$69 indicates that market sentiment strike price. Assume a spot price of US$83 a barrel felt that the spot price at the expiry date would be quite and a strike price of US$77 a barrel. In this case, high, so the options writer (the agent selling the call it will be profitable to exercise the option since option to the holder) would require a large premium that is the less expensive means of acquiring to offset an option price much below the expected the physical commodity. As described above, to spot price. The higher the strike price, the less likely obtain the guaranteed overall price, the agent the future spot price would be above this level and must close the position on the futures market by allow the premium to be reduced. selling a contract to expire on the contract expiry The option contract can be combined with the date, thus offsetting the position in the futures physical purchase in much the same way as a simple market. Since this sell price should be close to the futures contract. For example, an agent that knows spot price that will govern the physical purchase, it will purchase crude oil in March 2008 could have the net cost is that of the options contract--which purchased a call option in October with a strike price will equal the strike price plus the option price 5 Hedging 41 (US$77 + US$5.34). The sum of these two choose to exercise its right to sell will be greater at can be greater than the prevailing spot price. higher spot prices. If the spot price ruling at the time However, because the options price has already of exercise of the contract is lower than the strike been incurred, only the strike price is relevant price, then the holder of the put option will exercise in deciding whether it is better to exercise the it in order to maximize the gains. If the spot price is option. As with simple hedging described above, above the strike price, the holder of a put option would there is a basis risk on this transaction in that the allow it to expire. futures sell price, entered into to close the futures In sum, an options holder can obtain a more position, may differ from the spot price at the time favorable distribution of outcomes by allowing the of physical purchase. option to expire in high-regret circumstances (a low · The spot price in effect at the exercise time is below the spot price for call options and a high spot price for strike price. In this case, it is better to let the option put options), but there is an additional cost--that of expire and purchase crude on the spot market at the premium--to be paid whatever the outcome. To this lower price. The total costs will be the sum obtain a large margin of protection against regrets (a of the option price (paid regardless of whether very low spot price for buyers of crude) will require the option is exercised) plus the spot price at the a large upfront premium, which will reduce the time of the physical purchase. attractiveness of the strategy. Similar considerations govern the use of put options that might be utilized by an oil producer Issues in Operating an Oil Hedging wishing to lock in a floor price for a future sale, Program while not missing the opportunity to benefit from The primary purpose of an oil hedging program is an unforeseen increase in spot prices. The producer to reduce the risks from the volatility of crude oil entering into a put option pays the option price to or oil product prices. Oil-producing nations, facing the writer. The option price increases at higher strike uncertain future revenue streams, could hedge prices because the probability that the holder will revenues from future production, while importing countries could hedge purchases of gasoline or diesel. State-owned enterprises also may be large enough to Table 5.6 engage in a systematic hedging program. The United European Call Options for WTI Crude on NYMEX, Nations Conference on Trade and Development (2005) October 11, 2007 (US$) describes the possibility of a state transportation Option price for Option price for company using a swap agreement to reduce risks on Strike price Dec. 2007 Mar. 2008 the purchase of fuel supplies. Other agencies such as 69.00 11.71 10.97 power companies may similarly wish to reduce risk by means of these instruments. To date, however, there is 71.00 9.84 9.40 no evidence that governments and their agencies have 73.00 8.05 7.92 begun making use of this financial instrument much 75.00 6.35 6.56 more than in the past, and it appears that there are several factors to be considered before a government 77.00 4.81 5.34 would be willing to institute such a program. If the 79.00 3.45 4.27 main objective of the government is to stabilize public 81.00 2.39 3.39 expenditure or the balance of payments, it would be more appropriate to find a hedging instrument 85.00 1.02 2.01 that is highly correlated with variations in public 87.00 0.63 1.54 expenditure or the balance of payments. Only when Source: Author calculations. variations in the oil price are the dominant factor in 42 Special Report Coping with Oil Price Volatility their volatility will oil price hedging provide a large of the time when futures prices were available for degree of risk reduction. the specific duration. The percentage increases, and correspondingly the correlation coefficient with the Degree of Volatility of Crude Oil and Oil current spot price decreases, with increasing number Product Prices of months in the futures contracts. When data from The statistical tests reported in chapter 3 show that January 2004 are considered, the percentage rises to the volatility of crude oil prices, whether measured as much as 100 percent for 24-month futures contract daily, weekly or monthly, was lower in January 2004 prices. That is, a buyer of WTI crude oil would have to March 2007 than in January 1986 to December 1999 consistently benefited from locking into 24-month and January 2000 to December 2003. Gasoline, diesel, futures prices. and jet kerosene prices were slightly more volatile This ex post finding should not be taken as an in the most recent subperiod; heating oil, residual endorsement of the use of futures markets to mitigate fuel oil, and propane were less volatile compared to the adverse effects of large price increases. At the time January 2000 to December 2003, but not January 1986 of taking out the hedges, the futures prices may have to December 1999. In virtually every case, volatility been the best estimates possible of the spot price that was higher in the second subperiod than from the would be in effect at the time of closing out the futures beginning of the sample period to December 1999. The contract. Importing governments or their agents are changes in volatility and in correlation between spot unlikely to be able to make a systematically better and futures prices resulted in a decline in hedging estimate of the prices in the coming months than the efficiency in the most recent subperiod for both crude market itself. Hedging is designed to remove risk and oil and gasoline. The actual hedging efficiency for not to increase returns, and the ex post experience of a crudes and for oil products is not particularly high in periodofunhedgedreturnsexceedinghedgedreturns any period (except for a hedge of two-year duration is no gauge as to whether this will continue. For large which reaches close to 90 percent in two subperiods); oil-exporting countries with substantial experience in it is low for WTI crude and gasoline in the most recent selling crude on the international market, it is more subperiod. The basis risk is an increasingly important plausible that they on occasion may be able to make factor in the oil futures market, so the attractiveness of superior estimates of price movements in the coming hedging as an instrument to reduce risk (as measured months and hence be able to engage in a successful on an ex post basis) does not appear to have increased hedging program. in the recent period of higher oil prices. The calculations undertaken for hedging returns Duration of Available Hedges show that, during the periods considered and The futures markets have seen a steady lengthening especially the most recent subperiod, a sell hedger of the duration of futures contracts available. From would have been better off not to have hedged at the experience of the 1980s, when crude oil futures all but to have just sold on the spot market and contracts stretched out only to six months, the thereby benefited from the steady climb in prices. maximum duration of a contract is presently around Conversely, a buy hedger would have found it sevenyears,althoughnotallmonthsaretradedatsuch much more attractive to have hedged during this long durations. The duration of contracts for gasoline period, locking in the futures prices which generally and heating oil have also increased to around three turned out to be lower than the spot prices in effect years. This provides a much more flexible approach at the time of hedge closing. To illustrate, figure 5.1 to hedging and the possibility of reducing risks over compares monthly average spot prices of WTI crude a longer period, as the superior performance of two- with 6-month, 12-month, and 24-month futures year futures contracts in reducing risk illustrates. contract prices; table 5.7 summarizes statistics on the However, during the periods analyzed, and especially data shown in the figure. Since 1986, futures prices the most recent subperiod, the unhedged return (for proved to be lower than spot prices 63 to 79 percent a seller) greatly exceeded the hedged return. 5 Hedging 43 Figure 5.1 for many durations and subperiods, it is below 70 percent, indicating the magnitude of residual risk Spot and Futures Prices of WTI Crude even under relatively favorable circumstances. Governmentslookingtohedgeoilproductimports 100 Spot should note that for certain products (kerosene and 6-month futures automotive diesel), there are no direct futures trades; 80 lerrabrep 12-month futures consequently, a further basis risk would be involved 24-month futures 60 if gasoline or heating oil futures were used to hedge these products. The correlation between, for example, $SU 40 spot kerosene and futures heating oil prices would clearly be weaker than that between spot heating oil 20 and futures heating oil. 0 1986 1990 1994 1998 2002 2006 Actual Sale or Purchase of Physicals 6 12 24 The analysis of operations of a simple hedging Statistic mo. mo. mo. contract described above implicitly assumes that the % of months when futures prices were seller or purchaser of physicals will be making and lower than current spot prices, entire period 63 67 79 financing the futures contracts through the broker. In % of months when futures prices were lower than current spot prices, since Jan. `04 78 74 100 practice, this is often not the case (see, for example, Gerner and Tordo 2007). For a producing country, Correlation with spot price, entire period 0.93 0.88 0.77 the national oil company--if it is actually producing Correlation with spot price, since Jan. `04 0.81 0.80 0.69 and marketing the crude--would be able to carry Sources: U.S. EIA 2008a and Bloomberg.com; author calculations. out both operations. In some countries, the national Note: Spot prices are monthly averages; futures prices are those oil company or petroleum ministry will merely be quoted 6 months, 12 months, and 24 months earlier on NYMEX. receiving taxes and royalties on the sale of crude producedandmarketedbyinternationaloilcompanies. Where production levels and plans are not directly Basis Risk controlledbythegovernment,thereareadditionalrisks For all crude oil and oil products, there is a basis risk that inappropriate amounts might be hedged. For which leaves a residual uncertainty about revenues example, a shutdown or sudden decline inproduction to be received. Hedging efficiency calculations show not foreseen by the government could lead it to hedge that the basis risk is extremely large in the most recent more than was appropriate, with a possibility that its subperiod, reflecting the fact that the futures price for obligations through the closing-out buy hedge would immediate delivery (for the month ahead in which leave it with a temporary financing burden. Moreover, the contract was to be closed out) was not always sincetaxandroyaltypaymentslagcrudesales,revenue close to the spot price in the delivery month.5 The flow may be uneven to an extent that could not be two-year hedge has the greatest hedging efficiency. removed by a simple hedging strategy. The basis risk for crudes other than WTI (which forms Oil products may similarly lead to problems, the reference for NYMEX) is in most cases slightly even though governments rarely purchase these higher than that for WTI, but this gap is particularly themselves. Private sector purchases of oil products pronounced in the most recent subperiod. Gasoline in a country where government hedging is designed and heating oil have a similar residual risk to that of to smooth out the payment of subsidies through a crude. Hedging efficiency never exceeds 90 percent; price support scheme leads to the possibility that 5In practice, spot transactions are made on a particular day; thus, the monthly average price is not necessarily representative of a particular transaction. 44 Special Report Coping with Oil Price Volatility changes in private sector purchase plans would responsible for large losses serve as a warning as to result in inappropriate quantities being hedged by the difficulty of maintaining adequate oversight. the government. Legal Restrictions Financing Margin Calls In some countries, state oil companies or other Theoperationofthefuturesmarketrequiresthehedger government agencies are not permitted to use futures to be able to finance daily margin calls, depending or options because of their association with purely on the day-to-day price movements of the contract. speculative activities. Where such a ban exists, Some of these daily movements have been large in the government would have to consider whether recent years, and runs of successive price increases it wished to change the law and how to do so in a are not uncommon. Chapter 3 indicated that lengthy way that would limit risk from speculative trading runs of cumulative positive or cumulative negative by its agents. Commodity hedging programs may deviations were common even when looking at the require the passage of legislation authorizing the deviation of prices from a trend (the Hodrick-Prescott program and establishing boundary conditions for filter), and that in the extreme cases these lasted its implementation. Although active hedging may several years. If hedging decisions were made on the be more effective than rule-based hedging, it might basis of the filtered prices, the cumulative margin require a higher degree of autonomy on the part of calls could be large and persistent. Even though the the executive branch. Because spending authority is margin is eventually returned and earns interest, normally established by an existing budget law, the the temporary financing requirement could prove type and efficiency of hedging strategies available to unmanageable for the government. The resulting a government may be limited. short-term and immediate financing requirement when a large volume of crude is being hedged would Political Accountability result in highly variable outflows and inflows to the Ultimately, as numerous writers have pointed out, the government agency taking out the hedge. This lack of government is responsible for the success or failure of predictability could be difficult to handle in countries a hedging program. When prices rise, the use of a sell where there is only weak cooperation between the hedge can result in missing the opportunity to achieve hedging agency and the central bank. In addition, higher sale prices by avoiding the futures market extremely careful monitoring would be needed to and selling on the spot. The government could come ensure that appropriate amounts are transferred. under pressure to explain why its revenues have not risen in line with world oil prices. The extra certainty Oversight in the revenue flow provided by the hedge may not Becauseanactualhedgingprogramrequiresspecialist satisfy those who do not have to manage budget knowledge, oversight for the government becomes expenditures. Similarly, a buy hedger, in a period both important and difficult. If the hedging program when product prices actually fall, may pay more is carried out by government employees--whether in through the hedge than could have been achieved thetreasury,astatecompany,oradedicatedagency--a by waiting to purchase. If the government's critics layer of oversight will be needed with the authority were unaware of what could have been achieved to review all documents and trades. Agents given too through a hedge when product price had risen, there much latitude in running the hedging program may would not be a symmetric complaint concerning the be able to conceal for a long time trading mistakes government's lack of hedging to have captured such that have been made. There are incentives to cover gains. Any asymmetry of such pressure would reduce up losses by making even riskier trades in the hope the likelihood that a government would be willing to of incurring an offsetting profit. Recent examples in undertake a hedging program. It also suggests that if the private sector of single individuals apparently a government were to consider doing so, a widespread 5 Hedging 45 public education program should be conducted, as useful for such a complex operation, and one in which was done by the state government of Alaska when it large sums of money are involved. The fact that was considering whether to hedge oil production. (In governments do not now appear to be hedging sales the end, Alaska chose not to hedge.) or purchases on a broad scale indicates that hedging Some of these concerns can be addressed by the is not a simple solution for dealing with problems of use of options, which permit a seller to take account oil price volatility. of prices higher than initially anticipated or, for a Even very large and sophisticated companies buyer, prices lower than anticipated. However, the have on occasion lost large sums of money through size of premiums that may have to be paid to obtain a the use of derivates. Bailey (2005) describes the case substantial degree of cover against these possibilities of Metallgesellschaft Refining and Marketing whose could seem expensive in retrospect and provoke business centered on buying oil products (diesel, further opposition. heating fuel, and gasoline) at spot prices and selling to customers on long-term contracts. The company Lack of Models also traded in futures and swaps for which the For some governments, the lack of well-known and underlying assets were oil products. In late 1993, its successful examples in other countries that could losses on this business were more than US$1 billion, be studied and copied is a considerable drawback. of which a substantial fraction could be attributed to Learning from the actions of others can be particularly the injudicious use of derivates. 6 Security Stocks and Price Hikes In the absence of buffer stocks, physical disruptions to imports. Delays in shipments or unloading are fairly supply can cause temporary sharp spikes in end-user common but are not normally protracted; a modest prices. As a result, stocks of crude oil and oil products amount of stock is thus sufficient insurance against have been a common feature of the oil industry this type of supply disruption. worldwide. Coordinated use of stocks to smooth price Similar considerations explain why companies volatility is not unique to oil, and efforts have been hold stocks of oil products. Demand may experience made to do the same for other commodities (box 6.1). a sudden surge or supply a temporary dip (for example, from an unscheduled refinery shutdown). An adequate level of commercial stocks ensures that Supply Disruptions sharp price spikes, rationing, or both can be avoided. In countries that import or produce crude oil to supply In markets with several sellers, companies have a domestic refineries, crude stocks provide a necessary strong incentive not to run out of supplies, since a buffer to allow the refinery to be supplied at a constant temporary inability to supply the market may lead rate even if there are fluctuations in production or to a permanent loss of business to reliable-appearing rivals able to provide supply. Again, such disturbances tend to be small compared to sales, so stocks need not Box 6.1 be very large. Carrying stocks incurs costs--both in terms of the capital required to construct additional Experiences with Other Commodities storage facilities (tanks) and the interest costs forgone As noted in chapter 1, price volatility is not confined to on the value of the crude oil or oil product held in the oil sector. For example, there have been numerous stock. These costs need to balanced against possible attempts to smooth prices for agricultural and mineral benefits. Where the likelihood of a disruption is higher commodities through various stock schemes. Some of (for example, where alternative supplies cannot be these schemes have been designed to stabilize the brought in quickly, as in land-locked countries with world price through stock additions or withdrawals, no pipeline infrastructure), or where the costs of while others have focused on internal price adjustment being short are seen by a company as being more to consumers. Upon reviewing the literature, Dehn, damaging, the amount of precautionary stock held Gilbert, and Varangis (2005) concluded that, for export is likely to be higher. commodities, the crucial problem was that there were overoptimistic price expectations, leading to eventual On rare occasions, the oil market suffers large bankruptcy of many of the schemes. Although the disruptions of either an internal or external nature. current era of high oil prices is different from earlier A lengthy shortage of crude oil or oil product can episodes of falling export prices, the difficulty of be highly damaging to an economy, as users of predicting the general level of future prices is common oil products face rationing or even the complete to both oil and other commodities, and mistakes in unavailability of a crucial input. Two significant such forecasts can be just as expensive now as they users of crude oil and oil products are the power were earlier. sector--when electricity is generated from fuel oil or 47 48 Special Report Coping with Oil Price Volatility diesel--and the transport sector. Because power and In practice, major disruptions have rarely resulted transport typically play major roles in the production in complete unavailability of oil supplies, but rather structure of an economy, a complete disruption in price spikes when reductions in supply have forced of supply would have great adverse effects on the prices up. This was the case in Zanzibar when a economy. cargo failed to arrive on time in 2005. In other cases, In the case of the power sector, there may be however, inadequate transport capacity for alternative excess capacity of other forms of generation that can sources of crude oil or oil products has led to both be run more extensively. Diesel may serve as a backup markedly higher prices and actual physical shortages, fuel to fuel oil; it is also used for the small generators as experienced in 2005 by copper mines in Zambia. In used to supplement grid supply, which is subject to that case, fuel oil shortages were caused by a shortage outages. If the country were to experience shortages of rail tankers, and mines were forced to cut back of both fuel oil and diesel, the costs to the economy copper production drastically or stop production would indeed be large. In many countries, there are altogether (Bacon and Kojima 2006). no alternative fuel sources available in the short run, On the global front, Leiby (2004) and Harks (2003) and rationing would have to be imposed. The inability providedetailsofmajoroilmarketdisruptionsbetween to obtain continuous power supply--especially 1950 and 2003; this is summarized in table 6.1. if unanticipated--can impose very high costs on businesses that depend on power as a key input. The IEA Response costs of unserved power are often estimated as vastly Faced with the possibility of a large supply disruption exceeding the costs of served power.1 and the associated spike in international oil prices, In the transport sector, which covers goods many governments have established strategic oil transport (trucks and rail) and passenger transport reserves. In this regard, the member countries of (buses and cars), there are no short-run substitutes the International Energy Agency (IEA) created the available when a disruption in oil product supply International Energy Program, which includes rules occurs. Rationing may be used to direct limited for the amount of oil stocks to be held by member supplies to priority uses--such as away from private countries and rules for releasing such stocks onto the car use to public transport--but there will inevitably market. The arrangement requires that each member be a loss of production and welfare. hold stocks equivalent to at least 90 days use of net Table 6.1 Types of Oil Market Disruptions, 1950­2003 Type Number Duration (months) Size (% of world supply affected) Accident 5 5.2 1.1 Internal political struggle 9 6.5 2.3 International embargo/economic dispute 4­6 11.0 (6.1a) 6.2 War 4­7 Total number, average duration, and average size 24 8.1 (6.0a) 3.7 Source: Leiby 2004. Note: The duration and size of international embargoes and wars are combined here. Some of these events were difficult to classify, affecting the data in the number column. a. Excluding 44 months of Iranian oilfield nationalization. 1Estimates for the costs of unserved power vary widely and depend on the mix of household and business users. The East African (2000) quotes figures for Kenya of between US$0.50 and US$0.80 per kilowatt-hour for unserved power, while the Energy and Resources Institute (TERI 2001) estimates the production loss in two Indian states between Rs 7.2 and 24.7 (US$ 0.15 to US$0.52 using the average exchange rate in 2001) per kilowatt-hour. 6 Security Stocks and Price Hikes 49 imports (see Hale & Twomey Limited 2005 for an The use of security stocks to smooth the effects of operational discussion of this arrangement in New high international prices has attracted some attention. Zealand). Such stocks may be held by the government Ontwooccasions,theUnitedStateshasreleasedstocks directly,orcompaniescanbemandatedtoholdcertain tomitigatehighpricelevelsinanactionindependentof amounts of stocks beyond their normal commercial formal IEA criteria. The European Union considered, levels, as in Japan and the Republic of Korea. but did not legislate, a directive that would have made Under the original Agreement on an International price smoothing a direct target of stock use. If a large Energy Program, stocks could be released if one or stockholder or a bloc of countries such as the IEA more members sustained a reduction in the daily rate members were to release stocks onto the market, there of their oil supplies at least equivalent to 7 percent could be two effects on prices. First, the extra supply of the average daily rate of their final consumption. could be sufficiently large relative to global supply so as to lower the market-clearing price. Second, the The agreement was complemented in the 1990s by willingness to respond in this way could persuade the Coordinated Emergency Response Measures, those trading or hedging on the oil markets that which provide a rapid and flexible system of response higher prices will be met with stock drawdowns, thus to actual or imminent oil supply disruptions, reducing the chances that prices will rise further. including supply reductions below 7 percent. The agreement was superseded in the 1990s by the Implications of Security Stock Holding CoordinatedEmergencyResponseMeasures,whichis a consultation process among members of the IEA on As a result, the mere existence of the security stocks whether it is appropriate to recommend a coordinated means that futures prices are less likely to be driven stock drawdown. As discussed by Emerson (2006, up when there is a perception that the market will p. 3380), this provision has rarely been used, partly become tighter. Such a large-scale stock drawdown because "strategic oil reserves were to be saved in case creates important externalities for consumer countries that did not reduce stocks, since they benefit from they were more urgently needed later on." the general lowering of oil prices. This is due to the At the same time, it has become clearer to policy global nature of the oil market whereby a shock to makers that oil security is less a matter of volume one part of the market is quickly reflected in prices than of price. Indeed, Taylor and Van Doren (2005) throughout the market. concluded that the costs of running the U.S. Strategic For a small country or one whose stocks are not Petroleum Reserve had largely outweighed its large by global measures, stock releases could not benefits, and that this was likely to continue to be the be large enough to have a material effect on global case in the future. oil prices. However, such stocks could be sold into The use of security stocks to provide temporary the domestic market below the import price, thus domestic supply in the presence of a global supply protecting consumers in part from the impact of the disruption will depend on how such a disruption international price rise. The government might wish is defined. The IEA approach is to work through its to protect only certain groups (such as the commercial governing board to determine whether an actual or transport sector through its purchases of diesel), or potentially severe oil supply disruption is occurring, it might wish to provide some price protection to all and, if so, to recommend to member countries to take members of the society. To achieve the latter end, the a number of actions including stock drawdown. Such government would have to mandate a price at which an approach is quite distinct from a scheme that is all supply, whether from imports or stocks, would responsive only to price changes. For example, the have to be sold in order to avoid only select purchasers steady run-up in prices during the 2004­07 period, benefiting from the stock release. caused by market sentiment rather than a major and To operate such a scheme, the government has to unanticipated reduction in global supply, did not purchase stocks when prices are relatively low, store trigger an IEA stock release. them until needed, and then release some onto the 50 Special Report Coping with Oil Price Volatility market at times of higher prices. This cycle has to be the government, instead of purchasing oil, put an repeated if the scheme is to have a long-run effect. equivalent amount of money into a dedicated account. The timing and amount of purchases and releases When the rules indicate that oil should be released are critical, as are the costs of holding the inventory.2 onto the market at prices below the international price, Brathwaite and Bradley (1997) analyzed the operation money would be released from the fund to lower the of such a scheme for California, assuming that costs prices charged relative to those paid for the import of refilling would be less than the depressing effect on of crude oil or oil products. The basic features of the prices of the subsequent stock release, and that release operations of a security stock scheme designed to and refilling would occur each year. Their study smooth domestic prices are illustrated by a simple targeted a decrease of US$0.12 a gallon (US$0.032 a two-period example. liter) below market prices, and found that, if prices during restocking at annual intervals rose by more The Operation of a Two-Period Price- than US$0.02 a gallon (US$0.005 a liter, or US$0.84 a barrel), the scheme would not be worthwhile. Smoothing Security Stock Scheme The issue of how to purchase oil to place into the Two different schemes are illustrated: scheme A security stock has been analyzed by Yun (2006), who uses physical stocks that are purchased, stored, and evaluated various hedging strategies for purchases. then released; scheme B involves "virtual" stock, in The basic scenario assumed that when the oil price that cash is provided by the government to lower was higher than normal, stocks were released; oil prices in the country when international prices and, simultaneously, the stockpiler was assumed are too high. In both cases, the consumption of oil to buy forward in times of low oil prices to protect products in the country is 40 units per period. Two against price increases during the refilling period. scenarios for international prices are considered. In More complex hedging rules were also considered. both, the international market price (paid to import However, the study did not consider the more realistic oil) is US$40 per unit in the first period. In the second case of the stockpiler considering whether to replenish period, alternatives of US$60 per unit or US$35 per at a given moment depending on prevailing prices. unit are considered. The cost to the government of Aschapters3and4show,crudeoilandoilproduct storing one unit of oil for one period is 5 percent of prices appear to have become nonstationary in recent the value of the stock held. years and do not exhibit strong mean reversion. Scheme A, the physical stock scheme, is governed Consequently, the government often may have to by the following. wait a lengthy period before it can refill at prices that seem economic. Moreover, there is a distinct · If the price is less than US$45 a unit in the first risk that the inventory might be filled at a price period (floor trigger price), the government will that turns out to be higher than subsequent market buy 20 units in the first period and store them. prices. This circumstance would mean either that · In the second period the government will release stocks would have to be sold at a loss, or that a large 20 units from stock, if available, when the price inventory would have to be financed for a lengthy is above a trigger of US$55 a unit (ceiling trigger period. A formal analysis of the optimal operation of price). a commodity inventory when prices are stochastic but · The price charged to consumers during a stock mean-reverting is provided by Secomandi (2007). drawdown period will be the weighted average of Any scheme with given rules for the purchase, the amount released from the stock valued at the storage, and release of oil in relation to price signals ceiling trigger price and the balance purchased by could be mirrored by a "virtual" stock in which companies valued at international market prices. 2DynMcDermott (2005) quotes US$3.00 a barrel per year for the Japanese oil reserves, US$1.60 for the European oil stockpile, and US$2.40 for U.S. industry stocks. 6 Security Stocks and Price Hikes 51 A market unit price of US$40 in the first period is consumers is US$100 in total (US$2.50 per unit × 40 below the floor trigger, and the government purchases units).Ontheotherhand,thegovernmentfacesdifferent 20 units at a cost of US$800. If the international costs in the two schemes, as shown in table 6.2. price rises to US$60 in the second period (above the Using physical stocks, the government can benefit ceiling trigger), the government releases the 20 units from capital appreciation if prices rise and can pass from the stock at a price of US$55 per unit to the these benefits on to consumers. The net position of companies. The companies then sell 40 units priced the government depends on the magnitude of the at US$57.50 a unit, which is the weighted average price change and the costs of storage. If prices fall, the of the international market price and the stock sale government suffers a capital loss and also has to pay price: ([US$55 × 20] + [US$60 × 20]) 40. If the price for longer storage. If the government instead uses a instead falls to US$35, the government continues to virtual stock scheme, the cost will only be the amount hold the stocks. of subsidy provided when the price is high. In scheme B, the virtual stock scheme, whenever The foregoing example shows that a virtual the unit price of oil rises above the ceiling trigger price security stock scheme can protect consumers but will of US$55, the government offers a cash transfer to the bemoreexpensivetothegovernmentintimesofrising companies sufficient to allow the price to consumers oil prices, which is when such a scheme is needed. The to be set at the mean of the international market price capital gain on physical stocks is not available to help and US$55. In the first period, the government takes finance the lowering of prices when they are deemed no action and incurs no costs. In the second period, if undesirablyhigh.Viewedinthelongrun,however,the the international price rises to US$60, the government situation may be different. If prices are equally likely provides US$2.50 for each of the 40 units sold, at a cost to fall as to rise at any moment, then a security stock of US$100, allowing the market price to be US$57.50. scheme would suffer capital gains and losses equally, If prices instead fall to US$35, the government takes and incur the costs of storage and interest forgone. no action. However, security stocks can be used in the rare event In both cases, the consumers face the same prices ofanunavoidableshortagethatcannotimmediatelybe and therefore are indifferent between the two schemes. met by paying higher prices and are clearly superior to When the government caps the price, the benefit to the use of a virtual stock, which would be available to Table 6.2 Costs of Security Stock Operations in Two-Period Case Scheme Period Action US$60 per unit in period 2 US$35 per unit in period 2 1 Purchase/sale costs -800 -800 Storage costs -40 -40 2 Purchase/sale costs 1,100 0 A Storage costs 0 -40 Current value of remaining stock 0 700 Both 260 -180 1 Purchase/sale costs 0 0 Storage costs 0 0 B 2 Purchase/sale costs -100 0 Storage costs 0 0 Both -100 0 Source: Author calculations. 52 Special Report Coping with Oil Price Volatility transfer money to consumers but would be unable to · The sales volume per time period to be made when meet any absolute physical shortage caused by some the ceiling trigger price is exceeded. The maximum disruption in the supply chain. volume to be released each period has to be Thedesignofasecuritystockschemetobeusedto sufficient to make a meaningful reduction in combat higher prices requires several determinants. consumerpricespossible.However,alargerelease relative to the size of the stock could make a large · The nature of the price event to be ameliorated. Security downward adjustment to prices possible only for stocks can protect against two scenarios. One is a very short period and reduce the opportunity to a temporary disruption in the market in which have further stock on hand against the possibility prices suffer a very large but short-lived spike. that prices would temporarily rise even further. Such an occurrence is rare. The other scenario is a period of a more prolonged large price rise. In this Simulation of a Security Stock case, it is important not to dispose of the whole Scheme between 1986 and 2007 stockholding in one period, because of the risks that high prices will continue for some time. A simulation of a physical security stock scheme · The maximum size of the stock.Thestockheld should illustrates some of these issues and shows how choices beinproportiontothenormalrateofconsumption of the key parameters affect the scheme's overall of oil products. The IEA's recommendation to hold performance. The history of oil prices between 1986 the equivalent of 90 days net imports as security and 2007 provides the opportunity to simulate the stocks reflects this consideration. The larger operation of a security stock in two rather different the stock, the greater the impact it can have on contexts. Between January 1986 and December reducing a period of high prices--but the greater 1999, the average monthly price of WTI crude was the risk of a large capital loss if prices fall. Also, US$19 a barrel and was scarcely higher at the end the carrying costs of storage will increase with of the period than at the beginning. However, from the size of the stock. September through November 1990 oil prices spiked, · The floor trigger price below which purchases would be reaching a peak of more than US$36 a barrel. A very made if the stock is not full. The government has to different pattern was in evidence between January decide on a price that is lower than the expected 2000 and March 2007, during which time oil prices future shock price in order to be able to purchase climbed steadily and ultimately more than doubled. A and resell at a profit. If this floor price is too low, simulationofmonth-by-monthgovernmentpurchases the stock may never be filled; if it is too high, gains orsales,dependingoninternationalmarketpricesand from selling may be small and will not offset the the amount already in stock, is described below. costs of running the scheme. · A ceiling trigger price above which sales would be made. Security Stocks and a Price Spike The ceiling trigger price is a price that is thought (January 1986­December 1999) to be harmful and at which amelioration will A simulation for the first period was carried out with provide substantial benefit. When it is set high, the the assumption that the stocks would be used only in stocks would rarely be used; thus, the government the case of a truly exceptional market price increase. would be able to benefit from buying low and Based on the experience of prices over this period, an selling high less often. The choice of ceiling price exceptional event was defined as one that could be should be closely related to the overall strategy. If expected, on average, once in 100 months (once every the rare but extreme event is the target, the ceiling eight years). This exceptional price corresponded price would be correspondingly higher. approximately to US$29 a barrel.3 3The mean of log prices was 2.930 during the period, with a standard deviation of 0.188. The distribution of log prices was approximately normal, and the value of a one-sided normal distribution with a probability of 1 percent is 2.33. Hence, the critical log price is (2.93 + 0.188 × 2.33). 6 Security Stocks and Price Hikes 53 Operation of the security stock is governed by This scheme, with three consecutive large monthly the following: drawdowns (three-quarters of monthly consumption, and hence the relative weights of three to one) was · The monthly rate of consumption is 1 million designed to have a large moderating effect on prices barrels of oil. when the international market price spike was · The maximum monthly purchase into stock is exceptional. During the 14-year period, there were 1 million barrels. just three months when the price rose sufficiently · The maximum stock is three months' worth of to stimulate a stock drawdown. However, had consumption at 3 million barrels. world prices skyrocketed between November 1990 · If a decision is taken to release oil from the stock, and November 1993, this country would have been the monthly release is 750,000 barrels. without much protection. · The maximum floor trigger price for purchase is The cumulative monthly expenditure on the US$17 a barrel. scheme--including purchases, interest, and storage · The sale price for stock release is US$29 a barrel. costs and subtracting the values of sales--is tabulated · Duringstockrelease,consumerspaytheweighted to identify the maximum resources the government average of released stocks (at US$29) and the would have had to devote to the scheme, before then-prevailing international market price, the allowing for unsold stock valued at the current market weights being three to one in this illustration price at the end of the period. During the period, (see below). the cumulative financial outlays by the government · The monthly interest rate is 0.8 percent (10 percent change depending on purchases and sales. If there a year compounded). are positive stocks at any time, these would provide · The costs of storage are US$0.20 per barrel per a total or partial offset to these financial outlays. The month. net cost to the government at the end of the period is the cumulative financial outflow--that is, purchases The baseline operation of the security stock less sales, plus costs, less the closing value of unsold scheme is simulated using monthly prices of WTI stocks. The financial performance of the scheme is crude. The initial value of the stock is zero. The shown in table 6.3. simulation runs from January 1986 until the end of The security stock performed as planned, December 1999. The stock would have been filled seeing releases in just three months. During those completely between February and April 1986, when months, the price charged to consumers on average prices were low. No further movement would have would have been US$3.70 below the international taken place until September to November 1990, when market price. In October 1990, when international a stock release takes place, leaving just 750,000 barrels prices peaked at US$36 a barrel, the sales price to in store. The stock would then not have been refilled consumers would have been US$30.70. The terminal until the months of November 1993 to January 1994, net cost to the government of running the scheme when it would have been completely refilled. It would would have been US$31.1 million, while the total then have remained full until the end of the period. benefit to consumers would have been relatively Table 6.3 Costs and Benefits of a Security Stock Scheme Operated January 1986­December 1999 Monthly Max. buying Benefit to Max. financial End-of-period release price Selling price Final net cost to consumers exposure stock (barrels) (US$/barrel) (US$/barrel) gov't (US$ mil.) (US$ mil.) (US$ mil.) (mil. barrels) 750,000 17 29 31.1 11.2 109.4 3.0 Source: Author calculations. 54 Special Report Coping with Oil Price Volatility small at US$11 million. The government's financial the weights being determined by the size of the stock outlays would have reached the maximum value of release relative to the monthly demand. Had the US$109.4 million at the end of the period, but could same criterion for setting the ceiling trigger price as have been partially offset by selling the stocks at the that in the first period been used, the ceiling trigger then-current price. price would have been US$89 a barrel. In the base case (US$35 and US$65), with a sale amount of 150,000 barrels, the stock would have Security Stocks and a Sustained Price been filled during the first three months of 2000 Rise (January 2000­March 2007) with no change until September 2005, when the first The second detailed simulation covers a period in drawdown would have occurred. There would have which prices rose and stayed high for a sustained been further releases in January 2006, and then every period. It is assumed in this case that the objective month from April until August 2006. is to offer some relief to consumers but to keep The financial performance of the scheme under sufficient reserve in stock to maintain this for different assumptions is shown in table 6.4. In the several periods if necessary. Several different sets base case (the first three rows in the table), the scheme of operating conditions are considered. First, the with the largest monthly stock release would have floor trigger price is set at US$35 a barrel and the brought the largest benefits to consumers and to the ceiling trigger price at US$65, to give the government government through its ability to sell large amounts the opportunity to buy at low prices and to sell at at peak prices. Had the scheme been extended beyond higher--but not necessarily extreme--prices, as March 2007, the third scheme in the table would experienced during the period. For this price range, have had no further stock to combat even higher three different sales policies of increasing monthly prices. Because world oil prices have not fallen to amounts are considered, ranging between 150,000 the maximum selling price of US$35 a barrel since, and 500,000 barrels per month. Two additional this scheme would have ceased to operate short of trigger price scenarios are considered, one with a changing operating rules. narrower band between buying (US$40 a barrel) At a release level of 250,000 barrels, a narrow price and selling (US$55 a barrel) and the other with a band would have given larger benefits to consumers, wider band (US$30 a barrel for purchase and US$70 while a wider price band would have given the least a barrel for release). The other factors are kept the protection to consumers. For all three price bands at same as in the price spike simulation. The price to this stock release level, the government would have consumers is the weighted average of the trigger experienced a small net cost or even returned a net release price and the international market price, with gain. Table 6.4 Costs and Benefits of a Security Stock Scheme Operated January 2000­March 2007 Monthly Max. buying Final net cost Benefit to Max. financial Months End-of-period release price Selling price to gov't consumers exposure of stock stock (barrels) (US$/barrel) (US$/barrel) (US$ mil.) (US$ mil.) (US$ mil.) release (mil. barrels) 150,000 35 65 1.9 5.2 172.4 7 1.95 250,000 35 65 -7.2 8.7 172.4 7 1.25 500,000a 35 65 -24.8 13.4 172.4 6 0.00 250,000a 40 55 0.9 24.0 168.5 12 0.00 250,000 30 70 -1.0 2.31 182.7 4 2.00 Source: Author calculations. a. Stocks were exhausted by the end of the simulation period. 6 Security Stocks and Price Hikes 55 The second scenario indicates that a security price to be fairly high in order to obtain sufficient stock operation designed to ameliorate the impact of capital gain to cover some or all of the costs of higher prices on consumers can be successful during a running the scheme. Only if the international price period of rising prices. The degree of success depends were substantially higher would the welfare benefits on the ability to fill the stock at a time of relatively of lowering domestic oil prices toward the ceiling low prices, thus profiting from later opportunities to trigger price be worthwhile. The variation in prices sell at higher prices. However, the largest consumer is also an important determinant of the usefulness and government benefits were achieved by using the and cost-effectiveness of using stocks in this way. largest monthly stock release amount. Since there When variability is high, the chances of an extreme were several months that triggered a potential stock event are increased, so stocks may be more useful. release (a price of more than US$65 a barrel), stocks When variability is low, stocks would be used only were empty by March 2007. The subsequent history rarely. If prices fluctuate around a constant mean, the of oil prices, with the October 2007 monthly WTI operation of security stocks will almost inevitably be crude average reaching US$85.40 a barrel, illustrates extremely costly. the dangers of too early a release at a period when oil If prices were nonstationary instead of being prices are very volatile and on the rise. mean-reverting, they could drift lower as well as higher, so a scheme to hold stocks until a very high Assessment of the Two Periods price was experienced might need to run for a long Whatever the intended purpose of the scheme, the time before stock releases took place. The risks of the temporal behavior of oil prices will be the crucial government facing an increasingly large financing determinant of its likely success or failure. The scheme cost would be higher than in the case where prices is needed to ameliorate the impact of unusually high reverted to a mean. prices, so the probability of such prices occurring The second example illustrates the case where within a given period of time is important. If oil prices follow a generally rising path for much of the prices had a fixed probability distribution (with a period. If the government were able to anticipate the constant known mean and standard deviation) and price rise and buy stocks at a "low" price, it could use were independent from period to period, then an the capital gains from low-price purchases to support accurate assessment of the probability of a certain the reduction in prices to consumers when prices are price occurring could be calculated and would higher. Such a scheme could be entirely self-financing continue to be valid into the future. This situation was over the period in which the general price movement illustrated with the simulation for the period 1986 to is upward. The problem for the operation of this 1999, where the mean did not vary greatly during the approach is to determine beforehand when prices period, and where the probability of extreme events are likely to follow a rising pattern. One conventional could be reasonably calculated. tool for assessing market views of likely price trends Although the design of a security stock scheme is the futures prices for crude oil and oil products, as to cope with extreme prices could be successful in discussed in chapter 5. Often, a commodities market achieving price moderation, when prices fluctuate is in backwardation--futures prices are below current around a fairly constant mean value, the period prices--but at times, markets go into contango-- during which stocks have to be stored will be futures prices are higher than current prices. If there is lengthy; if refilling takes place, the government will a deep contango, or the futures prices increase steeply be holding stock throughout the period, except for a with the length of the contract, this serves to indicate very few months when prices are abnormally high. the market sentiment that actual prices will turn out Furthermore, in order to have sufficient stock on to be higher in the future. hand to make a significant difference in the price An alternative to basing views on the futures at such times, the inventory carried will have to be market is to track historical prices with a filter, as large. The government will want the ceiling trigger discussed in chapter 3. This technique can be used 56 Special Report Coping with Oil Price Volatility to constantly update the estimate of the trend price disruptions--such as those in early 2003, when as new data are added. Forecasting still requires there were strikes in Venezuela and Nigeria and the assumptions to be made about the course of prices. outbreak of war in Iraq--did not elicit any response The use of a filter (or any moving average price- from the IEA. smoothing technique) would respond to situations Countries outside the IEA are constructing such as that experienced from 2004 onward, when oil strategic petroleum reserves as well. China has begun prices began a steady climb. storage construction in a three-phase program (Oil The simulation results suggest that using a fixed and Gas Journal 2007a and 2007b). In the first phase, set of rules for purchases and sales is too limiting. to be constructed between 2004 and 2008, stocks are The rules that were adequate during the period 1986 planned to cover about 13 days of oil consumption to 1999 would have been completely inadequate after (100 million barrels); in the second phase, another 1999, because they would never have permitted any 200 millions barrels will by added by 2010; and, in purchase of stock, and the stock left over from before the third phase, another 200 million barrels are to be the beginning of 2000 would have been exhausted by added. Emerson (2006) and the Oil and Gas Journal early 2001 before the large price increase took place. indicate that the Chinese may consider using the The trigger prices would need to be updated as the strategic petroleum reserves to control price swings, mean price forecast is increased in order to provide as well as to provide a reserve against unexpected some relief against exceptional and above-trend supply shocks. variations. United States International Experience with Strategic At the end of October 2007, the United States held Petroleum Reserves 1,708 million barrels of crude oil and oil products in public and private stocks, which was equivalent to The 26 industrialized countries that are members of 130 days of net imports. Of these, nearly 700 million the IEA held public and commercial stocks of crude barrels were in the government-financed Strategic oil and oil products of 4.1 billion barrels in June 2007; Petroleum Reserve. This level of coverage gives the this was equivalent to nearly 150 days of net imports country the flexibility to release stocks even when (IEA 2007). Of this total, some 1.5 billion barrels the IEA has not decreed that an emergency situation were public stocks held exclusively for emergency exists; such was the case in 1996. The United States purposes, while the rest were industry stocks held has low-cost storage capacity available in the form of to meet government stockholding obligations and for salt domes located near the Gulf coast, allowing for commercial purposes. cheap storage and efficient drawdown. The operation Since its formation, the IEA has acted on two of the U.S. Strategic Petroleum Reserve is governed occasions to bring additional oil to the market through by the Energy Policy and Conservation Act.4 Under coordinated actions: in response to the 1991 Gulf this act, the president can determine whether a supply War and to the hurricanes in the Gulf of Mexico in shortage or high prices could affect national security 2005. At the time of Hurricane Katrina (September and, if so, authorize a drawdown. 2005), the IEA members agreed to make available to Nontest releases from the reserve have occurred the market some 60 million barrels of oil equivalent, on three occasions (test releases are small releases primarily through a stock release. (In fact, 29 million designed to test the operation of the system): barrels were drawn from public stocks and a further 23 million barrels were made available by lowering · 21 million barrels were released in 1990­91 stockholding obligations on industry.) Other supply because of Desert Shield/Storm 4For a description, see the U.S. Department of Energy Office of Fossil Energy Web site at www.fe.doe.gov. 6 Security Stocks and Price Hikes 57 · 28 million barrels were released in 1996­97 for Republic of Korea nonemergency reasons The Republic of Korea also holds stocks in excess · 11 million barrels were released in 2005 because of the IEA-recommended level. As of July 2006, of Hurricane Katrina. the public sector stocks were equivalent to 57 days of imports, while private sector stocks accounted The 1996­97 sales were designed to help reduce for another 69 days of imports. Private sector the budget deficit at a time when crude oil prices were companies must hold at least 40 days of cover for high. In addition, loans and swaps with commercial domestic sales. The operation of the Republic of companies have been made 10 times, including a Korea's stocks follows IEA guidelines. In addition, 30 million­barrel exchange of crude oil for heating oil the public stockpile, which is managed by the to be stored in the Northeast United States at a time Korean National Oil Corporation, uses time swaps when heating oil stocks were particularly low in that with the private sector in order to reduce costs and region. By lowering heating oil prices, however, extra keep reserves in circulation. Companies are invited importsfromEuropewerenotattracted,thusnegating to bid a user charge (premium) for a quantity of the desired effect of improving regional supply. stockpiled oil, which they must return within a stipulated period. Japan Japan holds stocks equivalent to about 170 days of domestic consumption, of which 320 million barrels Assessment of crude are in the state stockpile, while the private To date, government-owned or -mandated private sector holds 130 million barrels of crude and another sector security stocks have been held as an insurance 130 million barrels of oil products. Companies are against sudden supply shortages. The one exception required to hold stocks equivalent to 70 days of to this practice appears to have been the use by the domestic consumption, which is identical to the United States of government stocks to reduce prices country's net imports. Japan therefore also has the in the 1996­97 period. However, it is possible that flexibility to release stock even when there is no IEA countries now building security stocks will consider mandate, while keeping to its obligations to maintain their use for domestic price stabilization at times of 90 days of import coverage. Furthermore, under the unusually high prices, even when these are not linked country's Petroleum Stockpiling Law, the private to any sudden supply disruption. sector holds the equivalent of 60 days imports of The experience of the IEA scheme, which liquefied petroleum gas. Japan, according to its IEA depends on the IEA's Governing Board identifying obligations, released part of its private sector stockpile an episode of actual or potential substantial supply during the first Gulf War and Hurricane Katrina. It disruption, suggests that stocks held for this purpose did so by reducing the mandatory amount to be held will rarely be used. For high-income countries, the by the private sector. costs of filling and running the security stocks that Thepublicstockpileispartlystoredinunderground are rarely used will be affordable. For lower income and floating storage, which is substantially more countries, on the other hand, the costs may be too expensive than above-ground storage but gives high, and the number of days covered may need an insurance against natural disasters such as to be somewhat lower than the 90 days of imports earthquakesandtyphoons.Eventhoughprivatesector mandated by the IEA. stockholding is partly subsidized by the government, Simulations of the use of stocks to smooth out it constitutes an extra cost for oil companies and acts extreme price events indicate that this strategy is most as a barrier to market entry. Japan uses its stocks likely to be successful and operated at least cost in a strictly following the IEA model, with reductions period of rising prices. Conversely, the scheme would in stockholding permitted only when the IEA has be very expensive in a period of falling prices. Since indicated that an emergency situation exists. the behavior of oil prices has been extremely difficult 58 Special Report Coping with Oil Price Volatility to predict, any government considering using stocks of uncertainty about the likely costs and benefits of for this purpose may be dissuaded by the high degree such a scheme. 7 Price-Smoothing Schemes Many governments have operated schemes designed at a time of steadily increasing international market tosmooththepathofdomesticoilpricestoconsumers. conditions. Two different approaches to price control are widely There are several methods of determining used. One approach is to cap prices when they get price-smoothing scheme ceiling and floor prices too high, either by reducing product tax rates or by or the price band that will be used to reduce the providing direct subsidies. This scheme "slices the volatility of domestic prices around the target price. top" off high international prices, at the cost of loss These methods are described in detail by Federico, of government revenue or increased fiscal burden. Daniel, and Bingham (2001); LeClair (2006) analyzes It effectively has the dual outcome of lowering the a proposed scheme using variations in tax rates for average price paid over a period of time and reducing the United States. volatility. The second approach is to control prices A price-smoothing scheme can be judged in terms in such a way that the scheme is self-financing of three outcomes: over a period of time. In this latter approach, the government acts to reduce domestic prices when · The reduction in the volatility of domestic international oil prices are higher than some ceiling prices threshold; conversely, it maintains domestic prices · The reduction, if any, in the overall level of at the floor when international prices are below a domestic prices predetermined floor threshold. The costs of support in · The fiscal cost or forgone revenue high international price periods are balanced against extra receipts in times of lower international prices. A The magnitudes of these outcomes have to be price-smoothing scheme operates in a manner similar evaluated using a counterfactual of what the domestic to a virtual security stock, but instead of coping only prices would have been in the absence of the scheme. with spikes in prices, it aims to continually reduce the To carry out such a calculation from actual data would magnitude of any price swings. The nearer the ceiling require detailed information on the whole product- and floor prices are to each other, the more stable the pricing structure, so that international prices can be actual domestic price will be. linked to domestic prices set and to the exact point The key to both a price-capping scheme and in the product price chain at which the price control a price-smoothing scheme is the target price. For is imposed (ex-refinery prices, wholesale prices, or price capping, this target is the level of prices that retail prices). is the highest the government considers acceptable to the public at that moment; for a price-smoothing Setting a Target Price scheme, it is the price around which market prices are to be smoothed. In both cases, this price can Faced with steadily increasing international oil prices, evolve over time according to market conditions--in a number of developing countries are subsidizing fact, a price-smoothing scheme must follow market prices on some or all oil products (Bacon and Kojima conditions so that it does not run a persistent deficit 2006, IMF 2007). In the face of the general rise in oil 59 60 Special Report Coping with Oil Price Volatility prices since 2004, some countries that had not been sufficiently responsive to new higher prices, the using price caps, or had limited caps on certain fuels, fiscal burden should not increase unexpectedly. have introduced or widened the existing scheme. · The second approach is to use a fully automatic The continued rise in international prices has led pricing scheme whereby international prices are to mounting fiscal costs in these cases. As a result, continuously reviewed and new domestic prices some countries have more recently reversed this are regularly determined on this basis. The decision and abandoned price subsidies as being too review period could be daily, weekly, monthly, expensive. A particular problem with some of these or even less frequently. Once the review period schemes is that the price caps set have been ad hoc, and formula are determined, the domestic price bearing no systematic relation to the international is set accordingly. price. With such an approach, there can be a tendency for the capped price to increase less rapidly than A successful formula designed to track the the international price, with the increasing per unit general level of international prices while being less subsidy worsening the total fiscal costs of the scheme volatile than these prices will usually be based on against the backdrop of continuing international price some moving average of past actual prices and, where increases. suitable, futures prices. The simplest scheme is to use Governments that have set the regulated price a moving average of previous prices. For example, in through an explicit or implicit formula have usually setting prices each month, the target price might be donesoinawaythattracksmovementsininternational an average of the prices during the previous three prices, even if there is not a full pass-through of these months. This ensures that the target price is changed prices to consumers. This approach tends to limit the each month in response to recent price movements. magnitude of the total subsidy, while giving a signal Moreover, by taking an average over three months, to consumers that the cost of oil is rising and that the resulting series is smoother than daily, weekly, they should adjust their consumption accordingly. or monthly prices. A longer average, based on more The formula used for tracking the movements of months, will be less variable. However, in a time of international crude oil or oil product prices, while steadily rising (or falling) international prices, the limiting volatility of domestic prices, requires a built- longer the averaging period, the greater the difference in smoothing mechanism. Whether smoothing prices between the current international price and the is progressive or regressive depends on the range of moving average (figure 7.1) products considered and on the share of expenditures An extension of this approach is to use futures on these products in total household expenditure at market data as a better proxy for where prices might different income levels. For example, smoothing only beatthetimetheregulatedpricecomesintooperation. gasoline prices will tend to benefit the richer members An average of futures contracts at the current date of society in developing countries, because the poorer for several durations can be constructed (see annex members generally do not own cars or use gasoline. 6 for price-smoothing formulae) as such an index. Two approaches dominate the setting of regulated The absence of futures product markets apart from prices: in the United States and the United Kingdom--and these only for a small range of products--limits the · The first (semi-automatic) approach is to set applicability of this approach. a "reasonable" price based on current market Table 7.1providessummarystatisticsthatdescribe experiences and then review the target price the volatility of the various price-smoothing formulae periodically. When international prices have based on the logarithmic returns of different series. As risen by a sufficient margin and for a long enough well as three- and six-month moving averages based period of time, a new price is set. This approach on past data, a series based on the average of the three produces a series of step changes at irregular different futures contracts for the next three months intervals, but, provided the government is and another based on an average of the three-month 7 Price Smoothing Schemes 61 Figure 7.1 WTI Crude Monthly and Six-Month Moving Average Prices 80 80 70 a. Nominal WTI monhtly average spot price b. Six-month moving average price 70 lerrabrep 60 60 50 50 40 lerrabrep 40 $SU 30 20 $SU 30 20 10 10 0 0 `86 `88 `90 `92 `94 `96 `98 `00 `02 `04 `06 1986 1990 1994 1998 2002 2006 Sources: U.S. EIA 2008a; author calculations. Note: Six-month moving average prices are averages of the current spot price and the prices during the previous five consecutive months. moving average and the three months average of a maximum month-to-month increase of 13 percent. futures contract prices are constructed. The standard The returns on futures prices as averaged over three deviation of the returns (which, when multiplied by different contract durations (one, two, and three 100, approximate percentage changes) measures the months) are just as volatile as current spot prices, average volatility of the series, and the maximum while the average of the previous three months' spot and minimum measure the extremes of volatility. prices and the three contract months of futures prices Taking moving averages over increasingly long lags has comparable volatility to that of the three-month decreases the volatility of the series substantially. moving average of spot prices. Compared to the standard deviation of spot prices, The choice of the smoothing formula affects the which is equivalent to an average monthly change of difference between the formula price and the actual 8 percent, the standard deviation of the three-month international price ruling in the same month, which moving average is 5 percent; for the six-month moving in turn affects the cost of operating the smoothing average, it is 3.5 percent. The maximum monthly price scheme. For a country that is importing WTI crude, swings are also substantially reduced by averaging. the regulated price for a particular month has to Spot prices have a maximum monthly increase of be determined before the onset of that period. For nearly 40 percent, while the six-month average has example, using a three-month moving average Table 7.1 Summary Volatility Statistics for Returns of Current Prices, Moving Average WTI Crude Prices, and Futures Prices, July 1986­October 2007 Avg. of 1, 2, and 3 Avg. of 3-month spot Current monthly 3-month avg. of 6-month avg. months of futures prices and 3 months Statistic avg. spot price spot prices of spot prices contracts of futures contracts Mean 0.0072 0.0068 0.0061 0.0051 0.0070 Standard deviation 0.078 0.050 0.035 0.073 0.052 Maximum 0.392 0.238 0.125 0.285 0.227 Minimum -0.209 -0.150 -0.082 -0.329 -0.168 Sources: U.S. EIA 2008a and Bloomberg.com; author calculations. Note: Returns are based on differences in the logarithms of prices in US$ per barrel. 62 Special Report Coping with Oil Price Volatility approach, the regulated price for December would period of analysis, the longer the moving average have to be based on actual prices in September, the lower the volatility, but the higher the cost to the October,andNovember.Thisinevitablelagintroduces government for basing its regulated price on that a form of basis risk, in that the most recent actual moving average. The use of an average based on information is not incorporated. Cumulating the three past monthly spot prices and three monthly difference over the period between the international futures contract prices has almost identical volatility spot price and the regulated price derived from the and fiscal cost as a scheme based only on the past lagged three-month moving average produces the three monthly spot prices. The failure of the addition cumulated cost to the government of setting regulated of futures prices to improve the performance of the prices in this way. moving average indicates the weak link between Figure 7.2a and b illustrate the cumulated cost futures contract prices and the actual spot prices that for one barrel of crude based on this pricing scheme have emerged at the time of delivery. for three- and six-month lagged moving averages, A smoothing filter used to describe past data respectively.Between1986and1999,theschemeworks movements, such as the Hodrick-Prescott filter well, with the cumulated cost fluctuating around zero. discussed in chapters 2­4, is another method of From 2002 onward, the steady rise in international smoothing prices. Using this lagged smoothed series prices means that the regulated price based on a as a proxy for the current target price would have moving average is constantly behind the international resulted in a cumulative deficit of US$110 a barrel price, leading to an ever larger cumulative cost to the over the period. government--despite large increases in the regulated Even though crude prices did not begin their price itself. By October 2007, the cumulated cost per major run-up until 2004, the use of a moving average barrel using a three-month moving average reaches price-setting scheme resulted in very long sojourns in US$132, while that using a six-month moving average deficit for the financing of the regulated prices. With a reaches US$220 as a result of the longer moving three-month moving average, the scheme would have average falling further behind in a time of steadily been continually in deficit between December 1988 rising prices. A regulated price, based on the average and October 2007 (figure 7.2a). With a six-month of the lagged three-month moving average and moving average, the scheme would have been in the average of futures prices through one to three deficit since April 1994 (figure 7.2b). months, would have produced a cumulated cost to As LeClair (2006) points out, if consumers the government by the end of the period of US$128 a understand the price-setting mechanism, they might barrel. adjust their consumption behavior, which could affect Comparing the two moving average schemes the level of domestic prices in the market by changing based on past spot prices indicates that, over the demand. Also, where the short-run price elasticity Figure 7.2 Cumulative Cost of Regulating the Price of Crude Oil with Lagged Three- and Six-Month Moving Averages 140 240 120 a. Lagged three-month moving average, b. Lagged six-month moving average, l 100 200 April 1986­October 2007 160 July 1986­October 2007 arreb 80 60 barrel 120 per 40 80 per 20 40 US$ 0 US$ 0 -20 -40 `86 `88 `90 `92 `94 `96 `98 `00 `02 `04 `06 `86 `88 `90 `92 `94 `96 `98 `00 `02 `04 `06 Sources: U.S. EIA 2008a; author calculations. 7 Price Smoothing Schemes 63 of demand is above zero, the moderation of prices Table 7.2 through a formula will result in a higher demand than Fiscal Costs of Regulating WTI Prices through Three- would have occurred in the absence of regulation, Month Averaging for Different Price Bands, and this would have a second-round impact on the April 1986­October 2007 government tax take. 0% ±10% ±15% Federico, Daniel, and Bingham (2001) analyze Parameter band band band an extension of the moving average rule to allow for Cumulative cost per barrel ceiling and floor barriers to regulated prices. A target (US$) 132 37 26 price is defined through some form of moving average Standard deviation of scheme, and a ceiling and floor around this target are returns 0.050 0.062 0.070 then determined. The regulated prices are set equal to Source: Author calculations. internationalpricesaslongasthelatterarebetweenthe Note: Returns are based on differences in the logarithms of prices ceiling and floor. If the international prices are outside in US$ per barrel. the band, the regulated price is set equal to the ceiling (or floor), and the difference between the international price and the regulated price is financed by a tax Most governments wishing to smooth prices reduction (increase) or subsidy increase (reduction). are concerned with the prices of oil products to end A version of this scheme uses moving average price users. The mechanics of a price-smoothing scheme as the target and sets a band around this within ±X will depend in part on whether products are subject percent. This ensures that the ceiling and floor prices to taxes in the local market, or whether they are change with the target price. If the value of X were set implicitly or explicitly subsidized. In many countries, to zero, this would correspond to the simple moving oil products are an important source of fiscal revenue, average regulated price scheme described above. subject to sales taxes (or value added tax) and an In the next illustration, the target price is set additional excise tax. The tax structure can be varied as the three-month moving average of WTI crude so as to reduce the final price, providing the tax rates prices as determined in the previous period, while are larger than the desired subsidy. Since sales taxes the moving ceiling and floor prices are set 10 and tend to be universal across commodities, excise taxes 15 percent, respectively, above and below this level. are most likely to be varied. The government intervenes whenever the current Imports of oil products will normally be priced in WTI crude price is above (below) the target price U.S. dollars, but the smoothing scheme would need to ceiling (floor) by reducing (increasing) tax rates. The base the moving average on prices in local currency. cumulated fiscal cost of the scheme simulated from This would have the effect of also smoothing out April 1986 to October 2007 is calculated for one barrel fluctuations in exchange rates. The cases of Kenya of oil consumed every month. The results are shown and Ghana, described below, illustrate the impacts in table 7.2. of smoothing the prices of imported products in local The results demonstrate how a scheme based currency. on a moving average price, but with a ceiling and During the period 1986 to 2007, the Kenyan floor to contain extreme price movements, would shillingfluctuatedcontinuouslyagainsttheU.S.dollar, have reduced the cost of intervention. The wider without sudden movements due to a devaluation. In the bands, the lower the costs of the intervention January 1986, the exchange rate was K Sh 16.3 to to the government would have been. However, the US$1; by August 2007, the rate was K Sh 66.9 to the wider the price band, the more volatile would be the dollar. This simulation assumes that oil products are regulated price: regulated prices would be equal to imported from the Persian Gulf; hence, the prices are actual international prices for a larger part of the time, based on Gulf prices as quoted by Energy Intelligence and the ceiling and floor would be in operation for a (2008).Forcomparison,thepriceofDubaicrudeisalso smaller part of the time. analyzed. Table 7.3 presents the volatility measures 64 Special Report Coping with Oil Price Volatility for imported products, based on different moving 1986, the rate was C/80 to the U.S. dollar; by August averages, in both U.S. dollars and local currency. 2007, this had reached C/9,300 to the dollar. The AsisthecaseforWTIcrude,thelongerthemoving relevant market for products and crude oil for Ghana average,thelowerthevolatilityofallfueltypes.Volatility isassumedtobenorthwestEurope,andhenceproduct is slightly higher when measured in local currency for prices from Rotterdam are used. The relevant crude allproductsandforallpriceaverages.Thesmallsizeof is taken to be Brent. Table 7.4 presents the volatility this effect is explained by the fact that the volatility of measure for Ghana. the exchange rate (based on monthly returns) at 0.033 The pattern of volatility in Ghana is very similar is much smaller than those of oil prices measured in to that shown in table 7.3 for Kenya. The local U.S. dollars. Thus, the impact of this extra component currency volatility is higher than that in U.S. dollars, on the volatility in local currency is minor. but the difference is small. Again, the longer period In the case of Ghana, the movement in the moving averages in all cases reduce the volatility exchange rate during the period was larger. In January substantially. Table 7.3 Standard Deviation of Returns for Oil Products Imported to Kenya Based on Various Moving Average Prices, July 1986­September 2007 US$ K Sh Current monthly 6-month 3-month Current monthly 3-month 6-month Fuel type spot average average spot average average Crude 0.083 0.056 0.037 0.089 0.060 0.040 Gasoline 0.081 0.050 0.033 0.087 0.054 0.036 Gasoil 0.094 0.059 0.041 0.100 0.063 0.045 Kerosene 0.112 0.066 0.046 0.116 0.069 0.049 Fuel oil 0.129 0.076 0.051 0.132 0.078 0.052 Source: Author calculations. Note: Returns are based on differences in the logarithms of prices in US$ or K Sh per barrel. Table 7.4 Standard Deviation of Returns for Oil Products Imported to Ghana Based on Various Moving Average Prices, July 1986­September 2007 US$ C/ Current monthly 6-month 3-month Current monthly 3-month 6-month Fuel type spot average average spot average average Crude 0.088 0.056 0.038 0.090 0.060 0.043 Gasoline 0.094 0.059 0.040 0.101 0.066 0.047 Gasoil 0.086 0.055 0.039 0.091 0.062 0.046 Kerosene 0.087 0.057 0.040 0.092 0.063 0.047 Fuel oil 0.113 0.067 0.047 0.116 0.073 0.053 Source: Author calculations. Note: Returns are based on differences in the logarithms of prices in US$ or C/ per barrel. 7 Price Smoothing Schemes 65 Case Studies in Price Smoothing · The Fuel Price Stabilization Fund was established in October 2005, with an initial endowment of To illustrate different approaches to smoothing the US$10 million taken from Chile's copper fund. retail prices of oil products, the cases of Chile and Newmechanismsfordeterminingthetargetprice Thailand are described. Chile currently operates and the floor and ceiling prices were put in place. with an explicit formula for a target price and sets a The new target price was based on actual prices ceiling and a floor price around this target price to over a period of up to 52 weeks before the current contain large fluctuations in prices. The target price date, and on futures contract prices for delivery is set according to a moving average of international up to six months ahead. The length of the moving prices. Thailand, by contrast, has not used an explicit average could be varied, but a particular choice formula but has varied tax rates and subsidies to cap had to remain in force for at least four weeks. The retail prices. price band for intervention was narrowed from The Chilean government first established the 12.5 percent to 5 percent of the target price. The Petroleum Prices Stabilization Fund in 1991 (ENAP operation of the fund has twice been extended. 2007) in order to smooth domestic prices of gasoline, During the period July to November 2006, the diesel, kerosene, liquefied petroleum gas, and fuel oil. fund disbursed credits because international The operation of the scheme is described by Valdés prices were above the ceiling prices. Then, (2006) and Libertad y Desarollo (2006). There have between September and November 2006, the been three versions of the fund: Fund collected revenues by imposing a tax when the international price was below the floor · From 1991 to 2000, prices were set according to price. With respect to gasoline prices during this an average of the historic price and the long-term 22-week period, the fund disbursed for 8 weeks expected price, and taxes were kept at a fixed rate, and collected taxes for 11 weeks; for three weeks, while adjustments were made on an ad hoc basis. it did neither since the international price was The fund was endowed with resources to enable between the ceiling and floor values. In early 2008, it to support the domestic price when necessary. the government injected US$200 million into the When oil prices remained relatively constant, the fund to help lower prices. scheme worked well and withdrawals from the fund were balanced by inflows. However, the The evolution of the rules governing the pricing of rise in international prices in 2000 necessitated a oil products in Chile, through the use of the Petroleum revision in the fund's operation. Prices Stabilization Fund and Fuel Price Stabilization · In the second version of the fund, regulated Fund, illustrates some of the main issues associated prices were set weekly, taking into account with a price-smoothing scheme. The use of a long- expert views on future oil prices, and subsidies period moving average to determine the target price were to be limited to an amount that the fund was successful while international oil prices were could sustain for 12 weeks at current prices. The fairly stable. Once the fluctuations became larger, target price was calculated to reflect medium- however, the Petroleum Prices Stabilization Fund and long-term international oil market prices could not support such a scheme. The move to shorter based on 2 years prior and up to 10 years future moving averages reduced the chance that there would expected prices. The price band for the floor and be a series of substantial withdrawals from the fund. ceiling was set at 12.5 percent of the target price. At the same time, the use of a wider band to regulate The persistent rise in oil prices from 2004 meant volatility meant that, for much of the time, the prices that the fund was practically exhausted by the werenotregulatedandinsteadfluctuatedwithmarket time of Hurricane Katrina and the associated price. The tighter price band introduced in the Fuel sharp increase in oil prices in August and Price Stabilization Fund will have reduced volatility, September 2005. but, during periods of steeply rising prices in 2007, 66 Special Report Coping with Oil Price Volatility the moving average determination of the target price Figure 7.3 could have resulted in a long period of disbursements Thai Oil Fund Financial Status from the fund. From the calculations reported earlier in this chapter, it appears that the use of an average 30 5 Oi based partly on futures contract prices was not )B 15 likely to have safeguarded against underestimation onillib( 0 0 lfun d of the level of actual international prices during this -15 -5 period. lanceab -30 inflow Thailand's experience with capping and -45 -10 smoothing oil product prices is described by Bacon undfl -60 Oil fund inflow (billion and Kojima (2006). Prior to February 2003, the only -15 B Oi -75 Oil fund balance ) oil product subsidy was for liquefied petroleum -90 -20 gas. This was financed through the State Oil Fund, 1997 2000 2002 2004 2006 2008 which received levies from other oil products. At Source: EPPO 2008. that time, the fund had a deficit of US$96 million. Note: During the 1997­2007 period, the Thai baht fluctuated between a low of 31.36 to the U.S. dollar in 1997 to a high of Faced with an anticipated price spike in oil and 44.43 in 2001. oil products prices caused by the invasion of Iraq, the government reintroduced subsidies on other the period of rapidly increasing international prices, products, but these were phased out in April 2003. the fixed domestic prices resulted in a rapidly In January 2004, faced with a moderate increase escalating fiscal cost. Even though the regulated in crude oil prices, the government reintroduced a price was increased on a few occasions, it failed to price cap for an initial period of two months, with keep pace with international prices. The regulated the expectation that the price rise would be short price also exhibited a few very sharp increases. In lived and that the maximum cost to the government March 2005, the price of diesel was increased by would be B 5 billion (US$128 million at the time). The B 3 a liter (a 20 percent increase), which was much subsidy on gasoline was removed in October 2004, greater than any weekly change that would have but the much larger subsidy on diesel continued until occurred had prices been unregulated. A moving July 2005; indeed, diesel prices were actually frozen average target price would also have lagged behind between January 2004 and February 2005. By the international prices, but the accumulated costs need time the subsidy scheme was abandoned, the total not have risen so rapidly. The danger of fixing prices cost of the scheme was B 92 billion (US$2.2 billion was that it was difficult to change them. Only in at the time). Since then, the accumulated deficit on the oil fund has been steadily reduced through the levies on oil products (excluding liquefied petroleum Figure 7.4 gas) so that, by September 2007, the fund was almost Actual and Hypothetical Diesel Prices in Thailand, back in balance (figure 7.3). These levies could have January 2002­September 2007 been used to support other development objectives, 30 rather than repaying the past subsidies to consumers iter)l 25 of oil products. The course of actual retail diesel prices between 20 2002 and 2007, and the hypothetical prices that would perthab( 15 have emerged with the same tax structure and 10 Hypothetical price marketingmargins,butintheabsenceofcontributions pricel 5 Actual price from the oil fund, is shown in figure 7.4. Retai 0 Figure 7.4 illustrates the danger of excessive 2002 2003 2004 2005 2006 2007 smoothing of prices around a fixed level. During Sources: EPPO 2008; author calculations. 7 Price Smoothing Schemes 67 the face of unsustainable financing pressure did the Schemes that introduce a ceiling and floor price government feel able to pass some of the cost increase band around the moving average can offer a good on to consumers. trade-off between reducing the cost of support to the government while reducing volatility relative to international prices. The wider the price band, the Assessment less the cost of support but the greater the volatility Facedwithlargeoilpriceincreases,somegovernments of domestic prices. have sought to shield consumers from the effects Schemes that set a price cap on an ad hoc basis of the increased costs of oil and their increased run the danger of rapidly accumulating a substantial volatility. Price-smoothing schemes based on moving deficit in times of increasing international prices, averages of previous spot and futures prices can because the government is not forced by the use of be highly successful in reducing the volatility of an explicit formula to constantly revise the regulated consumer prices. When there is no strong trend in price. A regulated price that is infrequently changed the underlying international prices, such schemes can does reduce volatility--at least in the short run--but operate without incurring an excessive fiscal burden is likely to result in a few but very large price changes for the government in the long run. However, even as the government is periodically forced to reset in this case, the pattern of oil price changes can result the regulated price. Financing the deficit of such a in the scheme running a deficit for a lengthy period, scheme, which is not designed to capture any upside which may be politically difficult to support. when regulated prices are above international prices, The choice of moving average is important in this effectively faces a one-sided risk--if prices steadily context. The longer the moving average, the more increase, there will be a permanent deficit that will vulnerable the scheme will be to periods of sustained have to be financed out of other taxes. price increases, but the lower will be the volatility As with other schemes designed to reduce the of the regulated price. The incorporation of several impact of the volatility of oil prices, the emergence of futures prices into the moving average appears to a period of steadily increasing oil prices, which are make little difference to the scheme's ability to track largely unforeseen, is likely to result in the scheme's the general level of spot prices while simultaneously eventual failure and a substantial financial burden for reducing volatility. the government--and, ultimately, for the population. 8 Tackling Oil Intensity and Diversification The measures discussed in the preceding Oil Share of GDP and Intensity chapters are designed to reduce price volatility or uncertainties about future price volatility. This The oil share of GDP is defined in this study as the chapter considers managing oil price volatility by percentage of GDP in current U.S. dollars spent on reducing oil consumption, and thus reducing the oil consumption, where oil is valued--also in current relative importance of oil consumption. The greater U.S. dollars--at the average annual market price of the amount of oil a country consumes relative to its Brent, Dubai, and WTI. For ease of calculation, freight current gross domestic product (GDP), the greater the charges for importing countries are not included, consequences throughout the economy; the higher the and thus the calculations here may underestimate level of oil dependence, the greater the adverse effects actual expenditures on oil. For those oil-producing of oil price volatility felt by consumers and businesses countries that provide oil on the domestic market at any given percentage change in prices. The relative below world prices, the market price of oil would importance of oil consumption as a share of GDP can represent forgone economic opportunity costs rather be reduced by lowering demand for oil. This can be than actual expenditures. achieved by There are 163 countries for which oil consumption data are available for 2006 from the U.S. Energy · improving the efficiency of oil-consuming InformationAdministration(EIA).Although2005and activities (for example, by increasing vehicle fuel 2006 consumption figures are given as estimates and economy or improving the efficiency of power mayberevisedinthefuture,theyprovideanindication plants fired by diesel or fuel oil), of where countries stand. The distribution of the oil · restricting activities consuming oil (such as by share of GDP in 2006 is shown in table 8.1. Half of the restricting car use and raising thermostat settings countries spent more than 6 percent of GDP on oil for air conditioning in the summer), consumption. Ten percent spent more than 15 percent · diversifying away from oil. of GDP, and 4 percent more than 20 percent of GDP. Figure 8.1 plots the historical oil share of GDP Such demand-restraining measures can be since 1980 for select countries. In China, Japan, and implemented through exhortation, incentives, fiat, Kenya, oil share of GDP was at its highest in 1980 when or pricing mechanisms (making it more expensive oil prices in real terms were higher than in any other to drive, for example). More detailed examples, year during the period examined. As will be shown as well as a review of international experience to below, more than one-third of the countries for which mid-2006, are given by Bacon and Kojima (2006). This data are available experienced their highest oil share chapter complements that work by reviewing global of GDP in 1980. Almost as many countries, including trends in oil's share of GDP, oil intensity, and energy Jordan and Guinea Bissau, experienced their highest diversification. Throughout this chapter, oil refers to oil share in 2006. a basket of three marker crudes: Brent, Dubai, and Table 8.2 takes 135 countries that existed in 1980 WTI. and for which data are available to compute the oil 69 70 Special Report Coping with Oil Price Volatility Table 8.1 Distribution of Oil Share of GDP in 2006 Percentage share less than: Parameter 1 2.5 5 7.5 10 15 20 Number of countries 2 19 72 103 124 147 157 Percentage of countriesa 1 12 44 63 76 90 96 Sources: U.S. EIA 2008b; author calculations. Note: Oil share of GDP defined as the percentage share of current GDP in US$ spent on oil consumption, where oil is valued at the average annual price of Brent, Dubai, and WTI. a. Out of a total 163 countries. Figure 8.1 Historical Oil Share of GDP for Select Countries 20 Jordan 18 Guinea Bissau GDPfo 16 Kenya % China as 14 Mexico 12 Japan consumed 10 oilfo 8 6 value 4 Market 2 0 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 Sources: U.S. EIA 2008b; author calculations. Table 8.2 Maximum and Minimum Oil Shares of GDP, Selected Years, 1980­2006 Parameter 1980 1981 1986 1988 1998 2005 2006 No. of countries with maximum oil share of GDP 50 15 0 0 0 10 43 % of countries 37 11 0 0 0 7 32 No. of countries with minimum oil share of GDP 2 0 16 16 80 0 0 % of countries 1 0 12 12 59 0 0 Sources: U.S. EIA 2008b; author calculations. Note: Data shown are for 135 countries that existed in 1980 and for which data are available from 1980 or 1981 to 2004 or later. Only those years in which there were at least 10 countries with a minimum or maximum share are shown. 8 Tackling Oil Intensity and Diversification 71 share of GDP beginning in 1980 or 1981 to 2004 or U.S. dollars. Because the resulting numbers were later. The table gives summary statistics on when the small, they were multiplied by 1,000; this is the maximum and minimum shares occurred. For about equivalent of expressing barrels of oil per US$1,000 halfthecountries,theoilshareofGDPwasatitshighest of GDP in 2000 U.S. dollars. Table 8.3 shows the in 1980 or 1981. For nearly 40 percent of the countries, distribution of oil intensity in 2006. however,themaximumoilshareofGDPwasobserved Forthe132countriesforwhichdatawereavailable in 2005and2006.Notsurprisingly,for80countries, the to compute oil intensity between 1980 or 1981 and oil share of GDP was at its lowest in 1998, when world 2004 or later, historical oil intensity was computed for oil prices reached their lowest level in real terms. each year. Figure 8.2 shows the historical evolution for The oil share of GDP is affected by two factors: select countries. For many countries, oil intensity has the amount of oil consumed relative to GDP and the generally been declining. However, for some, it has price of oil. The former effect, termed oil intensity, increased in recent years. was here calculated by taking barrels of oil consumed Table 8.4 summarizes the statistics as to when oil and dividing by constant GDP expressed in 2000 intensity reached its highest and lowest levels. For Table 8.3 Distribution of Oil Intensity in 2006 Barrels per US$1,000 of GDP (2000 US$) Oil intensity less than: Parameter 0.1 0.25 0.5 0.75 1.0 1.5 2.0 Number of countries 1 3 15 32 66 103 120 Percentage of countriesa 1 2 9 20 41 64 75 Sources: U.S. EIA 2008b; author calculations. a. Out of a total 160 countries. Figure 8.2 Historical Oil Intensity for Select Countries 5 4 Jordan US$) Guinea Bissau GDP 3 Kenya 2000 China per of Mexico 2 Japan Barrels (thousands 1 0 1980 1985 1990 1995 2000 2005 Sources: U.S. EIA 2008b; author calculations. 72 Special Report Coping with Oil Price Volatility nearly half the countries, oil intensity was its highest Figure 8.3 in 1980 to 1984. For nearly a quarter, however, the Historical Oil, Gas, and Coal Prices lowest oil intensity was observed during the same period. Consistent with a general decline over time, 16 tsi Oil (Brent, Dubai, and WTI) oil intensity was at its lowest in 2006 for 41 countries. unl 14 U.S. natural gas For 47 percent of the countries (63), oil intensity 12 European gas in 2005, 2006, or both was more than 90 percent of Australian coal 10 the maximum oil intensity during this period. In ermahthsitirB 8 25 countries, oil intensity has peaked during this 6 decade. The high oil share of GDP in 1980 and 1981 can onliilmrep 4 therefore be explained by a combination of high oil 2 US$ pricesandhighoilintensity.Manycountries,however, 0 experienced a high oil share of GDP in 2005 and 2006 1983 1987 1991 1995 1999 2003 2007 Source: World Bank Development Economics Prospects Group. despite declining oil intensity, demonstrating the exacerbating effect of high oil prices. be noted that the spot market for coal accounts for about 10 percent of global coal trade; the remainder Relative Price Levels and Price is covered by long-term contracts and generally has Volatility lower, more stable prices. Coal prices are by far the lowest, and the price gap Price correlations between different fuels are useful between coal on the one hand and oil and gas on the in considering whether, and how much, to diversify other has been widening in recent years. That said, energy sources. In the extreme, if the prices of coal prices have been rising rapidly in recent months. different energy sources are perfectly correlated, Table 8.5 shows price correlations for different fuels then price volatility will also be similar between the between January 1983 and December 2007, divided two energy sources. Figure 8.3 shows monthly prices into subperiods. of Australian coal (spot price), crude oil, natural gas Taking the entire period between 1983 and 2007, in Europe (average of contract prices for imported the most tightly correlated prices are, not surprisingly gas indexed to oil product prices with a lag), and considering price indexation, those for crude oil and natural gas in the United States (spot price at Henry European gas. The pair is followed by oil and U.S. gas, Hub in Louisiana) since January 1983. The prices are European gas and U.S. gas, oil and Australian coal, expressed in nominal U.S. dollars per unit of energy, and European gas and coal. The least correlated pair in this case million British thermal units. It should is U.S. gas and Australian coal. Since 2000, the most Table 8.4 Maximum and Minimum Oil Intensity, Selected Years, 1980­2006 Parameter 1980 1981 1982 1984 1987 1988 1999 2000 2001 2006 No. of countries with maximum 42 6 9 4 2 2 6 3 6 5 % of countries 32 5 7 3 2 2 5 2 5 4 No. of countries with minimum 10 6 5 8 7 6 3 6 2 41 % of countries 8 5 4 6 5 5 2 5 2 31 Sources: U.S. EIA 2008b; author calculations. Note: Data shown are for 132 countries that existed in 1980 or 1981 and for which data are available to at least 2004. Only those years in which there were at least six countries with a minimum or maximum intensity are shown. 8 Tackling Oil Intensity and Diversification 73 Table 8.5 Fuel Price Correlation Period and fuel Australian coal Oil Gas, Europe Gas, U.S. 1983-2007 Australian coal 1.00 Oil 0.79 1.00 Gas, Europe 0.74 0.96 1.00 Gas, U.S. 0.51 0.81 0.80 1.00 1983-99 Australian coal 1.00 Oil 0.39 1.00 Gas, Europe 0.70 0.47 1.00 Gas, U.S. -0.22 0.21 -0.11 1.00 2000-07 Australian coal 1.00 Oil 0.85 1.00 Gas, Europe 0.75 0.95 1.00 Gas, U.S. 0.48 0.63 0.62 1.00 2000­03 Australian coal 1.00 Oil -0.19 1.00 Gas, Europe 0.41 0.37 1.00 Gas, U.S. 0.08 0.55 0.64 1.00 2004-07 Australian coal 1.00 Oil 0.54 1.00 Gas, Europe 0.27 0.89 1.00 Gas, U.S. -0.30 0.21 0.22 1.00 Source: Author calculations. Note: All prices are monthly prices shown in figure 8.3. The European gas price series starts in January 1991. tightly correlated pair remains oil and European gas, approximate percentage changes in prices from one followed by oil and coal, coal and European gas, and month to the next. The largest positive return is for oil and U.S. gas. Between 1983 and the end of 1999, U.S. natural gas at 48 percent, and the largest negative price correlations were fairly weak except between return is for oil at ­44 percent. coal and European gas. In the most recent subperiod Table 8.6 summarizes standard deviations of beginning in January 2004, the price correlation was the returns shown in figures 8.4 and 8.5 for different strong between oil and European gas, but not for subperiods. For every subperiod examined, U.S. others; price trends have been the opposite for coal natural gas is the most volatile price. Oil is the second and U.S. gas. most volatile, although coal price volatility has been Figures 8.4 and 8.5 plot the historical volatility catching up since the beginning of 2004. Coal and of the monthly prices of the above four fuels, where European gas prices had comparable volatility until volatility is expressed as returns on logarithms the end of 2003, after which coal volatility began of prices. As before, returns multiplied by 100 to increase while European gas volatility began to 74 Special Report Coping with Oil Price Volatility Figure 8.4 Table 8.6 Volatility of Historical Oil and Coal Prices Standard Deviation of Fuel Price Volatility 0.5 Gas, Gas, Period Coal Oil Europe U.S. 0.4 Oil (Brent, Dubai, and WTI) 0.3 Australian coal 1983-2007 0.04 0.08 0.04 0.12 pricesfo 0.2 1983-99 0.03 0.09 0.03 0.11 0.1 2000-07 0.05 0.08 0.04 0.15 0.0 2000-03 0.04 0.09 0.05 0.16 logarithms -0.1 2004-07 0.06 0.07 0.03 0.14 on -0.2 Sources: Price data from World Bank Development Economics -0.3 Prospects Group; author calculations. Returns -0.4 Note: Standard deviations are calculated on returns on logarithms of monthly prices expressed in nominal US$ per unit of energy. -0.5 Coal is Australian coal. Oil is the average of Dubai Fateh, Brent, 1983 1987 1991 1995 1999 2003 2007 and WTI crudes. The European gas price series starts in January 1991. Source: Author calculations. Figure 8.5 levels, with the highest correlation being 0.39--that Volatility of Historical Gas and Coal Prices is, at most, 15 percent (square of 0.39) of the returns 0.6 can be said to be explained by volatility correlation 0.5 U.S. natural gas between two fuels (coal and U.S. gas in 2000­03, and European gas 0.4 coal and oil in 2004­07). The low correlation squares pricesfo Australian coal 0.3 suggest that fuel diversification could help mitigate the price volatility of higher volatility fuels. msh 0.2 0.1 One approach in price risk management is to diversity the fuel portfolio to take into account risks ogaritl 0.0 associated with both price-level increases and price on -0.1 -0.2 volatility. In this approach, the lowest cost fuel is not assigned 100 percent of the fuel portfolio. A Returns -0.3 -0.4 simple illustration is given in table 8.8, where only -0.5 two fuels are considered: oil and coal. These two 1983 1987 1991 1995 1999 2003 2007 fuels are considered in varying proportions, ranging Source: Author calculations. from 100 percent oil to 100 percent coal. According to figure 8.3 and table 8.6, coal has consistently lower price levels and lower price volatility. For each decline. One observation is that oil and European gas combination examined, the standard deviations of prices have been tracking each other closely with a fuel price volatility are lower when coal is included growing offset since about 2004 (figure 8.3), but the in the fuel mix than if only oil is used. What may be price volatility of European gas has been much lower counterintuitive is the finding that using a mix of than that of oil. Therefore, diversifying away from oil 10 percent coal and 90 percent oil lowers the price to gas in Europe would offer protection against oil volatility of the fuel mix relative to using coal alone, price volatility, if not higher oil prices. although coal is consistently the less volatile of the Table 8.7 shows correlations between the four two fuels. During 2004­07, a mix of 25 percent oil fuels for returns of logarithms of monthly prices. The and 75 percent coal would also have lowered price correlations are much weaker than those for price return fluctuations. 8 Tackling Oil Intensity and Diversification 75 Table 8.7 Fuel Price Volatility Correlation Period and fuel Australian coal Oil Gas, Europe Gas, U.S. 1983-2007 Australian coal 1.00 Oil 0.19 1.00 Gas, Europe 0.01 0.05 1.00 Gas, U.S. 0.12 0.19 0.08 1.00 1983-99 Australian coal 1.00 Oil 0.09 1.00 Gas, Europe -0.01 0.02 1.00 Gas, U.S. 0.15 0.22 0.08 1.00 2000-07 Australian coal 1.00 Oil 0.22 1.00 Gas, Europe -0.05 0.04 1.00 Gas, U.S. 0.10 0.15 0.06 1.00 2000-­03 Australian coal 1.00 Oil 0.04 1.00 Gas, Europe -0.02 -0.04 1.00 Gas, U.S. 0.39 0.13 0.10 1.00 2004-07 Australian coal 1.00 Oil 0.39 1.00 Gas, Europe -0.12 0.17 1.00 Gas, U.S. -0.11 0.21 0.03 1.00 Source: Author calculations. Note: All prices are monthly prices shown in figure 8.3. The European gas price series starts in January 1991. Table 8.8 Standard Deviation of Fuel Mix Price Volatility Period Oil 75% oil/25% coal 50% oil/50% coal 25% oil/75% coal 10% oil/90% coal Coal 1983­2007 0.084 0.075 0.063 0.048 0.039 0.043 1983­99 0.086 0.075 0.061 0.043 0.033 0.035 2000­07 0.079 0.074 0.067 0.056 0.049 0.054 2000­03 0.087 0.081 0.071 0.055 0.042 0.044 2004­07 0.070 0.066 0.062 0.056 0.055 0.062 Source: Author calculations. 76 Special Report Coping with Oil Price Volatility Energy Diversification Index and Oil the number of energy sources with equal shares that Share of Primary Energy would have the same diversification index. For computing energy diversification, the The previous section suggests that fuel prices and last year for which data are available was 2005. price volatility of different energy sources are not Table 8.9 presents the distribution of HHDI for the necessarily well correlated even over a number 181 countries for which data are available. There are of years, and a diversified portfolio of energy only five countries with an HHDI smaller than 0.25, sources could thus mitigate the price volatility of equivalent to using four energy sources with equal a particular energy source. The literature on the shares. More than half the countries have an HHDI theoretical measurement of diversity is extensive, higher than 0.5, or equivalent to being dependent with substantial contributions coming from the on two or fewer energy sources with equal shares. field of ecology with its measures of biodiversity. Twenty-two countries have an HHDI index of unity, Jost (2006) gives an extensive analysis of such being dependent only on oil. Most, but not all, of these indicators. With respect to energy, the most popular countries are small island nations; this group also indicators are based on the Herfindahl-Hirschman includes small non-island African countries. index and the Shannon-Wiener index. This chapter The historical evolution of HHDI for select uses the Herfindahl-Hirschman index, calculating countries is shown in figure 8.6. The most diversified it from six sources of energy: oil, natural gas, economy in the world is Finland, with an HHDI of coal, hydropower, nuclear power, and other forms 0.21 in 2004, equivalent to using five energy sources of renewable energy (geothermal, solar, wind, equally. Some countries, such as China and Sri Lanka, and wood and waste electricity generation). AA have been showing an upward trend in HHDI, or significant omission is biomass outside of the power falling energy diversification, in recent years. sector. Small-scale biomass use is widespread in Summary statistics on the evolution of HHDI for developing countries, especially among the rural poor the 158 countries that have continuous data between and small commercial establishments. However, data 1980 and 2005 are given in table 8.10. Nearly two- limitations do not permit the inclusion of biomass in thirds of the countries have minimum diversification the present analysis. Its inclusion would lower all the in the early 1980s. A quarter of the countries, however, numbers presented in this section. have maximum diversification during the same To compute the Herfindahl-Hirschman period. Close to another quarter have maximum diversification index (HHDI), the fractional share diversification in 2004-05. The table also shows the of each source (standardized in energy units), pi, is difference between the maximum and minimum squared and summed to yield values of HHDI experienced by the countries between 1980 and 2005. Some experienced no difference, HHDI = (8.1) ipi , 2 and all of them are countries with an HHDI of 1.0 where i runs from 1 to 6. The higher the HHDI, the less throughout the period. diverse is the energy sector. The lowest possible value TheHHDImeasuresdiversityofallfuels,butdoes ofHHDI,representingmaximumdiversification,is0.17 not explicitly indicate how much oil is contributing to for six energy sources. For a given HHDI, its inverse is the overall index. Although the HHDI may suggest Table 8.9 Distribution of HHDI, 2005 Parameter HHDI < Ľ HHDI < ą/ł HHDI < ˝ HHDI < ľ HHDI > ľ HHDI = 1 Total Number of countries 5 27 77 133 48 22 181 Percentage of countries 3 15 43 73 27 12 100 Sources: U.S. EIA 2008b; author calculations. 8 Tackling Oil Intensity and Diversification 77 reasonable diversification, the oil share of primary more than half of their primary energy, and about a energy may nevertheless be high; the reverse could third of the countries rely on oil for more than three- also occur. To supplement the HHDI, a simpler quarters of their primary energy. Those countries with measure--the oil share of total primary energy--was an oil share of energy equal to unity are the same computed. This simply reports pi in equation 8.1. The countries that had an HHDI of unity. distribution of the oil share of primary energy in 2005 The historical evolution of the oil share of energy is shown in table 8.11. for select countries is shown in figure 8.7. They are For about a quarter of the countries, oil accounts the same countries as those in figure 8.6, except that for less than a third of total energy. Fifty-five percent Finland has been replaced by Trinidad and Tobago, of the countries, however, are dependent on oil for which is the country with the lowest dependence on Figure 8.6 Historical HHDI for Select Countries 1.0 0.9 Senegal 0.8 Jordan x 0.7 Sri Lanka deni Kenya oni 0.6 China catfiisersvid 0.5 India United States 0.4 Finland HH0.3 0.2 0.1 0.0 1980 1985 1990 1995 2000 2005 Sources: U.S. EIA 2008b; author calculations. Table 8.10 Maximum and Minimum HHDI, 1980-2005 Year of minimum diversification Year of maximum diversification Parameter 1980 1980-83 2004-05 1980 1980-83 2004 2005 Number of countries 74 102 9 27 40 15 21 Percentage of countries 47 64 6 17 25 9 13 Difference in HHDI between maximum and minimum Difference > 0.5 > 0.4 > 0.3 > 0.2 > 0.1 > 0.05 0 Number 1 9 22 53 102 123 20 Percentage of total 1 6 14 33 64 77 13 Sources: U.S. EIA 2008b; author calculations. 78 Special Report Coping with Oil Price Volatility Table 8.11 Distribution of Oil Share of Primary Energy, 2005 Parameter Share < Ľ Share < ą/ł Share < ˝ Share < ľ Share > ľ Share = 1 Total Number of countries 29 44 82 121 60 22 181 Percentage of countries 16 24 45 67 33 12 100 Sources: U.S. EIA 2008b; author calculations. Figure 8.7 Historical Oil Share of Primary Energy for Select Countries 1.0 0.9 Senegal 0.8 ygerney Jordan 0.7 Sri Lanka 0.6 Kenya arm United States prifoe 0.5 India 0.4 China sharliO Trinidad and Tobago 0.3 0.2 0.1 0.0 1980 1985 1990 1995 2000 2005 Sources: U.S. EIA 2008b; author calculations. 1 oil. (Equatorial Guinea and the Democratic Republic Although the HHDI and the oil share of energy of Korea have lower shares, but they are excluded are not comparable, it is worth noting that, in 2005, for seeming data problems and an unusual political there are 50 countries in which the oil share of energy situation, respectively.) There are notable differences is lower than its HHDI. Among them, there are between figures 8.6 and 8.7. The United States, despite 20 countries in which the HHDI is larger than 0.5 but its high energy diversification, shows a relatively the oil share of energy is lower than one-third. There high level of dependence on oil, reflecting its heavy are no countries in which the HHDI is smaller than consumption of gasoline as an automotive fuel. China, 0.5 and the oil share is greater than 0.75, but there are in contrast, despite having an HHDI close to 0.5, shows 19 countries in which the HHDI is smaller than 0.5 low reliance on oil. and the oil share is greater than 0.5. Summary statistics on the historical evolution of theoilshareofenergybetween1980and2005aregiven Policies for Reducing Dependence on in table 8.12. Half of the countries have the greatest Oil reliance on oil in 1980. Nearly a third of the countries have the least dependence on oil in 2003­05. On the Dependence on oil can be lowered by reducing oil whole, countries are diversifying away from oil. consumption per unit activity (such as fuel consumed 8 Tackling Oil Intensity and Diversification 79 Table 8.12 Maximum and Minimum Oil Share of Primary Energy, Selected Years, 1980-2005 Parameter 1980 1981 1982 2001 2003 2004 2005 Number of countries with maximum 79 11 9 2 4 5 5 Percentage of countries 50 7 6 1 3 3 3 Number of countries with minimum 25 3 6 9 9 12 25 Percentage of countries 16 2 4 6 6 8 16 Sources: U.S. EIA 2008b; author calculations. Note: Data shown are for 158 countries that existed in 1980 and for which data are available to 2005. Only those years in which there were at least nine countries with a minimum or maximum oil share are shown. by driving a certain distance), reducing the level of not only cost less than the other two approaches activity consuming oil (driving fewer kilometers), considered (both of which involved raising vehicle and fuel switching. Fuel switching is easier in power fuel economy standards) but would start reducing generation and much more difficult in transport, consumption immediately, and the market effect where suitable substitutes for gasoline and diesel are would gradually drive the transition to more fuel- not readily available. Car and appliance ownership efficient vehicles (Automotive Environment Analyst as a function of household income is S-shaped, with 2004). High transportation fuel prices in Europe have low uptake at very low income and ownership rising led to widespread adoption of fuel-efficient cars and steeply above a threshold income level before reaching an increasing switch to compression ignition (diesel) saturation at high income. This trend means that engines, which are inherently more efficient than low-income developing countries are particularly spark ignition (gasoline) engines. A recent review susceptible to steeply rising oil consumption in the of vehicle fuel economy from around the world medium term. indicates large differences in the fuel consumption Over the long run, pricing oil products high of new cars per unit distance traveled, with Japan through taxation is one of the most effective ways and Europe leading in fuel efficiency and the United of promoting efficient consumption of oil and States--where retail fuel prices are among the lowest discouraging nonessential use. The first step for of high-income countries--lagging considerably countries that are still subsidizing fuel prices is to behind (ICCT 2007). start phasing down the subsidies. High prices force Needless to say, high prices hurt consumers. Of consumers to conserve and look for alternative lower particular concern in developing countries is the cost energy sources. For example, high taxation impact on the cost of living of higher prices of diesel, on transport fuels will encourage the use of more which is used in both freight and passenger transport. fuel-efficient vehicles, reduce trip numbers and trip Increasing the price of diesel will increase input lengths, and favor public over private transport modes. A report by the U.S. Congressional Budget prices for major production sectors. Indirect effects of Office on instruments for improved fuel economy is higher diesel prices on the poor can be considerable. informative in this regard. The report examines three Earlier studies in Pakistan and Yemen found that, different approaches to decreasing fuel consumption as a percentage of household income, the adverse by 10 percent, and finds that the cheapest and most effect of increasing diesel prices was regressive and effective path would be a substantial increase in had the greatest impact on the poor (ESMAP 2001, the fuel tax. Simply raising the federally mandated ESMAP 2005). Additional tax revenue flowing to the fuel economy standard would be the most costly treasury from higher fuel taxation could be used to approachforconsumers. Raisinggasoline taxeswould target assistance to the poor. 80 Special Report Coping with Oil Price Volatility Policies that are not necessarily based on fuel analysis shows that this has been achieved mainly pricingandthatreduceconsumptionofoilarecovered through lowering energy intensity in each sector, in detail by Bacon and Kojima (2006). The report and not by structural changes in the economy--for discusses a number of measures that limit petroleum example, shifting out of manufacturing to the service fuel consumption in transportation, including sector (Lamech, Kojima, and Bacon 2007). · traffic management in urban centers; Fuel switching is another way of reducing · limiting the speed limit, for example, to below dependence on oil. In the transport sector, three 80 kilometers an hour; alternative energy sources are natural gas, electricity · setting fuel economy standards; (mostly hybrid vehicles), and biofuels. Compressed · parking policies that make parking expensive, natural gas is particularly suitable in countries with difficult (by limiting the availability of parking), domestic gas production and where urban centers or both; already have a network of pipelines. Conditions · promoting public transport as well as car- and that make use of natural gas economic are reviewed van-pooling; by Gwilliam, Kojima, and Johnson (2004). Hybrid · physical restraints on vehicle use, the best known gasoline-electric or diesel-electric vehicles are only scheme of which is an odd-even day restriction, now beginning to be deployed on a commercial scale. whereby vehicles are banned from use on certain Biofuels are being increasingly mandated in countries days depending on the terminal digit (odd or around the world, but the need for significant even) of their registration number; subsidies remains a barrier. Additionally, there are · road pricing; concerns about increasing correlations between oil · limiting workdays; and biofuel feedstock prices, and the upward pressure · promoting better driving practices that conserve that will have on food prices (Kojima, Mitchell, and fuel. Ward 2007). In the power sector, non-oil options are natural Measures limiting petroleum oil consumption in the gas, coal, hydropower, nuclear power, and renewable power sector, where oil is used as a fuel in power energy such as geothermal, solar, and wind. These are generation, include the following: not quick solutions but normally form part of a longer term power development plan: building a large-scale · Reducing the use of air conditioning, central hydroelectric power plant, for example, takes years. heating, and elevators The feasibility of switching to renewable electricity · Encouraging more energy-efficient practices by also depends on natural resource endowments (for setting efficiency standards, providing financial example, availability of geothermal power). incentives through tax differentiation based on Manycountriesareconsideringswitchingfromoil efficiency, and raising public awareness · Imposing earlier closing hours on retailing and and natural gas to coal for power generation. Some are offices and introducing daylight savings time evenexaminingsmall-scalecoalapplicationsinremote · Reducing the length of the working week areas and small island economies, where diesel is · Imposing power rationing (the most radical currently used. Given the large and possibly widening approach) price gap between coal and hydrocarbons, as shown in figure 8.3, this may make sense in financial terms. Globalexperienceindicatesthatincreasingenergy When environmental externalities, which are poorly efficiency is important. Bacon and Bhattacharya pricedatthemoment,aretakenintoaccount,switching (2007) show that, to the extent that rising fossil fuel to coal brings with it new problems. How to strike a consumption with rising GDP is offset, the offsets balance between affordability and energy security on have been largely due to falling energy intensity the one hand and environmental sustainability on the (energy consumed per unit of GDP). Subsequent other is a challenge that merits careful consideration. 9 Conclusions During the last 20 years, international oil prices have nonstationarity of prices has far-reaching implications experienced dramatic changes. From a period of for policymakers. Because current pricesare presently relative stability between the mid-1980s and the end giving only weak clues as to prices in the coming of the 1990s, prices remained near US$20 a barrel, with months, governments must consider a wide range of the exception of a short-lived price spike during the possible outcomes and plan accordingly. They also first Persian Gulf War. From the end of the 1990s until need to acknowledge that their policies may come into the beginning of 2004, prices fluctuated but not to the operation at a time when prices differ substantially extent of indicating the subsequent development in from those projected. which their levels rose in real terms to above their The magnitude of this uncertainty about price historic maximum. behavior is measured in this report by the volatility The path of price changes has not followed a of prices. This volatility is calculated as the standard smooth evolution over time; even during the last three deviation of returns (defined as the change in the years, there have been periods where prices declined logarithms of successive prices) and is used to by a large margin, only to rise further subsequently. compare prices in different subperiods and in various These variations in prices add to the difficulties of countries. Volatility is lowest measured on a daily planning ahead for governments, businesses, and basis, and highest measured on a monthly basis, consumers. which is relevant for governments making planning decisions based on average prices taken over longer time intervals. Statistical Analysis of Price Volatility For oil products, the volatility in daily prices A statistical analysis of prices over the period was lowest in the earliest subperiod. This finding 1986­2007 was able to establish certain important should be interpreted in terms of the measurement features. Both for the period as a whole and for of volatility: for small values, the average return is three subperiods within this range, crude oil and oil approximately the average percentage change in product prices in nominal and real U.S. dollars were, prices from subperiod to subperiod observed during in almost all cases, nonstationary with the exception of the period in question. Since prices were, on average, thefirstsubperiod.Therewasnomeasurabletendency substantially higher in the third subperiod, the for prices to return to a mean value. Cochrane test volatility in that subperiod corresponds to a larger statistics appear to suggest that shocks to the prices average absolute change in prices than in the second have both permanent and temporary components. subperiod. This finding was also confirmed for five developing The volatility of oil product prices was generally countries, when measuring prices in local currency. higher than that of crude prices, with gasoline The one exception to this general tendency was in exhibiting the greatest volatility. During the second the first subperiod (1986­99) when some product and third subperiods, the volatility of the monthly and crude oil prices were stationary and therefore average prices of most products approached a value showed a tendency to revert to a mean value. The of 0.1, indicating average month-to-month price 81 82 Special Report Coping with Oil Price Volatility changes of about 10 percent. This level of volatility, (sequencesofthesamesignforthedeviationsbetween coupled with the lack of mean reversion in the level of actual and trend) was significantly below expectation, prices, indicates why a successful policy to cope with especially for residual fuel oil and propane. However, volatility would be a valuable policy tool. based on monthly average data, the number of runs Studies in other markets have indicated that wasaswouldbeexpectedifsuccessivedeviationsfrom period-to-period measures of volatility show trend were independent. The monthly data for the five clustering--a large price swing in one period tends to developing countries again indicated that, generally, be followed by a large price swing in the next. Recent thenumberofrunswasnotsignificantlydifferentfrom history would then be a likely guide to the amount that expected in the independent case. of volatility to be expected in the near future. Tests Although the number of runs based on monthly for clustering of volatility for U.S. price data using a average prices was generally consistent with GARCH model indicated that, for data based on daily successive deviations from trend being independent, prices--and, to a lesser extent data based on weekly the cumulated value of the deviations exhibited some average prices--volatility exhibited mean reversion. lengthy sojourns (the period of time for which the That is, there was clustering, but the effect died down cumulative sum remained the same sign). Based on over time, and the volatility tended to return to a monthly data, the longest sojourns for crude and for mean value. It was difficult to establish any temporal oil products were in virtually all cases longer than pattern for volatility for monthly average price data, three years, and often between four and five years. and a tendency to clustering could not be clearly And again in virtually all cases, the longest sojourns identified. This pattern for monthly price data was corresponded to a period when the cumulative cycles also found in a sample of five developing countries, were positive. This finding has a very important most markedly for the period from 2000 to 2007. More implication for schemes in which the government tries complex statistical analysis might reveal whether to smooth prices through some form of target trend there is any underlying pattern in the sequential and plans to temporarily finance the differences from volatility of oil prices. At this point, however, it international prices. Such attempts could well remain appears that there is little to guide policy makers as in deficit for long periods, which could be politically to the magnitude of volatility in subsequent periods, difficult to handle. The maximum sojourns were beyond the levels most recently experienced. This much shorter and cumulative cycles were on average result has significance for those designing strategies negative if daily prices are traced. However, operating that require a quantification of volatility in future an oil account for price smoothing based on daily periods, such as hedging. prices would mean revising prices and transferring A further aspect of the temporal pattern of oil money in and out of the oil account on a daily basis, prices is that of the sequential patterns of deviations thereby increasing both end-user price fluctuations from the underlying trend. Fitting a Hodrick-Prescott and administration costs. filter to oil prices produces a series that follows all There can be large differences in the behavior the main fluctuations but with a smoother path of price levels between prices denominated in U.S. from period to period. This series can be taken as a dollars and those in other currency units due to representation of how price expectations might be exchange rate fluctuations. Price increases in the past continuously revised as new data become available, four years have not been as large in the countries and governments could take these trend values as where the local currency has strengthened against those around which to build policies. the U.S. dollar in the face of the dollar's recent The deviations from this trend measure the general depreciation. However, when price volatility temporary costs of basing policies on trend values is examined, exchange rate appreciation appears to rather than on international market prices. Tests have done little to moderate price volatility in the using daily and weekly data for the presence of runs five developing countries examined. In several cases, in these deviations indicate that the number of runs exchange rate fluctuations seem to have increased, 9 Conclusions 83 rather than reduced, the volatility of crude oil and oil the largest differences in returns between the two product prices. strategies were found in the most recent period. Anumberofpolicieshavebeenusedorconsidered For buyers of crude oil or oil products, hedging for possible use in reducing the adverse effects of price appears to have been a very attractive strategy, when volatility on economic agents. These policies fall purchasing forward could have both reduced risks into two classes. A first group of policies attempts to and secured a lower price than the spot market for the transfer the volatility of oil prices from the ultimate commodity itself. Crucially, this strategy would have purchasers of the oil or products to another party. In required agents to be able to anticipate the general the case of hedging, the counter-party is the futures rise in prices that occurred during the period. Since market itself; while for security stocks and price- the futures prices so consistently underestimated the smoothingschemes,thecounter-partiesareeffectively actual spot prices that emerged, it is difficult to believe taxpayers in the country who are temporarily that governments could have made better estimates of financing the costs of running the schemes. A the prices that would actually emerge. The possibility second group of policies looks to manage volatility of incurring large losses in the futures market, as must by reducing the level of oil consumption place the have happened to any seller using it consistently, is a burdenonindividualusersbyprovidingdisincentives clear indication of the dangers of relying on hedging or restrictions on its use. for a commodity whose prices are so volatile and whosemedium-termmovementsaresounpredictable. Hedging The possibility of consistently underestimating future prices in an upswing period, as has recently Hedging is widely used by the private sector to reduce been experienced, is well illustrated by the length of the risks arising from volatility, and thus it might sojourns of cumulative cycles. For countries that sell appear to be a prime candidate for governments to other crudes, or that need to purchase products other use as well. The statistical analysis of simple hedging than gasoline or heating oil, the basis risk created by strategies over the period studied in this report differentialsbetweenthesepricesandthosequotedon revealed important drawbacks to this approach. The the futures markets further reduces the attractiveness efficiency of hedging crude on the futures market of hedging strategies. increased with the length of the duration of the Options contracts are designed to reduce the hedge--contracts 24 months ahead provided the possibilities of regret by allowing contracts to expire greatest risk reduction--but, at the same time, the when they appear to turn out to be unfavorable. value of the unhedged return was much greater However, at a time of widely varying prices and than that of the hedged return for sellers of crude uncertainty about the general movement of prices in or of products. By the same token, the value of the the market, the upfront costs of using options may hedged return was greater than the unhedged return well be a strong disincentive to governments for using for buyers of crude. For gasoline and heating oil, optionsasalong-termstrategy.Thelackofwidespread which were evaluated over a three-month contract government endorsement of hedging strategies in duration, the hedged return was again greater than the oil market is an important indication that such the unhedged return for buyers of product. strategies appear to have substantial drawbacks. For sellers of crude oil or oil products, the gains Overall, futures or options are an important risk- of consistently selling on the spot market would have reducing strategy when there is strong evidence that been larger than those from consistently selling on prices will fluctuate around a mean value, or when the futures market at durations ranging from 3 to the agent is certain about the overall direction of 24 months. This difference was found for each of prices. The history of oil prices during the period, the three subperiods, including the first in which which did not exhibit mean-reversion, and when spot prices did not show a strong upward trend. However, prices failed to be predicted by earlier futures prices, 84 Special Report Coping with Oil Price Volatility indicates why this strategy has not been more widely The simulations carried out in the study indicate used as a long-run policy instrument. that price-smoothing schemes in which the target price is determined by a moving average of past spot Strategic Stocks (or futures) prices can be effective in reducing the volatility of domestic prices to consumers. The largest Many countries mandate the private sector to hold reductions were achieved with the longer moving stocks above the levels required for commercial averages. During periods of increasing international operations; in a few cases, the government finances prices, the moving averages lagged behind, and there its own security stocks. These stocks have been would have been an increasing financing burden for intended primarily as a buffer against rare but large the government. This effect was larger when longer disruptions of the physical supply of crude oil or oil moving averages were used. products. There has been some discussion of the use of these stocks to smooth out extreme price increases-- The use of a modified scheme with intervention themselves caused perhaps by sharp changes in the only when international prices are outside a ceiling actual or expected global supply of oil. Simulations of and floor price band (as is used in Chile) provides the benefits and costs of using security stocks to place a method of obtaining a trade-off between the a cap on these exceptional price increases suggest that costs during a period of increasing prices and the this policy is likely to be most effective in a period of reduction in volatility. The narrower the price band, broadly rising prices, when the government has been the more the reduction in volatility, but the greater able to buy low and sell high (but below international the financing costs to the government while prices are prices), thus obtaining a contribution to the costs tending to increase. The evidence from sojourns data of running the scheme. The history of oil price is particularly relevant to this approach. The cycles-- behavior indicates that it is difficult to identify such which are the difference between the international an episode before it happens. During a period of price actual price and the filter price, which is effectively a mean reversion, when there may be a short-lived but smoothed moving average of past prices--exhibited exceptional event, the security stock can be effective very lengthy periods in which their cumulative value in reducing the level and volatility of domestic prices. corresponds to a continuous government financing But the carrying costs of a scheme, where there is little deficit. Sojourns of five years or even longer were opportunity to make a capital gain on holding the exhibited by many of the crude oil and products stocks, will be substantial. values in U.S. dollars and in local currency. Persistent deficits of this nature in an oil account may well be politically unsustainable. Governments that rely on Price-Smoothing Schemes ad hoc increases in the target price, made at irregular intervals when the possibility of increasing domestic The most commonly used policy for reducing oil prices seems politically acceptable, run the risk of very price volatility is price smoothing. The government rapidly accumulating extremely large deficits, as was lowers domestic prices at times of higher than the case in Thailand. "normal" international prices by lowering taxes or by increasing subsidies; it balances these costs by raising domestic prices at times of low international Reducing the Importance of Oil prices by increasing taxes or decreasing subsidies. Consumption Governments have generally not attempted to smooth prices around a constant level, effectively recognizing A different policy response to oil price volatility that price behavior is not mean-reverting. Instead, is to attempt to reduce its impact by reducing the they have adjusted the target price, around which relative importance of oil consumption. In this case, domestic prices are to be smoothed to follow the the volatility could remain the same for each unit general trend of international prices. consumed, but with the reduction in the number 9 Conclusions 85 of units consumed, the aggregate significance of even from gas) by increasing the share of coal in those the volatility would be reduced. Schemes to reduce uses where the fuels can be substituted, in order to the impact of high oil prices by reducing demand lower both costs and cost volatility. An analysis of the therefore also reduce the aggregate effects of its overall diversity of six energy sources used in 2005 volatility. revealed that more than half the 181 countries in the In 2006, nearly one-quarter of the 163 countries sample had a Herfindahl-Hirschman diversification analyzed spent a sum greater than 10 percent of their index of greater than 0.5, which is the equivalent of current GDP on oil; for a quarter of the sample, 2006 being equally dependent on just two fuels with equal was the year when this ratio was greatest during market shares. Twenty-two countries were entirely the period 1980­2006. Many countries have not been dependent on oil, and 60 countries had a share of oil improving the ratio of physical oil use to real GDP in total energy use of greater than 75 percent. during the period--only one-quarter of the sample Some policies to reduce oil dependence revolve experienced the lowest value of this ratio in 2006. around pricing and taxation, but the higher domestic These two sets of statistics indicate the need for strong prices which may lead to lower consumption policies to reduce the use of oil relative to GDP in a inevitably place burdens on consumers. Other climate of very high prices and high price volatility. policies to limit the consumption of oil products in A statistical analysis of the prices of competing the transportation sector--or the use of electricity fossil fuels revealed that the volatility of oil prices has where this is substantially fueled by oil products--are been greater than that of gas prices in Europe (but widely discussed but do not yet appear to have been lower than that of gas prices in the United States) and implemented on a sufficiently broad scale to make of spot coal prices. Further, correlations between the an appreciable difference in oil consumption. Other price volatility of different fuels are weak. At the same studies have indicated that the most promising route time, the gap between oil and gas prices on the one to lowering oil consumption is to improve energy hand and coal prices on the other has been widening. efficiency, and that policies focusing on end uses that These findings point to the possibility that countries involve the use of oil products along the supply chain may plan to diversify away from oil (and possibly should be pursued. Annex 1 Impact of Fiscal Parameters on Government Oil Revenue This annex takes an oil-producing country and gives Figure A1.2 a simplified illustration of the impact of varying fiscal parametersongovernmentoilrevenue.Theannexexamines Aggregate Production Profile of All Fields the trade-off between revenue volatility and government 120 income. It considers two fiscal regimes, one regressive (whereby the government take in percentage declines with year100 increasing oil price) and the other progressive. The annex persl 80 takes a hypothetical field that, over 19 years, produces 60 100 million barrels of oil. It then overlays them so that a arreb field with the same production profile and cost structure is 40 coming on stream every two years until a steady production ionll 20 level is reached. The simulation also assumes a constant cost Mi structure in real terms. The combined effect of overlapping 0 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 producing fields and assuming a constant cost structure is Year to remove volume and production cost volatility and leave Source: Author calculations. oil price volatility as the main cause of revenue volatility. The production profile and associated costs are taken fromJohnston(2003).Theproductionprofileofeachfieldand Historical spot prices of a basket of three marker the sum of annual oil production from all producing fields crudes--Brent, Dubai, and WTI--expressed in constant are shown in figures A1.1 and A1.2, respectively. Calculation 2007 U.S. dollars are used for calculating government of government revenue starts in year 1 in figure A1.2, when revenue. They are taken from the annual average prices 14 fields are producing oil. By then, the first field to have between 1978 and 2007; for 2007 (year 15), the monthly come on stream is in the 16th year of operation. average price in October 2007 is used so as to amplify volatility. The prices are shown in figure A1.3. This annex considers two production-sharing agreements (PSAs). PSAs normally provide for the sharing Figure A1.1 of production rather than profits. The state, which owns all Production Profile of Each Field petroleum, transfers title to a portion of the extracted oil and gas to the contractor at an agreed delivery point. The 14 contractor is responsible for all financing and technology areyrepslerrabnoill 12 required for petroleum operations and bears the risks. 10 Typical revenue streams in a PSA are shown in figure A1.4. Oil produced is split into cost oil, profit oil, and royalty. The 8 payment streams in figure A1.4 are explained below. 6 4 · Royalties are based on the volume or value of oil extracted. They are paid as soon as commercial Mi2 production begins, thereby providing early revenue 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 to the government. They also ensure that contractors Year make a minimal payment. Simple royalties--for Source: Johnston 2003. example, 10 percent of the value of the oil extracted-- 87 88 Special Report Coping with Oil Price Volatility Figure A1.3 Oil Prices Used in the Calculations )$SU 90 80 0702tnatsno(clerra 70 60 50 40 30 l/biofoecirP20 10 0 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Year Source: Authors. are easy to administer, but do not take into account the that can be retained in a given accounting period. profitability of the project and hence are regressive. Costs that are not recovered are carried forward and As such, royalties deter investment. One way of recovered later; most PSAs allow virtually unlimited redressing this is to make the royalty rate depend on carry-forward. It is another avenue available to the the level of production or the price of oil, increasing it government to ensure early revenue. with increasing production or oil. The rationale is that · Profit oil is the share of production remaining after the larger production levels lead to greater profitability royalty is paid and cost oil has been retained by the because of economies of scale (this is not always the contractor. In its simplest formulation, the agreement case, because many factors other than the scale of may stipulate that the profit oil be split, for example, production affect a project's profitability), and similarly 30/70--the contractor's share being 30 percent and the higher oil prices lead to greater profitability. In those government's share 70 percent--irrespective of world cases, royalties are said to be on a sliding scale. oil price or production level. Production sharing can · Cost oil refers to the oil retained by the contractor to also be on a sliding scale: the government's percentage recover the costs of exploration, development, and share can increase with increasing production level, production. Most PSAs limit the amount of cost oil cumulative production, or rate of return. · Income tax is paid after production is shared in this figure; it is also possible to write a PSA in which Figure A1.4 income tax is paid before production sharing. In the Production-Sharing Revenue Flow figure, the contractor is subject to income tax based on taxable income. Production · Bonuses are the most regressive fiscal parameters Cost oil Profit oil Royalty and give early revenue to the government. Signature bonuses are paid when the contract becomes effective and can be considerable in highly prospective areas. Contractor's share Government's share The fiscal parameters used in this annex are given in Contractor's after-tax Income table A1.1. The first case considered is regressive: royalty, share tax tax, and production-sharing rates do not increase with increasing net-of-cost income. There is a signature bonus Total contractor's share Total government's share of US$20 million, the royalty rate is fixed at 10 percent, and cost recovery for production sharing is restricted to 60 Source: Authors. Annex 1 Impact of Fiscal Parameters on Government Oil Revenue 89 Table A1.1 Description of Two Fiscal Regimes Parameter Case 1 Case 2 Capital depreciation Five-year straight line Five-year straight line Royalty 10% Sliding scale as a function of oil price Signature bonus US$20 million None Taxable income Gross revenue - (royalty + bonus + Gross revenue - (royalty+ bonus + eligible production share + eligible expenses) expenses) Income tax 30% 30% Production share 70% Sliding scale as a function of IRR Cost oil ceiling 60% None Source: Authors. percent in any given accounting period. All these provisions the rest of the life of the field. The cumulative revenue to are designed to ensure early revenue. The government the government is US$2.85 billion in case 1 and US$3.21 receives 70 percent of profit oil. After these payments, billion in case 2. the contractor pays an income tax of 30 percent on profits On the other hand, the sixth field to come on stream derived from the remaining income. The second case does faces many years of low oil prices. In instances where project not have a signature bonus and has sliding scale royalty profitability is low, the regressive fiscal regime ensures early and production-sharing schedules (table A1.2). The royalty revenue to the government, as shown in figure A1.6, and a rate does not reach 10 percent (the rate set in the first case) slightly higher cumulative income to the government. until the extracted oil fetches at least US$25 a barrel. As Annual government revenues in the two fiscal cases the oil price increases, however, the royalty rate rises with from all fields, beginning in year 1 in figure A1.2, are shown it and reaches a maximum of 40 percent above US$60 a in figure A1.7. The difference is evident in the last few years barrel. The government's share of profit oil increases with when oil prices are high. increasing internal rate of return (IRR) of the project, TherevenueflowsgiveninfigureA1.7areanalyzedusing reaching 70 percent (the rate in case 1) when the IRR is four different discount rates (table A1.3). At a discount rate between 30 and 35 percent, and as high as 90 percent when of zero--equivalent to valuing income to future generations the IRR exceeds 50 percent. the same as income today--revenue volatility is greater in Government revenues from the first field to come on the more progressive of the two cases. As the discount rate stream in the two fiscal cases are shown in figure A1.5. is increased--which may be justified if there are urgent Year 1 in the figure corresponds to year -14 in figure A1.3. basic infrastructure needs such as provision of electricity Case 1 indeed gives higher early revenue to the government, and water for which the government needs funding now but, starting in year 6, when the project has recovered ratherthaninthefuture--thedifferenceinrevenuevolatility capital expendituresand become profitable, the government diminishes, and, at a discount rate of 15 percent, the two revenue surpasses that in case 1 and remains higher for cases give essentially the same results. Table A1.2 Sliding Scale Royalty and Production Sharing in Case 2 Oil price (US$/barrel) < 20 20­25 25­30 30­35 35­40 40­45 45­50 50­60 > 60 Royalty, % 5 7.5 10 15 20 25 30 35 40 IRR threshold, % < 20 20 30 35 40 > 50 Gov't share of profit oil, % 0 40 70 75 80 90 Source: Authors. 90 Special Report Coping with Oil Price Volatility Figure A1.5 Figure A1.7 Government Revenue from First Field to Come on Government Revenue from All Fields Stream 4,000 Case 1 600 3,500 Case 1 Case 2 500 Case 2 arey arey 3,000 anoill 2,500 400 anoillim 2,000 300 mi 1,500 $SU 200 US$1,000 500 100 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Year Year Source: Author calculations. Source: Author calculations. Figure A1.6 not narrow volatility markedly. For example, the ratio of maximum annual revenue to minimum annual revenue is 7 Government Revenue from Sixth Field to Come on under case 1 and 8 under case 2. The price the government Stream adopting case 1 pays for reducing volatility somewhat is 180 to forfeit about US$850 million (undiscounted) in income 160 Case 1 during the 15-year period. Case 2 140 In practice, the political pressure to maximize arey 120 government revenue in times of high oil prices is likely to anoillim leadtooppositiontoafiscalregimethatmayreducerevenue 100 volatilitysomewhat,butwillalsodiscouragethegovernment 80 from enjoying windfall income when oil prices are high. $SU 60 The degree of this political pressure has been evident in 40 recent months, when government after government in oil- 20 producingcountriesandprovinceshaveproposedrevisions 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 to the fiscal regime--all designed to allow the government Year to participate more in the gains from record oil prices. For this reason, rather than attempting to reduce Source: Author calculations. revenue volatility, it is generally recommended that governments focus on smoothing budget expenditures through long-term, well-planned, disciplined budget This simple illustration shows that the ability of planning and execution. A few oil producers have used fiscal parameters to reduce revenue volatility in the face an oil fund successfully for this purpose. Expenditure of widely fluctuating oil prices is limited. This annex smoothing faces enormous challenges of its own, but that considered two hypothetical cases that differed widely is a topic for another study. in their progressivity. But even these two extremes did Annex 1 Impact of Fiscal Parameters on Government Oil Revenue 91 Table A1.3 Cumulative Government Revenue at Different Discount Rates (US$ million) 0% disc. rate 5% disc. rate 10% disc. rate 15% disc. rate Parameter Case 1 Case 2 Case 1 Case 2 Case 1 Case 2 Case 1 Case 2 Min. annual rev. 445 449 341 343 264 266 207 208 Max. annual rev. 3,145 3,602 1,550 1,775 790 904 620 607 Max. difference 2,700 3,153 1,210 1,432 526 639 413 399 Median annual rev. 929 900 648 635 521 514 364 384 Avg. annual rev. 1,187 1,243 755 782 514 526 372 377 Standard deviation 771 910 318 388 137 166 117 117 Coefficient of variation 0.65 0.73 0.42 0.50 0.27 0.32 0.31 0.31 Cumulative rev. 17,802 18,649 11,330 11,726 7,714 7,894 5,584 5,658 Source: Author calculations. Annex 2 Statistical Methods This annex defines statistical terms and describes the root, chances of maintaining that there is a unit root will statistical methods used in the study. Consider a series that be high, and only with very lengthy time series of data is is a function of time. X(t) is used to designate the value of it possible to distinguish between a process with a unit the series at a given period t. X(t - 1) represents the value root and one that "almost" has a unit root. This point is of X at one period before t, and more generally X(t - k) the important because the long-run behavior of these two value of X at k periods removed from t in the past. models is different: the former has no tendency to revert to a long-run mean and all shocks are permanent, while the latter does revert to some value eventually and shocks Unit Roots are temporary. To provide more evidence on the extent to which A series X(t) has a unit root if it is generated by a process: shocks (changes in levels from one period to the next) are X(t) = X(t - 1) + (t), (A2.1) temporary, variance ratio tests introduced by Cochrane (1988) are used. These relate to the variance of the difference where is equal to unity and (t) is a stationary random in prices that are k periods apart. The test forms the disturbance term. When is less than unity, the process statistics is stationary. Rk = (1 k) Var [X(t + k)-X(t)] Var [X(t + 1)-X(t)], (A2.2) Augmented Dickey-Fuller Test where Rk is the Cochrane's variance ratio and Var is A test for a unit root in a series X(t) performs the least variance. If X is not stationary, Rk will tend to unity as k squares regression of the first difference in X on the lagged increases; if X is stationary, the ratio will converge to zero. value of X and, if desired, a constant, a linear trend, and If the process is more general, combining both permanent lagged values of the difference in X. Standard tables exist (nonstationary) and temporary (stationary) components, for testing the null hypothesis that the process has a unit the ratio will tend to a finite value less than unity but root (the coefficient of the lagged price level is zero). In this greater than zero. study, the equation included a constant and a trend, and the number of autoregressive terms (terms from previous time periods) was selected automatically by the program The Hodrick-Prescott Filter to minimize the Schwartz information criterion, which is a The HP filter is a smoothing method that is widely used to statistical criterion for equation specification selection. obtain a smooth estimate of the long-term trend component of a series. Given a time series X(t), the procedure constructs a filtered series S(t) that minimizes the following criterion: Cochrane's Variance Ratio Test T T-1 [X(t) - S(t)]2 + A number of authors, including Pindyck (1999) and t = 1 t = 2 {[S(t + 1) - S(t)] - [S(t) - S(t - 1)]}2, (A2.3) Reinhart and Wickham (1994), have noted that if the price level is generated by a stationary process--one whose where T is the end of the estimation sample and is a mean and variance remain constant over time--for which smoothing constant that depends on the length of the time the coefficient on the lagged price is near unity, standard aggregate used. Suggested values are 14,400 for monthly ADF tests have very little power. That is, if there is no unit data and 62,500 for weekly data. The difference between 93 94 Special Report Coping with Oil Price Volatility the actual value and the filtered value is termed the cycle mixed autoregressive/moving average process. The mean value C(t), which is given by C(t) = X(t) - S(t). equation might be represented by R(t) = + Trend + R(t - 1) + (t), (A2.7) Returns where , , and are parameters to be estimated, Trend is a linear trend, and the variance of (t) at time t is 2(t). With the exceptions of figures 3.4 and 3.5 and where runs The second (variance) equation in a GARCH(1,1) model tests are performed, the return of a price series X in this would be represented by study is calculated by 2(t) = + 2(t - 1) + 2(t - 1), (A2.8) Rlog(t) = log X(t) - log X(t - 1) = log [X(t) X(t - 1)], (A2.4a) where , , and are parameters to be estimated, and 2(t) is the variance of the error term in equation A2.7. Such where logarithms are used, thereby making returns an equation is interpreted as indicating that this period's dimensionless. The Taylor series expansion of log(1 + ), variance consists of a weighted average of a constant where is small, suggests that, if X(t) X(t - 1) is close to value, the new information about volatility experienced in unity, the return multiplied by 100 is proportional to the the previous period (the ARCH term), and the estimated percentage increase in X from period to period. Otherwise, variance in the previous period (the so-called GARCH returns are calculated by term). The GARCH term is in fact a weighted average of all R(t) = X(t) - X(t - 1) (A2.4b) past information of volatility to that date. The (1,1) refers to the presence of a first-order, moving-average ARCH Cycle returns, CR(t), are always calculated by term (the first term in the parentheses) and a first-order, CR(t) = C(t) - C(t - 1) (A2.5) autoregressive GARCH term (the second term in the parentheses). If the GARCH model reveals that there is because cycles can be negative, and hence it is not possible autocorrelation in the error variances--that is, if + is not to take logarithms of cycles. equal to zero--then equation A2.8 can be used to construct estimates of the systematic and predictable component of the variance period by period (parallel to the single variance Variance Equality Test in the homoskedastic model). Because (t) is based on past 2 This test splits the total sample into two subgroups and information on (t-1) or on both (t-1) and 2 2 2(t-1), it is calculates the sample variance of each. The test statistic for known as the conditional variance. variance equality based on Fisher's F-distribution is If ( + ) is equal to zero, there is no autocorrelation in the variance term and it is homoskedastic. A series F(T1 - 1, T2 - 1) = Var1 Var2, (A2.6) is homoskedastic if all its elements have the same finite where Vari is the variance of subsample i, Ti is the number variance. If ( + ) is equal to unity, the long-run variance of observations in subsample i, and T1 - 1 and T2-1 are their tends to infinity and the variance process is nonstationary. corresponding degrees of freedom. This is called the integrated generalized autoregressive conditional heteroskedasticity (IGARCH) process. All shocks to the variance would then be permanent. A Wald GARCH Models for Autocorrelation of test can be carried out to test either of these null hypotheses. Returns Variance The half-life (H) of shocks to the variance is given by H = log (0.5) log ( + ) (A2.9) TheGARCHapproachallowsforautocorrelation(correlation between the elements in a series at different points in time, Each equation can be checked for adequate specification also known as serial correlation) in the variances of the to ensure that the residuals from the estimated mean series in question over time. It specifies two equations. The equation and the estimated squared residuals do not exhibit first (mean) equation relates the variable of interest (the autocorrelation. returns) to possible explanatory variables plus an error Once statistically significant results are obtained, term. The variables might include a constant, a trend, lagged they can be subjected to further checks. One is a Lagrange values of thereturns, andanyeconomic variablesthat might multiplier test for ARCH in the residuals. This test is be thought relevant. The residuals are hypothesized to have motivated by the observation that, in many financial time a variance that is time dependent and can be modeled as a series where GARCH tests have been most extensively used, Annex 2 Statistical Methods 95 the magnitude of residuals appears to be related to the these tests may be less effective. Nonparametric tests can magnitude of recent residuals. Referred to as the ARCH test be used to test for less structured patterns. A test based on in the rest of this report, this tests for serial correlation in the sequences of positive or negative returns (runs) can be used residuals. Other checks are that both and are positive, to investigate this form of clustering in the data. and that , , and their sum do not exceed unity. A runs test--also called the Wald-Wolfowitz test--is a A further extension of the GARCH model has been nonparametric test that checks the randomness hypothesis explored in certain studies on volatility in the oil market. of a two-valued data series. In this study, signs of returns The threshold GARCH (referred to as TARCH) model (positive or negative) are subjected to runs tests. A run is considers asymmetry in volatility and changes the variance a sequence of consecutive equal values. For example, if equation by splitting the term in ARCH into two variables-- the signs of monthly returns from January to December in one for "good" news corresponding to a positive residual, a year are given by + + + +-- + + +-- -, then there are and one corresponding to "bad" news when the residual is four runs in total, consisting of one run of four positive negative. If bad and good news have different impacts on signs; two runs of, respectively, three positive signs and the future variance of the series, there is said to be a leverage three negative signs; and one run of two negative signs. effect. Tests for equality can be carried out. The Wald-Wolfowitz test is based on a normal distribution in which the actual number of runs (w) is compared to the expected number of runs and the standard deviation Runs Tests of the number of runs. For this purpose, the z statistic is (w-µ) , where µ, the expected number of runs, is given Autocorrelation tests will be most successful when there is by [2N+N- (N++ N-)] + 1, and , the standard deviation, a regular and constant relationship between observations equals (µ-1)(µ-2) (N+ + N--1). N+ is the number of a fixed number of periods apart. In the case where there positive values and N- the number of negative values in are sequential patterns but their strength varies over time, the series. Annex 3 Statistical Analysis of U.S. Gulf Coast Prices This annex complements the results presented in chapter 3. and prices are not stationary. The test equation includes It covers the analysis of daily, weekly, and monthly prices a time-trend variable that creates a series beginning at 0 of WTI crude and oil products in the U.S. Gulf Coast. in the first observation of the sample and increasing by 1 for each subsequent observation. The insertion of this trend variable allows for removal of a systematic increase Data Coverage in prices, thereby focusing attention on nonsystematic price changes. The price data used in this annex are taken from the Web site of the U.S. Energy Information Administration. U.S. Gulf Coast prices were chosen partly because of the Are Crude Prices Mean-Reverting? location's proximity to where WTI crude's prices are quoted The results for crude oil prices are shown in table A3.2. In (Cushing, Oklahoma). The data are not uniformly available most cases, the prices are consistent with a unit root and over all time periods. For each commodity type, the first the series not being stationary. Real and nominal prices month for which data are available is given in table A3.1. yield similar results. However, during the first subperiod, there is some evidence for the rejection of the unit root hypothesis, suggesting that prices appear stationary during Table A3.1 that subperiod. First Month When Price Data Are Available If the series "almost" has a unit root, with very slow mean reversion, the value may be sufficiently close to unity Commodity Start date to be included in the confidence interval based on the ADF WTI Jan. 1986 test. In that case, the test may not indicate the presence U.S. Gulf Coast regular gasoline June 1986 of mean reversion and falsely identify a series as being U.S. Gulf Coast jet kerosene Apr. 1990 nonstationary. To gain a better understanding of such U.S. Gulf Coast heating oil June 1986 borderline cases, Cochrane test statistics were calculated. U.S. Gulf Coast diesel May 1995a The results are given in table A3.3. According to table A3.2, only daily and monthly prices up to December 1999 are U.S. Gulf Coast residual fuel oil July 1993 stationary, and all others are nonstationary. For the price Mont Belvieu, Texas, propane July 1992 series identified as being nonstationary, in no case does Source: U.S. EIA 2008a. Rk converge to unity as k is increased, but neither does Rk a. Prices in the U.S. EIA database appear for the first time in rapidly decline to zero. Shocks to the prices appear to have May 1995, but consecutive daily prices are not available until both permanent and temporary components. September 1995. Are Oil Product Prices Mean-Reverting? Testing for Stationarity ADF tests were applied to nominal and real oil product ADF tests were performed on nominal and real prices. prices in the U.S. Gulf Coast market. The results are shown Real prices are expressed in constant January 2007 U.S. in tables A3.4 to A3.6. The results for daily and monthly dollars, adjusted using the consumer price index. The oil product prices are largely similar to those for crude oil null hypothesis is that the price series has a unit root. prices. With the exception of the first subperiod, all product If the ADF test statistic is larger than the critical value prices, whether nominal or real, are nonstationary. With (shown here for 5 percent), then the null hypothesis holds weekly prices, nominal gasoline prices in each subperiod 97 98 Special Report Coping with Oil Price Volatility Table A3.2 ADF Test Statistics for WTI Crude Oil Beginning­ Beginning­ Jan. 2000­ Jan. 2004­ Averaging period Mar. 2007 Dec. 1999 Dec. 2003 Mar. 2007 Daily, nominal -2.55 -3.56 -2.90 -2.44 Critical value at 5% -3.41 -3.41 -3.41 -3.42 Daily, real -3.15 -4.08 -2.89 -2.49 Critical value at 5% -3.41 -3.41 -3.41 -3.42 Weekly, nominal -1.98 -3.22 -2.83 -2.48 Critical value at 5% -3.41 -3.41 -3.43 -3.44 Weekly, real -2.49 -3.77 -2.43 -2.49 Critical value at 5% -3.41 -3.42 -3.43 -3.44 Monthly, nominal -1.77 -4.34 -2.12 -1.75 Critical value at 5% -3.43 -3.44 -3.51 -3.53 Monthly, real -2.30 -4.74 -2.08 -1.73 Critical value at 5% -3.43 -3.44 -3.51 -3.53 Source: Author calculations. Note: Values significantly different from a unit root are indicated in bold. Table A3.3 Cochrane Statistics for Nominal Crude Oil Prices Parameter Rk Days 20 50 100 200 350 700 1,000 1,500 Full period 0.75 0.67 0.56 0.40 0.43 0.38 0.31 0.25 To end 1999 0.70 0.74 0.68 0.40 0.31 0.17 0.12 n.a. 2000­03 0.72 0.52 0.36 0.29 0.26 n.a. n.a. n.a. Jan. 2004­Mar. 2007 0.81 0.68 0.53 0.31 0.28 n.a. n.a. n.a. Weeks 10 20 35 50 75 100 200 350 Full period 1.10 0.93 0.74 0.68 0.73 0.72 0.54 0.50 To end 1999 1.26 1.17 0.76 0.63 0.50 0.39 0.20 n.a. 2000­03 0.84 0.58 0.52 0.46 0.39 0.24 n.a. n.a. Jan. 2004­Mar. 2007 1.10 0.89 0.69 0.38 0.47 0.26 n.a. n.a. Interval in months 5 10 20 35 50 75 100 n.a. Full period 1.21 0.72 0.78 0.72 0.60 0.52 0.51 n.a. To end 1999 1.58 0.75 0.45 0.31 0.23 0.10 n.a. n.a. 2000­03 0.90 0.61 0.45 n.a. n.a. n.a. n.a. n.a. Jan. 2004­Mar. 2007 1.00 0.37 0.27 n.a. n.a. n.a. n.a. n.a. Source: Author calculations. Note: n.a. = not applicable. Annex 3 Statistical Analysis of U.S. Gulf Coast Prices 99 Table A3.4 Table A3.5 ADF Test Statistics for Daily U.S. Gulf Coast Oil ADF Test Statistics for Weekly U.S. Gulf Coast Oil Product Prices Product Prices Jan. Jan. Jan. Jan. Jan. Jan. Begin- 1986­ 2000­ 2004­ Begin- 1986­ 2000­ 2004­ ning­ Dec. Dec. Mar. ning­ Dec. Dec. Mar. Fuel Mar. 2007 1999 2003 2007 Fuel Mar. 2007 1999 2003 2007 Gasoline, -3.17 -4.22 -3.26 -2.75 Gasoline, -1.87 -3.72 -3.43 -3.55 nominal nominal 5% -3.41 -3.41 -3.41 -3.42 5% -3.41 -3.42 -3.43 -3.44 Diesel, -2.54 -1.11 -2.70 -2.89 Diesel, -2.29 -0.66 -2.93 -2.88 nominal nominal 5% -3.41 -3.41 -3.41 -3.42 5% -3.41 -3.43 -3.43 -3.44 Heating oil, -2.20 -3.65 -2.84 -2.62 Heating oil, -1.78 -3.53 -2.89 -2.04 nominal nominal 5% -3.41 -3.41 -3.41 -3.42 5% -3.41 -3.42 -3.43 -3.44 Jet kerosene, -2.69 -2.76 -2.82 -2.71 Jet kerosene, -2.24 -3.69 -2.85 -2.74 nominal nominal 5% -3.41 -3.41 -3.41 -3.42 5% -3.41 -3.42 -3.43 -3.44 Residual fuel -2.76 -2.21 -2.26 -1.67 Residual fuel -3.72 -3.08 -3.07 -2.73 oil, nominal oil, nominal 5% -3.41 -3.41 -3.41 -3.41 5% -3.42 -3.42 -3.43 -3.44 Propane, -3.10 -2.19 -2.96 -2.85 Propane, -2.87 -1.83 -2.59 -2.59 nominal nominal 5% -3.41 -3.41 -3.41 -3.42 5% -3.41 -3.42 -3.43 -3.44 Gasoline, -3.27 -4.49 -3.27 -2.82 Gasoline, -2.04 -3.99 -3.42 -3.52 real real 5% -3.41 -3.41 -3.41 -3.42 5% -3.41 -3.42 -3.43 -3.44 Diesel, real -2.64 -1.21 -2.70 -2.88 Diesel, real -2.41 -0.75 -2.89 -2.88 5% -3.41 -3.41 -3.41 -3.42 5% -3.42 -3.43 -3.43 -3.44 Heating oil, -2.25 -4.04 -2.84 -2.65 Heating oil, -2.19 -3.57 -2.85 -2.01 real real 5% -3.41 -3.41 -3.41 -3.42 5% -3.41 -3.42 -3.43 -3.44 Jet kerosene, -3.26 -2.84 -2.82 -2.72 Jet kerosene, -2.49 -3.89 -2.81 -2.73 real real 5% -3.41 -3.41 -3.41 -3.42 5% -3.41 -3.42 -3.43 -3.44 Residual fuel -3.22 -2.30 -2.23 -1.67 Residual fuel -3.98 -3.17 -3.02 -2.73 oil, real oil, real 5% -3.41 -3.41 -3.41 -3.42 5% -3.41 -3.42 -3.43 -3.44 Propane, -3.40 -2.28 -2.94 -2.97 Propane, -3.17 -1.91 -2.57 -2.72 real real 5% -3.41 -3.41 -3.41 -3.42 5% -3.42 -3.42 -3.43 -3.44 Source: Author calculations. Source: Author calculations. Note: For figures in bold, the null hypothesis is rejected at a Note: For figures in bold, the null hypothesis is rejected at a 5 percent confidence level and the price series is stationary. 5 percent confidence level and the price series is stationary. 100 Special Report Coping with Oil Price Volatility are stationary. In addition, nominal residual fuel oil prices Table A3.6 for the entire period are stationary. ADF Test Statistics for Monthly U.S. Gulf Coast Oil Cochrane test statistics were calculated, and the results Product Prices for nominal prices are shown in tables A3.7 to A3.9. The Jan. Jan. Jan. entire period is covered in these tables, from the time shown Begin- 1986­ 2000­ 2004­ in table A3.1 to March 2007. During this period, the only ning­ Dec. Dec. Mar. series that is stationary is that for weekly residual fuel oil Fuel Mar. 2007 1999 2003 2007 prices. However, the results show no clear patterns that Gasoline, -1.76 -3.36 -3.02 -2.67 would suggest that weekly residual fuel oil prices alone nominal are stationary. 5% -3.43 -3.44 -3.51 -3.53 Diesel, -2.03 -1.52 -2.15 -2.14 nominal Testing Returns and Their Variance 5% -3.44 -3.50 -3.51 -3.53 The basic mean equation related the return to a constant Heating oil, -1.54 -4.29 -2.19 -1.80 nominal and several lagged values, while the variance equation utilized a GARCH(1,1) or GARCH(1,0) formulation. 5% -3.43 -3.44 3.51 -3.53 Estimates were carried out for crude oil and all oil products Jet kerosene, -1.86 -4.59 -2.07 -2.25 in nominal terms for the entire time period as well as for nominal three subperiods. The order of the ARCH test was 9. For 5% -3.43 -3.45 -3.51 -3.53 the variance equation covering the entire period, various Residual fuel -2.67 -2.19 -2.07 -1.90 trend variables were tested, and the one giving rise to the oil, nominal highest coefficient of determination (R2) was selected. The 5% -3.43 -3.47 -3.51 -3.53 trend variables were Propane, -2.23 -2.94 -1.48 -3.47 nominal · @trend, a trend term, which is a linear time trend that 5% -3.44 -3.46 -3.51 -3.53 increases by one for each observation in the series · pd1, a dummy variable for subperiod 1 (beginning of Gasoline, -1.92 -3.62 -3.02 -2.71 real the price series to December 1999) · pd2, a dummy variable for subperiod 2 (January 2000 5% -3.43 -3.44 -3.51 -3.53 to December 2003) Diesel, real -2.12 -1.57 -2.10 -2.10 · pd3, a dummy variable for subperiod 3 (January 2004 5% -3.44 -3.50 -3.51 -3.53 to end March 2007) Heating oil, -2.15 -4.72 -2.06 -1.75 · pdmar, a dummy variable for the period from the real beginning of the price series to end March 1999 5% -3.43 -3.44 -3.51 -3.53 · pdjun, a dummy variable for the period from the Jet kerosene, -2.03 -4.83 -2.02 -2.21 beginning of the price series to June 1999 real The variable pdmar was selected based on the findings 5% -3.43 -3.45 -3.51 -3.53 by Lee and Zyren (2007) that the March 1999 change in Residual fuel -2.84 -2.27 -2.04 -1.88 OPEC production policy was found to have a statistically oil, real significant effect on the variance equation, which could be 5% -3.44 -3.47 -3.51 -3.53 captured by inserting this dummy variable. The variable Propane, -2.47 -2.97 -1.47 -3.42 pdjun was examined because prices in local currencies in real the five developing countries treated in annex 4 appeared 5% -3.44 -3.46 -3.51 -3.53 to have the first break approximately between June and Source: Author calculations. July 1999. Note: For figures in bold, the null hypothesis is rejected at a TARCH did not yield meaningful equations. Monthly 5 percent confidence level and the price series is stationary. data on OPEC spare capacity were available beginning in January 2001, but inclusion of a variable for OPEC spare capacity did not yield statistically significant coefficients. Annex 3 Statistical Analysis of U.S. Gulf Coast Prices 101 Table A3.7 Cochrane Statistics for Nominal Daily U.S. Gulf Coast Product Prices Days Fuel 20 50 100 200 350 700 1,000 1,500 WTI crude 0.75 0.67 0.56 0.40 0.43 0.38 0.31 0.25 Gasoline 0.73 0.61 0.42 0.24 0.23 0.18 0.15 0.12 Diesel 0.58 0.48 0.35 0.24 0.28 0.22 0.15 0.11 Heating oil 0.68 0.57 0.47 0.33 0.38 0.31 0.25 0.20 Jet kerosene 0.82 0.67 0.50 0.30 0.34 0.29 0.22 0.17 Residual fuel oil 1.52 1.23 0.96 0.84 0.78 0.31 0.32 0.12 Propane 0.79 0.70 0.53 0.38 0.37 0.24 0.18 0.13 Source: Author calculations. Note: Period covered is from beginning to end March 2007. Table A3.8 Cochrane Statistics for Nominal Weekly U.S. Gulf Coast Product Prices Weeks Fuel 10 20 35 50 75 100 200 WTI crude 1.10 0.93 0.74 0.68 0.73 0.72 0.54 Gasoline 0.81 0.58 0.38 0.28 0.30 0.26 0.20 Diesel 0.97 0.74 0.55 0.51 0.58 0.55 0.35 Heating oil 1.00 0.84 0.64 0.60 0.67 0.64 0.46 Jet kerosene 1.02 0.78 0.52 0.47 0.52 0.49 0.37 Residual fuel oil 1.10 0.83 0.81 0.75 0.70 0.52 0.31 Propane 0.92 0.71 0.55 0.51 0.50 0.43 0.24 Source: Author calculations. Note: Period covered is from beginning to end March 2007. Table A3.9 Cochrane Statistics for Nominal Monthly U.S. Gulf Coast Product Prices Months Fuel 5 10 20 35 50 75 WTI crude 1.21 0.72 0.78 0.72 0.60 0.52 Gasoline 0.90 0.38 0.38 0.32 0.28 0.24 Diesel 1.06 0.60 0.69 0.62 0.40 0.35 Heating oil 1.21 0.70 0.78 0.70 0.56 0.50 Jet kerosene 1.09 0.56 0.62 0.58 0.45 0.39 Residual fuel oil 1.00 0.76 0.64 0.29 0.32 0.15 Propane 1.15 0.67 0.62 0.43 0.33 0.26 Source: Author calculations. Note: Period covered is from beginning to end March 2007. 102 Special Report Coping with Oil Price Volatility In a number of cases, more than one formulation was The results for daily prices are reported in tables A3.10 statistically significant with meaningful coefficients--that to A3.15 for the entire period as well as for three subperiods. is, ARCH and GARCH coefficients are positive, their sum The tables show the sum of the ARCH and GARCH does not exceed unity, and there is no evidence of serial coefficients and the significance of the hypothesis that correlation for the mean equation. The set of equations their sum is not less than unity based on a Wald test, as that gave the simplest mean equation with the highest R2 well as the estimated half-life of shocks to the conditional was selected. If the first lag had a statistically significant variance of returns. coefficient, higher order lags were retained as long as they When data from the entire period are taken, inclusion were consecutive. Therefore, if lags 1, 2, 3, 4, and 5 all had of one of the time-dependent dummy variables in the statistically significant coefficients, they were retained; but variance equation increases the R2. In the case of heating if lags 1, 2, and 4 had statistically significant coefficients, oil, where the time-dependent variable is @trend, the then only the first two lags were retained, because 2 and 4 coefficient associated with this variable is positive, are not consecutive. Where GARCH(1,1) and GARCH(1,0) indicating that the conditional variance increases with formulations gave meaningful results, both are shown. increasing time. In all cases, the conditional variance Table A3.10 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices, Beginning­March 2007 Gaso- Jet Heating Residual fuel Pro- Parameter WTI line kerosene oil Diesel oil pane Statistically significant equation? Yes Yes Yes Da Yes Yes Yes Yes Yes Finite half-life? Yes Yes n.a. Yes Yes Yes Yes Yes Sum of ARCH + GARCH coefficients 0.99 0.99 n.a. 0.97 0.96 0.73 0.24 0.99 Half-life in days 87 101 n.a. 21 18 2.2 0.5 63 Lagged variables in mean equation 3 3 n.a. 1 1 1,2 1,2 None GARCH order (1,1) (1,1) n.a. (1,1) (1,1) (1,1) (1,0) (1,1) Trend variables in variance equation pd2 None n.a. Trend None pd2 pd2 pd2 Source: Author calculations. Note: n.a. = not applicable. pd2 is a dummy variable for subperiod 2 (January 2000­December 2003); trend is a linear time trend that increases by one for each observation in the series. a. Results are classified into the four categories defined on p. 13. Table A3.11 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices, Beginning­November 14, 2007 Gaso- Jet Heating Residual fuel Pro- Parameter WTI line kerosene oil Diesel oil pane Statistically significant equation? Yes Yes Yes Da Yes Yes Yes Yes Yes Finite half-life? Yes Yes n.a. Yes Yes Yes Yes Yes Sum of ARCH + GARCH coefficients 1.00 0.99 n.a. 0.97 0.96 0.76 0.24 0.99 Half-life in days 168 92 n.a. 24 19 2 0.5 75 Lagged variables in mean equation 3 3 n.a. 1 1 1,2 1,2 None GARCH order (1,1) (1,1) n.a. (1,1) (1,1) (1,1) (1,0) (1,1) Trend variables in variance equation pd3 None n.a. Trend None pd2 pd2 pd2 Source: Author calculations. Note: n.a. = not applicable. pd2 is a dummy variable for subperiod 2 (January 2000­December 2003); pd3 is a dummy variable for period 3 (January 2004­end March 2007); trend is a linear time trend that increases by one for each observation in the series. a. Results are classified into the four categories defined on p. 13. Annex 3 Statistical Analysis of U.S. Gulf Coast Prices 103 Table A3.12 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices, Beginning­December 1999 Gaso- Jet Heating Residual fuel Pro- Parameter WTI line kerosene oil Diesel oil pane Statistically significant equation? Yes Da Yes Yes Da Yes Yes Yes Yes Yes Da Finite half-life? n.a. Yes n.a. Yes Yes Yes Yes n.a. Sum of ARCH + GARCH coefficients n.a. 0.98 n.a. 0.97 0.97 0.45 0.08 n.a. Half-life in days n.a. 44 n.a. 21 17 0.9 0.3 n.a. Lagged variables in mean equation n.a. 3,5 n.a. 3 2 1,2,3 1,2,3,4 n.a. GARCH order n.a. (1,1) n.a. (1,1) (1,1) (1,1) (1,0) n.a. Trend variables in variance equation n.a. None n.a. None None Trend Trend n.a. Source: Author calculations. Note: n.a. = not applicable. Trend is a linear time trend that increases by one for each observation in the series. a. Results are classified into the four categories defined on p. 13. Table A3.13 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices, January 2000­December 2003 Jet Heating Pro- Parameter WTI Gasoline kerosene oil Diesel Residual fuel oil pane Statistically significant equation? Yes Yes Yes Yes Yes Yes Yes Yes Yes Finite half-life? Yes Yes Yes Yes Yes Yes Yes Yes Yes Sum of ARCH + GARCH coefficients 0.80 0.68 0.96 0.96 0.94 0.94 0.80 0.33 0.90 Half-life in days 3 2 19 19 11 12 3 0.6 7 Lagged variables in mean equation None None None None None None 1 1 3 GARCH order (1,1) (1,1) (1,1) (1,1) (1,1) (1,1) (1,1) (1,0) (1,1) Trend variables in variance equation None None None None None None Trend Trend Trend Source: Author calculations. Note: n.a. = not applicable; trend is a linear time trend that increases by one for each observation in the series. Table A3.14 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices, January 2004­March 2007 Gaso- Jet Heating Residual fuel Pro- Parameter WTI line kerosene oil Diesel oil pane Statistically significant equation? Yes Yes Yes Yes Yes Yes Yes Yes Finite half-life? No Yes Yes Yes Yes Yes Yes Yes Sum of ARCH + GARCH coefficients 0.91 0.96 0.96 0.94 0.94 0.71 0.39 0.86 Half-life in days n.a. 15 16 12 10 2.0 0.7 5 Lagged variables in mean equation 1 None None None None None 1,2 1 GARCH order (1,1) (1,1) (1,1) (1,1) (1,1) (1,1) (1,0) (1,1) Trend variables in variance equation None None Trend None None None Trend None Source: Author calculations. Note: n.a. = not applicable; trend is a linear time trend that increases by one for each observation in the series. 104 Special Report Coping with Oil Price Volatility Table A3.15 GARCH Analysis of Returns of Logarithms of Nominal Daily Prices, January 2004­November 14, 2007 Gaso- Jet Heating Residual fuel Pro- Parameter WTI line kerosene oil Diesel oil pane Statistically significant equation? Yes Yes Yes Yes Yes Yes Yes Yes Finite half-life? No Yes Yes Yes Yes Yes Yes Yes Sum of ARCH + GARCH coefficients 0.96 0.94 0.96 0.97 0.94 0.71 0.32 0.95 Half-life in days n.a. 11 15 23 11 2 1 15 Lagged variables in mean equation 1 None None None 1 None 1,2 1 GARCH order (1,1) (1,1) (1,1) (1,1) (1,1) (1,1) (1,0) (1,1) Trend variables in variance equation None None Trend None Trend None Trend None Source: Author calculations. Note: n.a. = not applicable; trend is a linear time trend that increases by one for each observation in the series. is stationary and has a half-life ranging from 0.5 days to Comparisonoftables A3.10andA3.11,andoftables A3.14 more than 100 days. Residual fuel oil has two identical and A3.15, shows that inclusion of data between the formulations, with and without the GARCH term. In the beginning of April and November 14, 2007, makes virtually GARCH(1,1) formulation, the half-life is quadruple that no difference. The equation derived for WTI crude, shown for the GARCH(1,0) formulation. in table A3.10, was used to perform out-of-sample testing The conditional variance generally is stationary in and forecast returns and the variance of returns during this the subperiods, except WTI crude in the third subperiod. period. The forecast results were also compared with the During the first subperiod, no set of meaningful mean actual price returns. These results are shown in figure A3.1. and conditional variance equations could be found for The mean absolute percentage error takes the absolute value WTI crude, jet kerosene, and propane. A longer half-life of the ratio of the difference between the predicted and associated with a GARCH(1,1) formulation compared to a actual values (price return in this case) to the actual value. GARCH(1,0) formulation for residual fuel oil is observed The result shows that the power of prediction is very poor. in each of the three subperiods. Thisistobeexpectedfromthefindingdiscussedinchapter3 Figure A3.1 Forecast of Returns of Logarithms of WTI Crude Daily Spot Prices and Variance of Returns, April 4­November 14, 2007 .06 a. Logarithms of spot prices .0008 b. Variance of returns .04 .0007 .02 .00 .0006 -.02 .0005 -.04 -.06 .0004 Apr. 24, May 30, July 5, Aug. 9, Sept. 14, Oct. 19, Apr. 24, May 30, July 5, Aug. 9, Sept. 14, Oct. 19, 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 Source: Author calculations. Annex 3 Statistical Analysis of U.S. Gulf Coast Prices 105 that the systematic, predictable component of the variance The results for weekly prices are shown in tables A3.16 has a weak correlation with historical variance and makes to A3.19. For the entire period, the conditional variance only a small contribution to the overall price volatility at is stationary and has a half-life ranging from less than a each point in time in every case. Under the Theile inequality week to 12 weeks, except for a GARCH(1,1) formulation coefficient, the bias proportion indicates how far the for propane. The GARCH(1,0) formulation, however, mean of the forecast is from the mean of the actual series; yields a stationary conditional variance. For the last the variance proportion indicates how far the variance subperiod, meaningful equations could not be found of the forecast is from the variance of the actual series; for WTI crude, diesel, and heating oil. Jet kerosene has a and the covariance proportion measures the remaining stationary conditional variance in all cases, except in the last unsystematic forecasting errors. These three components subperiod. Propane has a stationary conditional variance add up to unity. The results show that the forecast error is in all cases if a GARCH(1,0) formulation is employed, but dominated by the variance proportion. not GARCH(1,1). Table A3.16 GARCH Analysis of Returns of Logarithms of Nominal Weekly Prices, Beginning­March 2007 Jet Heating Pro- Parameter WTI Gasoline kerosene oil Diesel Residual fuel oil pane Statistically significant equation? Yes Yes Yes Yes Yes Yes Yes Yes Yes Finite half-life? Yes Yes Yes Yes Yes Yes Yes No Yes Sum of ARCH + GARCH coefficients 0.94 0.93 0.92 0.89 0.79 0.89 0.09 0.96 0.43 Half-life in weeks 12 10 8 6 3 6 0.3 n.a. 0.8 Lagged variables in mean equation 1,2 1 1,2 1 1 1,2 1,2 1 1 GARCH order (1,1) (1,1) (1,1) (1,1) (1,0) (1,1) (1,0) (1,0) (1,0) Trend variables in variance equation Jun99 pd2 None Jun99 None None Mar99 pd2 Trend Source: Author calculations. Note: n.a. = not applicable. pd2 is a dummy variable for subperiod 2 (January 2000­December 2003); Jun99 a dummy that is 1 for any week through June 1999; Mar99 a dummy that is 1 for any week through March 1999; trend is a linear time trend that increases by one for each observation in the series. Table A3.17 GARCH Analysis of Returns of Logarithms of Nominal Weekly Prices, Beginning­December 1999 Jet Heating Residual fuel Pro- Parameter WTI Gasoline kerosene oil Diesel oil pane Statistically significant equation? Yes Yes No Ca Yes Yes Yes Yes Yes Yes Finite half-life? No Yes n.a. Yes Yes Yes No Yes Yes Sum of ARCH + GARCH coefficients 0.95 0.95 n.a. 0.91 0.92 0.33 0.96 0.33 0.43 Half-life in weeks 13 13 n.a. 7 9 0.6 n.a. 0.6 0.8 Lagged variables in mean equation 1 1 n.a. 1 1 None 1 1 1 GARCH order (1,1) (1,1) n.a. (1,1) (1,1) (1,0) (1,0) (1,0) (1,0) Trend variables in variance equation None None n.a. None None None None Trend Trend Source: Author calculations. Note: n.a. = not applicable; trend is a linear time trend that increases by one for each observation in the series. a. Results are classified into the four categories defined on p. 13. 106 Special Report Coping with Oil Price Volatility Table A3.18 GARCH Analysis of Returns of Logarithms of Nominal Weekly Prices, January 2000­December 2003 Jet Heating Residual fuel Pro- Parameter WTI Gasoline kerosene oil Diesel oil pane Statistically significant equation? Yes Da No Ca Yes Yes Yes Yes Yes Yes Yes Finite half-life? n.a. n.a. Yes Yes Yes Yes No Yes Yes Sum of ARCH + GARCH coefficients n.a. n.a. 0.14 0.14 0.15 0.90 1.0 0.42 0.43 Half-life in weeks n.a. n.a. 0.4 0.3 0.4 6.8 n.a. 0.8 0.8 Lagged variables in mean equation n.a. n.a. None None 1 1 1 1 1 GARCH order n.a. n.a. (1,0) (1,0) (1,0) (1,1) (1,1) (1,0) (1,0) Trend variables in variance equation n.a. n.a. None None None None None None Trend Source: Author calculations. Note: n.a. = not applicable; trend is a linear time trend that increases by one for each observation in the series. a. Results are classified into the four categories defined on p. 13. Table A3.19 GARCH Analysis of Returns of Logarithms of Nominal Weekly Prices, January 2004­March 2007 Gaso- Jet Heating Residual fuel Parameter WTI line kerosene oil Diesel oil Propane Statistically significant equation? Yes Da Yes Yes No Ca Yes Da Yes Yes Yes Yes Finite half-life? n.a. Yes No n.a. n.a. No Yes Yes Yes Sum of ARCH + GARCH coefficients n.a. 0.51 0.88 n.a. n.a. 0.93 0.18 0.84 0.39 Half-life in weeks n.a. 1 n.a. n.a. n.a. n.a. 0.4 4 0.7 Lagged variables in mean equation n.a. None 1 n.a. n.a. 1 None 1 1 GARCH order n.a. (1,0) (1,1) n.a. n.a. (1,1) (1,0) (1,1) (1,0) Trend variables in variance equation n.a. None n.a. n.a. n.a. None None None Trend Source: Author calculations. Note: n.a. = not applicable; trend is a linear time trend that increases by one for each observation in the series. a. Results are classified into the four categories defined on p. 13. The results for monthly prices are given in tables A3.20 (entire period, first subperiod, and the subperiod beginning to A3.25; there is no table for the last subperiod because June 1995), and propane (first subperiod) only. no meaningful equations were found for any of the fuels. Tables A3.21 and A3.25 repeat GARCH analysis using GARCH analysis was also carried out between June 1995 datainclusiveofOctober2007.Aswithdailyprices,theresults and March 2007, which corresponds to the time when price areessentiallythesameasthosenotincludingthepriceseries data are available for all fuels, which begins in June 1995. A between April and October 2007. In particular, extending the meaningful equation could be found only for jet kerosene price series examined in table A3.24 by 46 months does not during thissubperiod witha common database. Statistically yield statistically significant and meaningful equations for significant equations exist in most cases, but they fail to fuels that found none in table A3.24. While propane now has satisfy the requirement that both the ARCH and GARCH a finite half-life in table A3.25, the form of the mean equation coefficientsbepositiveandsumtooneorlessorthattherebe in both tables A3.24 and A3.25 appears arbitrary, with lags of no serial correlation. The conditional variance is stationary twoandninemonths(table A3.24)andofoneandninemonths forheatingoil(entireperiodandfirstsubperiod),jetkerosene (table A3.25) needed to satisfy statistical requirements. Annex 3 Statistical Analysis of U.S. Gulf Coast Prices 107 Table A3.20 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices, Beginning­March 2007 Gaso- Jet Heating Residual Pro- Parameter WTI line kerosene oil Diesel fuel oil pane Statistically significant equation? Yes Yes Yes Da Yes Yes Yes Da Yes Da Yes Da Finite half-life? No Yes n.a. No Yes n.a. n.a. n.a. Sum of ARCH + GARCH coefficients 0.82 0.29 n.a. 0.87 0.20 n.a. n.a. n.a. Half-life in months n.a. 0.6 n.a. n.a. 0.4 n.a. n.a. n.a. Lagged variables in mean equation 1 1 n.a. 1 1 n.a. n.a. n.a. GARCH order (1,1) (1,0) n.a. (1,1) (1,0) n.a. n.a. n.a. Trend variables in variance equation None None n.a. None None n.a. n.a. n.a. Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. Table A3.21 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices, Beginning­October 2007 Heating Residual Pro- Parameter WTI Gasoline Jet kerosene oil Diesel fuel oil pane Statistically significant equation? Yes Yes Yes Da Yes Yes Yes Yes Da Yes Da Yes Da Finite half-life? No Yes n.a. No Yes Yes n.a. n.a. n.a. Sum of ARCH + GARCH coefficients 0.82 0.29 n.a. 0.87 0.34 0.21 n.a. n.a. n.a. Half-life in months n.a. 0.6 n.a. n.a. 0.6 0.4 n.a. n.a. n.a. Lagged variables in mean equation 1 1 n.a. 1 None 1 n.a. n.a. n.a. GARCH order (1,1) (1,0) n.a. (1,1) (1,0) (1,0) n.a. n.a. n.a. Trend variables in variance equation None None n.a. None None None n.a. n.a. n.a. Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. Table A3.22 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices, June 1995­March 2007 Gaso- Jet Heating Residual Pro- Parameter WTI line kerosene oil Diesel fuel oil pane Statistically significant equation? Yes Da Yes Da Yes Yes Da Yes Da Yes Da Yes Da Finite half-life? n.a. n.a. Yes n.a. n.a. n.a. n.a. Sum of ARCH + GARCH coefficients n.a. n.a. 0.31 n.a. n.a. n.a. n.a. Half-life in months n.a. n.a. 0.6 n.a. n.a. n.a. n.a. Lagged variables in mean equation n.a. n.a. 10,13,15 n.a. n.a. n.a. n.a. GARCH order n.a. n.a. (1,0) n.a. n.a. n.a. n.a. Trend variables in variance equation n.a. n.a. None n.a. n.a. n.a. n.a. Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. 108 Special Report Coping with Oil Price Volatility Table A3.23 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices, Beginning­December 1999 Gaso- Jet Heating Residual Pro- Parameter WTI line kerosene oil Diesel fuel oil pane Statistically significant equation? Yes Yes Da Yes Yes Yes Da Yes Da Yes Finite half-life? No n.a. Yes Yes n.a. n.a. Yes Sum of ARCH + GARCH coefficients 0.87 n.a. 0.83 0.40 n.a. n.a. 0.47 Half-life in months n.a. n.a. 4 0.8 n.a. n.a. 0.9 Lagged variables in mean equation 1 n.a. 1 1 n.a. n.a. 4 GARCH order (1,1) n.a. (1,1) (1,0) n.a. n.a. (1,0) Trend variables in variance equation None n.a. None None n.a. n.a. None Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. Table A3.24 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices, January 2000­December 2003 Gaso- Jet Heating Residual Pro- Parameter WTI line kerosene oil Diesel fuel oil pane Statistically significant equation? Yes Da Yes Da Yes Da Yes Da Yes Da Yes Da Yes Finite half-life? n.a. n.a. n.a. n.a. n.a. n.a. No Sum of ARCH + GARCH coefficients n.a. n.a. n.a. n.a. n.a. n.a. 0.91 Half-life in months n.a. n.a. n.a. n.a. n.a. n.a. n.a. Lagged variables in mean equation n.a. n.a. n.a. n.a. n.a. n.a. 2,9 GARCH order n.a. n.a. n.a. n.a. n.a. n.a. (1,0) Trend variables in variance equation n.a. n.a. n.a. n.a. n.a. n.a. None Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. Table A3.25 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices, January 2000­end October 2007 Gaso- Jet Heating Residual Pro- Parameter WTI line kerosene oil Diesel fuel oil pane Statistically significant equation? Yes Da Yes Da Yes Da Yes Da Yes Da Yes Da Yes Finite half-life? n.a. n.a. n.a. n.a. n.a. n.a. Yes Sum of ARCH + GARCH coefficients n.a. n.a. n.a. n.a. n.a. n.a. 0.49 Half-life in months n.a. n.a. n.a. n.a. n.a. n.a. 1 Lagged variables in mean equation n.a. n.a. n.a. n.a. n.a. n.a. 1,9 GARCH order n.a. n.a. n.a. n.a. n.a. n.a. (1,0) Trend variables in variance equation n.a. n.a. n.a. n.a. n.a. n.a. None Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. Annex 3 Statistical Analysis of U.S. Gulf Coast Prices 109 Table A3.26 compares the results from Lee and Zyren Table A3.26 (2007) and those obtained following the procedures in this report (outlined above). Though comparable, one difference GARCH Analysis of Returns of Logarithms of Nominal is that the weekly prices in Lee and Zyren represent prices Weekly Prices, January 1990­May 2005 on the last trading day of the week, whereas the weekly Lee and Zyren This report prices used here are averaged over the entire week. When Half-life in Half-life the sum of the ARCH and GARCH coefficients is close to Fuel Suma weeks Suma in weeks unity, as with WTI crude, a small difference in the sum WTI crude 0.93 10 0.95 14 leads to a noticeable difference in the half-life. Gasoline 0.93 10 0.92 8 Heating oil 0.88 5 0.86 5 Runs Tests Sources: Lee and Zyren 2007; author calculations. a. Sum of ARCH and GARCH coefficients. The results of a series of runs tests performed on nominal and real daily prices are shown in tables A3.27 to A3.32. As mentioned in annex 2, prices here are not in logarithms. cycles where they can differ by up to a factor of nearly two. As expected, the results for returns and cycle returns Taking the entire period, there are too few runs for gasoline, are similar. Nominal and real prices return comparable residual fuel oil, and propane (the first two rows of results results, except for maximum and minimum cumulative in tables A3.27 and A3.28). Table A3.27 Runs Tests on Nominal Daily Prices, Beginning­March 2007 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) 0.91 -2.86 -0.01 1.63 0.85 -14.17 -4.62 Cycle returns, (w-µ) 1.24 -2.19 0.53 1.63 0.44 -21.96 -6.64 Cumulative cycles Maximum (US$) 244 596 498 335 428 223 160 Minimum (US$) -291 -332 -328 -307 -315 -118 -171 Average (US$) 0 25 9 0.5 -12 7 0 Percentage negative 54 38 49 52 64 48 50 Maximum sojourn, months 9.3 4.7 4.6 5.9 6.5 4.7 7.2 Source: Author calculations. Table A3.28 Runs Tests on Real Daily Prices, Beginning­March 2007 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) 0.91 -2.68 0.11 1.74 1.01 -13.95 -4.79 Cycle returns, (w-µ) 1.44 -2.19 0.47 1.98 0.74 -21.12 -6.62 Cumulative cycles Maximum (US$) 304 608 494 324 414 223 204 Minimum (US$) -442 -332 -495 -465 -299 -112 -173 Average (US$) -4 34 12 1 -13 9 0 Percentage negative 56 37 48 52 64 47 50 Maximum sojourn, months 9.3 4.8 4.6 5.9 6.5 4.6 7.1 Source: Author calculations. 110 Special Report Coping with Oil Price Volatility Table A3.29 Runs Tests on Nominal Daily Prices, Beginning­December 1999 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) 0.76 -3.17 0.02 0.88 0.91 -10.73 -4.26 Cycle returns, (w-µ) 1.01 -2.45 0.24 1.45 0.79 -18.75 -6.96 Cumulative cycles Maximum (US$) 203 202 299 209 95 92 160 Minimum (US$) -291 -222 -328 -307 -106 -50 -135 Average (US$) -4 15 6 0 -5 6 0 Percentage negative 55 38 47 50 62 51 48 Maximum sojourn, months 9.3 4.7 4.6 5.4 5.5 4.7 7.2 Source: Author calculations. Table A3.30 Runs Tests on Real Daily Prices, Beginning­December 1999 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) 0.77 -3.01 0.19 1.08 0.91 -10.67 -4.39 Cycle returns, (w-µ) 1.38 -2.52 0.40 1.75 0.91 -18.39 -7.14 Cumulative cycles Maximum (US$) 304 306 453 315 122 115 204 Minimum (US$) -442 -332 -495 -465 -135 -61 -173 Average (US$) -9 22 9 0 -7 7 -1 Percentage negative 57 37 45 51 62 51 49 Maximum sojourn, 9.3 4.8 4.6 5.5 5.6 4.6 7.1 months Source: Author calculations. Table A3.31 Runs Tests on Nominal Daily Prices, January 2000­December 2003 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) -0.46 -1.44 -0.60 1.60 0.22 -6.77 -0.54 Cycle returns, (w-µ) 0.04 -1.50 -0.29 0.67 -0.06 -9.19 -1.09 Cumulative cycles Maximum (US$) 134 218 230 241 213 144 195 Minimum (US$) -99 -146 -145 -130 -134 -132 -68 Average (US$) 10 45 14 19 0 -26 44 Percentage negative 43 30 48 47 58 78 27 Maximum sojourn, months 1.9 2.1 2.4 5.3 6.3 3.8 9.3 Source: Author calculations. Annex 3 Statistical Analysis of U.S. Gulf Coast Prices 111 Table A3.32 Runs Tests on Nominal Daily Prices, January 2004­March 2007 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) 1.37 0.82 0.60 0.48 0.32 -5.98 -2.22 Cycle returns, (w-µ) Cumulative cycles 1.05 1.10 1.07 0.51 0.07 -8.16 -2.09 Maximum (US$) 275 684 538 360 486 205 203 Minimum (US$) -118 -245 -247 -207 -257 -137 -111 Average (US$) 43 137 59 21 35 -7 59 Percentage negative 33 23 37 44 44 60 27 Maximum sojourn, months 2.2 2.2 2.7 4.5 4.4 2.9 7.2 Source: Author calculations. The percentage of months when the cumulative cycles cumulativecyclesarenegativeislargerforweeklyWTIcrude are negative varies from fuel to fuel and from subperiod to andgasolinepricesthanfordailypriceswhenthefullperiod subperiod. The lowest is 23 percent for gasoline between and first subperiod are considered, but markedly smaller January 2004 and March 2007; the largest is residual fuel between January 2000 and December 2003. In all cases, both oil between January 2000 and December 2003. For the the maximum and minimum cumulative cycles are smaller former, the cumulative cycles average US$137 per barrel; in magnitude for weekly prices than for daily prices. for the latter, they average -US$26. The largest maximum The results for nominal monthly prices are given sojourn for cumulative cycles is nine months for WTI crude in tables A3.37 to A3.39. There are no cases with too few in 1986 and 1987, and the cumulative cycles are negative runs for price returns. Maximum sojourns for cumulative during that period. cycles are longer than weekly prices. The percentages of The results for nominal weekly prices are shown in the time when cumulative cycles are negative are markedly tables A3.33 to A3.36. When the entire period is considered, smaller for monthly prices than for other averaging periods there are too few runs for returns for every fuel. One betweenJanuary2000andMarch2007;correspondingly,the marked difference from daily prices is that the maximum percentage of months when cumulative cycles are positive sojourns for cumulative cycles are significantly longer. is high, which means that the balance of an oil account For example, when the entire period is considered, the for price smoothing based on an HP filter and started in maximum sojourns vary from 21 months to as long as January 2000 would have been negative most of the time. 46 months, compared to the range of 5 months to 9 months The maximum and minimum cumulative cycles are smaller observed with daily prices. The percentage of months when in magnitude than those for daily and weekly prices. Table A3.33 Runs Tests on Nominal Weekly Prices, Beginning­March 2007 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) -2.94 -4.97 -2.53 -4.25 -3.72 -9.19 -5.39 Cycle returns, (w-µ) -2.08 -4.97 -2.45 -3.38 -3.63 -8.06 -3.71 Cumulative cycles Maximum (US$) 95 186 129 115 154 81 92 Minimum (US$) -103 -120 -127 -96 -110 -96 -61 Average (US$) -10 0 0 0 0 0 0 Percentage negative 63 48 48 49 53 47 52 Maximum sojourn, months 26 24 46 26 26 21 25 Source: Author calculations. 112 Special Report Coping with Oil Price Volatility Table A3.34 Runs Tests on Nominal Weekly Prices, Beginning­December 1999 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) -2.28 -5.11 -2.20 -3.23 -1.63 -6.89 -3.03 Cycle returns, (w-µ) -1.35 -4.96 -2.45 -2.41 -1.89 -7.12 -1.26 Cumulative cycles Maximum (US$) 63 58 103 82 41 39 47 Minimum (US$) -103 -79 -127 -96 -69 -51 -55 Average (US$) -11 -1 -1 -1 -3 -1 -1 Percentage negative 63 48 43 48 50 48 48 Maximum sojourn, months 26 24 46 26 26 16 25 Source: Author calculations. Table A3.35 Runs Tests on Nominal Weekly Prices, January 2000­December 2003 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) -1.03 -0.81 -0.69 -2.37 -2.93 -5.44 -3.05 Cycle returns, (w-µ) -1.05 -0.42 -0.40 -2.37 -2.97 -3.79 -2.47 Cumulative cycles Maximum (US$) 108 164 143 141 135 112 138 Minimum (US$) -3 -4 2 0 -7 -24 -9 Average (US$) 54 76 71 70 66 42 50 Percentage negative 5 2 0 0 6 33 11 Maximum sojourn, months 25 47 48 48 29 20 30 Source: Author calculations. Table A3.36 Runs Tests on Nominal Weekly Prices, January 2004­March 2007 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) -1.87 -1.22 -1.22 -1.81 -2.09 -3.28 -3.66 Cycle returns, (w-µ) -1.65 -1.84 -1.02 -1.30 -1.61 -2.46 -3.51 Cumulative cycles Maximum (US$) 114 223 137 111 155 43 70 Minimum (US$) -54 -83 -113 -100 -110 -133 -48 Average (US$) 2 31 -1 -14 -10 -41 12 Percentage negative 63 37 51 62 67 90 26 Maximum sojourn, months 11 11 11 20 10 30 11 Source: Author calculations. Tables A3.40 to A3.42 compare the results of runs tests fuel oil and propane in the case of daily prices and none for forthelongestperiodwhenafullsetofpricedataisavailable monthly prices. The average of cumulative cycles is positive for all fuels and all averaging periods--September 1995 to for each fuel when monthly prices are used, but negative for March 2007. Runs on returns show that there are too few more than half the fuels with weekly and daily prices. The runswhenweeklypricesareexamined,butonlyforresidual greatest negative average cumulative cycles is -US$45 a Annex 3 Statistical Analysis of U.S. Gulf Coast Prices 113 barrel, observed with daily gasoline prices. The percentage thehypotheticaloilaccountforpricesmoothingbasedonan of months when cumulative cycles are negative is largest for HPfilterchangesonaveragefrompositivewhendailyprices daily prices, followed by weekly, and then by monthly. The are used to negative when monthly prices are used. To take maximum sojourns for cumulative cycles are 4 to 8 months advantage of the positive balance in the daily series, prices with daily prices, 21 to 28 months with weekly prices, and 27 wouldhavetobeadjustedonadailybasis,leadingtogreater to 40 months with monthly prices. The sign of the balance of price fluctuations as well as higher administrative costs. Table A3.37 Runs Tests on Nominal Monthly Prices, Beginning­March 2007 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) -1.63 0.41 -1.80 -1.99 -1.38 0.21 -1.56 Cycle returns, (w-µ) -0.99 1.03 -1.04 -1.32 -0.28 -0.53 -0.97 Cumulative cycles Maximum (US$) 41 76 65 61 70 39 53 Minimum (US$) -55 -59 -66 -65 -66 -47 -42 Average (US$) -8 0 0 0 0 0 0 Percentage negative 61 50 45 46 46 49 53 Maximum sojourn, months 35 39 35 42 36 30 33 Source: Author calculations. Table A3.38 Runs Tests on Nominal Monthly Prices, Beginning­December 1999 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) -1.01 0.23 -1.29 -1.57 -0.66 0.22 -1.48 Cycle returns, (w-µ) -1.31 0.79 -1.30 -1.25 -0.66 0.09 -0.62 Cumulative cycles Maximum (US$) 27 40 39 39 37 27 30 Minimum (US$) -55 -52 -58 -56 -55 -40 -42 Average (US$) -6 -1 -1. -1 -3 -1 -2 Percentage negative 62 51 48 50 55 54 53 Maximum sojourn, months 35 39 30 42 25 30 33 Source: Author calculations. Table A3.39 Runs Tests on Nominal Monthly Prices, January 2000­March 2007 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) -0.80 0.25 -0.91 -0.81 -0.80 -0.08 -0.91 Cycle returns, (w-µ) 0.32 0.61 -0.05 -0.39 0.32 -0.95 -0.95 Cumulative cycles Maximum (US$) 87 125 117 112 120 74 91 Minimum (US$) -4 -9 -14 -14 -17 -11 5 Average (US$) 40 51 54 52 51 37 39 Percentage negative 6 8 17 16 17 9 0 Maximum sojourn, months 54 89 53 53 53 61 89 Source: Author calculations. 114 Special Report Coping with Oil Price Volatility Table A3.40 Runs Tests on Nominal Daily Prices, September 1995­March 2007 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) -0.42 -0.60 0.24 1.78 0.85 -12.94 -3.34 Cycle returns, (w-µ) 0.08 -0.26 0.99 1.73 0.44 -18.71 -4.66 Cumulative cycles Maximum (US$) 230 512 497 333 427 216 156 Minimum (US$) -164 -417 -288 -234 -316 -125 -175 Average (US$) -10 -45 9 -2 -13 0 -4 Percentage negative 66 79 52 58 65 53 55 Maximum sojourn, months 5.3 6.5 4.6 8.0 6.5 4.7 5.6 Source: Author calculations. Table A3.41 Runs Tests on Nominal Weekly Prices, September 1995­March 2007 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) -3.15 -2.19 -1.93 -4.20 -3.91 -7.90 -5.72 Cycle returns, (w-µ) -2.00 -2.36 -1.38 -3.13 -3.82 -6.81 -4.02 Cumulative cycles Maximum (US$) 101 166 142 126 157 79 89 Minimum (US$) -68 -140 -108 -85 -107 -98 -65 Average (US$) -5 -21 13 10 2 -2 -4 Percentage negative 58 63 45 46 51 51 56 Maximum sojourn, months 24 23 28 27 26 21 25 Source: Author calculations. Table A3.42 Runs Tests on Nominal Monthly Prices, September 1995­March 2007 Parameter WTI Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Propane Returns, (w-µ) -0.73 0.13 -1.20 -1.20 -1.27 0.05 -1.69 Cycle returns, (w-µ) 0.56 0.19 -0.41 -0.72 -0.18 -0.73 -1.60 Cumulative cycles Maximum (US$) 61 86 84 80 79 43 64 Minimum (US$) -35 -49 -47 -46 -58 -42 -31 Average (US$) 12 10 19 19 9 5 11 Percentage negative 34 36 32 32 39 39 42 Maximum sojourn, 40 39 40 40 38 32 27 months Source: Author calculations. Annex 4 Statistical Analysis of Developing Country Prices This annex supplements chapter 4 and provides additional Table A4.1 results from the analysis of fuel prices in Chile, Ghana, India, thePhilippines,andThailand.Tothisend,internationalcrude First Month in the Price Data Series and oil product prices appropriate for each country were Commodity Start date examined in U.S. dollars and in the respective local currency. WTI Jan. 1986 These prices do not include taxes and other fuel charges or U.S. Gulf Coast regular gasoline June 1986 transportation, distribution, and retail costs and margins. U.S. Gulf Coast jet kerosene Apr. 1990 U.S. Gulf Coast heating oil June 1986 Data Coverage and Methodology U.S. Gulf Coast diesel May 1995 U.S. Gulf Coast residual fuel oil July 1993 The source of price information other than that in the U.S. Gulf Coast was Energy Intelligence, which provides only Mont Belvieu, Texas, propane July 1992 monthly data. U.S. Gulf prices were taken from the U.S. Indonesia Minas-34 Jan. 1987 Energy Information Administration Web site and used to Singapore premium gasoline Jan. 1987 compute equivalent domestic prices in Chile. Singapore Singapore jet kerosene Jan. 1987 product prices were used for the Philippines and Thailand, Singapore gasoil Jan. 1987 Rotterdam prices for Ghana, and Persian Gulf prices for Singapore residual fuel oil, Jan. 1987 India. For ease of comparison, all prices are given on a per 3.5% sulfur, 180 centistokes barrel basis. Table A4.1 gives the first month for which data Nigeria Bonny Light-37 Jan. 1987 areavailableforeachcommodityconsidered.ForallbutU.S. Gulf Coast prices, the data begin in January 1987. Rotterdam regular gasoline Jan. 1987 Differences in price level and price volatility were Rotterdam jet kerosene Jan. 1987 examined for three subperiods--the first beginning Rotterdam gasoil Jan. 1987 with the first month in which the prices were available Rotterdam residual fuel oil, 3.5% sulfur Jan. 1987 (table A4.1) to June 1999, the second from July 1999 to Dubai Fateh-32 Jan. 1987 December 2003, and the third from January 2004 to January Persian Gulf premium gasoline Jan. 1987 2008--and for the entire period. Augmented Dickey-Fuller tests, GARCH analysis, and runs tests were performed for Persian Gulf jet kerosene Jan. 1987 the period beginning with the first month in which prices Persian Gulf gasoil Jan. 1987 were available to March 2007. They were also conducted Persian Gulf residual fuel oil, Jan. 1987 for two subperiods, the first ending in June 1999 and the 3.5% sulfur, 380 centistokes second one beginning in July 1999 and ending in March Sources: U.S. EIA 2008a and Energy Intelligence 2008. 2007. The second subperiod was not split further because, when monthly prices were tested, most fuel prices did not yield meaningful equations even when the longer time span @trend (see annex 3) and pd1 (defined in this annex as from July 1999 to March 2007 was used; further subdivision covering the period from beginning through June 1999) thus would have yielded no meaningful equations. as dummy variables in the conditional variance equation The results of ADF tests are summarized in chapter in GARCH analysis, pd3 (covering January 2004 to March 4 and are not given here. This annex presents the results 2007) was also tested, and the equation with the highest R2, of GARCH analysis and runs tests. In addition to testing everything else being equal, is reported here. For runs tests, 115 116 Special Report Coping with Oil Price Volatility values for (w-µ) (defined in annex 2), are reported. January 2008) and for the entire period (beginning to Cycles in local currency are based on Hodrick-Prescott January 2008) are shown in table A4.2. The differences filters calculated from local prices. between U.S. dollar and Chilean peso price increases are given in table 4.1. Table A4.3 gives the ratio of fuel prices in January 2008 Chile to those in January 2004. The ratio is consistently lower for Chilean peso prices, signifying appreciation of the Chilean Mean prices in the three subperiods (beginning to June peso against the U.S. dollar. The largest price increase is 1999, July 1999 to December 2003, and January 2004 to observed with residual fuel oil. Table A4.2 Period Average Prices in Chile Price (units) Period Crude Gasoline Diesel Jet kerosene Gasoil Residual fuel oil 1 18.91 22.98 20.86 22.31 21.12 12.48 2 27.79 32.43 31.04 31.61 30.32 20.35 Nominal (US$) 3 59.76 70.07 72.65 73.32 69.15 40.55 Entire 28.27 36.15 42.01 33.64 31.88 19.28 1 6,584 9,046 9,038 7,741 7,336 4,316 2 17,436 20,340 19,469 19,806 19,024 12,821 Nominal (Ch$) 3 32,617 38,293 39,591 39,979 37,697 22,029 Entire 13,609 18,592 23,150 16,160 15,332 9,324 1 27.89 31.51 26.38 32.97 31.20 18.47 2 31.75 37.04 35.46 36.12 34.64 23.23 Real (US$) 3 60.51 70.97 73.50 74.21 69.99 40.96 Entire 34.71 41.94 45.55 41.24 39.07 23.60 1 15,093 15,933 12,128 17,875 16,909 9,999 2 19,849 23,151 22,165 22,557 21,657 14,577 Real (Ch$) 3 33,130 38,930 40,189 40,593 38,273 22,304 Entire 19,397 23,020 25,258 23,030 21,827 13,207 Nominal (% 2/1a 47 41 49 42 44 63 increase for 3/2a 115 116 134 132 128 99 prices in US$) 3/1a 216 205 248 229 227 225 Nominal (% 2/1a 165 125 115 156 159 197 increase for 3/2a 87 88 103 102 98 72 prices in Ch$) 3/1a 395 323 338 416 414 410 2/1a 14 18 34 10 11 26 Real (% increase 3/2a 91 92 107 105 102 76 for prices in US$) 3/1a 117 125 179 125 124 122 2/1a 32 45 83 26 28 46 Real (% increase 3/2a 67 68 81 80 77 53 for prices in Ch$) 3/1a 120 144 231 127 126 123 Sources: U.S. EIA 2008a; author calculations. Note: Subperiod 1 is from beginning to June 1999; subperiod 2 is from July 1999 to December 2003; subperiod 3 is from January 2004 to January 2008; the entire period is from beginning to January 2008. Real prices are in January 2007 currency units. a. The price increase from subperiod 1 to subperiod 2 (percentage increase in subperiod 2 over subperiod 1) computed in U.S. dollars is subtracted from the price increase between the same two subperiods in Chilean pesos. Annex 4 Statistical Analysis of Developing Country Prices 117 Standard deviations of returns for logarithms of the presence of lags 1, 2, 4, and 7 for the ARCH (1,1) monthly prices and exchange rates are shown in table A4.4. formulation for the conditional mean equation for gasoil Aside from the first subperiod, price volatility was the in the first subperiod appears arbitrary, but retaining same or greater in Chilean pesos. Volatility increased with fewer terms does not yield a statistically significant increasing exchange rate volatility. equation. For this reason, the GARCH(1,0) formulation The results of GARCH analysis of the returns of seems more credible. logarithms of local monthly prices are given in tables A4.5 The results of runs tests on prices in U.S. dollars and to A4.7. The presence of lag 15 in the equation for in Chilean pesos are shown in tables A4.8 to A4.13. On residual fuel oil in the first subperiod appears arbitrary, the whole, runs on returns yield similar results, while but this is the only formulation that does not exhibit cumulative returns tend to be more positive in local serial correlation and passes the ARCH test. Similarly, currency than in U.S. dollars. Table A4.3 Ratio of January 2008 Prices to January 2004 Prices in Chile Currency Crude Gasoline Diesel Jet kerosene Gasoil Residual fuel oil US$ nominal 2.7 2.3 2.7 2.6 2.6 3.1 Ch$ nominal 2.3 2.0 2.2 2.2 2.2 2.6 US$ real 2.4 2.1 2.3 2.3 2.3 2.7 Ch$ real 1.9 1.7 1.9 1.9 1.9 2.2 Sources: U.S. EIA 2008a; author calculations. Table A4.4 Standard Deviation of Returns for Logarithms of Prices and Exchange Rate in Chile Jet Residual Exchange Price (units) Period Crude Gasoline Diesel kerosene Gasoil fuel oil rate 1 0.087 0.102 0.081 0.091 0.086 0.130 n.a. Nominal 2 0.081 0.120 0.089 0.088 0.089 0.118 n.a. (US$) 3 0.070 0.116 0.086 0.091 0.080 0.090 n.a. Entire 0.083 0.110 0.086 0.091 0.086 0.121 n.a. 1 0.087 0.099 0.079 0.090 0.087 0.130 0.015 Nominal 2 0.087 0.124 0.095 0.095 0.095 0.121 0.025 (Ch$) 3 0.074 0.116 0.088 0.093 0.081 0.092 0.021 Entire 0.085 0.110 0.088 0.092 0.087 0.122 0.019 1 0.086 0.101 0.080 0.090 0.085 0.130 n.a. 2 0.080 0.119 0.088 0.088 0.088 0.117 n.a. Real (US$) 3 0.068 0.113 0.084 0.088 0.078 0.088 n.a. Entire 0.082 0.108 0.084 0.090 0.085 0.120 n.a. 1 0.085 0.097 0.079 0.089 0.084 0.129 n.a. 2 0.086 0.123 0.095 0.095 0.095 0.121 n.a. Real (Ch$) 3 0.073 0.116 0.087 0.091 0.080 0.091 n.a. Entire 0.083 0.108 0.087 0.091 0.086 0.121 n.a. Source: Author calculations. Note: n.a. = not applicable. Subperiod 1 is from beginning to June 1999; subperiod 2 is from July 1999 to December 2003; subperiod 3 is from January 2004 to January 2008; the entire period is from beginning to January 2008. 118 Special Report Coping with Oil Price Volatility Table A4.5 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Chilean Pesos, Beginning­March 2007 Gaso- Jet Residual Parameter Crude line Diesel kerosene Gasoil fuel oil Statistically significant equation? Yes Yes Yes Da Yes Da Yes Yes Yes Yes Finite half-life? No Yes n.a. n.a. Yes No Yes Yes Sum of ARCH + GARCH coefficients 0.84 0.30 n.a. n.a. 0.18 0.90 0.16 0.33 Half-life in months n.a. 0.6 n.a. n.a. 0.4 n.a. 0.4 0.6 Lagged variables in mean equation 1 1 n.a. n.a. 2 1 1 1,2 GARCH order (1,1) (1,0) n.a. n.a. (1,0) (1,1) (1,0) (1,0) Trend variables in variance equation None None n.a. n.a. None None None pd3 Source: Author calculations. Note: n.a. = not applicable; pd3 is a dummy variable that is 1 for any data from January 2004 to end March 2007. a. Results are classified into the four categories defined on p. 13. Table A4.6 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Chilean Pesos, Beginning­June 1999 Gaso- Jet Residual Parameter Crude line Diesel kerosene Gasoil fuel oil Statistically significant equation? Yes Yes Yes Da No Ca Yes Yes Yes Yes Finite half-life? No Yes n.a. n.a. Yes No Yes Yes Sum of ARCH + GARCH coefficients 0.87 0.50 n.a. n.a. 0.21 0.87 0.30 0.26 Half-life in months n.a. 1 n.a. n.a. 0.4 n.a. 0.6 0.5 Lagged variables in mean equation 1 1 n.a. n.a. 2,4 1,2,4,7 1 15 GARCH order (1,1) (1,0) n.a. n.a. (1,0) (1,1) (1,0) (1,0) Trend variables in variance equation None None n.a. n.a. Trend None None None Source: Author calculations. Note: n.a. = not applicable; trend is a linear time trend that increases by one for each observation in the series. a. Results are classified into the four categories defined on p. 13. Table A4.7 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Chilean Pesos, July 1999­March 2007 Jet Residual Parameter Crude Gasoline Diesel kerosene Gasoil fuel oil Statistically significant equation? Yes Da Yes Da Yes Da Yes Da Yes Da Yes Finite half-life? n.a. n.a. n.a. n.a. n.a. Yes Sum of ARCH + GARCH coefficients n.a. n.a. n.a. n.a. n.a. 0.42 Half-life in months n.a. n.a. n.a. n.a. n.a. 0.8 Lagged variables in mean equation n.a. n.a. n.a. n.a. n.a. 1,2 GARCH order n.a. n.a. n.a. n.a. n.a. (1,0) Trend variables in variance equation n.a. n.a. n.a. n.a. n.a. None Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. Annex 4 Statistical Analysis of Developing Country Prices 119 Table A4.8 Runs Tests on Nominal Monthly Prices in Chile, in U.S. Dollars, Beginning­March 2007 Parameter Crude Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Returns, (w-µ) -1.63 -0.49 -0.89 -1.72 -1.52 -2.07 Cycle returns, (w-µ) -1.00 -0.23 -0.23 -1.76 -11.84 -1.10 Cumulative cycles Maximum (US$) 67 92 12 -2 103 -5 Minimum (US$) -97 -111 -227 -225 -136 -158 Average (US$) -7 0 -98 -101 0 -85 Percentage negative 60 48 97 100 40 100 Maximum sojourn, months 57 41 182 254 36 254 Source: Author calculations. Table A4.9 Runs Tests on Nominal Monthly Prices in Chile, in Chilean Pesos, Beginning­March 2007 Parameter Crude Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Returns, (w-µ) -1.42 -0.99 -1.02 -1.73 -0.86 -2.32 Cycle returns, (w-µ) -0.50 -0.80 -0.48 -1.76 -0.40 -1.13 Cumulative cycles Maximum (Ch$) 23,234 38,703 19,462 15,069 33,556 9,726 Minimum (Ch$) -34,127 -36,098 -66,056 -63,368 -51,432 -35,523 Average (Ch$) -1,591 0 -14,134 -14,202 0 -9,519 Percentage negative 48 38 82 83 41 84 Maximum sojourn, months 92 96 93 92 36 124 Source: Author calculations. Table A4.10 Runs Tests on Nominal Monthly Prices in Chile, in U.S. Dollars, Beginning­June 1999 Parameter Crude Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Returns, (w-µ) -0.85 -1.14 -0.24 -1.15 -0.40 -1.13 Cycle returns, (w-µ) -1.13 -1.31 0.08 -1.49 -6.89 -0.50 Cumulative cycles Maximum (US$) 43 57 -8 -5 63 -5 Minimum (US$) -48 -45 -167 -171 -41 -116 Average (US$) -2 9 -93 -96 26 -82 Percentage negative 60 40 100 100 16 100 Maximum sojourn, months 57 39 161 161 36 161 Source: Author calculations. 120 Special Report Coping with Oil Price Volatility Table A4.11 Runs Tests on Nominal Monthly Prices in Chile, in Chilean Pesos, Beginning­June 1999 Parameter Crude Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Returns, (w-µ) -1.50 -1.10 -0.47 -1.49 -0.50 -1.08 Cycle returns, (w-µ) -0.85 -1.12 -0.24 -2.40 -0.40 -0.55 Cumulative cycles Maximum (Ch$) 23,234 27,959 15,078 14,697 33,556 9,726 Minimum (Ch$) -32,625 -34,859 -48,531 -47,594 -27,926 -33,800 Average (Ch$) 1,967 6,117 -9,834 -9,941 14,769 -7,108 Percentage negative 39 14 85 85 16 86 Maximum sojourn, months 92 96 93 92 36 124 Source: Author calculations. Table A4.12 Runs Tests on Nominal Monthly Prices in Chile, in U.S. Dollars, July 1999­March 2007 Parameter Crude Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Returns, (w-µ) -0.78 0.66 -0.81 -0.81 -0.78 -1.86 Cycle returns, (w-µ) 0.09 0.94 -0.43 -0.89 -9.92 -1.15 Cumulative cycles Maximum (US$) 115 137 151 139 144 69 Minimum (US$) -49 -66 -88 -83 -95 -43 Average (US$) 32 34 33 32 29 26 Percentage negative 28 26 30 31 32 22 Maximum sojourn, months 49 50 47 46 48 59 Source: Author calculations. Table A4.13 Runs Tests on Nominal Monthly Prices in Chile, in Chilean Pesos, July 1999­March 2007 Parameter Crude Gasoline Jet kerosene Heating oil Diesel Residual fuel oil Returns, (w-µ) -0.20 -0.20 -0.99 -0.31 -0.13 -2.42 Cycle returns, (w-µ) 0.37 0.09 -0.43 0.51 0.15 -1.15 Cumulative cycles Maximum (Ch$) 54,454 73,563 67,993 62,663 61,477 43,034 Minimum (Ch$) -1,502 -1,238 -17,525 -15,774 -23,506 -1,723 Average (Ch$) 24,875 27,558 26,953 26,016 21,098 20,107 Percentage negative 5 6 24 23 26 4 Maximum sojourn, months 56 62 50 50 50 66 Source: Author calculations. Annex 4 Statistical Analysis of Developing Country Prices 121 Ghana in nominal terms--signifying high inflation rates during the study period. For real prices, the price series had to be Prices averaged over each subperiod as well as over the terminated in November 2007 because the consumer price entire period and percentage price increases between index was available only up to that month. subperiods are shown in table A4.14. Nominal price Table A4.15 gives the ratio of fuel prices in January increases in local currency units are extremely large, 2008 to those in January 2004. The ratios are consistently reaching as high as 3,000 percent in the third subperiod over higher for nominal cedi prices, and lower for real cedi the first subperiod--or 15 times the percentage increases prices. Table A4.14 Period Average Prices in Ghana Price (units) Period Crude Gasoline Jet kerosene Gasoil Residual fuel oil 1 18.25 21.78 23.77 22.14 13.42 2 26.33 30.72 32.96 30.59 20.81 Nominal (US$) 3 59.56 66.01 74.82 69.95 40.87 Entire 27.97 32.25 35.62 33.21 20.31 1 16,263 19,272 21,140 19,783 12,420 2 181,950 211,561 227,680 212,032 144,100 Nominal (C/) 3 548,207 606,956 688,294 643,567 376,502 Entire 154,652 174,134 194,435 181,628 111,039 1 26.52 31.67 34.54 32.15 19.49 2 30.08 35.11 37.67 34.95 23.77 Real (US$) 3 58.96 65.85 74.39 69.44 40.15 Entire 33.36 38.81 42.67 39.73 24.28 1 181,372 215,909 236,412 220,173 134,006 2 375,426 437,910 471,619 438,033 295,460 Real (C/) 3 572,464 641,074 723,990 675,490 388,461 Entire 296,353 343,283 378,314 352,302 216,388 Nominal (% 2/1 44 41 39 38 55 increase for 3/2 126 115 127 129 96 prices in US$) 3/1 226 203 215 216 205 Nominal (% 2/1 1,019 998 977 972 1,060 increase for 3/2 201 187 202 204 161 prices in C/) 3/1 3,271 3,049 3,156 3,153 2,932 2/1 13 11 9 9 22 Real (% increase 3/2 96 88 97 99 69 for prices in US$) 3/1 122 108 115 116 106 2/1 107 103 99 99 120 Real (% increase 3/2 52 46 54 54 31 for prices in C/) 3/1 216 197 206 207 190 Sources: U.S. EIA 2008a; author calculations. Note: For definitions and calculations, see the notes to table A4.2. 122 Special Report Coping with Oil Price Volatility Table A4.15 Ratio of January 2008 Prices to January 2004 Prices in Ghana Currency Crude Gasoline Jet kerosene Gasoil Residual fuel oil US$ nominal 3.0 2.5 2.7 2.9 3.2 C/ nominal 3.3 2.7 3.0 3.2 3.5 US$ reala 2.7 2.3 2.5 2.6 3.0 C/ reala 2.1 1.8 2.0 2.1 2.4 Sources: U.S. EIA 2008a; author calculations. a. Ratio of real prices in November 2008 to those in January 2004. Standard deviations of returns for logarithms volatility seemingly amplifying the local currency unit- of monthly prices and exchange rates are shown in price volatility. In real terms, prices in cedis were more table A4.16. In nominal terms, local currency prices volatile except for the residual fuel oil price in the third were consistently more volatile, with exchange rate subperiod. Table A4.16 Standard Deviation of Returns for Logarithms of Prices and Exchange Rate in Ghana Residual fuel Exchange Price (units) Period Crude Gasoline Jet kerosene Gasoil oil rate 1 0.086 0.083 0.089 0.083 0.119 n.a. Nominal 2 0.098 0.105 0.087 0.088 0.105 n.a. (US$) 3 0.083 0.103 0.072 0.071 0.075 n.a. Entire 0.089 0.092 0.086 0.083 0.109 n.a. 1 0.095 0.093 0.094 0.089 0.123 0.045 2 0.106 0.113 0.098 0.099 0.111 0.033 Nominal (C/) 3 0.083 0.104 0.072 0.072 0.075 0.003 Entire 0.095 0.099 0.091 0.088 0.112 0.039 1 0.086 0.082 0.089 0.083 0.118 n.a. 2 0.097 0.104 0.086 0.087 0.104 n.a. Real (US$) 3 0.081 0.101 0.070 0.069 0.073 n.a. Entire 0.088 0.091 0.085 0.082 0.108 n.a. 1 0.097 0.092 0.099 0.093 0.126 n.a. 2 0.107 0.112 0.097 0.098 0.113 n.a. Real (C/) 3 0.084 0.102 0.072 0.072 0.072 n.a. Entire 0.097 0.098 0.094 0.091 0.115 n.a. Source: Author calculations. Note: n.a. = not applicable. Subperiod 1 is from beginning to June 1999; subperiod 2 is from July 1999 to December 2003; subperiod 3 is from January 2004 to January 2008; the entire period is from beginning to January 2008. Annex 4 Statistical Analysis of Developing Country Prices 123 GARCH analysis of local prices is shown in The results of the runs tests are shown in tables A4.17 and A4.18. The results of the second subperiod tables A4.19 to A4.24. During the first subperiod, are not shown because no meaningful equations could cumulative returns in cedis tend to be more positive, be found for any of the fuels. No valid equation could be but this trend appears to be reversed during the second found for gasoil in any of the subperiods examined. No subperiod. Cumulative returns in local currency are, equation appears arbitrary, with the possible exception on average, positive in each of the three subperiods of that for gasoline in the first subperiod. examined. Table A4.17 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Ghanaian Cedis, Beginning­March 2007 Jet Parameter Crude Gasoline kerosene Gasoil Residual fuel oil Statistically significant equation? Yes Yes Yes Yes Da Yes Yes Finite half-life? Yes Yes Yes n.a. No Yes Sum of ARCH + GARCH coefficients 0.25 0.25 0.90 n.a. 0.90 0.23 Half-life in months 0.5 0.5 7 n.a. n.a. 0.5 Lagged variables in mean equation 1 1 1b n.a. 1,2 1,2 GARCH order (1,0) (1,0) (1,1) n.a. (1,1) (1,0) Trend variables in variance equation pd3 None None n.a. None pd3 Source: Author calculations. Note: n.a. = not applicable; pd3 is a dummy variable for period 3 (January 2004­end March 2007). a. Results are classified into the four categories defined on p. 13. b. An equation with lags 1, 2, and 3 passes all the tests (statistical significance of each coefficient, ARCH test), but the half-life becomes infinite. Table A4.18 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Ghanaian Cedis, Beginning­June 1999 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Statistically significant equation? Yes Yes Yes Yes Da Yes Finite half-life? Yes Yes No n.a. Yes Sum of ARCH + GARCH coefficients 0.45 0.51 0.97 n.a. 0.37 Half-life in months 0.9 1 n.a. n.a. 0.7 Lagged variables in mean equation 1 4 1,2 n.a. 1,2 GARCH order (1,0) (1,0) (1,1) n.a. (1,0) Trend variables in variance equation None None None n.a. None Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. 124 Special Report Coping with Oil Price Volatility Table A4.19 Runs Tests on Nominal Monthly Prices in Ghana, in U.S. Dollars, Beginning­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -0.77 -1.99 -2.27 -2.23 -1.25 Cycle returns, (w-µ) -1.03 -1.53 -2.06 -1.55 -1.27 Cumulative cycles Maximum (US$) 73 99 97 86 35 Minimum (US$) -99 -95 -141 -137 -85 Average (US$) -1 0 -15 -14 -10 Percentage negative 46 48 57 56 61 Maximum sojourn, months 42 51 47 48 40 Source: Author calculations. Table A4.20 Runs Tests on Nominal Monthly Prices in Ghana, in Ghanaian Cedis, Beginning­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -2.67 -1.88 -2.72 -2.23 -2.57 Cycle returns, (w-µ) -1.67 -1.38 -3.99 -1.67 -1.92 Cumulative cycles Maximum (C/) 456,515 620,504 667,971 605,049 238,336 Minimum (C/) -758,411 -755,834 -1,048,142 -1,020,468 -608,976 Average (C/) 389 3,898 2,095 1,591 3,646 Percentage negative 32 40 40 35 21 Maximum sojourn, months 102 103 101 102 143 Source: Author calculations. Table A4.21 Runs Tests on Nominal Monthly Prices in Ghana, in U.S. Dollars, Beginning­June 1999 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -1.17 -1.39 -1.81 -1.52 -0.89 Cycle returns, (w-µ) -1.83 -1.39 -1.81 -1.87 -0.90 Cumulative cycles Maximum (US$) 52 54 55 55 35 Minimum (US$) -47 -74 -99 -89 -44 Average (US$) 4 2 -11 -10 -8 Percentage negative 42 44 54 54 68 Maximum sojourn, months 42 51 47 48 38 Source: Author calculations. Annex 4 Statistical Analysis of Developing Country Prices 125 Table A4.22 Runs Tests on Nominal Monthly Prices in Ghana, in Ghanaian Cedis, Beginning­June 1999 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -3.07 -1.04 -1.94 -1.53 -2.22 Cycle returns, (w-µ) -2.51 -1.56 -3.45 -1.75 -1.39 Cumulative cycles Maximum (C/) 327,500 353,255 407,297 389,427 232,827 Minimum (C/) -163,681 -219,123 -199,347 -171,245 -176,838 Average (C/) 74,560 86,444 95,035 89,855 55,177 Percentage negative 18 26 30 23 4 Maximum sojourn, months 102 103 101 102 143 Source: Author calculations. Table A4.23 Runs Tests on Nominal Monthly Prices in Ghana, in U.S. Dollars, July 1999­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) 0.58 -1.26 -0.59 -0.92 -0.64 Cycle returns, (w-µ) 0.88 -0.76 -0.76 -0.01 -0.81 Cumulative cycles Maximum (US$) 117 145 154 136 71 Minimum (US$) -55 -49 -83 -86 -42 Average (US$) 34 42 37 30 31 Percentage negative 28 26 31 31 20 Maximum sojourn, months 52 50 46 46 60 Source: Author calculations. Table A4.24 Runs Tests on Nominal Monthly Prices in Ghana, in Ghanaian Cedis, July 1999­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -0.37 -1.72 -1.77 -1.59 -1.26 Cycle returns, (w-µ) 0.51 -0.34 -1.79 -0.34 -1.24 Cumulative cycles Maximum (C/) 620,196 839,627 867,318 776,294 415,174 Minimum (C/) -594,730 -536,711 -848,795 -849,223 -432,138 Average (C/) 45,237 90,771 52,540 31,425 97,924 Percentage negative 47 42 45 46 35 Maximum sojourn, months 37 35 35 35 47 Source: Author calculations. 126 Special Report Coping with Oil Price Volatility India Table A4.26 gives the ratio of fuel prices in January 2008 to those in January 2004. The ratios are consistently lower Prices averaged over each subperiod as well as the entire for Indian rupee prices in both nominal and real terms. period and the percentage price increases between Crude oil prices rose the most for the set of benchmark subperiods are shown in table A4.25. Nominal price fuels selected for India. increases in Indian rupees in the third subperiod over the Standard deviations of returns for logarithms of first subperiod are about three times those in real terms. monthly prices and exchange rates are shown in table A4.27. Table A4.25 Period Average Prices in India Price (units) Period Crude Gasoline Jet kerosene Gasoil Residual fuel oil 1 16.10 22.37 22.59 21.36 12.35 2 24.46 30.46 28.77 27.53 21.28 Nominal (US$) 3 53.90 62.85 69.37 69.05 41.69 Entire 25.21 31.93 32.97 31.91 19.94 1 430 602 597 567 331 2 1,136 1,414 1,336 1,279 991 Nominal (Rs) 3 2,348 2,739 3,025 3,009 1,814 Entire 952 1,189 1,225 1,192 759 1 23.35 32.33 32.81 30.99 17.91 2 27.94 34.81 32.89 31.44 24.30 Real (US$) 3 54.48 63.62 70.19 69.83 42.09 Entire 30.36 38.92 40.06 38.61 23.96 1 965 1,343 1,355 1,284 738 2 1,434 1,785 1,687 1,613 1,248 Real (Rs) 3 2,444 2,857 3,154 3,136 1,886 Entire 1,351 1,731 1,774 1,713 1,069 Nominal (% 2/1 52 36 27 29 72 increase for 3/2 120 106 141 151 96 prices in US$) 3/1 235 181 207 223 238 Nominal (% 2/1 164 135 124 126 200 increase for 3/2 107 94 126 135 83 prices in Rs) 3/1 446 355 406 431 449 2/1 20 8 0 1 36 Real (% increase 3/2 95 83 113 122 73 for prices in US$) 3/1 133 97 114 125 135 2/1 49 33 24 26 69 Real (% increase 3/2 70 60 87 94 51 for prices in Rs) 3/1 153 113 133 144 156 Sources: U.S. EIA 2008a; author calculations. Note: For definitions and calculations, see the notes to table A4.2. Annex 4 Statistical Analysis of Developing Country Prices 127 Table A4.26 Ratio of January 2008 Prices to January 2004 Prices in India Currency Crude Gasoline Jet kerosene Gasoil Residual fuel oil US$ nominal 3.1 2.5 2.9 3.0 3.0 Rs nominal 2.7 2.2 2.6 2.6 2.6 US$ real 2.7 2.2 2.6 2.6 2.6 Rs real 2.2 1.8 2.1 2.1 2.1 Sources: U.S. EIA 2008a; author calculations. In real terms, local currency prices have higher volatility retained, and the conditional variance has a finite half-life. for every fuel and every subperiod. In nominal terms, local In the second, where only one lag (lag 3) is kept, the null currency prices have the same or greater volatility than hypothesis cannot be rejected. prices denominated in U.S. dollars. The results of the runs tests are given in tables A4.31 GARCH analysis results are shown in tables A4.28 to A4.36. For the entire period, cumulative returns in local to A4.30. In table A4.28, the equation for residual fuel oil currency are negative more frequently than in U.S. dollars; looks quite arbitrary, but retaining fewer lagged terms for this occurs primarily during the first subperiod. However, the mean equation makes the equation fail the ARCH test. the average cumulative cycles are negative in U.S. dollars During the first subperiod, two GARCH(1,0) formulations and positive in local currency for every fuel. Maximum are shown for jet kerosene. In the first, lags 4 and 6 are sojourns are longer for prices in local currency. Table A4.27 Standard Deviation of Returns for Logarithms of Prices and Exchange Rate in India Residual fuel Exchange Price (units) Period Crude Gasoline Jet kerosene Gasoil oil rate 1 0.086 0.076 0.109 0.093 0.145 n.a. Nominal 2 0.085 0.083 0.094 0.093 0.100 n.a. (US$) 3 0.062 0.066 0.119 0.071 0.074 n.a. Entire 0.082 0.076 0.108 0.089 0.125 n.a. 1 0.089 0.079 0.112 0.097 0.146 0.024 2 0.085 0.083 0.095 0.094 0.100 0.006 Nominal (Rs) 3 0.064 0.067 0.120 0.072 0.074 0.014 Entire 0.084 0.078 0.110 0.092 0.126 0.020 1 0.086 0.075 0.109 0.093 0.144 n.a. 2 0.084 0.081 0.093 0.091 0.099 n.a. Real (US$) 3 0.061 0.063 0.117 0.069 0.072 n.a. Entire 0.081 0.075 0.107 0.088 0.124 n.a. 1 0.089 0.080 0.112 0.097 0.146 n.a. 2 0.086 0.085 0.096 0.094 0.100 n.a. Real (Rs) 3 0.064 0.066 0.120 0.072 0.073 n.a. Entire 0.084 0.078 0.110 0.092 0.126 n.a. Source: Author calculations. Note: n.a. = not applicable. Subperiod 1 is from beginning to June 1999; subperiod 2 is from July 1999 to December 2003; subperiod 3 is from January 2004 to January 2008; the entire period is from beginning to January 2008. 128 Special Report Coping with Oil Price Volatility Table A4.28 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Indian Rupees, Beginning­March 2007 Jet Residual Parameter Crude Gasoline Diesel kerosene Gasoil fuel oil Statistically significant equation? Yes Yes Yes Yes Yes Da Yes Finite half-life? No Yes Yes Yes n.a. Yes Sum of ARCH + GARCH coefficients 0.91 0.31 0.65 0.74 n.a. 0.38 Half-life in months n.a. 0.6 2 2 n.a. 0.7 Lagged variables in mean equation 1 1 1,4 1 n.a. 1,2,4,8, 11,14,16 GARCH order (1,1) (1,0) (1,0) (1,1) n.a. (1,0) Trend variables in variance equation None None None pd3 n.a. Trend Source: Author calculations. Note: n.a. = not applicable; pd3 is a dummy variable for period 3 (January 2004­end March 2007); trend is a linear time trend that increases by one for each observation in the series. a. Results are classified into the four categories defined on p. 13. Table A4.29 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Indian Rupees, Beginning­June 1999 Residual Parameter Crude Gasoline Jet kerosene Gasoil fuel oil Statistically significant equation? Yes Yes Yes Yes Yes Yes Yes Yes Yes Finite half-life? No No No No Yes No No Yes Yes Sum of ARCH + GARCH coefficients 0.99 0.86 0.88 0.77 0.48 0.93 0.97 0.35 0.39 Half-life in months n.a. n.a. n.a. n.a. 1 n.a. n.a. 0.7 0.7 Lagged variables in mean equation 4 1 1 1 4,6 3 4 4,6 1,2,4,5 GARCH order (1,1) (1,0) (1,1) (1,0) (1,0) (1,0) (1,1) (1,0) (1,0) Trend variables in variance equation None None None None None None None None None Source: Author calculations. Note: n.a. = not applicable. Table A4.30 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Indian Rupees, July 1999­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Statistically significant equation? Yes Da Yes Da Yes Da Yes Da Yes Finite half-life? n.a. n.a. n.a. n.a. No Sum of ARCH + GARCH coefficients n.a. n.a. n.a. n.a. 0.58 Half-life in months n.a. n.a. n.a. n.a. n.a. Lagged variables in mean equation n.a. n.a. n.a. n.a. None GARCH order n.a. n.a. n.a. n.a. (1,0) Trend variables in variance equation n.a. n.a. n.a. n.a. None Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. Annex 4 Statistical Analysis of Developing Country Prices 129 Table A4.31 Runs Tests on Nominal Monthly Prices in India, in U.S. Dollars, Beginning­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -1.49 -2.54 -2.25 -2.95 -1.90 Cycle returns, (w-µ) -0.93 -2.31 -2.16 -2.49 -1.73 Cumulative cycles Maximum (US$) 67 70 84 83 32 Minimum (US$) -98 -86 -128 -130 -85 Average (US$) -2 -7 -13 -6 -13 Percentage negative 46 57 55 49 64 Maximum sojourn, months 40 50 47 47 47 Source: Author calculations. Table A4.32 Runs Tests on Nominal Monthly Prices in India, in Indian Rupees, Beginning­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -0.93 -2.45 -2.28 -2.40 -1.82 Cycle returns, (w-µ) -1.54 -2.57 -2.52 -3.08 -3.04 Cumulative cycles Maximum (Rs) 2,873 2,466 3,423 3,162 1,279 Minimum (Rs) -4,140 -3,541 -5,636 -5,954 -3,593 Average (Rs) 2,873 2,466 3,423 3,162 1,279 Percentage negative 43 68 69 65 69 Maximum sojourn, months 42 66 75 74 108 Source: Author calculations. Table A4.33 Runs Tests on Nominal Monthly Prices in India, in U.S. Dollars, Beginning­June 1999 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -1.54 -2.20 -2.21 -1.89 -2.05 Cycle returns, (w-µ) -1.22 -2.18 -2.21 -1.21 -1.71 Cumulative cycles Maximum (US$) 45 47 64 74 32 Minimum (US$) -38 -86 -99 -83 -52 Average (US$) 3 -6 -10 -2 -12 Percentage negative 43 56 54 49 72 Maximum sojourn, months 40 50 47 47 47 Source: Author calculations. 130 Special Report Coping with Oil Price Volatility Table A4.34 Runs Tests on Nominal Monthly Prices in India, in Indian Rupees, Beginning­June 1999 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -1.17 -2.51 -2.21 -1.55 -2.00 Cycle returns, (w-µ) -1.83 -2.86 -2.54 -1.55 -2.71 Cumulative cycles Maximum (Rs) 1,505 985 1,970 2,172 996 Minimum (Rs) -1,909 -2,347 -2,585 -2,328 -2,392 Average (Rs) 105 -492 -499 -356 -317 Percentage negative 38 72 75 70 81 Maximum sojourn, months 42 66 75 74 108 Source: Author calculations. Table A4.35 Runs Tests on Nominal Monthly Prices in India, in U.S. Dollars, July 1999­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) 0.00 -0.99 -0.15 -1.96 -0.37 Cycle returns, (w-µ) 0.15 -0.70 -0.47 -2.47 -0.76 Cumulative cycles Maximum (US$) 105 101 128 112 76 Minimum (US$) -60 -40 -84 -101 -35 Average (US$) 29 22 25 16 36 Percentage negative 30 34 34 38 18 Maximum sojourn, months 53 49 48 46 61 Source: Author calculations. Table A4.36 Runs Tests on Nominal Monthly Prices in India, in Indian Rupees, July 1999­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) 0.32 -0.70 -0.31 -1.70 -0.47 Cycle returns, (w-µ) 0.15 -0.34 -0.47 -2.93 -1.61 Cumulative cycles Maximum (Rs) 4,782 4,581 5,846 5,134 3,671 Minimum (Rs) -2,231 -1,427 -3,213 -3,982 -1,200 Average (Rs) 1,598 1,388 1,429 1,019 1,852 Percentage negative 27 30 33 37 15 Maximum sojourn, months 56 53 50 47 63 Source: Author calculations. Annex 4 Statistical Analysis of Developing Country Prices 131 The Philippines Table A4.38 gives the ratio of fuel prices in January 2008 to those in January 2004. The ratios are consistently lower Prices averaged over each subperiod as well as over the for Philippine peso prices in both nominal and real terms. entire period and the percentage price increases between Crude oil prices rose the most for the set of benchmark fuels subperiods are shown in table A4.37. Nominal price selected for the Philippines. increases in local currency units are larger in every case Standarddeviationsofreturnsforlogarithmsofmonthly examined, and especially relative to the first subperiod. prices and exchange rates are shown in table A4.39. Prices in Table A4.37 Period Average Prices in the Philippines Price (units) Period Crude Gasoline Jet kerosene Gasoil Residual fuel oil 1 17.84 23.56 23.96 22.87 14.23 2 26.37 30.07 30.38 29.11 23.61 Nominal (US$) 3 58.06 67.25 71.33 68.63 45.61 Entire 27.45 33.41 34.51 33.07 22.31 1 472 623 634 605 378 2 1,300 1,482 1,495 1,436 1,164 Nominal (P)= 3 2,954 3,435 3,640 3,499 2,317 Entire 1,129 1,351 1,400 1,343 921 1 25.90 34.29 34.80 33.18 20.64 2 30.11 34.35 34.72 33.25 26.96 Real (US$) 3 58.70 68.10 72.20 69.44 46.10 Entire 33.15 40.85 42.02 40.22 26.92 1 1,126 1,497 1,514 1,442 895 2 1,696 1,933 1,954 1,874 1,518 Real (P) = 3 3,087 3,602 3,811 3,663 2,421 Entire 1,627 1,998 2,053 1,964 1,324 Nominal (% 2/1 48 28 27 27 66 increase for 3/2 120 124 135 136 93 prices in US$) 3/1 225 185 198 200 221 Nominal (% 2/1 175 138 136 137 208 increase for 3/2 127 132 143 144 99 prices in P) = 3/1 526 451 474 478 514 2/1 16 0 0 0 31 Real (% increase 3/2 94 51 95 98 108 for prices in US$) 3/1 144 156 127 99 107 2/1 51 29 29 30 69 Real (% increase 3/2 82 86 95 95 60 for prices in P) = 3/1 174 141 152 154 170 Sources: U.S. EIA 2008a; author calculations. Note: For definitions and calculations, see the notes to table A4.2. 132 Special Report Coping with Oil Price Volatility Table A4.38 Ratio of January 2008 Prices to January 2004 Prices in the Philippines Currency Crude Gasoline Jet kerosene Gasoil Residual fuel oil US$ nominal 3.1 2.3 2.7 2.7 2.8 = P nominal 2.3 1.7 2.0 2.0 2.1 US$ real 2.7 2.0 2.4 2.4 2.5 = P real 1.8 1.3 1.6 1.6 1.6 Sources: U.S. EIA 2008a; author calculations. Table A4.39 Standard Deviation of Returns for Logarithms of Prices and Exchange Rate in the Philippines Residual fuel Exchange Price (units) Period Crude Gasoline Jet kerosene Gasoil oil rate 1 0.082 0.080 0.101 0.087 0.120 n.a. Nominal 2 0.079 0.105 0.090 0.088 0.089 n.a. (US$) 3 0.092 0.090 0.076 0.071 0.062 n.a. Entire 0.083 0.088 0.094 0.085 0.105 n.a. 1 0.085 0.084 0.103 0.090 0.121 0.023 2 0.080 0.107 0.094 0.092 0.089 0.017 Nominal (P)= 3 0.093 0.092 0.078 0.074 0.062 0.013 Entire 0.086 0.091 0.096 0.087 0.105 0.021 1 0.081 0.079 0.100 0.087 0.119 n.a. 2 0.078 0.104 0.089 0.086 0.088 n.a. Real (US$) 3 0.090 0.088 0.074 0.069 0.059 n.a. Entire 0.082 0.087 0.093 0.084 0.104 n.a. 1 0.086 0.086 0.103 0.090 0.121 n.a. 2 0.080 0.107 0.094 0.093 0.089 n.a. Real (P) = 3 0.093 0.092 0.078 0.074 0.062 n.a. Entire 0.086 0.092 0.097 0.088 0.106 n.a. Source: Author calculations. Note: n.a. = not applicable. Subperiod 1 is from beginning to June 1999; subperiod 2 is from July 1999 to December 2003; subperiod 3 is from January 2004 to January 2008; the entire period is from beginning to January 2008. localcurrencyunitsforallfuelsareconsistentlymorevolatile equation fail the ARCH test. Similarly, in the first subperiod, for each subperiod, both in nominal and real terms. retaining fewer lags in the equation for residual fuel oil GARCH analysis results are shown in tables A4.40 makes it fail the ARCH test. and A4.41. The results from the second subperiod are not The results of the runs tests are given in tables A4.42 to given because no meaningful equations could be found A4.47. The cumulative cycles in local currency are negative for any of the fuels. In table A4.40, retaining fewer terms for every fuel for the entire period. With the exception of in the GARCH(1,0) formulation for jet kerosene and in the crude oil, the cumulative cycles are negative more than GARCH(1,1) formulation for gasoil makes each respective half the time. Annex 4 Statistical Analysis of Developing Country Prices 133 Table A4.40 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Philippine Pesos, Beginning­March 2007 Jet Residual Parameter Crude Gasoline Diesel kerosene Gasoil fuel oil Statistically significant equation? Yes Da Yes Yes Yes Yes Yes Da Finite half-life? n.a. Yes Yes Yes No n.a. Sum of ARCH + GARCH coefficients n.a. 0.31 0.90 0.61 0.97 n.a. Half-life in months n.a. 0.6 7 1 n.a. n.a. Lagged variables in mean equation n.a. 1,2 1,2 1,2,3,4,6 1,2,4,6 n.a. GARCH order n.a. (1,0) (1,1) (1,0) (1,1) n.a. Trend variables in variance equation n.a. None None None None n.a. Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. Table A4.41 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Philippine Pesos, Beginning­June 1999 Jet Residual Parameter Crude Gasoline Diesel kerosene Gasoil fuel oil Statistically significant equation? Yes Yes Yes Yes Yes Da Yes Finite half-life? Yes Yes No No n.a. Yes Sum of ARCH + GARCH coefficients 0.62 0.65 0.98 0.91 n.a. 0.30 Half-life in months 1 2 n.a. n.a. n.a. 0.6 Lagged variables in mean equation 1 4 1,2,3,4 1,2 n.a. 1,2,4,6 GARCH order (1,0) (1,0) (1,1) (1,0) n.a. (1,0) Trend variables in variance equation None None None None n.a. None Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. Table A4.42 Runs Tests on Nominal Monthly Prices in Philippines, in U.S. Dollars, Beginning­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -3.19 -1.54 -2.47 -3.90 -2.23 Cycle returns, (w-µ) -2.94 -1.03 -2.29 -3.98 -1.99 Cumulative cycles Maximum (US$) 73 80 92 89 38 Minimum (US$) -101 -94 -131 -108 -85 Average (US$) 0 -7 -11 -1 -10 Percentage negative 43 51 53 47 60 Maximum sojourn, months 42 48 46 48 47 Source: Author calculations. 134 Special Report Coping with Oil Price Volatility Table A4.43 Runs Tests on Nominal Monthly Prices in Philippines, in Philippine Pesos, Beginning­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -3.14 -0.23 -2.97 -3.93 -1.79 Cycle returns, (w-µ) -2.70 0.00 -3.31 -3.48 -1.71 Cumulative cycles Maximum (P) = 3,142 3,326 3,708 3,307 1,836 Minimum (P)= -4,662 -5,129 -7,318 -6,403 -3,996 Average (P)= -18 -667 -760 -535 -485 Percentage negative 36 55 57 52 57 Maximum sojourn, months 95 55 48 52 38 Source: Author calculations. Table A4.44 Runs Tests on Nominal Monthly Prices in Philippines, in U.S. Dollars, Beginning­June 1999 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -2.37 -1.89 -2.16 -2.37 -2.37 Cycle returns, (w-µ) -2.71 -1.69 -2.20 -2.38 -2.36 Cumulative cycles Maximum (US$) 52 53 68 80 38 Minimum (US$) -44 -93 -100 -81 -52 Average (US$) 5 -3 -7 3 -9 Percentage negative 38 46 52 45 65 Maximum sojourn, months 42 48 46 48 47 Source: Author calculations. Table A4.45 Runs Tests on Nominal Monthly Prices in Philippines, in Philippine Pesos, Beginning­June 1999 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -2.05 -0.71 -2.55 -2.37 -1.98 Cycle returns, (w-µ) -2.35 -0.35 -2.88 -1.75 -2.03 Cumulative cycles Maximum (P) = 1,214 1,100 897 1,307 481 Minimum (P)= -1,827 -3,271 -3,519 -3,046 -2,431 Average (P)= 286 -333 -420 -174 -284 Percentage negative 26 48 53 44 50 Maximum sojourn, months 95 55 48 52 38 Source: Author calculations. Annex 4 Statistical Analysis of Developing Country Prices 135 Table A4.46 Runs Tests on Nominal Monthly Prices in Philippines, in U.S. Dollars, July 1999­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -1.93 0.15 -0.15 -2.87 -0.70 Cycle returns, (w-µ) 0.88 -0.76 -0.76 -0.01 -0.81 Cumulative cycles Maximum (US$) 117 118 136 118 88 Minimum (US$) -57 -56 -87 -79 -33 Average (US$) 35 26 27 21 39 Percentage negative 28 32 34 40 17 Maximum sojourn, months 52 46 47 44 60 Source: Author calculations. Table A4.47 Runs Tests on Nominal Monthly Prices in Philippines, in Philippine Pesos, July 1999­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -2.30 0.66 -1.26 -3.04 -0.47 Cycle returns, (w-µ) -1.35 0.51 -1.56 -3.27 -0.34 Cumulative cycles Maximum (P) = 4,969 5,396 5,979 5,151 4,267 Minimum (P)= -2,836 -3,060 -5,047 -4,559 -1,564 Average (P)= 1,323 868 967 731 1,625 Percentage negative 29 33 33 37 18 Maximum sojourn, months 47 43 43 40 57 Source: Author calculations. Thailand GARCH analysis results are shown in tables A4.51 to A4.53. In table A4.51, although the GARCH(1,0) formulation Prices averaged over each subperiod as well as over the for jet kerosene appears arbitrary, retaining fewer lagged entire period and the percentage price increases between variables makes the equation fail the ARCH test. Similarly, subperiodsareshownintable A4.48.Inbothnominalandreal in the first subperiod, if fewer lagged variables are retained terms, the percentage price increases in the third subperiod in the equation for residual fuel oil, the equation fails over the second subperiod were 20 to 25 percent. the ARCH test. Lastly, in the second subperiod, keeping Table A4.49 gives the ratio of fuel prices in January 2008 fewer lagged terms for residual fuel oil, including omission to those in January 2004. The ratios are consistently lower of all lagged variables, makes the equation statistically for Thai baht prices in both nominal and real terms. In real insignificant. terms, fuel prices effectively doubled in the intervening The results of the runs tests are shown in tables A4.54 four years. to A4.56 for local prices. The results for prices expressed in Standard deviations of returns for logarithms of U.S. dollars are in the Philippines section of this annex. For monthly prices and exchange rates are shown in table A4.50. the whole period, cumulative cycles in local currency tend Local currency prices exhibited the same or greater to be more positive, with the exception of crude oil. During volatility in both nominal and real terms, except for the the first subperiod, however, cumulative cycles tend to be nominal residual fuel oil price during the first subperiod. more positive in U.S. dollars. 136 Special Report Coping with Oil Price Volatility Table A4.48 Period Average Prices in Thailand Price (units) Period Crude Gasoline Jet kerosene Gasoil Residual fuel oil 1 17.84 23.56 23.96 22.87 14.23 2 26.37 30.07 30.38 29.11 23.61 Nominal (US$) 3 58.06 67.25 71.33 68.63 45.61 Entire 27.45 33.41 34.51 33.07 22.31 1 484 639 649 619 388 2 1,103 1,257 1,271 1,219 987 Nominal (B) 3 2,182 2,533 2,687 2,583 1,713 Entire 945 1,138 1,176 1,127 773 1 25.90 34.29 34.80 33.18 20.64 2 30.11 34.35 34.72 33.25 26.96 Real (US$) 3 58.70 68.10 72.20 69.44 46.10 Entire 33.15 40.85 42.02 40.22 26.92 1 782 1,036 1,048 1,000 624 2 1,276 1,453 1,470 1,409 1,141 Real (B) 3 2,234 2,598 2,754 2,647 1,753 Entire 1,168 1,428 1,469 1,406 953 Nominal (% 2/1 48 28 27 27 66 increase for 3/2 120 124 135 136 93 prices in US$) 3/1 225 185 198 200 221 Nominal (% 2/1 128 97 96 97 154 increase for 3/2 98 102 112 112 74 prices in B) 3/1 350 296 314 317 341 2/1 16 0 0 0 31 Real (% increase 3/2 95 98 108 109 71 for prices in US$) 3/1 127 99 107 109 123 2/1 63 40 40 41 83 Real (% increase 3/2 75 79 87 88 54 for prices in B) 3/1 186 151 163 165 181 Sources: U.S. EIA 2008a; author calculations. Note: For definitions and calculations, see the notes to table A4.2. Table A4.49 Ratio of January 2008 Prices to January 2004 Prices in Thailand Currency Crude Gasoline Jet kerosene Gasoil Residual fuel oil US$ nominal 3.1 2.3 2.7 2.7 2.8 B nominal 2.7 1.9 2.3 2.3 2.4 US$ real 2.7 2.0 2.3 2.4 2.4 B real 2.3 1.6 1.9 2.0 2.0 Sources: U.S. EIA 2008a; author calculations. Annex 4 Statistical Analysis of Developing Country Prices 137 Table A4.50 Standard Deviation of Returns for Logarithms of Prices and Exchange Rate in Thailand Residual fuel Exchange Price (units) Period Crude Gasoline Jet kerosene Gasoil oil rate 1 0.082 0.080 0.101 0.087 0.120 n.a. Nominal 2 0.079 0.105 0.090 0.088 0.089 n.a. (US$) 3 0.092 0.090 0.076 0.071 0.062 n.a. Entire 0.083 0.088 0.094 0.085 0.105 n.a. 1 0.085 0.084 0.102 0.089 0.118 0.032 2 0.084 0.107 0.094 0.092 0.092 0.017 Nominal (B) 3 0.093 0.091 0.078 0.073 0.064 0.014 Entire 0.087 0.090 0.096 0.087 0.104 0.026 1 0.081 0.079 0.100 0.087 0.119 n.a. 2 0.078 0.104 0.089 0.086 0.088 n.a. Real (US$) 3 0.090 0.088 0.074 0.069 0.059 n.a. Entire 0.082 0.087 0.093 0.084 0.104 n.a. 1 0.085 0.084 0.102 0.088 0.119 n.a. 2 0.082 0.105 0.092 0.091 0.091 n.a. Real (B) 3 0.092 0.088 0.076 0.071 0.062 n.a. Entire 0.086 0.090 0.095 0.086 0.104 n.a. Source: Author calculations. Note: n.a. = not applicable. Subperiod 1 is from beginning to June 1999; subperiod 2 is from July 1999 to December 2003; subperiod 3 is from January 2004 to January 2008; the entire period is from beginning to January 2008. Table A4.51 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Thai Bahts, Beginning­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Statistically significant equation? Yes Da Yes Yes Yes Yes Yes Yes Finite half-life? n.a. No Yes Yes No No No Sum of ARCH + GARCH coefficients n.a. 0.81 0.25 0.89 0.84 0.97 0.35 Half-life in months n.a. n.a. 0.5 6 n.a. n.a. n.a. Lagged variables in mean equation n.a. 1 1,2 1,2 1,2,4,6 4 2 GARCH order n.a. (1,1) (1,0) (1,1) (1,0) (1,1) (1,0) Trend variables in variance equation n.a. None None None None None Trend Source: Author calculations. Note: n.a. = not applicable; trend is a linear time trend that increases by one for each observation in the series. a. Results are classified into the four categories defined on p. 13. 138 Special Report Coping with Oil Price Volatility Table A4.52 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Thai Bahts, Beginning­June 1999 Jet Residual Parameter Crude Gasoline kerosene Gasoil fuel oil Statistically significant equation? Yes Da Yes Yes Yes Da Yes Da Yes Finite half-life? n.a. Yes No n.a. n.a. Yes Sum of ARCH + GARCH coefficients n.a. 0.70 0.77 n.a. n.a. 0.42 Half-life in months n.a. 3 n.a. n.a. n.a. 0.8 Lagged variables in mean equation n.a. 3,5,6 3,5 n.a. n.a. 1,2,3 4, 6,13 GARCH order n.a. (1,0) (1,0) n.a. n.a. (1,0) Trend variables in variance equation n.a. None None n.a. n.a. None Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. Table A4.53 GARCH Analysis of Returns of Logarithms of Nominal Monthly Prices in Thai Bahts, July 1999­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Statistically significant equation? Yes Da Yes Da Yes Da Yes Da Yes Finite half-life? n.a. n.a. n.a. n.a. No Sum of ARCH + GARCH coefficients n.a. n.a. n.a. n.a. 0.68 Half-life in months n.a. n.a. n.a. n.a. 0.7 Lagged variables in mean equation n.a. n.a. n.a. n.a. 2,9,16 GARCH order n.a. n.a. n.a. n.a. (1,0) Trend variables in variance equation n.a. n.a. n.a. n.a. None Source: Author calculations. Note: n.a. = not applicable. a. Results are classified into the four categories defined on p. 13. Table A4.54 Runs Tests on Nominal Monthly Prices in Thailand, in Thai Bahts, Beginning­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -2.82 -0.99 -2.19 -3.14 -2.16 Cycle returns, (w-µ) -2.96 -0.51 -2.04 -2.71 -2.54 Cumulative cycles Maximum (B) 502 907 998 751 504 Minimum (B) -459 -566 -490 -481 -336 Average (B) -11 28 62 59 8 Percentage negative 58 47 39 36 48 Maximum sojourn, months 97 96 97 96 96 Source: Author calculations. Annex 4 Statistical Analysis of Developing Country Prices 139 Table A4.55 Runs Tests on Nominal Monthly Prices in Thailand, in Thai Bahts, Beginning­June 1999 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -2.66 -1.71 -1.54 -1.40 -2.33 Cycle returns, (w-µ) -2.71 -1.04 -1.88 -1.19 -2.04 Cumulative cycles Maximum (B) 1,146 1,192 792 1,305 278 Minimum (B) -1,959 -2,603 -2,750 -2,237 -2,406 Average (B) 151 -384 -530 -218 -409 Percentage negative 26 62 63 51 77 Maximum sojourn, months 61 51 47 49 48 Source: Author calculations. Table A4.56 Runs Tests on Nominal Monthly Prices in Thailand, in Thai Bahts, July 1999­March 2007 Parameter Crude Gasoline Jet kerosene Gasoil Residual fuel oil Returns, (w-µ) -1.13 0.66 -0.78 -3.11 -0.70 Cycle returns, (w-µ) -1.35 0.41 -0.70 -2.96 -1.73 Cumulative cycles Maximum 4,905 4,739 5,808 5,050 3,740 Minimum -1,907 -1,902 -3,117 -2,806 -1,017 Average 1,715 1,366 1,505 1,247 1,874 Percentage negative 24 27 27 31 12 Maximum sojourn, months 52 49 49 45 63 Source: Author calculations. Annex 5 Hedging Parameters This annex derives the values of the risk-minimizing and Equation A5.2 can be rewritten by incorporating the optimal hedge ratios as well as other associated hedging certain initial value of wealth, as determined by the spot performance parameters for an agent that has physical price of the physical asset at time 0, W(0) = p(0) × N. The crude oil or oil products to sell. It is assumed that the agent change in wealth over the life of the hedge is1 has N units to sell on the spot market and desires to hedge W = W(1)-W(0) = [p(1)-p(0)] × N M (where M is smaller than or equal to N) of these units + [f(0,1)-f(1,1)] × M, (A5.3) through a futures transaction. In the first case, the goal is to choose M to minimize the overall risks as measured and the change in the value of the wealth per unit of by the variance of the return to the portfolio of M futures production is contracts and N spot sales. W N = [p(1)-p(0)] + h × [f(0,1) - f(1,1)], (A5.4) Let where h denotes the hedge ratio, the proportion of physical · f(0,1) denote the futures prices quoted at current time units for which futures contracts are taken out. This 0 for delivery at time 1, equation can be rewritten as · f(1,1) denote the futures price at time 1 for delivery at time 1, W N = p-h × f, (A5.5) · p(0) denote the spot price at time 0, where p = [p(1)-p(0)] and f = [f(1,1)-f(0,1)]. · p(1) the spot price at time 1. The objective of hedging in this case is to minimize the Without a hedge, the oil producer would receive the total risk on the sale of oil. Measuring risk by the variance uncertain amount p(1) at time 1. To effect a hedge, the of the change in wealth per unit sold requires that the producer sells M futures at time 0, and offsets this position variance of equation A5.5 be minimized. The variance can at time 1 with the purchase of M units for immediate be written as delivery at time 1. At time 1, the gain (loss) on the futures Var [ W N] = Var p-2h Cov [ p, f ] contracts is + h2 Var f, (A5.6) [f(0,1) - f(1,1)] × M. (A5.1) where Var p and Var f are the variances of p and f, The overall value of the hedged portfolio, denoted W(1), is respectively, and Cov [ p, f] denotes the covariance of p and f. The variance-minimizing value of the hedge ratio W(1) = p(1) × N + [f(0,1) - f(1,1)] × M. (A5.2) is given by If the hedged commodity and the physical commodity h* = Cov [ p, f ] Var f. (A5.7) are identical in all respects (quality, location, and timing) then p(1) = f(1,1), and a choice of M = N would eliminate Alternatively, all price risk from the contract. It is important to note that h* = (Var p Var f), (A5.8) the change in futures prices is the change in the price at a fixed time (1) between the dates of opening and closing where is the (unsquared) correlation between the two the hedge. changes in prices. The hedge ratio determined in equation 1The equation formulation is not intended to imply that the seller is weighing the option of selling today versus a few months from now. Subtracting W(0) from equation A5.2, which introduces a constant, is a device for expressing the equations that follow in terms of p and f. 141 142 Special Report Coping with Oil Price Volatility A5.7 is termed the risk-minimizing hedge ratio. The value increment in the return due to hedging, relative to this set of the minimum risk attainable is given by of fixed prices, is therefore accounted by the second term on the right-hand side of equation A5.12. When futures Var [ W N] = Var p-(h*)2 Var f. (A5.9) prices rise (as the closing date approaches), the return to If the two price changes ( p and f) are perfectly the hedger falls depending on how much was hedged. correlated, the hedge is perfect and removes all uncertainty. Equation A5.11 can be estimated by using historical Where the correlation is substantially less than unity, the data on changes in prices. The use of sample data to fraction of the physical commodity that should be hedged estimate a theoretical concept relies on there being no to minimize risks will be correspondingly lower. The shifts in the underlying variances and covariances. If existence of the basis risk that leads to this lack of perfect there had been such a structural shift, the regression correlation means that the producer must balance the risk coefficient would also change over the period as would of not hedging part or all of the production against the the risk-minimizing hedge ratio and the effectiveness of risk entailed from the basis on the part that is hedged. hedging. More sophisticated models use dynamic hedging Hedging efficiency is measured by the percentage reduction strategies where the risk-minimizing hedge ratio changes in the variance of the unhedged portfolio achieved by the over time and are estimated through a model such as a portfolio of physical and futures. At the risk-minimizing GARCH process. value, the ratio of the variance of the hedged portfolio to The estimation of the risk-minimizing hedge ratio from the variance of the unhedged portfolio is given by a given data period can be used to simulate the benefits of a hedging strategy for that same period--the ex post Var [ W N] Var p = 1- . 2 (A5.10) hedge in which the agent has made an estimate of the risk- The squared correlation between the two changes in minimizing hedge ratio using data from that period itself. It prices thus measures hedging effectiveness. It is assumed can also be used to simulate a hedging strategy outside that that the short hedger is constrained not to hedge more than period--the ex ante hedge in which it is assumed that the is available to sell of the physical commodity. If the value of same hedge ratio would minimize risks if all the data were the risk-minimizing hedge ratio is greater than unity, this available to estimate it. If the data changed over time such is assumed to be an infeasible portfolio; a value of unity is that the regression coefficients in equation A5.11 changed, taken as the feasible risk-minimizing hedge. then the ex post and ex ante hedges would give different Equation A5.7 gives the key to estimating the risk- risk reductions and returns. The results of calculations for minimizing hedge ratio. Since the formula given is identical ex post risk-minimizing six-month hedged and unhedged to that used to estimate the regression coefficient when returns for various crudes covering the period February the change in the spot price is regressed on the change in 1988 to December 2006 are given in table A5.1. the futures price, the risk-minimizing hedge ratio can be An extension to the risk-minimizing hedge is to take obtained by the regression into account the expected returns from hedging versus not p = y + h f + , (A5.11) hedging. To balance risk against return, a utility function must be specified. The utility function U to be maximized where the estimated return on the portfolio is given by is usually assumed to be of the form y* = E( p)-h*E( f), (A5.12) U = E[ W N]- Var [ W N], (A5.13) and E( p) and E( f) are the expected values of the where is a measure of the preference for risk. The higher arguments p and f, respectively.2 the value of , the more important it is to choose a hedged Using previous data for futures and spot prices for portfolio that reduces risk. The optimal hedge ratio, h^, can the commodity in question, the regression coefficient can be shown to be be estimated. Hedging effectiveness is estimated by the h^= h*-E( f) (2 Var f ) (A5.14) squared correlation coefficient from the regression, and the risk-minimizing hedge ratio by the regression coefficient and is estimated from the value of the risk-minimizing on the change in futures prices. The estimated value of y* hedge ratio, the mean and variance of the change in futures is the expected return from the risk-minimizing portfolio prices, and the risk preference parameter . over the period, measured relative to the set of opening The value of the optimal hedge variance is given by spot prices at the beginning of every futures contract. The substituting equation A5.14 into equation A5.6: 2This can be seen by noting that regressions pass through the point of means. Annex 5 Hedging Parameters 143 Table A5.1 Ex Post Risk-Minimizing Six-Month Hedged Return and Unhedged Return for Various Crudes, February 1988­December 2006 Feb. '88­Dec. `06 Feb. `88­Dec. `99 Jan. `00­Dec. `03 Jan. `04­Dec. `06 Hedged Unhedged Hedged Unhedged Hedged Unhedged Hedged Unhedged Crude, country return return return return return return return return Brega, Libya -0.58 0.74 -0.37 0.50 -1.56 0.94 0.16 1.44 Cabinda, Angola -0.52 0.71 -0.33 0.51 -1.38 0.90 0.12 1.31 Cossack, Australia -0.57 0.76 -0.37 0.46 -1.50 1.25 0.02 1.32 Dukhan, Qatar -0.50 0.75 -0.35 0.45 -1.24 1.05 0.26 1.48 Es Sider, Libya -0.58 0.72 -0.38 0.49 -1.53 0.91 0.10 1.35 Forcados, Nigeria -0.62 0.74 -0.43 0.47 -1.46 0.99 0.14 1.47 Iran Heavy, Iran, Islamic Rep. of -0.52 0.64 -0.35 0.45 -1.30 0.72 0.22 1.33 Iran Light, Iran, Islamic Rep. of -0.55 0.67 -0.39 0.45 -1.30 0.79 0.22 1.39 Kole, Cameroon -0.58 0.77 -0.38 0.51 -1.10 0.97 0.14 1.52 Mandji, Gabon -0.58 0.74 -0.34 0.52 -1.15 0.84 0.15 1.51 Marine, Qatar -0.50 0.70 -0.36 0.45 -1.24 0.95 0.21 1.37 Murban, Abu Dhabi, UAE -0.50 0.75 -0.35 0.46 -1.28 1.08 0.23 1.46 Oriente, Ecuador -0.65 0.57 -0.35 0.49 -1.90 0.55 -0.21 0.94 Saharan, Algeria -0.60 0.73 -0.42 0.48 -1.57 0.96 0.15 1.42 Urals, Russian Federation -0.57 0.67 -0.42 0.45 -1.29 0.80 0.22 1.40 Widuri, Indonesia -0.61 0.68 -0.37 0.46 -1.82 0.86 0.07 1.33 WTI, U.S. 0.10 1.22 -0.31 0.51 -1.54 1.16 3.20 4.12 Sources: Futures prices from Energy Intelligence 2008; author calculations. Note: UAE = United Arab Emirates. Var [ W N] = Var p + (h^2-2 h^h*) Var f (A5.15) hedges with an immediate buy hedge coupled with an The expected return on the optimal hedged portfolio is equivalentsellofthefuturescontractforimmediatedelivery at the time of expiration of the original futures purchase, the y^= E( p)-h^E( f). (A5.16) overall change in the value of the portfolio is given by the The risk reduction (hedging efficiency) of the optimal negative of equation A5.3. The risk-minimizing hedge ratio hedge can be derived by dividing equation A5.15 by the continues to be given by equation A5.8, the expected return variance of the spot price change. on the hedge is equal to the negative of equation A5.12, and For a long hedger that intends to buy the physical the expected unhedged return is equal to the negative of the commodity after a specified number of months and that change in the spot price over the duration of the hedge. Annex 6 Price-Smoothing Formulae This annex accompanies chapter 7 and uses the following The average futures price at time t taken over the next definitions: m contract durations is · i = m p(t) is the spot price of a commodity (crude oil or oil p(t,i)] m. product) at time t Pf(t,m) = [i = 1 · p(t, i) is the futures price at time t, for delivery i periods The average of n past prices and m futures prices set in the future. in period t - 1 to be used as a target price for period t is given by The n month moving average of past prices at time t is i = n i = n i = m Pm(t,n) = [i p(t - i)] n. Pv(t) = [i p(t - i)] + p(t,i)] (n + m). = 1 = 1 i = 1 145 Glossary Arc-sine law A theorem, also known as the law of long leads, that shows that, when a coin is tossed repeatedly with equal chances of heads and tails, the proportion of the time that the total number of heads is greater than the total number of tails follows a certain mathematical function. This theorem implies that often very large numbers of trials are needed before the lead switches from heads to tails (or vice versa). Autocorrelation The correlation of a variable measured at a number of successive time intervals with the values of the same variable a fixed number of periods earlier Barrels A unit of volume, equal to 42 U.S. gallons and equivalent to 159 liters Brent crude One of the major crude oil classifications used as a benchmark for pricing, produced in the North Sea Basis risk The risk associated with imperfect hedging using futures, arising from differences in the qualities of the commodity to be hedged and of the reference commodity underlying the futures (for example, West Texas Intermediate or Brent crude) Conditional variance The forecast of the variance of a series at a point in time based on information available in the previous period Correlation A measure of the extent to which two variables move together or oppositely over time Cumulative sum The sum of all past values of a series until that time Cycle The difference between a given data series and a trend fitted to that series ("the filter") Distillate fuel oil Products of refinery distillation, sometimes referred to as middle distillates, consisting of kerosene, diesel fuel, and heating oil Filter A smooth estimate of the long-term trend of a data series F-test A test that checks if the variances of two separate series are equal GARCH Generalized autoregressive conditional heteroskedasticity--a statistical model to represent a situation in which the variance of shocks to a given series changes over time Gasoil European designation for the medium oil from the refining process used as a fuel in diesel engines, burned in central heating systems, and used as a feedstock for the chemical industry Heating oil A distillate fuel oil used for domestic heating and in medium-capacity commercial- industrial burner units Heteroskedasticity The nonconstancy of the variance of a series over time Homoskedasticity The constancy of the variance of a series over time Lagged variable With respect to the current value of a series, the value lagged k periods is the value of that same series k periods earlier Mean The average of a set of data 147 148 Special Report Coping with Oil Price Volatility Mean reversion A series is mean-reverting if values eventually return to the average Nonparametric test A nonparametric or distribution-free test is one that makes no assumption about the underlying frequency distribution of the variable being assessed Nonstationary A process is nonstationary if its probability distribution varies over time; the mean or variance of such a process can therefore be nonconstant Null hypothesis A hypothesis set up in statistics to be invalidated (nullified) in order to support an alternative hypothesis. A null hypothesis is presumed true until statistical tests indicate otherwise. One-sided 5 percent Also called a one-tailed test of significance. A statistical hypothesis test in which the test values for rejecting the null hypothesis are located entirely in one tail of the probability distribution (for example, all values are positive instead of covering positive and negative numbers), and the null hypothesis is rejected if there is only a 5 percent or lower probability that it is true. Propane One of two important components of liquefied petroleum gas, the other being butanes Random walk A process where each successive step is in a random direction. It can be shown that the distance from the starting point in a one-dimensional random walk (moving forward and backward on a straight line) with n steps asymptotically approaches 0.8 n. Return The difference between the current and previous value of a variable (typically the price); in chapter 5 and annex 5, a change in the value of an investment or a portfolio over a given period of time Residual fuel oil Heavy fuel oil produced from the residue in the fractional distillation process Runs test A test for the randomness of a series of data over time utilizing information on the number of unbroken sequences of positive or negative values Shock Any external factor that causes an unpredicted change in the variable under consideration, typically prices Sojourn The number of periods a cumulative sum stays positive (or negative) before changing sign Standard deviation The square root of the variance of a series Stationary A process is stationary if its probability distribution does not vary over time; the mean and variance of such a process are constant Time series A series of data points measured at successive times, typically at uniform time intervals Unit root A series has a unit root when the current value is equal to the previous value plus a random term U.S. gallon A unit of volume, equivalent to 3.79 liters Variance A measure of the dispersion or variability of a series based on the average squared values above and below the mean West Texas One of the major crude oil classifications used as a benchmark for oil pricing, with Intermediate (WTI) price settlement in Cushing, Oklahoma References Alaska Department of Revenue. 2002. 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Special Report Series RENEWABLE ENERGY THEMATIC AREA East Asia and Pacific (EAP) Sustainable and Efficient Energy Use to Alleviate Indoor Air Pollution in Poor Rural Areas in China (002/07) Latin America and the Caribbean Region (LCR) Nicaragua Policy & Strategy for the Promotion of Renewable Energy Resources (003/07) Global (GLB) Considering Trade Policies for Liquid Biofuels (004/07) ENERGY POVERTY THEMATIC AREA Global (GLB) Risk Assessment Methods for Power Utility Planning (001/07) ENERGY SECURITY THEMATIC AREA Global (GLB) Coping with Oil Price Volatility (005/08) Energy Sector Management Assistance Program (ESMAP) Purpose The Energy Sector Management Assistance Program is a global technical assistance partnership administered by the World Bank and sponsored by bilateral official donors since 1983. ESMAP's mission is to promote the role of energy in poverty reduction and economic growth in an environmentally responsible manner. Its work applies to low-income, emerging, and transition economies and contributes to the achievement of internationally agreed development goals. ESMAP interventions are knowledge products including free technical assistance, specific studies, advisory services, pilot projects, knowledge generation and dissemination, trainings, workshops and seminars, conferences and roundtables, and publications. ESMAP's work focuses on four key thematic programs: energy security, renewable energy, energy-poverty, and market efficiency and governance. Governance and Operations ESMAP is governed by a Consultative Group (the ESMAP CG) composed of representatives of the World Bank, other donors, and development experts from regions that benefit from ESMAP assistance. The ESMAP CG is chaired by a World Bank Vice President and advised by a Technical Advisory Group of independent energy experts that reviews the Program's strategic agenda, work plan, and achievements. ESMAP relies on a cadre of engineers, energy planners, and economists from the World Bank, and from the energy and development community at large, to conduct its activities. Funding ESMAP is a knowledge partnership supported by the World Bank and official donors from Australia, Austria, Denmark, France, Germany, Iceland, the Netherlands, Norway, Sweden, the United Kingdom, and the U.N. Foundation. ESMAP has also enjoyed the support of private donors as well as in-kind support from a number of partners in the energy and development community. Further Information For further information, a copy of the ESMAP annual report, or copies of project reports, please visit the ESMAP Web site, www.esmap.org. ESMAP can also be reached by email at esmap@worldbank.org or by mail at: ESMAP c/o Energy, Transport and Water Department The World Bank Group 1818 H Street, NW Washington, DC 20433, USA Tel.: 202-458-2321; Fax: 202-522-3018 ENERGY SECURITY Energy security is of critical importance to developing countries. Reliable, affordable energy is a key ingredient to economic growth and poverty alleviation. Sustained efforts must be made to address the increasing risks to energy security now seen around the world. Energy Sector Management Assistance Program A primary challenge is high fossil fuel prices. Importing 1818 H Street, NW countries are paying an increasing share of national Washington, DC 20433 USA Tel: 202-458-2321 incomes to satisfy domestic demand, with often grave Fax: 202-522-3018 consequences for economies and government budgets. Internet: www.esmap.org It is the poorest countries and communities that suffer the Email: esmap@worldbank.org most from high fossil fuel prices. In addition, existing energy supply infrastructure is all too often insufficient to meet growing demand. Without this physical infrastructure in place, adequate and reliable electricity and other energy supplies will not be consistently delivered. Numerous ESMAP projects explore ways in which client countries can best deal with these energy security risks. From novel approaches to dealing with high oil prices, to sharing lessons on successful regional integration, to creating the best institutional frameworks to foster needed investments, ESMAP is delivering concrete policy options to client country governments to bolster their energy security as a key tool to achieving sustainable economic growth.