-e'I ANCE :--: ; and Roal C. .Duncan editor- s * ~ ~ ~ g b . * . .* . .. .. . . .~~~1 ' . . .W . . . . ~~~~ ~ ~~~~~~~ . .. .'. Wo Bank blication . . . Commodity Risk Management and Finance Commodity Risk Management and Finance Theophilos Priovolos and Ronald C. Duncan, Editors Published for the World Bank Oxford University Press OXFORD NEW YORK TORONTO DELHI BOMBAY CALCUTTA MADRAS KARACHI PETALING JAYA SINGAPORE HONG KONG TOKYO NAIROBI DAR ES SALAAM CAPE TOWN M.1ELBOURNE AUCKLAND and associated companies in BERLIN IBADAN © 1991 The International Bank for Reconstruction and Development / The World Bank 1818 H Street, N.W., Washington, D.C. 20433. U.S.A. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the priot permission of Oxford University Press. Manufactured in the United States of America First printing June 1991 The text of this book is printed on paper containing S0 percent virgin pulp, 45 percent recycled preconsumer waste, and S percent recycled and deinked postconsumer waste. The findings, interpretations, and conclusions expressed in this study are the results of research done by the World Bank, but they are those of the authors and do not necessarily represent the views and policies of the World Bank or its Board of Executive Directors or the countries they represent. The World Bank does not guarantee the accuracy of the data included in this publication and accepts no responsibility whatsoever for any consequences of their use. Library of Congress Cataloging-in-Publication Data Commodity risk management and finance / edited by Theophilos Priovolos and Ronald C. Duncan. p- cm. "Published for the World Bank." Includes bibliographical references and index. ISBN 0-19-520867-6 1. Commodity-backed bonds. 2. Debts. External-Developing countries. 1. Priovolos, Theophilos. 11. Duncan, Ronald C., 1936-. Ill. International Bank for Reconstruction and Development. HG4651.C694 1991 90-25115 332.63'23-dc2O CIP Foreword As has been made painfully obvious during the 1980s, the developing countries face great difficulties in raising external finance and in servicing their external debts, due in large part to the sharp fluctuat ons in the prices received for their primary commodity exports. Their terms of trade are also very susceptible to import price shocks, especially from the most important primary commodity import for most of them-petroleum. In turn, the terms-of-trade shocks from primary commodity price fluctua- tions are a major problem for the management of firms and, probably most important, for the macroeconomic management of the developing countries themselves. It is probably fair to say that the effort that has had to be devoted to macro management of these economies in the wake of such shocks has detracted seriously from the effort that would have othervise been given to getting on with the process of development. As the chapters in this volume showv, there are now commodity price-related financial instruments that can be used to manage the volatility in export earnings and import payments and -o shift the risks from the developing countries to those more capable of bearing them in world markets. As a result, revenue and expenditure streams can be made more stable, debt servicing can be made more reliable, creditworthiness can be improved, and macroeconomic management can be made less onerous. The use of commodity price-related instruments for hedging commod- ity price risks and for raising finance has expanded :apidly in recent years in industrial countries. Their use has been minimal in developing countries, however, in part because they are new, but also because of the lack of understanding by the countries of their risk exposure and lack of knowledge about private market-based risk management practices. This lack of knowledge presents an opportunity for the World Bank Group to v Vi CONMMODITN- RISK MANAGEMENT AND FINANCE provide tec.< X .%.' assistance to developing countries. A unit has been formed in 1, .,national Economics Departmenlt to undertake such technical asska.,:.e to make developing countries, institutions, and enterprises that fare substantial commodity price risk more aware of commodity pric;-related instruments; to help them obtain training and experience in the use of the various risk management instruments available; and to hielp them to develop appropriate strategies for com- modity risk management. Technical assistance of this nature is presently being undertaken in several countries. D. C. Rao Director, International Economics Department The World Bank Con ten ts Contributors x Acknowledgments xi 1. Introduction 1 Th)eophilos Priovolos and Ronald C. Duncan Part I. The Pricing of Commodity-Linked Securities 2. Experience with Commodity-Linked Issues 11 Theeophilos Priovolos Introduction I 1 Gold-Linked Financing 14 Silver-Linked Financing 30 Crude-Oil-Linked Financing 31 Other Commodity-Linked Issues 37 Notes 38 3. The Demand for Commodity Bon;' 39 Moctar A. Fall The One-Consumption Good Case 39 The Determinants of the Demand for Commodity Bonds 48 The Mulngood Case 51 4. A Review of Methuds for Pricing Commodity-Linked Securities 56 Tbeophilos Priovolos Case 1: Uncertain Commodity Price 58 Case 2: Default Risk 58 Case 3: Interest Rate Risk 58 Notes 60 iii viii CONTENTS 5. Pricing Commodity Bonds Using Binomial Option Pricing 61 Ragburatn Rajan The Model 62 Parameter Determination 67 Extensionis 70 Comparative Analysis of Binomial Model and Schwarrz Model Results 70 Conclusion 78 AppendixS -1. The Continuous-Time M,del 79 Appendix 5-2. Proof That the Distribution of the Binomial Model Tends to thc Bivariate Normal Distribution 79 Notes 81 Part 1I. Commodity Contingency in the Internal Lending of Developing Countries 6. Optimal External Debt Management with Commodity-Linked Bonds 85 Robert J. M)ers and Stanley R. Thomipson A lklodel of Optimal External Debt Allocation 86 Estimation 89 The Case of Costa Rica 90 Concluding Comments 93 Notes 94 7. Integrating Commodity and Exchange Rate Risk Management: Implications for External Debt Management 95 Stijn Claessens Issues in joint Commodiry and Exchange Risk Management 97 An Analytical Model for Commodity Risk and Exchange Rate Management 103 Empirical Applications in Indonesia and Turkey 106 Conclusion 110 Notes 111 8. Hedging with Commodity-Linked Bonds under Price Risk and Capital Constraints 115 Richard J. Ball and Robert J. Myers Hedging with Commodity-Linked Bonds When Producers Are Capital-Constrained 116 Hedging with Commodity-Linked Bonds and Conventional Loans 121 Conclusion 123 CONTENTS i. 9. Financial Instruments for Consumption Smoothing by Commodity-Dependent Exporters 124 Brian Wriobt and David Newvberv Sovereign Borrowing and Default Prevention 125 The Costs of Income Variability 125 Consumption Smoothing by Bcrrowing and Lending 126 Commodity Bonds issued by 'over,'ign Leniders 127 Optimal Dynamic Smoothing Strategies 128 Conclusion 131 Notes 132 10. Securitizing Development Finance: The Rolc of Partial G'iarantees and Commodity Contingencv 134 Ronald Andersoni, Christopher Gilbert, Und AIUrei.v ozvell Sovereign Risk 136 Securitization 140 Securitizing Developing Country Obligations 142 The Design of Commodity-Contingent Instrtiments and Associated Guarantees 145 Conclusion 149 Notes 151 11. Conclusion 152 Theophilos Priovolos and Ronald C. Duncan Bibliography 157 Inrdex 169 Con tributors Ronald Anderson, Department des Sciciices Economiques, Universite Catholique de Louvain, Belgium Richard J. Ball, Department of Agricultural and Research Economics, University of California, Berkeley Stijn Claessens, Debt and International Finance Division, World Bank Ronald C. Duncan, International Trade Division, World Bank Moctar A. Fall, Capital Markets Group, Salomon Brothers Inc., New York Cb-;stopher Gilbert, Department of Economics, Queenl Mary and Westfield College, London Robert ,. Myers, Department of Agricultural Economics, Michiga4n State University, East Lansing David Newbery, Department of Applied Economics, University of Cambridge Andrew Powell, Department of Economics, Queen Mary and Westfield College, London Theophilos Priovolos, Elf Trading S.A., Ger.zva Raghuram Rajan, Sloane School of Management, Massachusetts Institute of Technology, Boston Stanley R. Thompson, Department of Agricultural Economics, Michigan State University, East Lansing Brian Wright, Department of tgricultural and Research Economics, University of California, Berkeley Acknowledgmen ts We owe a substantial debt to the colleague., who have contributed their papers to this volume. Special thanks also go to Don Lessard and Todd Petzel who commented on several of the papers in the book and to the three anonymous reviewers of the Editorial Committee of the World Bank. We also thank the copyright owners of reproduced articles in the boo.s who gave permission to reprint the articles and the American Economic Association and American Agricultural Economics Associa- tion for allowing us to present several of these articles at their December 1988 Conference in New Yo; E.K We are grateful for the financial support of the World Bank and, in particular, of its R.search Committee. We acknowledge with many thanks the encouragement and support of Stanley Fischer, chief economist of the World Bank xvhen this volume was written, for the risk management work in the International Com- modity Markets Division. We have also benefited from the comments and suggestions of a number of others in the World Bank Group, including Jean Baneth, David Bock, Kemal Dervis, Ishac Diwan, Enrique Domenge, Robert Graffam, Ishrat Husain, Ronald Johannes, Peter Jones, Ruben Lamdany, Charles Larkum, Johannes Linn, Carl Ludvik, Herbert Morais, Barbara Opper, Sanjivi Rajasingham, Lcster Seigel, Andrew Steer, John Taylor, Anthony Toft, John Underw;ood, Frank Vita, Dimitri Vittas, and all our colleagnes in the International Commodity Markets Division. In addi- tion, we would like to thank Gerry Pollio of Chemical Bank; Gaylen Byker and John Grobstein of Paribas; Tony Singleton and Sykes Wilford of Ch. e Manhattan Bank; Neil-Thalheim of Bankers Trust; Srini Vasan of First Boston; Ian Giddy and Frank Ocwieja of Drexel; Viktor Filatov of Morgan Guaranty; Bob Hormatz, John Goldberg, Mike Schwerin, and Tom Demeure of Goldman Sachs and J. Aron; John Rinaldi, Heinz xi Introduction Tbeophibos Priovolos and Roniald C. Duincanz Developing countries are expos i to major financial risks and, in particular, to commodity price risks. Their exposure to these risks and their limited ability to deal with the risks effectively was obvious in the 1980s, when sustained declines in commodity prices and sharp increases in interest rates were followed by increases in indebtedness and debt- servicing difficulties. One form of financing that has expanded greatly in the financial markets of industrial countries in the second half of the 1980s and that appears to offer considerable potential for risk management in develop- ing countries is commodity-linked financing. This book brings together a series of papers that examines the various uses of commodity-linked financing by entities in industrial countries and analyzes the merits of their use in developing countnres. The exposure of developing countries to instability in commodity prices is illustrated in table 1-1 by their dependence on commodity exports. This dependence is the highest in Africa, Oceania, and Latin America, while less so in Asia and southern Europe. The share of commodity exports accounts for 42 percent of developing country exports, but only 25 percent of industrial country exports. The exchange rate and interest rate exposure of developing countries is illustrated in figure 1-1, with information on the debt composition of developing cotiuitries. Most public and publicly guaranteed debt is still in U.S. doilars, although increasingly less so since 1982. The shares of U.K. pound, Japanese yen and German deutsche mark (DM) public and publicly guaranteed debt are increasing. These four currencies account for almost all borrowing by developing countries. The noted shift in the past 10 years toward borrowing at variable interest rates underlines the dependence of developing countries on interest rates in the United States, I COMMODITY RISK MANAGEMENT AND FINANCE Table 1-1 Share of Exports of 33 Primary Cotmmnodities fhom Developing Countries by Region, 1982-S4 Average (number of countries) Share of exports (percent) Region 0-25 25-30 5S-75 7S-1 00 Total Latin America 3 10 t1 3 27 Africa 6 13 10 14 43 Asia 8 5 3 3 19 Oceania 0 1 2 1 4 Southern Europe S 0 0 0 5 Total 22 29 26 21 98 Source: World Bank, 1988a. United Kingdom, Japan, and Germany. The followving two examples illustrate the difficulties that many developing countries faced in the 1980s in n:anaging tneir commodity exposure. Coffee, bananas, and beef account for 50 percent of total Costa Rican exports. This country was hit by a series of severe trade shocks from 1978 to 1982. These shocks resulted from falling prices in its major export commodities. The initial response appears to have been to treat the downturn in export earnings as temporary and borrow externally to maintain domestic consumption and investment levels. With the onset of the debt crisis in 1981, however, this strategy was no longer sustainable. The ensuing restrictions on new external borrowing precipitated a disastrous economic slump that began around 1981 and continued to 1983. Costa Rica has become a highly indebted country; at present, its growth potential is handicapped by its debt-servicing requirements. The secondary market for Costa Rican debt, which trades at a large discount, reflects the market's perception of Costa Rica's ability to service its debt. To ensure that the country does not return to a debt-burdened situation will require a debt reduction scheme, such as the Brady Plan, accompa- nied by good macroeconomic management and the implementation of hedging programs. In Algeria, there was a substantial trade shock in 1986 with the decline in oil prices. Algeria's hydrocarbon exports account for some 90 percent of total exports. In this case too, the country tried to stabilize its consumption path by borrowing from abroad. In contrast to the Costa Rican situation, the Algerian economy (despite reaching a higher level of indebtedness than in the past) has been able to absorb the impact of the shock to its terms of trade. Nevertheless, the oil shock has alerted the authorities to the vulnerability of the economy to the variability of INTRO DUCT I(ON hydrocarbon prices and to the need to hedge the doxvnside exposurc of the economy to reduce the chances of a future deterioration in growth. Although for some developing coUntries (in particular, those that are highly indebted) the first priority is to reduce their indebtediness, almost all net . to maintain sound macroeconlomic policies-including imple- mentation of effective risk managcment progr"ms. There are, in fact, maniy commodity risk managemenit instruLmileits available to developing coulitries. They can be categorized into three groups: self-insurance instruments, third party insurance instrumeints, and other instrumenits. The first group includes instruLImenlts such as reserve management schemes, domestic stabilization scilcimCes, macroeconomnic policies, and Figure 1-1 Curre'icy Composition of Public and Publicly Guaranteed Deveilping Country Debt (billiors of U.S. dollars) 475.3 548.9 593.1 690.7 800.1 905.2 Percent 10 - - - - - --; 90 80 70 . N~~N 50 -!!-~ 40 - 30 - - ' 20 1982 1983 1984 1985 1986 1987 F1 Other ED French francs E Deutsche marks El Yen EJ LSTG W U.S. dollars Source: World Bank (1988). 4 COIMMODITY RISK MANAGEMENT AND FINANCE diversification programs. The second group includes financial market instrLuments such as futures, forwards, options, swaps, and long-term contracts. among others. The third group includes all other schemes such as international commodity agreements and compensatory financing schiemes, including th'e STABE,-VS'S33AiN schemes Cof the LLCurp UUU C.11 om_UiUcI Community (EEC), for example. One instrument that combines risk inanagement with finance, wvhose use has greatly expanded in the late 1980s, is commodity-linked fi- nancing. This financial market instrument (belonging to the second group of risk management instruments) can help industrial and developing countri2s alike raise funds, while linking revenues xvith expenses and assets with liabilities. Commodity-linked financing is a hybrid instru- ment: It Is a risk mnanagement instrument as well as a financing instrument. As commodity-linked financings extend beyond one year, their risk mannaement nronerties are of strategic imnPortance to the commodity price exposures of the organizations involved. Commodity- linked financing conies in many forms, such as commllnodity bonds, commodity loans, and others. The chapters in Part I cover the issue of the pricing of commodity- linked securities. Chapter 2 reviews the different forms of commodity- linked financing. A conventional bond makes semiannual coupon pay- ments, determ.ined by a coupon rate, and pays out the principal amount at maturity. The nominal return to the investor is known, but, with the uncertainty of the infiation rate over time, tne reai return is uncertain. With commodity bonds, investors have sought to link their investment to real assets. Commodity bonds exist in two different forms: those of a forward tVDe. often called convertible or indexed bonds. and those of the option or warrant type. In commodity bonds of the forward type, the coupon andlor principa -a...t -r link.d --- z ttdqatt f - I.AJjJUI UILl!vL P) Il.lj)dIFI F4Y III%lLa atLL ILLINL%U t'.i1 a Lat..4 -..jUaIILJLY iJl aX commodity. A commodity bond of the option type makes normal coupon payments (just as conventional bonds do), but, upon maturity, the holder of these bonds has, in addition to the principal, the ..ption to buy or sell a predetermined quantity of the commodity at a predetermined price. Because of rhe inherent value of such an option- the counon navments of this bond are lower than they would be in a conventional bond. U L0 LIC1NE 1libLLU1IICILb VZ ULILN& dL' leasL ,,LUY. LiIIL1a Use of theeisuet sbc a; les;a centuy iThr I h'as b..en a recent awakening of interest in commodity-linked bonds, however, building in late 1986 and 1987. Several dozens of commodity bonds (most linked to gold, silver, and oil) have been issued, at an approximate value of US$3 billion-4 billion. Most have been issued in the Euromar- ketc hernicle of i,ncPrtiintv bnout the I.S1. reoildatorv environment Since the October 1987 stock market crash, however, the retreat of institu- INTrRODUCT ION S tional investors from the Euromarkets has led to a reduction in the vnliime of rnmmondity-!inkied bondscl isiised in thorse mirkets. The decline of commodity bond issues has been compensated by a draml atic increase in the numuer and volume of commodity loans and private commodity bond and note placements. Because commodity loans and private placements are less transparent, the volume of commodity- linked financing is unknown. Commercial banks estimate the volume to be in excess of US$4 billion per annum. T)p demand for com,mnA-t, bonds cones frm. Crispecators aInA hedgers. Chapter 3 discusses a theoretical model of the demand for commodity bonds. This is an extension of the work done by O'Hara (1984). O'Hara showed that if commodity bonds are priced fairly, they will be demanded only if there is a minimum necessary consumption quantity or the bond's payoff negatively correlates with the individual's portfolio return. The bond is valuable because it provides a form of insuanc in___ hegig i!_ s f future cons;.mption. In chap--, Fall1 1113UI,2iiL_% fit IILUr,1li5 L13r3 UL L LIU . i U IZk)LiJ1i. III ~II."FL%~& -J, L UII shows that the demand function for commodity bonds has two compo- nents, a speculative component and a hedging component, and tnat the demand for commodity bonds is positive when the investor has a lowver relative modified risk tolerance than the market (i.e., a higher relative modified tisk aversion). In part 1, different approaches to pricing commodity bonds are discusse.d4 i- chapters 4 aznd 5. A review of tlhe Q, uij (A1982)metho is presented by Priovolos in chapter 4. The Schwartz model considers the impact on bond pricing of commodity risk, default risk, and interest rate risk. In chapter 5, Rajan bypasses the mathematical complications of the Schwartz model when default risk is introduced by the use of binomial pricing theory. Neither of these chapters considers sovereign risk. however. The introduction of such risk is particularly important for developing countries, and it is discussed in the last chapter of part 11. There are five chapters in part II. The issues addressed in this section provide insights on three levels: those that apply to commodity-iinked finance whether or not the borrower is a sovereign with the related limitations of contract enforceability, those that apply to a sovereign with a clean financial slate, and those that apply to sov-ereign borrowing in the presence of an exisdng debt overhang. The chapter by Myers and Thompson focuses on the first level computing commodity hedge ratios for a country facing variance in commodity output, as well as in the price of its commodity exports. They derive the optimal conditions tor the use of commodity bonds of the for-ward type in a hedge of the external debt requirements of a hypothetical commodity-dependent country. In chap- tfr 7, Claessens introduces exchange rate risk, in addition to commodity price risk, in hedging external debt requirements. 6 COMMODITY RISK MN1ANAGEMENT AND FINANCE The next two chapters by Ball and Myers and WVright and Newbery make important contributions at the first two levels. In chapter 8, Bali and Myers extend the analysis by Thompson and Myers to a sovereign with a clean financial slate. In chapter 9, Wright and Newbery, without reference to the limits of enforceability, quantify the magnitude and welfare costs of export revenue variance for counltries characterized by concentrated exports. They also analyze and quantify the relative per- formance of reserve management versus commodity hedging in reducing fluctuations in the foreign income of such countries. Estimates of the cost of price variability and the potential benefits from risk reduction as a result of employing these two mechanisms clearly demonstrate the importzance of risk management. Wright and Newbery also show, within the context of sovereign borrowinig, the way in which alternative types of commodity-linked contracts affect the probability of default and, hence, access to external finance in an idealized rational world. In chapter 10, Anderson, Gilbert, and Powell begini with the problem of sovereign borrowing and the comparative advantage of lenders in bearing particular forms of risk. They find that the required insurance premiums for guaranteeing sovereign risk are minimized when the insuring body has a comparative advantage in bearing sovereign risk and when the contractual terms of any new financing are contingent on factors affecting the borrower's present and future earnings. They show that assets that are contingent on commodity prices may be the most suitable form of obligation; for many developing countries. Commodity bonds and loans, long-term commodity options, forwards, and swaps have proliferated in the developed countries in the past few years. The liquidity of these commodity-risk management instruments, although still not comparable to that of similar foreign exchange or interest rate instruments, is growing at a very fast pace. Why is it then that developing countries do not hedge their commodiry exposure wvith these financial instruments? In part, it is because developing country organizations (with the exception of some multinational organizations) do not have the knowledge or the institutional basis to hedge their short-term operational and long-term strategic commodity exposure. Moreover, the hedging cost for developing countries is substantially higher than that of indus- trial countries. This is due to the perceived sovereign risk of developing countries. While chapters 6 and 7 address the issue of how much of one's exposure to hedge, chapters 8-10 explore the reasons commodity-linked finance is important for program and project finance in developing countries. Here it is shown that the two parts of commodity finance-risk management and finance-can be structured in such a way that they maximize the welfare (however defined) of an organization. Further- INTRO DUC-r ON 7 more, in chapter 10, it is show n that within a debt .structuring framework, where negative pledge clauses could be waived, the sovereign risk assumed by a commercial bank with a properly structured commod- ity-linked bond or loan is much less than with a conventional bond or loan. In other wvords, the capital of a bank can be better used xvhen its clients commit to hedge their commodity exposure xvith properly struc- tured commodity loans. In turn, the bank would '.ave to hedge its commodity price exposure in the financial markets, here it is presumed to do so at a lesser cost than its clients. The final chapter summarizes the findings in this volumlle and addresses the costs and benefits of commodity-contingent financinig instruments, from the viewvpoint of both the issuer and the investor. Finally, the possible role of international development agencies in this area of development finance is disCussed. c ') (m i n sL, (t ,)1 Z I0 m0 zr .io r* M Experience w"th Commodity-Linked Issues Theophilos Priovolos In response to the appetite of investors eager to participate in the possible upswing of long-underperforming commodities and in response to the risk management needs of primary commodity producers-in particular, precious metal producers-commodity-linked securities proliferated in the late 1980s. Securities linked to the prices of silver, gold, and oil wvere particularly popular wvith investors. Almost all conmmodity-linked financ- ings were issued by corporations and governments in the developed world. In developing countries, however, very few offerings occurred. This chapter reviews recent experiences with commodity-linked issues. Introduction These kinds of bond issues are by no means a novelty. The first known commodity bond, which is the most common form of commodity-linked financing, was issued by the Confederate States of America in 1863 (see Fall, 1986). The Cont'ederates were fighting a costly war against the United States of America; their principal asset was cotton and, for that reason, they decided to issue a bond 'whose payoff would be linked to the price of cotton. Commodity bonds may also be linked to conimodities other than the traditional primary ones. In 1945, for example, the French government's Caisse Nationale d'Energie issued a bond indexed on the price of electricity to pay for the nationalization of utilities. Investors were paid a 3 percent coupon and additional income from a fund that comprised 10 percent of the gross utilir-- revenues in France. As stated earlier, commodity bonds ,ay be of two kinds: forward (often called commodity-indexed or conv,ertible bonds) and option (often called commodity warrant bonds). For example, a conventional 12 COMMODITY RISK MANAGEMENTr AND FINANCE US$1,000 10 percent coupon bond would make annual payments of USS5100, while a similar oil bond of a forward type would, for instance, make coupon payments equal to the current monetary valuc of 5 barrels of Brendt oil. The payoffs to these bonds reveal that they are similar to a conventional bond and a set of forward contracts. Each coupon payment is analogous to a forward contract; howcver, there is one major difference. In a forward contract, the agreement is that the monetary settlement will take place at maturity. In a commodity bond, the investor who holds the long side has already fulfilled his obligation by buying the bond. Forwvard contracts are negotiated betwcen two parties and are not always easily traded. In a commodity bond of the option type, one or several call or put options are attached to the coupon or princ.pal paymients. In this case, the investor receives the US$1,000 face value and, in addition, has the option of buying or selling a predetermined quantity of oil at a predetermined price. Because these bonds include an option feature that has a market value, the coupon rate is generally lower than it wvould have been for a conventional bond. Thus, the advantage to the issuer of ti. optionl type is loNver interest payments, with a tradeoff of sharing an appreciation in the price of the commodity by wvriting a call option on the commodity. Issuers of commodity bonds are typically governments or corporations that have ready access to the underlying commodity and that seek a better hedge of their liabilities with their assets. The advantage to the investor is the ability to take a liquid and divisible position in a commodity, thus benefiting from a price hike (or fall) yet receiving a guaranteed minimum return on the investlilent (through the fixed coupon payments). Commodity bonds of both the option and forward type allow the holder to take a iong-term commodity position. Thus, it would seem that commoditv bonds would be popular with investors and issuers when commodity prices are expected to change significantly in either direction. The proliferation of commodity bonds linked to precious metals (gold and silver) and to oil in recent years can be attributed to their image as an inflation hedge, their storability, and the natural position of several commercial banks in these markets. Uncertainty as to which U.S. agency-the Comnodity Futures Trading Commission (cFrc) or the Securities and Exchange Commission (SEC)-should regulate these issues has caused most of the commodity-linked financings to take place in the Euromarkets. Since the October 1987 crash, Euromarket activity has subsided. At present, most commodity-linked financings are placed in the private markets. Australian and Canadian Lflnks have become very active in these markets because of the im-)ortance of commodities to the Australian and Canadian economie-. Data on pxivate placements are EXPERIENCE WITH COMMNODITY-LINKED 'SSUES 13 scarce, but recent reports indicate that commodity-linked financings amount on an average of USS0.3 billion monthly.' It is noteworthy that commodity-linked financing has taken forms other than those of the forward or option-type bonds. Some of these forms include those listed below. Commodity- Indexed Certificates ot Deposit A banik-issued certificate of deposit (CD) typically pays interest to a depositor based on a percentage of the rise or decline in the price of a commodity or the value of an index during a specified period of time. The matutity, denomination, and manner in which interest is calculated on ant indexed CD can vary substantially, and these differences reflect the disparate needs of savers In the United States, regulatory problems caused the abortion of gold CD issues by banks oni the East and West Coasts in 1987. (See, for example, the Wells Fargo CD offering of Septeuiber 1987.) In other countries, however, and, in particular, in Hong Kong, bear .^nd bull gold CDs are available. (See, for example, the Banque Indosuez issue of February 1988.) Commodity Variable-Rate Loans A commodity variable-rate loan is made at an irterest rate that is indexed to or correlates with an accepted benchmark of current market rates. The borrower's interest payments are adjusted at specified dates to reflect subsequent interest rate fluctuations. Such loans may have mini- mum or maximum rates set at the time of origination. Variable interest payments may be indexed to the value of a commodity produced by a borrower (see bullion loans below). Gold Repos Gold repos refers to an entity wvith excess gold that borrowvs cash from a bank for a specified period. Gold is used as collateral for the loan and is later repurclased by the b. rrower at a margin above a specified interest rate, but less than the cost of carrying gold during the relevant period. Thus, an entity with excess gold is able to meet a short-term funding requirement, and the bank makes a fully collateralized short-term loan at a rate higher than the market interest rate. Bullion Loans A bank may extend financing to a mining co:;.pany indexed to bullion orices. The producer can use this comparatively low-cost financing to meet it, working capit.i needs and deliver bullion (or thc cash value thereof) to satisfy the loan repayment obligation. 14 COMMODI-rY RIsK MANAGEMENT AND FINANCE Swvaps Swaps are privately negotiated transactions in which two parties, directly or through an intermediary bank, agree to exchanige a series of payments calculated on different bases: fixed-rate interest payments for floating-rate payments, one type of floatinig-rate paymcut for another type of floating-rate payment, dollar-denominated payments for nondol- lar-denominated payments, fixed for floating comnmodity price payments, or payments tied to the price of one index for payments tied to the price of another. An exchange is arranged between tw%o counterpaf:ics with comp;ementary needs, and the payments due on the spe^ified dates are netted. Swap transactions have been structured in innumerable forms and variations.3 Caps, Floors, and Collars Caps and floors on commodity prices or other financial instruinents are similar to swap transactions, except that the commodity price is fixed at a maximum (cap) or a minimum (floor). The seller of a cap agrees to pay the buyer the price differential bet-ween t!Ac capped and a floating price, with respect to a specified notionml amount, in exchange for the payment of a fee. The seller of a floor agrees to pay the buyer the price differential between the floor and the floating price, with respect to a specified notional amount, in exchange for the payment of a fee. A collar is a transaction in which the purchaser of a cap simultancously sells a floor to the seller of the cap, thereby deftaying the cost of the cap. Swaps, caps, floors, and collars are not financing instruments per se. Their hedging properties, however, have made zheir use increasingly important in commodity financing. As previously noted, in 1988, com- modity financing relied more heavily on the types of financial instruments described above than on the more traditional Eu':obond types. The following sections discuss particular experiences w ith gold, silver, oil, and other commodity-specific issues. Gold-Linked Financing Gold-linked financing has been ihe most widespread among forms of commodity-linked financing. The forward (or indexed) type and the option (or warrant) type have been the most typical forms of gold-linked financing. One of the best-known cases of gold bonds was that of the Giscard bond. In 1973, the French government appealed to investors with a gold-indexed bond issue. The "Giscard," as this bond is com- monly referred to-named after the then-French finance minister (and Table 2-1 Gold Warraid Issues, 1986-88 Implied Strike All-in volunir pre- pre- Issue at ir ue mWin' iniu?? Coverage Issue ;;ead Exercise pnrce 1're,niumt (per- (per- (per- ratio Spot date managerJ) Host bun I Warrant atid period issue level cent) cent) cent) (percent) US$1OZ 9/12/86 American - 4 n; Wrts eacih US$9.:'0/0.02 oz USSI.50/0.02 oz 15 7 24 - 430 Barrick to buy 0.02 oz (US$4iO/oz) (US$75/oz) Resources gold 4 ycars (Merrill . (9/12/86- Lynch 9/25/90) Canada) 9/27!86 Echo Bay Sfr 110 m To each bond US$560 Sfr 542/Nrr 15 30) 42 86 431 Mines due 10/29/96 of Sfr 5,000 is 1 5 years approx. (Sfr 90 3/8/oz) Ltd. ci'.s: J.875% Wrt, exercisable (11/30/86- (US$54/oz) (Credit Host bond into 6 oz of/or 9/30/91) (US$90.73/oz) Suisse) and Wrt dollar equivalent (Spot FX = iSSu'd at 1()( of gold sfr 1.6595/US$) 10/11/86 Standard Sfr ISO In To each bond USS565 ZO) Sfr 500/Wrt 28 30 50 48 435 Oil Co. due 11/6/93 of Sfr S,000 is 4 years (SIr 151!5/oz) (Morgan %7I'N: 3.125'Xt attached 1 Wrn, (11/6/87.. (US$90.73/oz) Guaranty) I-lost bond cntitrlitig the 11/6/91) (Spot l:X = and W!t holder to Sfr 1.67/USS) issued at purchase 3.3 oz 100 of gold or receive thie difference between spot price of goJd ard exercise price (1Jii,le ccntin*,es on the fullouving page.) Table 2-1 (continued) Implied Strike All-in volume pre- pre- Issue at issue miuma miumb Coverage Issue (lead Exercise price Premium (per- (per- (per- ratio Spot date manager) Host bond Warrant and period issue level cent) cent) cent) (percent) US$Ioz 2/25/87 Credit Sfr 200 m To each bcnd US$565.20 Sfr 500/Wrt 42 15 40.3 50.2 407 Suisse due 2/20/97 of Sfr 4,000 are (USS467.98 oz) (Sfr 162/oz) (Credit CPN: 2.875% attached 10 3 years (US$10S.3/oz) Suisse, Host bond Wrts, allowing (3/20/87- (Spot FX = Zurich) and Wrr together the 3/20/90) Sfrl.5385/USS) issued at purchase of 100 I OOg oi finc gold (I e = 31.1035g) 3!3/87 Citibank - 10,000 Wrts US$430/oz Sfr 1,050/Wrt 25 6½/2 23.5 - 403 (Citibank exercisable into 2 years (Sfr 105/oz) NA, 10 oz of fine (4/16/87- (US568.2/oz) Zurich) gold or equiv. 4/16/89) (Spot FX = cash amount Sfrl.5395/USS) 3/5/87 Financiere Sfr 100 m To each bond Sfr 2.335/lOOg .ir 540/10 Wrt 40 13 43 41 412 Credit due 3/30/97 of Sfr 5,000 are (US$465.7/oz) (Sfr 167.95/oz) Suisse CPN: 3.25% attached 10 3 years (US$107.7/oz) First Host bond Wrts, allowing (3/30/87- (Spot FX = Boston and Wrt purchase of 3/30/90) Sfrl.56/US$) (Credit issued at lOOg of fin.c Suisse) 100 gold (1 oz = 31.1035g) 3/5/87 Citibank - 10,000 Wrts, US5420/oz Sfr 9SI50[Wrt 24 2 18 - 412 (Citibank each exercisable 15 months (Sfr 95/oz) NA, into 10 oz of (4/22/87- (US$60.9/oz) Zurich) fine gold or 10/3/88) (Spot FX = equivalent cash Sfrl.56/USS) 3/6/87 Banque - 15,000 Wrts, US5410/oz Sfr 1.380/Wrt 29 0.Y61 21.7 - 406 Indosuez each entitling 2 years (Sfr 138/oz) (Goldman holder to buy (4/16/87- (Spot FX = Sachs) 10 oz gold 4/16/89) Sfr 1.55/USS) 3/18/87 Morgan - 12,000 Wrts, US$425/oz Sfr 995/Wrt 26.5 4.41 35 - 407 Guaranty each to bring 5 41/4 years (Sfr 191/oz) Trust oz of fine gold (4/30/87- (US5124.6/oz) (MG, AG, 7/31/91) (Spot FX = Switzer- Sfr 1.5335/USS) land) 3/25/87 Electricitc Sfr 100m To each notc of Sfr 2.350/lOOg Sfr 4.489/15 Wrr 45 15 44.4 28.6 418 de France due 4/20/95 Sfr 50,000 are (US!481/oz) (Sfr 186/oz) (Credit CP'N: 3.375%/o attached 15 gold 3 years (US$122.5,'oz) "uisse Host b-snd Wrts issued by (4/30/87- (Spot FX = Zurich) and Wrt Credit Suisse, 4/04/90) Sfrl.5195/USS) issued at each exercisable 100 into 50g of fine gold 4/9/87 Kingdom Sfr 100m To each note of Sfr 2,450/lOOg Sfr 3.666/15 Wrt 39 19 43 30.8 427 of due 4/20,194 Sfr 50,000 are (USS509/oz) (Sfr 152/oz) Belgium CPN: 3.375% attached 15 gold 3 ycars (USSIOI.5/oz) (Credit Host bond Wrts, each (4/30/87- (Spot FX = Suisse and Wrt exercisable into 4/20/90) Sfrl.4972/USS) Zurich) issued at 100 SOg of fine gold (Table continues on the following page.) Table 2-1 (continued) Implied Strike All-in volutne pre- pre- Issue at issue miuma miumb Coverage Issue (lead Exercise price Premium (per- (per- (per- ratio Spot date manager) Host bond Warrant and period issue level cent) cent) cent) (percent) US$/oz 4/14/87 Citibank - 20,000 Wrts US$440/oz Sfr 610/Wrt 25 - 18.5 - 444 NA each to bring 5 21 months (Sfr 122/oz) (Citicorp) oz of fine gold (5/4/87-214/89) (US$82/oz) (Spot FX = Sfr 1.4878/USS) 4/15/87 Saint- ECu 75m To each bond US$490/oz US$135[Wrt 39.5 10 41 49.5 444 Gobain due 5/6/92 of ECU 1,000 is 3 years (Spot FX = (Salomon CPN: 4.50% attached a gold (5/6/87-516190) US$1. 1154/Ecu) Bros.) Host bond Wrt, exercisable and Wrt into 1 oz of fine issucd at gold 100 4/15/87 BNP USSlOOm To each bond USS496/oz US$1SO/oz 45 12 45.5 44.4 444 (CSFB) due 5/13/92 of US$1,000 is 3 years CPN: zero attached 1 Wrt (5/13/87- Host bond to buy I oz of 4/16/90) and Wrt gold issued at 80 4/16/87 Hoffman Sfr 250m To each bond Sfr 2.510/lOOg Sfr 238.5/oz 52 21.7 55 42.2 429 La Roche due 9/30/90 of Sfr 5,000 \USS522.2/oz) (US$158.5/oz) (Credit CPN: zero are attached 31/2 years (Spot FX= Suisse) Host bond 10 Wrts, (5/15/87- Sfr 1.495/US$) and Wrt exercisable into 9/30/90) issued at lOOg of fine 80.5 gold 4/16/87 Kingdom Sfr SOm To each note Sfr 2.520/100g Sfr 472/ 34 16.7 38.5 32.4 449 of due 4/20/92 of Sfr 50,000 (US$524.3/oz) 3 lOOg = 147/oz Belgium CPN: 3% are attached IS years (US$98.3/oz) (Credit Host bond gold Wrts, each (4/20/87- (Spot FX = Su .j and Wrt exe;cisable into 4/20/90) Sfr 1.495/USS) issued at 50g 100 5/14/87 Aegon Sfr 100m To each bond US$500/oz US$113/oz 37 7.8 32 36.5 46A. (Citicorp) due 6/16/92 of Sfr 50,000 23 months CPN: 2.S% are attached 5 (6/17/87- Host bond Wrts, each 5/15/89) and Wrt exercisable into issued at S oz 100 5/20/87 Eastman US$ 130m To each bond US$470/oz US$1 18/oz 32 _ 25 47.06 470 Kodak & due 6/25/90 of US$5,000 are 23 months Co. CPN: 9% attached 5 Wrts, (6/25/87- (uBs) IP: 113.175 each exercisable 5/19/89) (cum Wrts) into I oz 101.375 (ex Wrts) 5/21/,7 Eksport- US$100m To each bond US$475/oz US$120/oz 32 _ 25 47.5 476 finans due 6/22/90 of US$5,000 are 23 months (UBS) CPN: 9% attached 5 Wrts, (6/23/87- r: 113.18 eachi exercisable 5/22/89) (cum Wrts) into I oz 101.18 (ex Wrts) (Table continues on the following page.) Table 2-1 (continued) Implied Strike All-in volume pre- pre- Issue :t issue mium' miumb Coverage Issue (lead Exercise price Premiuin fper- (per- (per- ratio Spot date manager) Host bond Warrant and period issue level cent) cent) cent) (percent) US$/oz 5/21/87 General SMr I 2ni To cach bond US$510/oz US$99/oz 38 8.1 29 37.23 472 Motors due 6/30/92 of Sfr 50,000 17 months Canada CPN: 2.750% arc attached S (Citicorp) Host bond Wrts, each and Wrt exercisable into issued at S oz 100 5/21/87 uBs Sfr 200m To cach bond Sfr 2.575/lOOg Sfr 495/10 Wrts 34 16 38 44.3 472 (UBS) due 6/15/97 of Sfr 5,000 are (Sfr 801/oz) (Sfr 154/oz) CPN: 31/4% attacihed 10 (US$548/oz) (US$10S/oz) Host bond Wrts, together 3 years (Spot FX = and Wrts exercisable into (6/15/87- 1.4600) issued at lOOg of fine 6/15/90) 100 gold 5/29/87 Chris- 'r 50m To each bond Call: strike = Call: USS83.2/oz Call: - Call: Call: 451.25 tiania due 7/8/94 of Sfr 5,000 are US$490 Put: US$46.1/oz 34 27 27.1 Bank CPN: 21/2% attached 3 call 18 months (until (Spot FX = Put: Put: Put: (Gutz- Host bond and 4 put Wrts 11/30/88) 1.4600 313/4 17 36.1 willer) and Wrts on difference Put: strike = Sfr/US$) issued at London fixing US$420 100 and strike per 1 3 years (unitil oz fine gold 5/31/90) 6/30/87 DNC Sfr 50m To each bond Call: strike = Call: US$83.2Voz Call: - Call: Call: 45: .10 (Gutz- due 6/20/94 of Sfr 5,000 are US$440 Put: US$41.7/oz 34 26 27.3 willer) CPN: 21/l% attached 3 call 18 months (Spot FX = Put: Put: Put: Host bond and 4 put Wrts Put: strike = 1.5010 Sfr/US$) 31½/2 19 36.4 and Wrts on difference US$410 issued at London fixing 3 years 100 and strike per 10 oz fine gold 7/25/87 Citibank - 10,000 naked US$420/oz Sfr 1.4901Wrt 32 - 13 - 457 NA gold warrants, (until (USS963.89IWrt) (Citicorp) each Wrt allows 10/11/88) (US$96.38/oz) the holder to (Spot FX = purchase 10 oz 1.5495 Sfr/US$) of fine gold 8/4/87 Rhone Sfr 100m To each bond US$475/oz Sfr 897.7/Wrr 41 - 29 61 475 Poulenc due 918195 of Sfr 5,000 is (9/11/87- (Sfr 213.7/oz) (Shearson CPN: 2% attached I Wrt, 5/22V89) ('JS$137.'/oz) Lehman) Host bond exercisable into (Spot FX = and Wrts 4.2 oz of gold 1.5523 .fr/USS) issued at (public issue) 100 8/6/87 Olivetti Sfr IOOm To each bond US$465/oz Sfr 988.3/Wrt 44 - 28.5 67 469 (uBs, SBC, due 9/21/96 of Sfr 5,000 is (until (Sfr 214.85/oz) Shearson CPN: 2% attached 1 Wrt, 5/22/89) (US$137.77/oz) Lehman) Host bond exercisable into (Spot FX = and Wrts 4.6 oz of gold 1.5595 Sfr/US$) issued at (public issue) 100 (Table continues on the following page.) Table 2-1 (continued) Implied Strike All-in voltf,ne pre- pre- Issue at issue ?nium' ?niurmn Coverage Issue (lead Exercise price Premium (per- (per- (per- ratio Spot date manager) Host bond Warrant and period issue level cent) cent) cent) (percent) US$/oz 8/11/87c SEK Sfr lOOm To cach bond IJS$460/oz Sfr 437.1/Wrt 29.5 - 23.4 42 463 (Warburg due Gf Sfr S,000 is 2 years (Sfr 174.9/oz) Soditic) 10/15/94 attached I Wrt, (US$111.34/oz) CPN: 23/s8/. exercisable into (Spot FX = Host bond 2.6 oz of gold 1.5705 Sfr/US5) and Wrts (public issue: issued at fees 17/8%) 100; 20% amortization yearly from 1990-94 FBDB C$50m To cach bond US$463.1S/oz CS140.79/Wrt 26.5 - 23.2 61 463 (Domin- due 11/4/91 of C$5,000 arc 2 years (US$106.98/oz) ion CPN: 101/4% attached S Wrts, (until 9/21/89) Securities) Host bond each one and Wrts exercisable into issued at 1 oz of gold 113½/2 (public issue) 9/23/87 ATT (UBS) US$100m To each bond US$463/oz IJS$120/oz 35 - 26.2 46 462 due of US$5,000 are 2 years 10/22/90 attached 5 Wrts, (10/22/87- CPN: 9¼/4% each one 9/21/89) Host bond exercisable into and Wrts 1 oz of gold issued at (public issue: 112-/4 fees 1 l/8%) - Not available. m = million. a. Defined as strike price/spot price. b. Defined as (exercise price + option premium)/spot price of goldc. The spot price of gold has to increase by this percentage from its current level for the investor to break even (i.e., recover the option premium). c. This deal was pullcd an(d replaced by a series of zero couponi traniches. Source: Goldman Sachs, London, February 1988. Table 2-2 Gold Indexed and Convertible Issues Issuer Issue (lead Amiount Issue Coupons Conversion Conversion date manager) (denoms) price (percent) Maturity details price Comments 1/16/73 French FFr 6.5 m 100 7 1/16/88 -- - R^demption and coupon govern- (FFr 1,000) are indexed to: ment (I) The price of 1 kg of gold in Paris on issue date, i.e., FFr 10.483 (2) The average price of I kg of gold for the 30 business days before January 1. Coupon (per bond) = (70/10,483) x (2) Redemption (per bond) = (1,000/10,483) x (2) 10/4/86 American US$50 m 100 5¼14 10/31/91 into gold fronm $530/oz Redemption price = Barrick 10/31/91 111V2½ Resources (Banque Paribas) 1/24/87 Barrick US$50 m 100 2 2/29/92 Into gold or US$ $406.94/oz -- Resources each equivalent guaran- with corn ersion teed by price reducing American by $16 per 1COg Barrick per year Resources cominencing (Banque 2/26/89 (i.e. Paribas) about $S/oz) Pegasus Sfr 60 m 100 5¾/4 10/10/96 (1) Into shares: (1) Into shares: Gold (Sfr 5,000) until 9/19/96 at Corp. (2) Into cash $9.607/share (Banque equivalent of at FX (Sfr Gutzwiller) gold during last 1.6S76/US$) tlhree years of corresponding maturity to 314 sharcs/ bond (Premiunm = 10.069%) (2) Into gold: to b .y 4.89 oz of fine godAbond at 5617.25/oz (Premium = 50'O) 9/19/86 Kingdom US$120 m 1001½ 3 10/20/93 Rccemption linked to of Two price of gold: Denmark tranchs s: Bull = Par x 1.158 (Societe Bull-$6(U m Price of gold at Generale) Bear-$60 m maturiry/ Price of gold at issue (M426.5/oz) Bear = Par x 2.78-1.158 Price of gold at maturity/Price of gold at issue ($426.5/oz) (Table continues on the following page.) Table 2-2 (continued) Issuer Issue (icad Amount Issue CopotJ Conversion CoJlversion; date tnanager) (denoins) price (percent) Maturity details price Comments 4/16/87 Interna- US$50,001,107 100 3'/s 5/12/92 (1) Convertible (1) Convertible tional of bonds into gold from into gold at Corona convertible into 5/15/88 to $16.91/g Resources gold witlh 5/15/92 (=$526.02/ (Banque attached gold (2) 1 Wrt is oz-20% Paribas) call warrants attached to each premium of bond-a 3-year spot) call on gold .'2) Call on gold at c 17.62/g (= S54 /.y4/ oz-25% premium of spot) 5/5/87 Hycroft US$12.152 m 105 5 5/28/92 (1) Conversion (1) Conversion (Banque mi,nimum to period: 12V1/87 price = $540/oz Gutzwiller) 17.361 m to maturity: (20% over maximum changeable for premium over l1Og gold spot gold) bullion or (2) For amount equal to current market value of I OOg gold bullion - Not available. m=million. Sou-ce: Goldman Sachs, London, February 1988. EXPERIENCE WITH COIIMMODITY-LINKED ISSUES 29 estimated, however, that since 1986, there have been loans totalilng approximately 7 million ounces, some 50 percent of which have becen arranged since October 1987. Gold loans arc used primarily to fuxid mine developments and expansion. Some loails, howeve., have been used to refinance corporate debt. The unresponsiveness of the equity markets to the hedging needs of the mining community and -the proliferation of know-how in the pricing of these loans have made them increasingly acceptable to the industry. The average length of gold loans has also increased in the past few years. T-his resulted from the needs of the mining industry. Capit.l1 costs increased with the exploi;z.tion of deeper or lower quality ores, anid some exogenous factors 'such as the introduction of income taxes for gold mining in Australia) affected the rate of return of the projects. The loan terms have lengthened, but they remain limited by th life of a borrower's ore reserves. The increasing size of loans has led to some dianges in lending and pricing practices. The practice of capping interest rates on gold loans has all but disappeared. Increasing competition and fluctu- ating borrowing costs have reduced lender's margins, making stable interest rates a matter of history. As the size of loans has increased, lenders have also begun to spread risks by syndicating loans to other lenders. The move away from single-!;.,der loans 1, moving gold lending toward a cost-plus-margin basis (analogous to currency lending). A variety of references are in use, including agent bank bare rate, lead bank gcoup reference race, ard tender panel and benchmark reference rate. A cu,F.x-reference borrowing rate is determined by Lubtracting a futures market contago from -a relevant London interbank offered rate (LIBOR). The contago may rel.ect a spot-to-forvard or a forward-to- fonvard contango. The LIBOR rate used has a term similar to that of the longest futures contract used in the contango calculation. The volatility of gold borrowing rates and average rates have increased recently. Scarce physical stocks and other factors have often caused rates to reach high levels. Sourcing of gold for Japan's Hirohito cein and the Taiwanese Central Bank gold purchases have depleted exchange stocks, leading to temporary increases in borrowing rates. There is a general agreement among market participants that interest rate levels have increased betwvc - 0.5 percent and 0.75 percent during 1988. Loan -greements now routinely contain provision for automatic conversion of debt to do%'Ars ii the event of a gold market disruption. As far as is known, there have L-en few defaults on gold loans. In November 1988, a small Australian producer, Solomon Pacific Resources NL, was reported to have fallen behind on its gold loan repayments, apparc.ntly due to higher-than-expected operating costs. In Canada, Pacific Trans- Ocean Resources reportedly ran into problems in meeting its loan EXPERIENCE WITH CO.Mt.1oDI .Y-LINKED ISSUES 3) Company decided to issue commodity bonds to try to hedge variations in wvorking capital. In 1980, the -rmpany raised USS2S mi.ihon with the issue of 81/ pe-cent silver-indexed bonds due April 1.5, 1995. The bonds make sem.annual coupon payments, and the largest principal payments are USS1,000 or the market value of 50 ounces of silver. The boids trade on the New York Stock Exchange. Under the terms of issue, the bonds can be redeemed on or a.ter April 15, 1985 if the average silver price for 30 consecutive days is greater than USS40 per ounce. The companv has the right ro p.opose redemption of 70 percent of its original issue from 1982 and t'nereafter. T-he company is not restric 1 from the creation of senior indebtedness, but must ma3ntain qualiie. reserves equal to or higher than 400 pelcent of thf aggregate amount of silver required by all outstanding si!ver-backed and silver-related securities. The investors can tal-e a position in the silver market %vhJ.e earning a good return from their investment, and the silver producer raises funds at a cost lowser than otherwise would have been possible. Sunshii'e IMining Corporation Msued a se:ond silver bond totaling USS40 million in April 1985 for April 2004 maturity. The coupon was 93,'. percent, and the principal is the greatest of callable USS1,000 or 58 ounces oc silver. The issue has properties simi!ar to the previous one. (See table 2-3.) Contrary to the case w-ith gold, the volumr of silver loans is not significant. The most important reason for the iack of development of silver-linked financing is because silver prices have changed little since 1980, trading in the range of USS6-8 per ounce during that time. At these prices, silver producing companies do not invest in new projects. Operating costs of new venti, es are in the USS4-5 per ounce range. When financing costs and a 20 percent pretax profit margin are added to chese costs, there is little incentive for silver pcoducers to undertake new ventures. As with gold, silver-linked financing would increase if silver rices increase substantially from theni present level. In the absence of such price increases, investment activity wvill only focus on refinancing existni g ventures and on hedging existing profit margins. Crude-Oil-Linked Financing Crud. -oil-iinkcd bonds and other forms of oil-linked financing began in the !ate 1970s after substantial petroleum price increases, but thei; u se became popular oniY in recent years. Indeed, the Reagan administration considered seriously the issuing of bonds l;nl:.d to oil to finance an increase in the U.S. strategic petroleu- reer^ in early 1981. Amorng the Table 2-3 Silver-Linked Issues, 1985-88 Issuer I! sue (lead issue Coupon c ite manager) Amount price (percent) Maturity Indexation Coinment April Sunshine US$40 ni 100 91/4 4/J 5/2004 Each $1,000 bond is The bonds are redeemable 1985 Mining redecmed at maturity in whole from 4/1S/90 at (Drexel at the. greate- of the option of the company, Buinham) $1,000 or the average at the IPA plus accrued Lambcrt) market price of 58 oz interest, if the IPA is greater of silv.-r ("Indexed than or equal to $2,000 Princip.il Amount") for a period of 30 consecutive calend-. days Source: Goldman Sachs, London, February 1988. EXPERIENCE WITH COM1.MODITY-LINKED ISSUES 33 first known oil bond issues were those by the Mexican government. The "Petrobonds," as the Mexican oil bonds are known, were issued in bearer form by a trust fund set up by the National Financicre S.A. (NAFINSA). NAFINSA is a development bank owned by the Mexican govern- ment. The Petrobonds are listed on the Mexican Stock Exchange. The objective in issuing these bonds was to entice back the money that fled the country following the 45 percent devaluation of the Mexican peso in 1976. The first issue took place in April 1977. Almost 2 billion pesos were raised, and the funds were used to finance Mexican oil development. The bonds had a maturity of three years and carried a coupon of 12.66 percent payable quarterly. The coupon was subject to a 21 percent Mexican wvithholding tax. After tax, the coupon netted approximately 10 percent. At maturity, the bondholder received the peso value of a pre-specified number of barrels of Mexican oil net of the nominal value of coupon receipts. The average oil export price for the 25 'days preceding the maturity date was used for the calculation of the payment. Each bal rel of Mexican oil per bond used in the calculation was worth 1,000 pesos zr the time of the issue. With this issue, the government was not only raising new monev at low nominal cost, but also was hedging a part of its oil production. The investors in these bonds were participating in the possible upswing of oil prices. The Mexican government has made five successful issues of Per:obonds. The importance of oil for the development of the Mexican economy was also recognized by the International Monetary Fund (INIF) restructuring agreement of the mid-1980s, under which the U.S. govern- ment was committed to increasing the availability of financing to the Mexican economy when oil prices dropped below a certain benchmark and reducing U.S. credit availability when oil prices increased above another. In 1981, Petro-Lewis Corporation, a Denver-based company in oil exploration and production raised US$20 million with oil-linked notes. The notes carried a 9 perce:? annual coupon rate, and they matured in five years. At maturity, the investors received the principal, its annual coupon, and an option. The option exercisable at maturity was based on average spot prices of several oil types. It was of the call variety and had a cap. By exercising this option, an investor could make at most an additional US$589 per bond. This kicker makes this type of bond attractive to investors. The borrower raises funds at lower cost than would otherwise have been possible, while foregoing some of the upside revenur potential from part of its oil assets. A Ic ng-term call or put commodit', option resemble. a zero commod- ity-linked bond of the option type. In this case, the "cc nventional bond" share in the commodity bond is reduced to zero. Sevcral of these Table 2-4 Oil-Linked Issues, 198S-88 Issue Issuer Host bond date (lead manager) (debenture) Warrant Description Comment 9/27/85 Phibro-Salomon Inc. (naked issue) (1) 16,000 call A-exercisable on 5/13/86 at Holder of warrants can (Salomon) Wrts offered in $28/bbl choose between four series of AA-exercisable on S/13/86 physical and net 4,000 per series, at $30/bbl settlement. If net each Wrt to buy B-exercisable on 11/14/86 ar settlement, the 1,000 U.S. barrels $28/bbl following formulae of wri BB-exercisable on 11/14/86 apply: at $301bbl (1) Call net settlement-- 3-day (2) 16,000 put C-exercisable on 5/13/86 at aveme = 3utre Wrts offered in $23/bbl average call futures oil-price x 1,000 price four series of CC-exercisable on 5/13/86 (2) Put net 4,000 per series, at $21/bbl settlement = put 3-day each Wrt to sell D-exercisable on 11/14/86 at settle p utures 1,000 $23/bbl oil0average price-futures DD-exercisable on 11/14/86 oil x 1,000 price at $21/bbl 6/16/86 Standard Oil Co. CPN: 6.30% (s.a.) (1) Indexed Note 1 Redemption = 100 + (wri Bonds issued in (Goldman Sachs) Amt: $300 m CPN: Zero price - 25) x 170" "units," each of which Denoms: $1,000 Amt: $37.5 m consisted of 8 iP: 100% Denoms: $1,000 debentures of $1,000 Mat: 6/15/2001 IP: 100% denoms, 1 oil indexed Mat: 12/15/92 note I (due 1990), and 1 oil indexed note 2 (due 1990) (2) Indexed Note 2 Redemption = 100 = (W1l CPN: Zero price - 25) x 200a Amr: $37.5 m Denoms: $1,000 ip: 100% Mat: 3/15/92 7/8/87 Kredintbank CPN: 3% (ann) Attached to each Exercise period: 2 years Private placement (Goldman Sachs) Amt: Sfr 50 m Sfr 50,000 note Exercise price: US$21/bbl Denoms: Sfr 50,000 are 2 Wrts, each to Ip: 100.5% buy 250 U.S. Mat: 8/14/92 barrels of w-n crude oil (American calls) 7/8/87 Christiania Bank CPN: 25/s% (ann) Attached to each Exercise period: 3 years Public issue that was (Banque Gutzwiller) Amr: Sfr 20 m Sfr 5,000 bond is Exercise price: US$23/bbl pulled (i.e., never Denoms: Sfr 5,000 1 Wrt to buy 100 actually materialized) iF: 100% U.S. barrels of w-n crude oil (American calls) 7/12V87 Montedison Finance CPN: 47/A% (ann) Attached to each Exercise period: 3 years Public issue (Morgan Stanley) Amt: Sfr 75 m Sfr 5,000 bonds Exercise price: USS23.55/bbl Denoms: Sfr 5,000 are 7 Wrts, each to and 100,000 buy 20 U.S. barrels Ip: 122% of wri crude oil Mat: 8/27/92 (American calls) - Not available. a. Tlhere is a cap on the West Texas Intermediate (wn) crude oil price of $40 per barrel. Source: World Bank data. 36 COMMODITY RISK MANAGEMENT AND FINANCE long-term (more than a year) commodity options have been written in the last three to four years. Gold, silver, and oil products were not the on;y commodities for which long-term options were written. Well-known cases include nickel, copper, aluminum, and other metals. Unfortunately, because most of these contracts take place outside official exchanges, it is very difficult to have an accurate estimate of the liquidity of these markets. It is, nevertheless, well known that an increasing number of commercial and investment houses are willing to quote a price for creditworthy organizations. The increased use of these option instru- ments, particularly with oil, has also helped the development of the oil swap markets. These long-term oil options are used for hedging pur- poses. In 1985, for example, Phibro-Salomon Inc., a New-York-based investment and trading house, offered its clients 16,000 West Texas Intermediate (xri) oil puts and as many calls with expiration dates of 8 and 14 months. In conjunction with a straight financing arrangement, long-term commodity options can compose the two parts of a commod- ity-linked financing. (As discussed later, however, there are important benefits to investors to have the two parts of a commodity-linked financing in one contract rather than in two.) During the past three years, several oil bond issues took place. (See table 2-4.) Almost all were of the forward type. Because of the uncer- tainties of the regulatory environment, only one took place in U.S. financial markets. This was the Sohio Oil Company issue. Sohio, a major U.S. oil producer, decided to use this method to finance a common venture with BP and to hedge their oil assets. Sohio issued oil-indexed units (olus). The offer wvas composed of (1) US$300 million, 6.3 percent oil-indexed debentures (OIDS), due in 2001, priced at 747, and yielding 9.59 percent; (2) US$37.5 million detachable oil-indexed notes (OINS) due in 1990; and (3) US$37.5 million detachable OINS due in 1992. Each oiu consisted of nine OIDS, one 1990 OIN and one 1992 OIN. For the OINS, if the spot price of oil exceeds US$25 per barrel, the note holder gets the excess multiplied by 170 barrels for each 1990 note and the excess multiplied by 200 for each 1992 note-with the excess not to exceed US$15 per barrel. Therefore, the effective yield on each oiu varies from a low of 8.3 percent, if the oi! price is below US$25, to a high of 13.9 percent when oil is US$40 per barrel. Each US$1,000 oIN is effectively a combination of a zero coupon bond priced at US$747 and an attached call option with an initial value of US$253. The option was coupled to the zero because the cFrc prohibits the existence of naked or securitized options with greater than 18 months' maturity, unless the security option is less than 50 percent of the value of the bond. The proposed 1989 cFrc ruling on hybrid instruments recommends a lower threshold percentage. Oil bond issues are expected to increase sharply in the years to come. EXPERIENCE WITH COMMODITY-LINKED ISSUES 37 The median cost of production of crude oil is still very low in comparison with the present prices of crude oil. Oil bonds can help finance the exploration and development of new projects or restructure the finances of existing oil companies. Other Commodity-Linked Issues There have also been commodity-linked financings in nickel, copper, zinc, and other commodities. The motivations for these issues were multiple. The most often quoted reasons, however, were to raise funds at low nominal cost and to hedge part of production from commodity price risks. Inco, the world's most important nickel producer and an important producer of copper, silver, cobalt, and platinum, issued a Can$90 million bond indexed to nickel or copper prices in 1984. TIhe issue came with a 10 percent coupon. The bonds mature in 1991. The bondholders have the privilege of either requesting the principal at par or to be paid the monetary equivalent of prefixed quantities of nickel or copper. The exchange right of the investors could have been exercised prior to 1987 if the nickel London Metal Exchange (LNIE) cash price exceeded USS2.90 per pound or the copper (LNIE cash) price exceeded US$0.80 per pound. Inco had the option to repay in cash or in common shares. In 1984, Inco was experiencing financial difficulties. With this issue, the company was able to raise funds at a cost substantially below what it would have had to pay otherwise. In 1988, Inco considered the issue of a second nickel bond. Its reason for doing so this time was to reduce its exposure to nickel price fluctuations. In 1988, nickel prices had reached unprecedented levels; the company was in a strong financial position and did not need to borrow additional funds. Inco found it more appropriate, however, to hedge its nickel price risks through long-term contracts with its major customers- thereby locking 25 percent of its production during the next three years to prices substantially higher than its average costs. In 1987, Cominco Ltd., an important Canadian mining company in the copper and zinc business, raised US$54 million for the financing of its investment program through the sale of preferred shares 2.nd commodity- indexed common share purchase warrants (cis). Each cis orovides the holder with the right to exchange the warrant on or before August 1992 for a number of common shares of the corporation to be determined based on the average market price of zinc or copper and on the average market price of common shares on the date of the exercise. Each unit was 38 COMMODITY RISK MANAGEIMENT AND FINANCE offered at US$18, of which US$11.75 was allocated for the preferred shares and US$6.25 for each warrant. In 1988, Magma, the largest copper producer in the United States, issued an even more innovative structure of notes linked to copper prices. The Us-$200 million issue, due in 1998, linked interest payments to copper prices. The quarterly interest payments were paying 18 percent at the time of the issue. The copper-indexed interest rate will range from 21 percent per annum at average copper prices of US$2 per pound and above to 12 percent per annum at average copper prices at US$0.80 per pound and below. The proceeds of the offering wvere used to restructure the liabilities of the company. The indexing of the interest payments to copper prices makes this issue one of the best examples of corporate balance sheet refinancing for risk management purposes. With this issue, Magma .iucceeds in linking expenses with revenues and, in the process, assuring stability in profitability and net worth. The nominal cost of financing makes this a high yield offering. Institutional and other investors in the high yield market were attracted to this issue. Several commodity-linked issues have taken place in developing coun- tries. Citibank is reported to have underwritten a small loan linked to palm oil prices in Malaysia. Mletallgesellschaft is reported to have financed its copper investments in Papua New Guinea with copper-linked financing. Lack of transparency in privately arranged financings makes it very difficult to determine an accurate number and amount of commod- ity-linked financings in both developing and developed countries. Con- fidential reports from major banking and commodity trading houses, however, do, indicate extensive use of these methods for financing or refinancing investment programs in the commodities industries. Notes 1. One billion equals one thousand million. See proceedings from the Fifth Mineral Economics Symposium, 1989, Toronto, Canada. 2. A version of this CD type-the College Sure cD-provides a return on maturity based on a multiple of the average cost of a college education to enable depositors to cover the costs of their children's college education. 3. Swaps are written oii forward and amortizing bases and may include various option-like features. The latter are referred to as swap options or "swaptions." Swaps can also be participating, extendable, or callable and have drawdown provisions. 4. Goldman Sachs has kindly provided us with these tables. S. See Woodward (1989) and Stone (1989). The Demand for Commodity Bonds Moctar A. Fall One of the most important models in finance theory, the Sharpe-Lintner Capital Asset Pricing Model (cAr.\i), is based on a single-period model with very restrictive assumptions (Sharpe, 1964). Although the model has been widely criticized and widely tested by the academic community, it is still extensively used in the nonacademic world. This chapter derives the demand funcrions for commodity bonds using a continuous-time inter- temporal model similar to the one derived by Merton (1971, 1973). The model applies a dynamic programming technique to the consumption- portfolio problem for a household whose income is generated by capital gains on investments in tradable assets. The derivations are done in nominal terms. The chapter begins with a one-consumption good version of this model and continues with a multigood extension. The One-Consumption Good Case Assumptions The general assumptions retained for this analysis are similar to the ones made in Merton (1973a). Households are assumed to behave as price takers in a perfectly competiti-ve market, and trading a!ways takes place at equilibrium prices. Households can buy and sell as much of an asset as they want at market prices and may short-sell any asset with full use of the proceeds. It is further assumed that households hold wealth in the form of risky assets and an instantaneously riskless assct for which the borrowing and lending rates are equal. All assets are assumed to be perfectly divisible and have limited liability. Households can trade continuously and face no transaction costs or taxes. Finally, asset prices are assumed to be stationary and log-normally distributed. 39 40 COMMODITY RISK MANAGEMENT AND FINANCE Most of the assumptions made are the standard assumptions required to make a perfect market. 1These have been widely discussed in the finance literature and are mainly retained for the sake of simplicity, while doing no damage to the analysis. Nevertheless, Fama argues in Cootner (1964) that srock and commodity price changes follow a stable Paretian distribution with infinite second moments, It is important to note, however, that nothing has been said about the homogeneity of house- holds' expectations, as is required in the derivation of the CAPM and similar models. Asset Returns In this section, there is a single consumption good, the commodity whose price is assumed to be generated by an Ito process: (3-1) p= idt + oridzi where a, is the expected percentage change in the commodity's price per unit time and al is the instantaneous variance per unit time. The instantaneously riskiess rate of interest is assumed to follow the following differential equation: (3-2) dr = ardt + 0a,dZr Each individual can hold three assets in the portfolio: a commodity bond, equity, and a default-free bond. The value of the comnmodity bond depends only on the price of the commodity, the rate of interest, and time until maturity. (3-3) Q, = Q1(PI, r, T) The value of the default-free bond, Q3, depends only on the rate of interest and time until maturity. (3-4) Q3 = Q3(r, T) The x..niaining asset, in the form of equity, is also assumed to be generated by an Ito process: (3-S) dQ2 = R2dt + a2dZ2 Ito processes, --though continuous, are not differentiable, and, thus, a tool is needed to manipulate functions that involve Ito processes. A thorough description of Ito processes is given in Ito and McKean (1964), but this discussion will focus only on Ito's lemma. THE DENMAND FOR COMMIOUITY BONDS 41 LEMMA Let F + F(X1, . . ., X,,, t) be a function at least twice differentiable where the Xi's are generated by Ito processes, then its differential is given by: H "~OF I oa2F (3-6) dF= E -X dX, + Fdt + E dX- ,= X d ' at 2 .= I ,= dX, dX,dX, where the product dX,dX, is defined by the rule (3-7) dz,dzj = p,xdt i, 1,... and (3-8) dz,dt = C i - 1, .. and pi, is the correlation coefficient betv-wcn the (Gauss-Weiner processes dz, and dz,. Now, equipped with Ito's lemma, the percentage change in the commodity bond's price can be determined, as well as t!-at of the default-free bond. (3-9) dQ = Q dPQ + IQ' 2Q dP;dP OPI O aT 2ap 2 dr2Q dr + dP-d dPdr 2 Or2- aP1dr However, T is defined as time until maturity, so that dT --dt. Furthermore, as an application of the multiplicatioi, rule v yen in Ito's lemma, the following products are obtained: (3-10) dP2 = P2[a Idt + sldz1]2 = P2s2dt (3-11) dr2= [a,dt + crdzz] = ardt (3-12) dP,dr = P1[o-1dt + sldzi][ardt + 0rdZ,] = PIS107prP dt With these new expressions, equation 3-9 becomes: OQl PI ar', a arOQ 1 P2SI 21 + 1 ar2 aQ (Qi [ C)l O: dP Q O r 2 Qi ap2 2 Qi ar2 PIS10ar 02QI 1 QI + Plr0 d r d t + SiP QdP dz. + Q dZr, Similar derivations for the default-frce bond, yield: (3-14) dQ3 = dr dr + - dT + 2- -2 dr2 ar 1T 2 ar2 42 COMMODITY RISK MANAGEMENT AN.) FINANCE and dQ3 [ar dQ3 1 tf 02Q3 1 aQ31 (Jr d (3-15) -- dt+--dz Q3 [Q3 ar 2 Q3 ar2 Q-3 'T I Q3 ar Furthermore, it is assumcd that interest rates are nonstochastic so that or. = 0. The commodity bond's price elasticity is defined as Pi dQl el = Q dP . As a result of these new specifications, asset returns are now fully expressed by: dQIC r a Ql 1 P I2Q I 1 d +Q (3-16) Q = ale, + Q d + 2 dt + eSdz Qi Q, r 2 Q' P Q, aT (3-17) dQl -- Rdt + oJldz1 Qi dQ2 (3-18S) -u- = R2dt + ..rdz2 (3-19) Q3 [a-Q3 Qr aQ-- dt= R3dt= Rfdt Budget Equation To derive the individual's budget equation, the framework followed is one in which all the wealth is held in the assets, income is generated by capital gains, and the individual must reduce asset holdings to consume. A discrete model with time periods of length h is first developed before the continuous model is derived by taking h to 0. Let W(t) and Qi(t) be wealth and asset prices at the beginning of period t. Ni(t) represents the number of shares of asset i held at date t. Thus, 3 (3-20) W(t)= 2 N5(t)Qi(t) i = I To consume between dates t and t + h, the individual must reduce asset holdings at date t. All of that consurrmption is in the form of the commodity, according to this model, and C,; is the rate of consumption per unit time. Consumption is thus given by: 3 (3-21) 2'[Ni(t) -N,(t + h)]Q,(t) = PI(t).C(t).h THE iDEMAND FOP. COmMODITY BONDS 43 Thus, 3 3 (3-22) W(t + h) - W(t)= N,(t + h)Q,(t + b) - X N,(t)Q,(t) *;1 i= I = N,{t + h)[Q2(t + h) - Q,(t)] - PI(t'.C(t).h ,=, and (3-23) W(t + h) - W(t) 3 r Qi(t + b) - (323) N#h = E N,(t + h ] -P(t).C(.t) As h? goes to 0, the continu.'us version of this equation is as follows: 3 (3-24) dW(t) = N,(t)dQ,tt) - P1(t).C(t).dt Now introduced is co,, the proportion of the portfolio held in asset i. (3-25) N{t) W(t) W(t) Equation 3-24 becomes: (3-26) dW= ,W -i- P.C.dt 2 Using equation 3-18 and o3 =1- cwi, the budget equation becomes: 2 2 (3-27) dW = wi,W(Ri - Rf)dt + (WRf - P1C)dt + v w IWo,dz1 t= l i= I Maximization Problem Each individual is f.ced with the problem of choosing a portfolio and consumption parern that will maximize the expected value of a time- additive von Ne .mann-Morgenstern utility function and bequest func- tion. The problem is formulated as: (3-28) Max Eo U1jjC(t), t]dt + B[W(T), T] subject to equation 3-27 and W(O) = WO. The utility function U is assumed to be strictly concave in C, and . 4e Original page # 44 is missing. THE DFIAND FOR COMMrIODITY BONDS 45 T1she terms of the covariance mairices defined by aoi = p,,or,o, and the condition o3 = 0, however, imply that a3i = 0 for ail i. For a similar reason, V,j = piiS*Uj implies Vb3 = 0. The first-order conditions thus become: (3-381 Uc = PlJw (3-39) 0 = (RI - Rf)Jw + WJ,wX( u13'1) + PiJ 2 (3-40) 0 = (R2 - R/)Jw + WJ-Ww 0 O214i + P1!1wV!2 .= I (3-41) A R'WJw (3-42) I = ,c Demand Functions The analysis just described the portfolio choice problem faced by an individual and enables the opcinal asset portfilio to be derived. Equation 3-38 states that, at the optimum, the mirginal utility of consu mption must equat; the' marginal utility of *vealth. In matrix form, equations 3-39 and 3-40 can be rewritten: 34) l tIl2 W,W i =1XV RI - R _ PIJIw I V1l Cl 2 022 tc2W Jww { - - Rf JWW I V121 The %arious terms of the variance-covy.riance matrix are defined by: (3-44) a,j = po-a,a p denotes the correlation coefficient between the commodity and the equity asset, so that (3-45) 12 = Ppor (3-46) C1ll = tI (3-47) (r22 = 02 Furthermore, it is assumed that p2 # 1, so that the variance-covariance matrit - .s nonsingular. The demand functions -an now be derived for the vanious assets by matri;c inveis;on in equation 3-43. (3-48) IO1W I- -JW 22 - pCaIC2 RI -Rf| tw)2W I Jw l2(1 _-p2) -Po122 oj I R2- Rf 2 PJIXw -2 PCr1a2 | ll Jwwcq2 2(1 - p2) -parC, 2 - O JWWO-Y.72 -PO-ltT2 SI ol~~~Cr 46 COMMODITY RISK MANAGEMENT AND FINANCE and (3-49) wOW = W --_ wW- Cw2W After simplifications, these equations are written: -Jw [(RI - Rf) (R2 - Rf)l PlJiw s1 (3-50) CIW = _~ p' _P _lO2 Jw -Jw !-(R, - Rd) (RI - Rf) (3-SI) ,,W V -- 2 I=l J2 (3-52) W., W - COIXW - 2W To express the last term of equation 3-SO as a function of the other variables, Fischer (1975) points out that the consumption decision by the individual is guided by commodity price changes rela.ive to wealth, so that consumption is a functicn of real wealth. (3-53) C = C(W/P,, t) By differentiating this equation to W and to PI, one obtains: (354) dC= C d(W/P1) C 1 (355) ac d(WIP,) _ w (3-55) dP=Cl-d = Cl p2 and thus the followir relationship holds: (3-56) aC -PI aC d_W _W dP, Furthermore, when equation 3-38 is differ: fiated relative to W and to PI, it yields: (3-57) Uccac =Jw + PIJIW (3-58) Uc PIPJ-U J ac_ -PI Ucc dW=Pljww =Ucc W dP -W (Jw + PiJlw) ac w ap, w (wP1w As a result, (3-59) = w W Jwvw Jww The individual's absolute risk tolerance T is defined as T- -UI/U 0 because more is better (Uc > 0), and the utility function is assurred to be concave in C or the first units of consumption are worth more to the individual than the subsequent units. rHE DEMAND FOR COMMODITY BONDS 47 Thus, MT=-JwIJw;.V is defined as the individual's "mo.iified" risk tolerance. (3-60) JW W U a T a T Jww 8cc ac ac c CC8W a W High values of this variable are obtained for high values of T and/or low values of the marginal propensity to consume. Cw can be expected to be a decreasing function of W. There could conceivably exist individuals for whom Clv = 0. These individuals have so much wvealth that any increase in that wealth would not induce them to consume more. At the other extrcme, very poor individuals would consume all of their additional gains, and, for them, Cw = 1, for at least W lower than a certain subsistence level. With these simplifications, the demand equations for each individual k can be written: wkWk k (RI Rd~ (R2 - Rfl WK k (3-61) MTI ( , (R2 - K -,) (l MT) (1 kp )R2 (1 - R ''I - (3-62) w4Wk = MTk[ (R2 R) ( p Rl-R,) [(I _ P2) (I - P')0'102J (3-63) w~kWk = Wk _- kWk - wOkWk (3-63) W3W = t. ,1* W 2 T, A look at the demand equations reveals that the demand for the equity asset is only comprised of a speculative component and is equal to the demand for a risky asset by a single period mean-variance maximizing investor. The demand for the: commodity bond, liowever, is also com- prised of a similar speculative component and a hedging component. A and B denote the bracket terms in equation 3-61 and 3-62, and these equations become: (3-64) w)Wk = MTk. A + (Wk - MTk)el (J-65) w10 Wk = MTk.B We define MTM " ' MTk as the market's modified risk tolerance. k By aggre.gating equations 3-64 and 3-65, one obtains: (3-66) @AS. M = MTM. A + (M - MT"')e (3-67) w2M. M = MTM. B Substituting the values of A and B obtained from these equations back iito equat:ons 3-64 and 3-65, one is able to derive anothier expression for the demand functions: 48 COMMODITY RISK .1MANAGEIMENT AND FINANCE kWk CI MT' wvk r MTkIWk1 ;3-68) w1W = wA. M + W[1_ M7 IW ] MTM el P MT"'IM (3-69) coWk 2 MTk- The Determinants of the Demand for Commodity Bonds Now consider the case in which the equity asset is the market portfolio before the introduction of commodity bond:.. Modern portfolio theory indicates that investors would hold the marktr portfolio, levered up or down according to their aversion to risk. 1-wo approaches can be taken here. One can analyze the change in the individual's portfolio mix after the introduction of a positive amount of commodity bonds or one can analyze and determine who would want to issue or hold such bonds, if they did not exist. The latter approach will be taken here in justifying the introduction of such bonds. In this case, W= 0, and equation 3-68 becomes: (3-70) ,.Wk = W [1 _ MTk/W k I el[ MTAI/M Thus, if MTk/Wk < MTm/M, then A Wk > 0. This is the result that is intuitively expected: When individual k has a lower relative modified risk tolerance than the market or a higher relative modified risk aversion, the individual would have a positive demand for commodity bonds. A comparison of equations 3-70 and 3-64, however, reveals that, even in this case, the demand for commodity bonds is not limited to the hedging component. Samuelson (1985) points out that sellers of such bonds will be those least averse to price risk as they are bribed to take on some of the irreducib.. variability by an appropriate market-clearing premium. For such individuals, their attitude toward commodity bonds will be guided by their speculative demand. Samuelson also notes that if the supply of commodity bonds were to come only froin individuals wzi!ling to take a little more risk for a premium, the market for commodity bonds would not be viable. This market must also be driven by a commercial function with the involvement of major players, big corporations, or governments, which are seeking to hedge the variations in their production costs or revenues. Now tal:e a closer look at the determinants of the demand for commodity bonds. Fronm equation 3-61, it can be seen that the determi- nants depend on the required rates of return for three assets: the correlation between the commodity and the market, their respective volatilities, and the individual's modified risk tolerance. THE DEMAND FOR COMMODITY BONDS 49 From this point on, Dk will denote individual k's demand for asset i: (3-71) Di = cowWk In taking the partial derivative of equation 3-61 with respect to R1, one obtains: (3-72) - > ° This is a general property of most demand functions as they are decreasing with respect to price. Equation 3-72 indicates that if R1 increases or the price of the commodity bond goes down, the demand for it will go up. Before taking the partial of equation 3-61 with respect to R2, note that whenever p > 0, the market serves as a hedge against inflation in the sense that the value of this asset goes up at the same time that investors need it the most: when commodity prices go up. (3-73) =I_~pT (R2 (1 - p2)alr.2 aD' Therefore, if P > 0, is implied. In other words, whenever R2 de- creases or Q2 goes up, the demand for commodity bonds will also go up. Thus, when p > 0, commodity bonds and the market act as substitutes. (3-74) aR 1- oo aRf (1- p2)a - (Pal - 2) The commodity bond's market beta is introduced and defined as: (3-7S) 1 cov (R, E2) pal1 var (i2) 02 and notice that when /31 > 1, it irnplies poa - o2 > 0. Equation 3-74 indicates that when default-free bond prices go down so that Rf goes up, there will be a greater demand for commodity bonds when their market beta is greater than 1. Remembering that o = elsl, the commodity bonds' market beta is el times the commodity's market beta. aD'i MTk [ (R2 - Rf) (RI -R)R (3-76) = p - -2 - dsrl (1p2)0. a 02 al By using a continuous-time framework, Breeden (1979) derived an intertemporal pricing relationship that must hold at each instant in time: J) U t-OMMODITY KISK MANAGEMENT AND tINANCE (3-77) R1 - Rf= (R2 - R) 132, where p3j, is the consumption-beta for asset i, defined by: (3-78) ~~~~coy (ij, din Q (3-78) 13k= var (d In C) With the use of these relationships, equation 3-76 becomes: dD_ MTk. (R2 - Rf) [L,1 Ž1 (3-79) a-1 (1 - p2) _[o _I a32cJ This still assumes p > 0. A similar analysis can be made for p < 0. In general, 12, > 0 as individuals increase their rate of consumption when the market is going up. The sign of 3,l is ambiguous, however. If commodity prices and consumption are correlated negatively, which is what would happen if higher commodity prices induced individuals to reduce their rate of consumption, equation 3-79 indicates a greater demand for commodity bonds when commodity prices become more volatile. Such would be the case as long as (3-80) I1c < PJP2cC71/202 Furthermore, (D_ pMT'(R2 - Rd) (3-81) O2 (1 - Aao- (1 - p2)0-10-2 When p is positive, it has been shown that the market and commodity bonds act zs substitutes. As the market becomes more volatile, it is a less accurate hedge against price changes. This increases the demand for commodity bonds. -D- MT (rR I..~ -1d(2-R (3-82) M1T _ [ - (1 + p2) (R- Rf) ap cr1(1 - 2) 2[P O7 In using Breeden's intertemporal pricing relationship, equation 3-82 becomes: 3 aD MT'(R2 - R) [2p Pc6 _ (1 - (3-83) P c(1-p) ['1t2 2J dp orl(l _r 2.2 L 1 . 2, Oa2 With the above-stated assumptions of p > 0 and Plc < P f32c o-1/2o2, one notes that aDi/Op>O. An intuitive explanation lies in the fact that when the commodity's correlation with the market decieO.ses, the market becomes a less desirable hedging tool. Furthermore, it can easily be shown that when p decreases, the variance of the total portfolio decreases TIIE DEMAND FOR CO.MMb1ODITY BONDS Si due to the inclusioni of commodity bonds. As a result, the latter become more attractive. The previous analysis derived in the case of a single-good economy is also valid when relative commodity prices are fixed and individuals consume the same consumption bundle. In that case, the commodity bond described would be a cpi-bond. These assumptions are very restrictive, however, because commodity prices are known to fluctuate somewhat independently, and individuals have differing tastes. The next section thus extends the analysis to the case of a multigood economy with stochastic consumption opportunities. The Multigood Case The model presented in this section is a multigood extension of the previous analysis. There have been verv few attempts to extend Merton's intertemporal asset pricing model and incorporate the case of many consumption goods. Long (1974) took such an approach, but only in the case of a discrete-time economy. A satisfactory extension was made by Breeden (1979, 1984) in the derivation of a consumption asset pricing model and in the examination of the allocational roles of futures markets in a multigood and multiperiod economy and by Cox, Ingersoll, and Ross (1985). The Model All the assumptions made in the single-good case are repeated in this section for a description of the economy. One can now examine the case in which there are m consumption goods, among which I are commodity goods with I s mi. The price dynamics for these goods are assumcd to be generated by Ito processes. (3-84) dpi -=adt + s,dx j1,...,m where a, and s, are constant. There are n assets with returns that are also assumed to be generated by Ito processes. The first I assets are commodity bonds with I s m ' n. (3-8S) dQQ'= R,dt + oa,dz, i = 1, . . . , n Qi The default-free bond's return is given by (3-86) dQ, l = Rn + Idt = Rfdt + i 52 CONIMODITY RISK MANAGEMENT AND FINANCE Along the same lines as the single-good case, each commodity bond is a function of its own commodity price, the interest rate, and the time until maturity. (3-87) Q,=Q(P, r, T) I = 1, . . .,I As an application of Ito's lemma, it is easy to see that dx, = dz, forj= 1, . . , I and that each commodity bond is perfectly correlated with its own commodity price. CI denotes the rate of consumption of good j by individual k by C*, and i= I is defined as the individual's rate of nominal expenditure. An analysis similar to that of the previous section shows that individual k's budget constraint is given by n n (3-88) dWk >,R - Rf)Wkdt + (WkRf - ek)dt + > aWYo,dzi i=1 i= 1 or in matrix form (3-89) dWk = wk(R - Rf)Wkdt + (WkRf - ek)dt + WIkWoadza where ck is the portfolio weights vector for individual k, Ra the assets return vector, o-J, the P. x n diagonal matrix of assets standard deviation, and dza the Gauss-Weiner processes vector. At each instant, individual k is assumed to maximize a time additive von Neumann-Morgenstern utility function given by, (3-90) E[f T ku (Ck, Y)dy + pk[Wk (T), T7J] where Ck denotes the rate of consumption vector for individual k: Ck (Ct),. Let Uk(ek, P', t) = Max uk(Ck, t) describe individual k's indirect utility function for consumption expenditures and P' the transpose of the consumption-good price vector. The dynamic programming methodol- ogy described in the previous section, yields the following first-order conditicns: (3-9 1) UI(ek, P', t) = Jkw(Wk, S', t) (3-92) ekwk = a (3-9) kw -jkVJ(Ra Rd- V;1-- V w Jw. iw kwW where S' is the transpose of the state variables vector (that is, variables that describe the investment, income, and consumption opportunities THE DEMAND FOR COMMODITY BONDS 53 sets), V,a is the n x n variance-covariance matrix of asset returns, and Vas the n x m covariance matrix of asset returns with the state variables. The Demand Functions From this point onward, the ce,nmodiry prices are chosen to be the state variables. By differentiating equation 3-91 with respect to W, one obtains: (3-93) U' (ek, P', t) * e' = J' w(Wk, S', t) Equations 3-91 and 3-93 combined, yield: (394) -A-T ik W 7 Jww V¢e.eU The last term in equation 3-92 denoted Mt- -JAW Atw was shown by Merton (1973a) to represent individual k's hedging demands against adverse changes in the consumption-investment oppor- tunity set. Equation 3-92 thus becomes: (3-95) &JkWk = MTVaL(Ra - Rf) + VaL'VsMHs by aggregating across all individuals, one obtains: (3-96) wMWM = MTMVa'(Ra - Rf) + VL2VasH;" where (3-97) H1?= HSi. k Equations 3-9S and 3-96 together present a new expression for the asset demand functions: (3-98) wtskWk = MT'. M HM + itk- MTk (3-98) MTM 'lV.V(HS MTM With an argument similar to that of the previous section, the net demand for any commodity bond acreos -he market should be ze.o, thereby yielding at( = 0 for i = 1, . .. , /. Furthermore, Breeden (1979) has shown that VL'VVa5 has, for column!, the portfolio of assets most highly correlated with the state variables; here, those state variables are the .ommodity prices. Hence, column j gives the portfolio that has the maximum coirelation with state vari:"I' Pi. As an application of Ito's lemma, it is evident that this price is periectly correlated with commodity bond Qj. Thus XjV,, = (s), where F is an I x I diagonal matrix that can 54 COMMODITY RISK MANAGEMENT AND FINANCE be normalized to unity by proper scaling of state variables. With these new results, equation 3-98 can be rewritten: (3-99) &w*Wk = Hk --MTH i 1, ... ., and (3-100) ZWIk Wm MT'i(M = I + 1, . . . , n MTkM M These equations are similar to equations 3-69 and 3-70 derived in the single-consumption-good case. To obtain the exact link between the two sets of equations, Hi must be expressed in terms of known parameters. To that effect, the additional assumption that individuals have time- additive isoelastic utility functions is introduced. Under this condition, Dieffenbach (1976) has shown that individual k's vector of percentage compensating variations in wealth for changes in the state variables is not a function of k's wealth lcvel. or: J4 (3-101) Wk = -A where Ak does not depernd on Wk, but does, in general, depend on the P,s. By differentiating with respect to Wk, one obtains: {. ,02) jk Wkj& j]k[jl + Wkjk W] = ° ('02) Jrwkf~ I t W~w] Replacing Jk with its expression from equation 3-101, the condition becomes: (3-103) Ji = -At[Jl + WkJlWW] or (3-104) Hk =-= A(Wk -MTk) JAw By aggregating across individuals, one obtains: (3-105) HIM= A M M-Am MTM where AM = M 'kA*WkandAA, = 1 M A kMTk. The-efore, the M k MTM k demand for commodity bonds is given by (3-106) &);jk = A4Wk - AMTk _ MT . M AM + MTkAM I I I ~~MTM £i,T By rearranging these terms, a more useful expression for the demand for commodity bonds can be derived. THE DEMAND FOR COMMODITY BONDS 55 (-_107) wzWk = AsW [I- MT/WM + A4Tk (M -l)(A -1 A) L MT'I/M (T + MTk(Am -AM)] The demand for commodity bonds is thus comprised of three terms, the first of which is similar to the expression obtained in equation 3-70. The reason for this is that if all individuals consumed the same bundle in the same quantities, A!' would be equal across individuals, and Ak = A, implies both AM = Ai and A'- = A, so the last two terms of equation 3-107 cancel out. Futhermore, when all individuals consun;e the same bundle, it can be considered as one consumption good, and the same results are found as in the previous section. This first term examm:ed has a positive contribution to the demand for commodity bonds whenever individual k has a lower relative risk tolerance than the market or a higher relative risk aversion. T he second term reveais that when the market is relatively more risk averse than unity, individua! k would have an additional demand for commodity bond i when the individual is more affected than the average individual by changes in that commodity's price. This would tend to be the case for commodities for which individual k has a very inelastic demand. The sign ^Žf the last term is the same for all individuals and does not play a major r--!c in the analysis of the demand for commodity bonds. 4 A Review of Methods for Pricing Commodity-Linked Securities Tk:eophilos Prio volos The model for pricing commodity-linked securities uses the option pricing framework as pioneered by Black and Scholes (1973), extended by Merton (1973b) and Cox and Ross (1976), a-d furti er refined by Schwartz (1982). The model for pricing commo:., -convertible bonds uses the option pricing framework of commodity-linked bondsl or the model of pricing convertible bonds as presented among others by Brennan and Schwartz (1980). As commodity-convertible bonds are equivalent to appropria'.-ly specified commodity bonds without war- rants, the discussion here focuses only on the latter type of bonds. The key assumption of the rrodel is that the underlying commodities, the commodity-linked bonds, and the equities of the firm issuing the bonds are continuo.isly tzaded in frictionless markets. The Schw; rtz model considers commodity price risk, default risk, and interest rate risk and takes the form of a second-order partial differential equation in four variables that governs the value of the commodity- linked boiid at any point in time. Let P be the value of the reference comn..odity bundle, V the value of the firm issuing the bonds, and r the instantaneously riskiess rate of interest and assume that they follow continuous paths described by the following stochastic differential equa- tions: (4_1) dP ap dt + op dzp (4-2) dV= Da-(V' t) dt + o-,dz, (4-3) dr ar(r) dt + ar,(r) dZr S6 METHODS FOR PRICING COMMODITY-LINKED SECURITIES S7 where D is the rate of total payouts of all the security holders of the firm (dividends, interest, etc.); crp, a,. are constants; and dzp, dzv, and dz, are Gauss-Weiner processes with (4-4) dzp * dzv = p dt, dzp * dzr = Pp * dt, dz * dz,r = p,, dt The total value of the commodity-linked bond can be expressed as (4-5) B = B(P, V, r, T) where T is the time until mO -urity. If a portfolio is formed by investing X, in the underlying commodity, P X2 in the firm, V X3 in a risk'.ss discount bond, G X4 in the commodity-linked bond,2 B then the instantaneous total retu;n on this portfoiio dY will be (4-6) dYXdP dV+ Ddt dG dB + Cdt (4-) dY=X,p+X2 V4 B G is assumed to depend only sn r and T, that is, G(r, T); c is the COUSron payment of the commodity bond. By applying Ito's lemrma, one obtains: (4-7) dG dt + aG dZr If we apply Itc's lemma in 4-S and introduce the result in 4-6 with 4-1, 4-2, and 4-7 and choose XI, X2, X3, X4 so that the portfolio return becomes riskless, the following partial differential equation governing the value of the commodity-linked bond at every point in time is derived: (428) 1 2P2P B + 1 a2V2BLv, + I r2Brr + OrpvPVBpv + 0p,PBp, + o-,VB", + rPBp + (rV - D)BV, + (a, - A cr,)B, - BT - rB + C = 0 The value of the bonds will be independent of the exptcted return on the commodity and on the firm; it will only depend on the current values of the reference commodity bundles and the firm (P, V). The promised payment on the bonds at maturity is equivalent to the face value of the bond (F), plus an option to Luy the reference commodity bundle at a specifizd exercise price (E). The promised payment can be made only if the value of the firm at maturity is greater than that amount. It is assumed that in case of default, the bondholder takes over the firm. The boundary condition at maturity can be expressed as (4-9) r ^' V, r, 0) = min [V, F + max (0, P - E)] Because the solu:.jn of 4-8 and 4-9 is very difficult, the following three simplified versions of the model can be obtained. METHODS FOR PRICING COMNMOI)DITY-LINKED SECURITIES 59 appropri; tely replaced in 4- 3, then the derived new 4-S function r,may be solved suliject to the boundary .onditioll (4-15) S.P, r, 0) = F + -max (0, P - E) If the commodity-linked bond is o; the Jiscourit type, its vIJue can be exp-,ssed as (4-1 6) B(P, Q, r) = F Q + W(P, Q, T) where the value of optio; X'(P, Q, T) can be obtained from Merton (1973b). Several numerical examples by Schwart-7 (1982) using -ases I to 3 sihow interesting properties of comrnodit' bonds. In case 1, the higher the standard deviation of the comInG. ty price (op), the higher the value of the oprion (W) and the lower the icquired coupon ratc (C/F). When the value of the reierence bundle (Plf) becomes zero, the bond becomer riskless, and U/F equates to r. When PIF = 1, that is, the value of the refe-ence bt"ndle equals the face value of the bond, the equilibrium _ol:pon rate is negativ:. 'n case 2, h boi!ndai)e :,r iition indicates that default at maturity depends not only or. che value of the firm, but aico on the value of the commodity bundle. X higher stanaXird deviation on the return on the commodity (a.) has two opposing effects on bond values: First, it is well known that the value of an option increases with the stand ard deviation of its underlving security; second, the probability of default a'so increases with ar, and this tends to iower bond values. The first effect dominares the second for low comnmodity bundle prices, for high firm values, and for shorter maturity dates. Default risk thus has a significant impact on bond values, and most of this r.- cories not Lrom the ficm being unable to nay the face value of the cc r.modity bonds, as in the case for regular corporate bonds, but from the firm being unable to pay the value of the opticn for high commodity prices even under substantial increases in the value of the firrr :A higher correlation be;ween the return on the comr. 'dity and the return on the firm increases bond values. As the risk of dfault decreases, the value of the bond approaches the solution for the no-default, constant-i -ercsc-zate case. The analysis involving case 3 sho;-.s that when pricing commodity bonds, it is quite safe to use the constant i.-:rest rate model as long as the relevant interest rate used is the one to the matunri of the bond. It is noteworthy that seime of the assumptions used to derive the Schwartz mode; :re questionable. The model assumes, for example, that the iuiderlying comr-idity is pe:fecdly tradable. The model neglects taxes corrpletely. Also, like most of the option pricing literature, the model assumes c^nstan. variances. More complex capital structures and bond 60 COMIMODITY RISK MANAGEMENT AND FINANCE characteristics-such as call features, sinking funds, and convertibility into the reference commodity bundle before maturity if convertible commodity bonds ate considerd-could be introduced at the cost of havkng to use complicated numerical procedures to solve th. appropriate partia! differential operations.4 Tlhe next section describes pricing commodity bonds with the use of binomial option pricing. This method has a number of advantages over the Schwartz ai,proach. Notes 1. A commodity-convertible bond can be shown to be e.uivalent to an appropriat-ly specified commodity bond with "American"-type warrants. 2. The commodi-y-linked bond is a conventional bond with commodity (call) warrants attached to coupon or principal payments. 3. The Black-Scholes fcrmula is W(P, T) = PN(x) - E:-TN(x - aoVT where log (PlEr7)! IT X o-VT 2- 4. Fall (1986) extends the Schwartz model by including the convenience yield of holding and scoring the commodity. He argues that his version is more reliable. Brer.nan (1986) has, nowever, shown that conv-.nience yields ar very difficult to estimat. This could be the reason for the differences in the pricing ot commodity bonds berweern Schwartz and Fall. Pricing Commodity Bonds Using Binomial Option Pricing Raghuram Rajatn Interest in commodity-linked securities has increased considerably re- cently. For the developing countries, these securities offer the possibility of hedging against commodity price risk, thereby enhancing their cred- itworthiness. Such instruments also link debt repayments to abilitv to pay (Priovolos, 1987a). Conventional bonds pay a stated interest rate (coupon) and a fixed principal redeemable at maturity. A commodity bond makes repayments subject to the fluctuations in the price of the underlying commodity. Thus, both the coupon and the principal repayment may be a function of the commodity price. A variety of commodity-bond-type instruments can be devised, resulting in different kinds of risk sharing and return. Two of the more popular variants are the Commodity Convertible Bond (ccB) and the Commodity Linked Bond (CLB). With the CCB, the holder can choose on redemption day either the nominal face value or a prespecified amount of the commodity bundle. The CLB consists of a conventional bond with an attached option or warrant to buy a certain amount of the commoditv at a predetermined exercise price. In some markets (not in the United States), the option can b! detached and sold separately. In return for the convertibility/option feature, the issuer receives a lower interest rate. Issues of commodity bonds can assist liability management by tailoring payments to ability to pay. In a ccB/cLB, the coupon provides a "floor" yield. When the price of the commodity increases, however, the yield to maturity for the bond increases and vice versa when the commodity price falls (limited by the floor level). Formulas for pricing commodity-linked bonds have been developed by Schwartz (1982) and Carr (1987). Both use the standard continuou s-time option pricing method to arrive at a differential equation. The extended 61 62 CO.MMODITY RISK NIANAGEMENT AND FINANCE form of the differential equation (incorporating convenience yields) is shown in appendix 5-1. Schwartz states that the solution to the general problem is difficult even by numerical methods and proceeds to make simplifying assumptions about the nature of the bond to obtain a solution. Even thc simplified form of the bond has a mathematically complex, closed-form solution. The need for a simpler, more intuitive, and flexible formulation has been felt. This chapter presents a method for pricing commodity-linked bonds in the presence of default risk and commodity price risk. The advantage of this method is that extensions are very simple. Fulther, the method is more intuitive than the continuous-time method, although it is equivalent in the limit. Most important, it is flexible and comprehensive. Finally, it can be used to model any bond instrument based on two or more stochastic processes. Evnine (1983) first extended the Cox, Ross, and Rubinstein option pricing model to incorporate an option on two or more stocks. The model developed here is basically a simplification and reformulation of Evnine's model and an application of the model to commodity bonds. In "The Model," a simple version of the bond is priced to make the process transparent. In "Parameter Determination," the parameters of the model are derived from real world values. In "Extensions," the model is extended to incorporate the various features that these bonds can include. In "Comparative Analysis of Binomial Model and Schwartz Model Results," some values obtained by the model are compared with those obtained by Schwartz. Further, some of the additional features are added and priced, and observations about some interesting phenomena are made. While appendix S-1 describes the differential equation that has to be solved and Schwartz's solution to the simplified form, appendix 5-2 shows the logic behind the values of the chosen parameters. The Model Assumptions (1) The commodity-linked bond consists of a zero coupon paying face value F at maturity, plus an option to buy a predefined quantity of the commodity with value at maturity date equal to P* at an exercise price of E., The option is European,2 with the maturity date the same as the redemption date. (S-1) B* = F + max [O, F'-] where B* is what the bond ought to pay at maturity. (2) At maturity, however, the firm's value V* (consisting of the total PRICING COMMODITY BONDS USING BINOMIAL OPTION l)RICING 63 value of its assets to its creditors) may be greater than or less than B'. If the firm is unable to pay, the bondholders get the residual value of the firm.3 Thei-iore, the value of the bond is equal to: (5-2) min [V*, F + max (0, P° - E)] (3) There are no payouts from the firm to the shareholders or bondholders before the maturity date of the bond. (4) The commodity bundle price and the firm value follow multiplica- tive binomial processes4 over discrete periods. (5) The interest rate is constant and positive. (6) The firm's debt consists only of Lommodity bonds; that is, there is no senior debt. (7) No taxes or transaction costs exist, and short sales are allowed. i:urther, assets are perfectly divisible. (8) There is no convenience yield from the commodity. Assumptions (1), (3), (5), (6), and (8) can be relaxed. Let the price of the commodry bundle and the value of the firm follow the continuous-time diffusion processes describci below: (5-3) dP pdt + o dzp (5-41 dsX = V ,, dt + or. dz,1 (5-5) dzp dz, = or. dt Where crp is the volatility of the commodity price, oa, is the volatility of the firm value, and op, is the covariance between the two. Also ,tlp and ,, are the drifts of the corresponding price movements. In this model, the continuous-time diffusion processes will be approx- imated with binomial jumps. If the commodity price and firm value moved independently, it would be easy to mode] the two as a two-step sequence of independent jumps. To introduce the covariance term, however, a third step is needed in which the price of the commodity bundle and the firm value move together (i.e., because there are two underlying stochastic processes and the processes are not independent, a three-step process will be assumed), Assume three assets: the commodity bundle with price P, the firm with value V, and a risk-free bond of face value B. Let ; be 1 + the riskiess rate of return per period. (Each jump is considered to occur in a period.) SEP 1. Price of commodity bundle P moves up by uW with probability q1 or down by d, with probability (1 - ql). The value of the firm V accrues at the riskless rate ;. This is because there is no uncertainty about 64 COMMIODITY RISK MANACEMENT AND FINANCE Vigure 5-1 The Binomial TPee At the end of each three-step unit, the values of the twvo state variables Pand Vare as follows. A if C q3 ul u3 Pr, u2 u3 V q2 Ui Pr, u2 Vr (I ) ul d3 Pr d2 d3 VF ____-- Pd2V q3 uI u3 Pr d2 u3 VF q1 ~u1 ) Vr (.q)u1 d3Pi d2d3 Vr 1~v ~ IZZZj d1 uPr d1P~u2Vi (1-q3) ud d~ (I dle Vrq3 U3.Pi 2 2d3 Vr (I d 1 23Vr (1 U2 d3 l (1-q2) dPr,d2 Vr ddu3lP 2 3V ( -q3) d)d3P d2d3VF Trhe bond values at the end of the third step are as shown below. A B C D Culu2u3 C41u2 l-q3 Culu2d3 Cu1d2u3 C q2 Culd2 1 ql Cu1 1 q3 Culd2d3 3zZ2EIZI Cdlu2u3 q2 CdIu2 1-q3 Cd1u2d3 I q2 Cdd2 q3Cd23 1q3 Cd1d2d3 Step 1 Step 2 Step 3 PRICING CONMMODITY BONDS USING BINO.MIAL OPTION PRICING 65 the value of the firm in this step; hence, it is a riskiess asset. Therefore, it should accrue at the riskless rate. STEP 2. Value of firm moves up by U, with probability q2 or down by d2 with probability (1 - q2). The commodity bundle accrucs at the riskless rate ;. STEP 3. P and V together n,OvC Llp by 143 with probability q3 or down by d3 with probability (1 - q3). Now folding the tree backward, one can find the expected value of the bond at node A. (See figure 5-1.) This would require knowledge of the probabilities of the upward and downward movement at eaC: step. Surprisingly, by creating equivalent portfolios and applying the con- dition that if two assets have the same value in all possible states of the Nvorld, in the next period they should have the same value as in the current period, one finds the value at node A of the bond without ever having to know the probability of upward or dowvnward movement. At node C, a portfolio is created that contains A * u1il of the commodity bundle and A u12; of the firm and B risk-free bonds paying ; per period. (B indicates both the risk-free bond and the quantity thereof; A is some numter.) Choose A and B such that this portfolio, if formed at C, has the same value as the commodity bond at D. That is, choose A and B such that A[u1Pi + u2V;Ju3 + iB = C,,4. , where C,lu ,, is the valuc of the bond after three steps, when the price of the commodity bundle has moved up oy uju3r and the value of the firm by U21u3;. Also, (5-6) 51 uIPr + u2V ]d3 + iB = C", ,d, We get (S-7) A = _ _ _ _ _ _ _ _ _ (U3 - d3)(u1, P; + U2 V) UI3Cu,u,d, d3u- u (5-8) B (3= -d3i - (U3 -d3); If there are to be no riskless arbit' age opportunities when the bond in the next period has the same valt .. in all states as the portfolio, the value of the bond in the present period must equal the value of the portfolio in the present period. (5-9) Cu= C5u,42 (u41P; + 42VA)A + B 3 -d3) +( d3) C /+ 66 COMMODITY RISK MANAGEMENT AND FINANCE Setting P, = (r - d3/u3 - d3) and 1 - P3 = (U3 - ;3 - d3), one can write (5-10) C.u,1 = [P3C.1,.,1 + (1 - P3)CuXu1d/ Similarly all the bond values at nodes below C in figure 5-1 can be found in terms of values at the terminal nodes D. At node B, a portfolio containing Al of firm value V and B1 risk-free bonds can be created. Using the same procedure as above, one finds (S-11) Cu' = [(X2 - d,)C,ul2 + (U2 - dCu1djl/r = [P2C.J, + (1-P2)C.,dll where (5-12) P2 - d2 ) Finally, using a portfolio of A2 of commodity and B2 of bonds, one can show (5-13) C = [PIC., + (1 - PI)Cd1]/; where (5-14) P1 = r di r - di Joined, one gets the recurrence relation for the bond value at period i in terms of the bond values at period i + 3. (5-15) C = [PIP2P3C.IU2UJ + PIP2(1 - P3)Cuud, + PI( - P2)P3C.,d,., + P1(1 - P2)(1 - P3)C,,d2d + (1 - Pl)P2P3Cd,u.xJ + (1 - P)P2(1 - P3)Cd,.,d, + (1 - P1)(1 - P2)P3Cd,d1,, + (1 - P1)(1 -PJ * (1 -P3)Cd,d,]/;3 where (5-16) CU,12U, = min [u2u3;V,F + max (u1u3PP - E,O)] The formula for the bond price after 3n periods is derived below. PRICING COMMODITY BONDS USING BINOMIAL OPTION PRICING 67 (S-17) C = -3n{ 2 2 2 (.1 n! Pli( - Po)'n i* .=0 j'=o k=o 0i(n W) ___ ,________ _____________ _ __ ) )* !(n-)~ ~~ _ n! 3 !(n - k) mm Pi( 2) (! k)! PI'(1 )f min [uutd V, F + max (0 uiu3d7id3ykiP - E)]} Parameter Determination Having derived the recurrence relation for the value of .ne bond after the three-step process-and thus the bond price after n in such three-step sequences-one must discover how the parameters can be derived from the obs ;ved variables. After 3n periods, assuming that there are i steps for process P alone and j steps for process V alone and k steps jointly: (5-18) P =u * din -. 3d3in (5-19) log = i log- + n log d + k log + n log d3 t-n logr (5-20) E[lo ()] P E[i] g ()+ E[k] log (23) + d1d3i (-20) E[log (p)] [ log (d) + n3log (dl) + log d jd3ijn (5-22) var [log (p)] = var i[log d2 + var k[logo d] + 2 cov [i, k] log [ru] log [3] = nql(1 - ql)olog d + nq3(0 - q3) * [log ]2 (As covariance, (i, k) = 0 because the two steps are independent.) Similarly, the mean and the variance for the return on V at the end of 68 COMMODITY RISK MANAGEMENT AND FINANCE the third step can be found by substituting u2 and d2 for ul and d1 and q2 for q, in the above equations. Finally, to find the covariance term, (S-23) Covariance {log ( p ), log (2V )} = E{log (ip*) log (l V) -Elg(p ) jElo ( ] After substituting and then taking expectations (and sparing some tedious algebra), one gets: (S-24) = [k2 - (nq3)2]4log [Ž]]2 = ivariance [k] log [U3]]2 = nq3(1 - q4) log (d)12 For the covariance of the binomial process to equal the covariance of the continuous-time process, in the limit is designated as n o o (5-5 cy[lg (p), (lV)] = nq3(1 - q3)[log(3)] crP ,t Further, for the means to be equal: (5-26) [q3 log U) + log d3n =i3t where O-p is Lhe covariance and A3 is the mean contributed by the third process, t is the time left for maturity of the bond, and 3n is the totai number of steps. (Because there is ns real equivalent of p.3, it is set as equal to A,, - r/3.) Setting the values of the other parameters at (reasons for specific values for parameters can be clearly seen in appendix 5-2) (5-27) q3 = + O'Pv 2 and (S-28) U3 = e + / -v d3 = e - / nv n n the covariance is provided by the third step (5-29) o-pn = [-pv - 3(t) PPICING COMMODITY BONDS USING BINOMIAL OPTION PRICING 69 that in the limit tends to the required value (5-30) opn opvt as n - X For the other two binomial processes, include [ udi)]2 23) = 2t Or ini the limit as n -. o (5-32) n[q!(l - qlj(log (Ud))2] = [p -pt Similarly, (5-33) n[q2(1 - q2)[1og (d2) ] [cv opL]t For the means of the distributions to be equal it requires that (5-34) lim [q log (u) + q3 1og + log did3j n =ipt and similarly for A.,t. The discount rate per period r should satisfy 3n = e" where r is the annualized risk-free rate and t the time to maturity in years. By setting (5-35) -j d = e (S-3 6) q(j+ (p - (±3 + r/3)1 (t) (5-36) 41 = 2[1 + ( -2 _ O,) /(~n) (5-37) u2 = e -(2 - 0rw)v d2 = e - and (5-38) q2 =[1+ - + /3(t) the required values hold in the limit. Note that ;L3 is arbitrary, and q, and q2 play no part in the valuation of the bond except to reassure that the processes are identical. So far, all that is assured is that the means and the variances of the binomial process can be made to tend to the required values. In appendix 5-2, it is demonstrated that the p,-r ceF .ends in the limit to the same probability distribution as the bivariate normal. 70 C(MMODI . IY RiSK .\IANAGE.MEN AND FINANCE iy) Payouts by firn. If I is the fraction of firm ValUC paid out aS dividcnd every ycar, it can bc incorporatecd by dinnishing the firm valuIC every nlt iteranionls by 8V. Pan kruptcV Would not occur as the '1 aluc of the firim could never go to zero as a rcsuilt of a fractional pay out. (2) Coupon paymnients on ondl. If . the yearly fixed coupon payment on thc bond, it could be dpictued by diminishing the vallIC of the firm every nit periods by C (and chcckinig for default). T-he nt coupon (after default) could be added to the bond valu2 at that node, and the standard process could be follou%ed to evaluate the bond Value. (3) Stochastic interest rate. Iihis could bc incorporated by having a fourthi step (plus more for covariancc terms). (4) Senior clebt. Senior debt could be Incorporated by changinig the terminal conditions: That is, if S be the amount of senior debt, the bond value at maturity (5-39) = IMII [ V - S, F - max [0, P - E]] (5) ConzIeniLncc yield. Convenienice yield on the cornmoditv option can be treated in the samie way as dividends on a stock option 'Fall, 1 9S6). If C, is the convenicnce yiced per period, it diminlishies the value of the conmmodity price by (I - C1) ^verv period. (6) Terminal conditions. Different terminal conditions could be incor- porated by mcrely changing the functioni that describes the bond value on teriminal date. Nothinig clse will have to change. Hencc, an lnc\eJ Commodity Option Note, which has a sliding stream of pavrnc::L.> on maturity date with the underlying amount itself being a funcr:o:i of the price, ca basily h priced. Pricing a cap is a trivial extern, Comparative Analysis of Binomioal Model a.nd Sctlhwartz ,Model Results The miodel describcd earlier was prograrmmed using Turbo Basic on an International Business Machines (IB,M) A-F Personal compLter (rc). First, the case assumed by Schwartz was ulsed as a check. The extensions possible with this nodc' were then incorpora-ted and priced. Checks were made by taking extreme cases in which the expected resLult is known. The basic case assumed by Schwartz is that of a company having issued a zero coupon with face value F = 100, maturing in five years. At maturity date, the bondholder has the right to buy a certain commodity bundle with initial value P and price volatility cr,. and is correlated with the commodity price movement v ith correlation coefficient p. PRICING COMMODITY BONDS USING BINOMIAL OPTION PRICING 71 Table 5-1 Commodity-Linked Bond Values for Different Commodity Bundle Prices, Firm Values, and Correlations Usinig the Binomlial Pricing A_'w!el /E = F = 100, r = 0.12, T = 5.0, a =,0.4, a-, = 0.3, number of iterations N = 10) Commoditv Pricing p Default pnrce model 0.0 0.3S 0.70 free Firm value, V - 200 P = 100 Binom;al 86.22 93.59 103.19 Schwartz 85.45 93.34 102.54 Difference (%) 0.90 0.27 0.63 P = 80 Binomial 77.48 83.46 89.46 Schwartz 77.34 83.20 89.26 Diffet.nce (%) 0.18 0.31 0.22 P = SO Binomial 65.38 67.83 69.76 Schwartz 65.01 67.67 69.62 Difference (%) 0.57 0.24 0.20 Fi,!n -t!_, V = 400 P = 100 Binomial 99.89 105.00 109.16 Schwartz 99.00 104.66 108.70 Difference (%) 0.90 0.32 0.42 P = 80 Binomial 86.88 90.53 92.30 Schwartz 86.57 90.02 92.35 Difference (%) 0.36 0.57 -O.OS P = 50 Binomia! 69.30 70.22 70.59 Schwartz 68.89 70.14 70.58 Difference (%) 0.60 0.11 0.01 Firm value, V = 1,000 P = 100 Binomial 107.95 109.08 109.58 109.41 Schwartz 107.15 108.92 109.40 109.41 Difference (%) 0.75 0.15 0.16 0.00 P = 80 Binomial 91.59 92.50 92.42 92.42 Schwartz 91.45 92.41 92.60 92.60 Difference (%) 0.15 0.10 -0.20 -0.19 P = 50 Binomial 70.64 70.58 70.61 70.61 Schwartz 70.39 70.61 70.64 70.64 Hifference (%! 0.36 -0.04 -0.04 -0.04 Table 5-1 shows the rrice of the bond tor various values of the covariance between the commodity price and the valuc of the firm, as well as various values of the firm and the commodity bundle. The average difference in the prices obtained from the two models is about 0.3 percent with the maximum being 0.9 percent and the minimum being 0. This is after 10 iterations of the binomial model. In the limit, the binomial model tends toward the Schwartz model. The advantage is not just simplicity: The binomial method enables the incorporation of senior debt, payouts Original page # 72 is missing. PRICING COMMODITY BONDS USING BINOMIIAL OPTION PRIC.NG 73 'able 5-3 Fffect of a Cornmncdity Pr.ce C.-o on the Commodity Bond Value Firm: valf- C.ise A Case B (V) (with c ap = 105) (no cap) Case C 200 66.97 93.5' 26.62 400 68.32 105.00 36.68 1,000 68.40 109.08 40.38 Note: Nack-Scholes va'ec of cap = 39.74. however, the valuP is not dimirished by the fLll valuLe of the option. This is because the issuer would r.at pay for the high com-nodity price status when barikriptc- is declared. Thercfore. an increase in the risk of default on the bona would decrease the value of ? -ap. In the limit, a cap would ilave no value if the bond alway;s defaulted a.ad paid nozhing, although it woulA equal the value of tLe optiov 'f there was no default risk. Now, in moving beyvonie th-, Schwi rtz model, additions are maae that are permitted bv th: biromial model. T1he startin6 point will be the basic bond, and features wili be addcd so that each fearjre's effect on the price o' ii: botl can be seen. Ilhe followirng assumptions -,re made: Face value = F = 100 Time *o maturity = 4 years Fxerci: price = 100 Inizial commodity pricc = 100 Coupon =- 103 a 0.4 o,, = 0.3 p 0.7 Risk-fr- rte - 0.12 No a-fault risk is assum. d initia"Iy. Table 5-4 shows that i coupon adds value to the bond, ane convc- nience yitld diminishes t!E valuc of the bond. A can, in the ALsence of default risk, reduces the value or the bond by the vaiie of an option with TaDic 5-4 li-pact nf Additional F?atures on Bond Vaiuc idond value Incremen:al value Original bond 110.62 Additic. ! fat: res Coup- i at 10 pe.rcent 14C.'2 29.90 Conv-'.jcr,ce yiela at ' pemcent 124.94 -15.58 Cap at lS0 iO3.34 -21.60 Default ris-z ( - 200) 100.70 -2.64 Scnio: debt (=50) 93.46 -7.24 Payout ratio (1.0) of firm 80.5 -13.01 74 COMMODITY RISK MANAGENMENT AND FINANCE exercise price equal to the cap. (The value of the cap is estimated at 21.28 in the Black forn!'ia as compared with 2i.60 here.) Increased payout and senior debt have no effect if default risk is not considcr. d. In the presence of default risk, however, senior debt diminishes the value of the bond, as do pavouts to equi:y or other bonds. Tlh cap, however, will be worth less. Some Comparative Statics The various parameters will be now varied for the bond above, and the va'ues of the zero-bond (principal and option repayment) and coupons will be established. The effects of varying are as follows: (1) Firm value. Coupons are paid whenever they are due. Therefore, the defauilt on the coupon is only likely when the firm value is comparable to the size of coupon ',ayments. This car be seen in figure 5-2 where default on the coupon starts only when .! initial firm value is below SO. Above SO, however, the coupon is no: defaulted on and maintains a constant value. Similarly, default on the principal and o; .ivn repayment becomes negligible at a firm value higher thar 600. Figure 5-2 Bond Valuesfor Different Firm Values Zero bond and coupon value 1:0 100 _ 90 _ TotalW 80 / Bond 60 _ / 50 4 / ,'Coupon 30 - -… 20 _ ,' 10 0 0 0.2 0.4 0.6 0.8 1 Initial firm value (thousands) PRICING COMMODITY BONDS USING BINOMIAL OPTION PRICING 75 Figure 5-3 Bond ValuesforDiff>rent Coupon Rates Zero bond and coupon value ltO) 90 Total (zero + coup:Jn) 80 70 60 6 . . Zerobond 50 40 30 - Coupon 10 _ , , ,, , , , , . , I 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Coupon rate (2) Coupon rates. Higher coupon rates increase the present value of the coupon, but simultaneously decrease th: value of the zero bond. (See figure 5-3.) This is because a higher coupon diminishes the value of the firm more and leaves a lower amount to repay the principal/option. The net effect is that a higher coupon does not increase the value of the bond as much in the presence of defau!t risk as it would a default-free bond. (3) Convenience yields. The effect of convenience yields is important as these are fairly volatile for some commodities, such as oil. From figure 5-4, it can be seen that a sharp charge in convenience yields, for example. from 20 to -20 percent, changes the total bond value by about 10 percent. (4) Senior debt. Here, senior debt refers ro debt maturing at the same time as the bond, but being senior to the bond. The larger the senior debt, the greater the chance of default on the principal/option, as seen in figure 5-5. Dividend or other payouts earlier than the bond maturity have a similar effect. (See igure 5-6). (5) Caps. Caps are effective as long as they are at price levels that have hig.h probabilities of being attained; at higher levels, they are of negligible value. (See figure 5-7.) 76 COMMODITY RISK MANAGEMF.NT AND FINANCE Figure 5-4 Bond ValuesforDifferent Convenience Yields Zero bond and coupon value 85 84 83 - 82 T Total (zero + coupon) 81- 80- 79- 78 77 l l_l -0.2 -0.1 0 0.1 0.2 Convenience yield Figure 5-51 BG .-, Valuesfor Different Senior Debt Amounts Zero bond and coupon value 110 100 _ 90 eIo Total (zero + coupon) 70- 60 ''- Bond\ 50 40 30 ______________''_,_- Coupon 20 10 0 20 40 60 80 100 120 140 Amount of senior debt PRICING COMMODITY BONDS USING BINCMIAL OPTION PRICING 77 Figure 5-6 Bond Values for Different Payout Ratios Zero bond and coupon value 110 900 ~ = oupon) 90 80 60 Bond -. 50 40 30 - - - - - - - - - - - - - - - - - - 20_ Coupon 10 -0.1 -0.06 -0.02 0.02 0.06 0.1 0.14 0.18 Payout ratio Figure 5-7 Bond Values for Dfferent Caps Zero bond and coupon value 100 f - 90 _ 80 70 - Bond 60 - ---- - - - -- .--- - - - - -- - - - - 50 _ 40 Coupon 20 10 0 , , * . , 0.1 0.3 0.5 0.7 0.9 Cap value (thousands) 78 COMMODITY RrsiS MANAGEMENT AND FINANCE Figure 5-8 Bond 1l}uesforDifferent Correlations Zero bond and coupon value 81 0 808 806 - Total (zero ± coupon) O.-I. 80.2 80.0 79.8 79) 6 79.4 79.2 79.0 i 0.3 0.4 0.5 0.6 t7 Correlation (6) Correlation. Cor:elation between the firm value and the commod- ity bundle price decreases the default risk and, hence, the value of the bond. (See figure 5-8.) Conclusion The binomial model is an effective way ot pricing a commodity bond in the presence of commodity price risk and default risk. Extensions to incorporate other sources of risk can be made easiiy. The limiting factor in all this is computationa! powcr, but it becomes significant only in the presence of features like fixed coupon payments or fixed payouts. Vlie application of this intuitive method to commodity-linked bonds is just one of the many applications possible. For example, secondary mnarket developing country debt could be priced by suitably redefining V (the value of the firm) and P (the price of the commodity). PRICINNG COMMIODITY BONDS USING BINOP,IAI. Ol'TION PRICING 79 Appendix 5-1. The ContinLuouis-Time Model Using the traditional continLous-time option pricing method, it can be shown that if the price of the commnodity bundle P and the value of the irm V follow stochastic processes: (5-40) dp1Pdt + ao dZp (5-41) d dt + V,Zv and (5-42) dZpdZ. = rp,Ldt the differential equation to be solved is (5-43) cjI'-Bpp + !o.2V2B,., + op.l)VBP, + PBp(r - 8} + B,{rV- D] - Bz - rB + C- 0 where B is the value of the bood, Z is the time to expiration, 8 is the convenience yield, D is the total payout by firm per year, and C is the yearly coupon attached to the bond. The boundary conditions are: (5-44) B(P, V, 0) = min [V, F + max (0, P -- E)] where F is the face value of the bond. If payout D is assumed to be a fixed fraction d of the firm value V and the coupon C is a fixed fraction c of the face value of the bond, default must be checked every time the coupon is paid; that is, V Ž C. The solution to this equation (if at all possible) would be very curnbersome, even by most numerical methods. Appendix 5-2. Proof That the Distribution of the Binomial Model Tends to the Bivariate Normal Disvribution To show that the binomial model tends in the limit to the bivariate norri;al distribution, the characteristic function of -he former is shown to tend toward the lat.er. Consider the three-step process in figure 5-1. There are eight terminal nodes at D that are numbered from top to hottom 1 to 8. Al ;he top-moct node, the commodity price is PuIu3r. Therefore, the log of the return on the commodity over the three steps at node 1 is (5-45) log RI = log ul + log U3 + log1 80 COMMODITY RISK MANAGEMENT AND FINANCE Similarly, the log return on the firm is (5-46) log R2 = log u2 + log U3 + log To determine the characteristic function of joint returns (log RI, log R2), denoted as 0(0,, 0-) (5-47) P(01, 0-) = E [exp (i0i log RI, iO2 log R2)] The expectation over the three-step process is the sum of eight terms, each arising from a particular outcome of (log R1, log R,) (5 48) 'k(t01,u2)= D where (5-49) DI = qlq2q3 exp [iOi(log ul + log U3 + log ;) + i02(0og U2 + log U3 + log ;)] _qIq2[11 + A3 b 2 0 X3 Pe; [iUi(r3/h + aa/h + log rt/3n) + i02(0-3Vh + ObIh + log rt/3n)] where h = tln.03 = V/cppv,ria = /(ap - OV),cb = oAw,2)- ap) (5 50) DI = qIq2 11 t A3ih2 exn {/h[i 1(cr3 + a,) + i02(o3 + Ab)] + h[iO1r/3 + i82r/3]} Expanding the exponential as a power series, multiplying out, and rearranging, one gets: (5-51) = qq21 + + iO.(C-3 + a) + iO2(03 + ab) DI=2 1 L Vb ba + h[-iO,(a3 + 'a) + ai82(a3 + ab) + iO1r/3 + iB2r/3- 2 (0- 3 + aa)2 -+ + )2 ( + C)2+ -0102(CT3 + Ua.)(0r3 + 0_b) - -f(0'3 + 0-b) + o(b)} PRICING COMMODITY BONDS USING BINOMIAL OPTION PRICING 81 where o(h) indicates power of h higher than 1, which will be negligible in the limit. Summing over all the eight nodes (i.e., finding the corresponding expression to DI above one for D2:D8 and then adding them all together), a tedious but necessary process, and then simplifying, one gets: (5-52) 0(01,92) = I + V/h[io1co,(2q, - 1) + i02Ob(2.'12 - 1)] + + h[iSlll3 + iO2/u3 + ilr/3 + i02r/3 + 021 (cy2 + _42) 0- 2 (oj + crI) + 0102(0r2) + (2q, - 1)(2q2 - 1)0affb] + o(h) Setting 2 [ ( p (+ r13)) q2 = 1- rl3 and substituting back for 7a, o,s, o'3 one gets: (5-53) k(01, 02) = 1 + h{[iGlp. + i02A2] _ 1 [020uf2 + 0_ia2 + 20102apJ} + o(h) After n such sequences, it is known that (5-54) fn(09,02) = 0-[4(v,02)]" occurs from the independenc- of successive processes. Therefore, allow- ing n -+ x such that h = tin -. 0, one gets (5-55) liM 0(01,02) = 1 + t{i0i,iL + i07p. -2 (02a2 + 02jo + 20iG2upV)} But the characteiist;c function for the joint lognormal diffusion process with parameters up, A., op, a0 is (5-56) 11(001,02) = 1 + (i611 It + i62j2t)0 (-122t + 2oa-vt + 20102apvt) that is the limit of the binomial. Notes 1. All starred (') terms are values on the date of maturity. 2. The European option differs from an Amcrican one in that it can be exercised only .upon eYpiration, rather than at any time. 3. This is not the case 'or a sovereign isje. In a developing country, when a corporate bondholder defaults, government authorities often assume foreign obligations. 4. See COA, Ross, and Rubenstein (1979). Original page # 82 is missing. Original page # 83 is missing. PART II Commodity Con tingency in the Internatioonal Lending of Developing Countries 6 Optimal External Debt Management with Commodity-Linked Bonds Rober yJ. Myers and Stanley R. Thompson MIuch of the spectacular growth in cxtcrnal borrowing by developing countries t...t occurred during .he 1970s was in the forr.i of general obligation loans denominated in U.S. dollars at floating interest rates. It is now well understood that this strategy involved substantial risks in respect to exchange rates, interest rates, and commodity prices. These risks became all too clear follom ing the developing country debt crisis that began in 1982. The deterioration in the developing countries' terms of trade quickly eroded their ability to service their burgeoning debts. In turn, this led to restricted access to new external credit and a period of forced adjustment in consumption and investment. A disturbing number of heavily indebted countries have not yet emerged from the resulting difficulties. This chapter examines the way in which commodity-linked bonds couid be used by developing countries to hedge the risks associated with their external debt position. Commodity-linked bonds are bonds that have principal, and possibly coupon payments, linked to future realiza- tions of a specified set of commodity prices. By issuing bonds linked to the prices of commodities that they export, developing countries would be hedging against the risk of a deterioration in export earnings because of a fall in these prices. If developing country debt had been issued in the form of commodity-linked bonds, debt service obligations would have fallen along with commodity prices, thus easing the burden of adjusting to the external shock. Of course, other commodity-linked financial instruments, such as futures and options contracts, could be Lsed for similar hedging purposes. Futures and options, however, do not exist for many commodities and typically have only short maturities. Thus, for 8S 86 COMMNIODITY RISK MANAGEMENT AND FINANCE many developing countries, commodity-linked bonds show considerable potential as a financial risk management instrument. The characteristics of alternative international financial instruments, including commodity-linked bonds, have been discussed extensively elsewhere. (See Lessard, 1977a; Lessard and Williamson, 1985; and O'Hara, 1984.) The specific purpose hicre is to provide an operational rule for choosing an optimal external debt portfolio consisting of commodity-linked bonds and conventional debt. To begin, a simple dynamic model is used to derive optimal rules for issuing commodity- linked bonds and conventional debt in a small, open economy. Next, estimation methods that allow these rules to be operationalized are presented. The approach is then illustrated with an application to Costa Rica, where the optimal external debt portfolio wvould contain a signif- icant proportion of commodity-linked bonds. A Model of Ootimal External Debt Allocation Consider a small, open economy in which all external debt is issued by the government. The government has a utility function, u(mr.), defined over real imports of goods and services per capita in period t. This utility function is meant to capture the contribution that imports make to domestic consumption and growth. It satisfies the von Neumann- Morgenstern axioms, as well as the conditions u'(m,) > 0 and u"(mt,) < 0. Commodity exports by the country are assumed to follow an exogenous stochastic process that is not influenced by t'ie government's external debt decisions. Real exports per capita in period t are denoted xr Without external finance, the value of imports must equal the value of expo-ts so thar the current account is in balance each period. It is assumed, however, that the government has access to two sources of extern. ! finance. First, it can take out conventional loans at the constant real interest rate r. Real rotal debt per capita held in the form of conventional loans at the end of period t is denoted d,. Second, the government can issue bonds linked to each of n commodities. When issued, th-ese bonds have real prices w, = (wlt, w2t, . . . , w,,) and the real prices of the u.iderlyi- g commodities are denoted P, = (pit, P2t, - . ,Pnt) Future commoc'ity pi ices are stochastic when the government issues the bonds. The bonds mature in one period and require a financial paymen. at maturity that is equal to the price of the underlying commodity.l TcG simplify the analysis, no coupon payments on the bonds are assumed. T.e per capita quantity of bonds issued by the government at time t is denoted b. - (bit, b2,... , bni)'. MANAGEMIENT WITH CO.MMODITY-LINKED BONDS 87 With these assumptions, the constraint facing the government when it chooses an external debt portfolio is (6-1) mt + rdt - I + p1b, -xt + (dt - dt I) + wvtb,. The government is also restricted in that it cannot borrow indefinitely to finance ever-increasing current account deficits. This constraint is im- posed by requiring (6-2) lim dT = rim bT= -- The go%ernnient's problem is now to choose issues of conventiona' debt and commodity-linked bonds that maximize thc discounted time-additive expected utility function (6-3) E,3 v BtIr subject to the sequence ot constraints in equation 6-1 and the transver- saliry conditions in equa'!:;i! 6-2. The solution to the governiment's problem must satisfy 6-1 and 6-2, plus thc Euler equations (6-4) u'(m;) - j3(1 + r)E,u'(mr, l) = 0 and (6-5) u'(m,)uw, - I3E[4u'(int + I)Pt + = 0. Finding a closed form solution is generally impocsible without placing strong restrictions on the form of the uti!ity function and on the probability distribution of prices and exports. Here, however, in accor- dance with the literature on the permanent income theory of consump- tion, it is assumed that the optimal import path can be defined2 as (6-6) mt = a [ (I + r) - 'E,(x, 4 )- , I -(1 + r)d, Notice that this is just a version of the permanent income theory of consumption--imports are set equal to some proportion, a, of "perma- nent" exports (a discounted sum of expected fu:-ure export revenues, minus current external debt). Equation 6-6 is not yet a decision rule because the terms E,(x,.i) must be eliminated by expressing them as a function of variables known by the government at time t. Suppose that x, is the first element of a vector, Yt = (x^, Plts P2,, ..., pnt, se)', that also contains the commodity prices and any other state variables useful for predicting future exports. The vector y, is assumed to follow the autoregre~ sive process (6-7) A(L)y,= et Original page # 88 is missing. MANA.UE.ENTr wuvrii COMMOD!TY-LINKED BONDS 89 are important, however, and the optimal portfolio must be; eiglited accordingly. Estimation Estimation of thc optima. conmodirv-linked bond portfolio revolves around the vector autoregressive process A(L)y, w which was defined in the previous section. Remenibering that , contains all of the com- modity prices that are linked to bonds (as well as x, and other state variables helpful in p:edictirg futrure export revenucs), thenl the condi- tional covariance matrices Qp,. and f2) in 6-13 are clearly just compo- nentr of fQ, the covariance matrix of T. Thus, estimation of the vector aut-regressive process for y, will provide an estimate of Q that, in turn, can be usei directly to operationalize 6-13. Estimation of the vector autoregressive process for Y, is also useful for another reason. To compute opt;rnal bond issues from 6-13, one needs to know the parameter vector y. From 6-8, recall that y represents coefficients on y, in the optimal prediction of a discounted sum of future realizations of export revenues, given current and past values of v,. From a formula derived by Hansen and Sargent, this optimal predictor is (6-14) 2 (1 + r) - 'E,(x, + 1) = A[I4/(1 - r)] - l'v + B(L)y, - 2 wvhere X is a row vector with a one in the first column and zeros elsewvhere, and B(l' satisfies (6-15) B(L) = OA[1/(1 + r)]7 (1 + rYkAk]Li+ 1 Thus, y is simply the first row of A[ 1/(1 + r) -f'. Evidently, estimation of the autoregressive pararneters in A1(L) provides a direct estimate of y (conditional on knowledge of the real interest rate r). Actual estimation of the parameters in A(L.) and fl can be accomplished via vector autoregression.4 The final piece of the estimation puzzle lies in obtaining an estimate of the real interest rate, r. Once r has been found, and A(L) and fl have been estimated, then cornputing the optimal commodity-linked bond issues is straightforward using 6-13. In many cases, prior information will be available on real interest rates. In the following application to Costa Rica, optimal external debt portfolios for a number of different real interest rates are presented, and the results indicate that they are not sensitive tor ;.s value. YU (COMMODITY KISK IMANAGEMENT AND PINANCE The Case of Costa Rica Costa Rica is a small country that depet;ds on a handful of agricultural commodities for the bulk of its export earnings. In recent years, coffee, beef, and bananas have accounted for more than half of total export revenues. Figure 6-1 shows gross national product (GNP), consumption, and investment for Co, A Rica betveen 1966 and 1986, all in real per capita terms. The pronounced slump that began around 1981 and continued into 1983 is indicative of the problems that many developing countries have experienced since the onset of the debt crisis. Figure 6-2 shows Costa Rica's terms of trade index and their total foreign debt in U.S. dollars. The data suggest that the economic slump of 1981-83 was preceded by a sharp negative terms of trade shock and a dramatic increase in debt servicing requirements. By linking debt service require- ments to conmnodity price realizations, commodity-linked bonds might help facilitate adjustment and avoid future slumps of this severity. Figure 6-1 Real per Capita Gross National Product Consumption and Investment for Costa Rica, 1966-86 1980 Colones per capita 20,000 18,000 GNP 16,000 - 14,000 -/- 12,000 _ / ~ Consumption 10,000 8,000 6,000 - Investmnent 4,000 - 2,000- 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 Source: World Bank data. MANAGENIENT WITH COMMODITY-LINKED BONDS 91 Figure 6-2 Terms of Rhade and Per Capita Total External Debtfor Costa Rica, 1966-86 Tenns of trade (1980 = 100) 150 2,000 140 - Terms of trade / 1,500 130 / Exteral debt 120 1 1,eOo 110 / 1~~~~~ ~-500 100 1IQ6i 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 Source: World Bank data. To illustrate the estimation of optimal external debt portfolios, a Costa Rican portfolio of conventional loans and bonds linked to three major export commodities-coffee, beef, and bananas-was examined. Real prices of these commodities are denoted Pa, Pb,, and Pat respectively. The first task was to estimate the vector autoregressive process for real exports and the three real commodity prices. To simplify, the possibility of including other variables in the model was not considered. Nominal prices and nominal export revenues, all in U.S. dollars, were each deflated by an index of import prices for Costa Rica. The commodity prices were obtained from World Bank (1985), and all other data are from World Bank (1988). The data are annual, and the sample runs from 1966 through 1985. In view of Lhe small number of available observations, an equation- by-equation approach to model specification was used. Preliminary investigations revealed no strong evidence of nonstationarity or hetero- 92 COMMODITY RiSK MANAGEMENT AND FINANCE Table 6-1 Estimation Results x, = 219.55 + 0.63 x, I - 0.11 xt - 2; K2=0.36 (3.78) (4.14) (0.78) pc = 2.82 + 0.42 pc - 0.10 p_ ; R2=0.23 (3.92) (2.63) (0.65) pb = 0.61 + 0.84 pb_ - 0.05 pb 2; 20.57 (1.13) (3.87) (0.22) pf = 0.05 + 0.48 p, -+ 0.65 pa - 2 0.04 pb 1; R2=0.58 (1.12) (3.11) (3.75) (4.14) [ 2,238.4 39.2 9.9 0.9 1 n- 39.2 0.99 0.15 0.02 9.9 0.15 0.44 - 0.019 _ 0.9 0.02 - 0.081 0.001 J Note: Values in parcnthcess are t-values. scedastic errors, so the models were estimated in the levels of each variable, assuming a constant conditional covariance matrix. Initially, an overfitted equation was specified with lags of all four variables included. len F-tests were used to test zero restrictions on sets of coefficients. Estimation results for the final model specification are shown in table 6-1, where the system was estimated using seemingly unrelated regression. Table 6-1 also contains the resulting estimated conditional covariance matrix. The optimal external dt'Nt portfolio was computed for 1985, the last year of the sample. The n:atrices QY,, and flpp come directly from table 6-1, and the parameter vector y is computed from the estimates in the table (as shown above). Each optimal commodity-linked bond issue was Table 6-2 Optimal Portfolios in 1985 as a Proportion of Total External Debt General obligation r loans Coffee Beef Bananas 0.00 .655 0.144 0.035 .0.166 0.05 .652 0.145 0.036 0.167 0.10 .649 0.147 0.036 0.168 MANAGENIENT WITH COMMODITY-LINKED BONDS 93 multiplied by an estimate of its price. This estimat. as obtained by using the vector autoregression to forecast commodity prices into 1986 (given information available in 1985) and then discounted back using the rei! interest rate. The final revenue figure was then expressed as a proportion of the actual level of total external debt in Costa Rica in 1985. The estimated optimal external debt portfolio is presented in table 6-2 under three different real interest rate assumptions. Clearly, the portfo- lios are not very sensitive to the real interest rate used. The results suggest that more than 30 percent of total debt should be issued in the form of commodity-linked bonds, with the bulk of these issues being split between coffee and bananas. The optimal portfolio of external debt for Costa Rica in 1985, therefore, appears to contain a significant proportion of commodity-linked bonds. Concluding Comments This chapter provideK a simple dynamic model that can be used to estimate optimal portfolios of external debt. It focuses on the potential role of commodity-linked bonds in hedging against the possibility of a deterioration in a country's terms of trade. The approach wvas applied to Costa Rica, where it was found that a significant proportion of external debt should be issued in the form of commodity-linked bonds. The framework could be extended in a variety of directionis. In particular, although optimal portfolios of external debt have been computed, the extent of reductions in the variance of real imports has not yet been determined. This information is critical in determining the hedging effectiveness of commodity-linked bonds. Future research might also examine expanded portfolios, perhaps looking at other commodity- linked instiuments, such as futures, options, and bonds linked to indices of commodity prices. There are a number of practical difficulties associated with commodity- linked bonds that deserve add:tional attenzion. In this paper, it has simply been assumed that markets for these instruments exist, and that such markets have no risk premia. It seems likely that commodity-linked bonds would be priced at a discount, however, especially if issued by developing countries subject to sign, icant default risk. In fact, the size of risk premia may be an important reason why there is currently such little use made of commodity-linked bonds. Nevertheless, the analysis pre- sented above suggests a potential hedging role for commodity-linked bonds, provided that diversified markets for these contracts can emerge and grow. 94 COMMODITY RiSK MANAGFIMENT AND FINANCE Notes 1. For simplicity, attention is restricted to bonds with a one-period maturity. An extension to longer-term maturities, however, would be relatively straightforward. 2. Assumptions sufficient to guarantee this equation is an exact solution are: (I) the expected real return to holding bonds is equal to the real interest rate E,[W,.1 - P, ,+,(1 + r) = 0 for i = 0, 1, . . . ; and cither (2) utility is qua .atic or (3) utility features constant absolute risk aversion and m, is normally distributed with a variance that depends only on i or (4) utility features constant relative risk aversion and log mi, is normally distributed with a variance that depcnds only on i. See Evans (1988) and the refcrences therein for more details on the latter three conditions. A complete derivation of equation 6-6 under these conditions is available from the authors on request. 3. This implies that there are no risk preniia in commodity-linked bond prices. If investors are risk adverse and cannot diversify all of the risks of investing in the bonds, then the bonds may be priced at a discount to conventional debt. (Schwartz, 1982) 4. No discussion of vector autoregression estimation techniques is included here. Those interested should consult Engle and Bollerslev (1986), Engle and Granger (1977), Sims (1980), and others. 7 Integrating Commmodity and Exchange Rate Risk Manlagement: Implications for External Debt Management Stijn Claessens Other things being equal, a strengthening of the dollar will worsen the terms of trade of net commodity exporters and hence reduce their welfare. For net commodity importers, the reverse pattern will hold.I ... for some countries, the fall in the dollar increased the burden of debt relative to their economies.2 Who is right, ex ante and ex post, about the effect of a cross-currency movement on the welfare of developing countries? Even though both quotations are, of course, deliberately placed out of context, they do illustrate some of the unresolved issues regarding the effect of cross- currency movements on the welfare of developing countries. The aim of this chapter is to at least clarify, and potentially resolve, some of these outstanding issues. Furthermore, the chapter attempts to present concep- tual and practical guidelines that will help with external debt manage- ment generally. During the past decade, many developing countries have been affected by the large volatility in cross-currency exchange rates and commodity prices as a result of the impact of these changes on the relative burden of 95 96 COMMODITY RISK MANAGEMENT AND FINANCE their external deF- service. Cross-culrrency exchange :.- lhanges have affected the struct re, as well as the level, of many de . i ; countries' external debt. This is, for instance, demonstrated by .; uncertainty of the real effective costs in a particular currency-where th. costs are related to the ability of and the opportunity costs to the country in generating foreign Original page # 102 is missing. INMPLICATIONS FOR EXTERNAL DEBT MANAGEMENT 103 An Analytical Model for Commodity Risk and Exchange Rate Managemenit Consider a world that consists of a small, open economy (the home country) and N developed countries.)7 Let each of the N developed countries, in whose currencies external debt can be denominated, have an exchange rate e(i), i = 1, . . . , N, which follows the diffusion process:18 (7-1) de() = v,(,)dt + oe(,)dZe,), i = 1,..., N e(i) Here e(s) is written in terms of the home country's currency per unit of the foreign currtncy (e.g., pesos per U.S. dollar), and dZ,(,, is a Wiener process. So E(dZ) = 0 and VAR(dZ) = dt. Thus, this differential equation says that the expected value of the depreciation of the ith exchange rate during the time period dt is v(,) and its standard deviation is 'Te(,. It is assumed that the exchange rate depreciations are approxi- mately normal for small intervals dt and that the exchange rates themselves are lognormal.19 Surpose also that the means and standard deviations Ve(,) and ¢e(,) are a)'owed to depend on bor,i time and a vector of state variables (which will be defined later). co, (7-2) Ve(j S = , t) and o.,p, = e,(S, t) where S is a (S x 1) vector of state variables that are assumed to follow It6 processes. Thus, there are N foreign currencies in which the home country can denominate its liabilities and invest its wealth, which are assumed to follow the process (7-3) = de,)(S, t)dt + oe,,(S, t)dZd,, Suppose that each country in the "world" hzE one no,ninal riskless (instantaneous) bond. Let B*( j) be the price in the jth currency of the foreign country j's riskless bond and B be the price in the home currency of the home country's riskless bond. The dynamics for B*(j) are- given by (7-4) =dB*(i) R*(j)dt, j = 1, .. . , N (74) ~~B*(j) where R*(j) is the instantaneous nomninal rate of return on the jth bond in cLrrency j, which is assumed to be constant. Also, let R be the instantaneous nominal return on the safe domestic bond. All interest rates are assumed to be constant. DJefine the excess return of the jth foreign bond for a domestic investor, dP(B-(J))1H(B*(i)), as the return on one unit of domestic currency 104 COMMODITY KI' ..: .',UANAGENIENT AND FINANCE invested in the foreign bond, financed by borrowing at the interest rate R in the domestic country, that is, (7-5) dH(B*(j)) = R*(j)dt + (() - Rdt, j=1, ...,N -(R*(1j) + Ve(j) - R)dt + Oe(j)dZe(;) Notice that the foreign bonds are risk-free in their own country, but exchange rate risks make them risky for investors from the "home country" and that their excess returns are perfectly correlated with the changes in the corresponding exchange rate.20 Next, suppose there are K commodities consumed in the home country, whose domestic currency prices follow the differential equation (7-6) dP(i) = vp(I)dt + op(,)dZp(a,) i = 1, . .. , K P(i) =lpjd Again, vp(,) and up(,) are allowed to be functions of both time and a vector of state variables. So the commodity price changes have a mean of vp(,,(S, t) and a standard deviation of qp(,j(S, t) over short time intervals dt.21 The first K elements in the (S x 1) vector of state variables are assumed to be the changes in the logarithms of the commodity prices; the next N elements are assumed to be the changes in the logarithms of the exchange rates, and the remaining (S - K - N) elements are assumed to be other unspecified exogenous variables. r ially, it as assumed that the domestic investor maximizes a time- ac:aitive von Neumann-Mcrgenstern lifetime expected utility function that depends only on the consumption of the K commodities and time, that is, Et{f7 U[cj(z), . . . , ck(z)]e-' dz} where 6 is the intertemporal rate of time preference and c; is the consumnption rate of good i. This assumption completes the model, and allows one to solve for the optimal liability portfolio.22 Let b be the optimal amounts of foreign liabilities; let V be the (N x 1) vector of excess returns; let Vaa be the (N x N) covariance matrix of excess returns to the foreign bonds; and let V, be the (N x S) matrix of covariances between the excess returns and changes in the state variables, which include the K commodity prices. Notice that, because the excess returns on foreign liabilities are perfectly correlated with changes in the exchange rate, Vaa is the same as the covariance matrix of exchange rate depreciations, and Va, is the same as the matrix of covariances between the exchange rate depreciations and changes in the states variables- where the first K state variables are the commrodity prices.23 It can be shown (see Svensson, 1987; Stulz, 1981; or Breeden, 1979) that the optimal F ,s of foreign bonds b = 1/C,,[-Uc/Uc,V-'v - VJ VasCS, IMPLICATIONS FOR EXTERNAL DEBT MANAGEMENT 105 where C = C(W, S, t) is the consumption expenditure function of the investor, W is wealth, and subscripts refer to partial derivatives. Notice that this is a linear combination of (s + 1) column vectors, each of which (when appropriately scaled) can be interpreted a; a mucual fund portfo- lio. The first portfolio is a mean-variance ehicient portfolio (i.e., a speculative portfolio), given by V-'v, and the remaining s portfolios are hedging portfolios, given by the s columns of (7-7) aa as The weights in the linear ce-nbination depend on the parameters of the utility function (such as degree of risk aversion and the consumption shares of the different goods), although the portfolios themselves do not. The weight on the speculative portfolio is - lCw(U,'Uc/) where UJU,, is the inverse of the coefficient of absolute risk aversion, and the we;ghts on the hedging portfolios are -Cs/Q,. For a country with a high degree of (relative) r.sk aversion, the hcdging mutual funds will clearly be relatively more important in the overall optimal holding of foreign bonds than the speculative mutual fund. Assuming that most developing countries are relatively risk averse, and using the assumption that the expected costs of borrowings in different currencies, after adjusting for exchange rate changes, are all equal (i.e., v = 0), the focus of the rest of this chapter will be on hedging portfoiios.24 The hedging portfolios are the portfolios that provide the maximum correlation with the state variables S; hence, they can be used to hedge against unanticipated changes in the state variables. This is because, after a shock to a state variable, the hedging portfolio leaves the investor's wealth and welfare "as near as possible" to what it was originally, where "nearness" depends on the degree of correlation of that portfolio with the state variable. The state variables that are of most concern here, and against which a commodity exporting developing country would want to hedge most, are the K commodity prices that determine its welfare level. The model says that the optimal way to hedge the K commodity prices (and, thus, the consumer's welfare) against changes in the exchange rates is to borrow according to the first K elements of the matrix V-1V because then a change in each currency leaves the investor's net welfare the least affected and would insulate the country from relative prices shocks, which are assumed to be the only external shocks affecting the country.25 The hedging portfolio has to be determined in light of the interaction between exchange rates and relative (commodity) prices movements. In the empirical application of this model, the K commodities p.. have been collapsed to one price-the difference between the logaritihrii of the export price and the logarithm of the import price, that is, the 106 CONMMODITY RISK MANAGEMENT AND FINANCE country's terms of trade.26 The terms of trade indicate the opportunity costs of foreign good consumption in terms of foreign goods earnings. The hedging portfolio of foreign liabilities will then insulate the country as well as possible against increases in the prices of import goods relative to the prices of export goods.27 Empirical Applications in Indonesia and Turkey The Econometric Model On the basis of the theoretical model, a portrolio of foreign assets is desired that has maximum correlation with the changes in the terms of trade.28 This optimal hedging portfolio can be found by solving equation 7-7, where V,,, is now the vector of covariances between the changes in the termr,s of trade and the changes in the exchange rates. Notice that Va'VaV is a simple ordinary least squares (o0s) regression (without intercept' -,f the changes in the state variable on changes in the exchange rates. Sui one could calculate the optimal portfolio shares by running a simple oLs regression of the terms of trade changes on the exchange rate changes and use the parameter estimates for the slopes as the shares. This procedure implicitly assumes that the variances and covariances of the exchange rate changes are constant through time, however, an assump- tion that has been proven false many times in the literature. It would seem appropriate, then, to use an estimation procedure that allows the covariance matrix to change with time. Autoregressive Conditional Heteroskedasticity (ARCH) is an economet- ric technique developed by Engle (1982) to do just that. In the univariate version that he presents, the conditional variance of a time series is allowed to depend on lagged squared residuals in an autoregressive manner. This means that during periods in which there are large unexpected shocks to the variable, its estimated variance will increase, and, during periods of relative stability, its estimated variance will decrease. Kraft and Engle (1982), Bollerslev (1986), and others have generalized the ARCH model in much the same way that an Autoregressive model is generalized to an Autoregressive Moving Average (ARMA) model. This model, called Generalized ARCH or GARCH, is the same as an ARMA model in squared residuals. Just as the ARMA model allows the mean to change with time, the Acti- (and GARCH) model allows the variance to change with time. The generalization of the univariate ARCH models to multi- variate ARsCH models involves allowing the whole covariance matrix to change with time, instead of allowing just the variance to change with time. The model used in the application reported here was developed by Bollerslev (1987). Although somewhat restrictive (because it imposes the IMPLICATIONS FOR EXTERNAL DEBT MANAGENMENT 107 restriction that the correlation matrix is constant through time, while the covariance matrix changes), it is relatively simple to estimate. The Optimal Portfolios The GARCH process was estimated for weekly exchange rates for the five major lending currencies: Japanese yen (-Y), deutsche mark (DM), Swiss franc (SwF), pound sterling (£), French franc (Ff) and U.S. dollar (US$) for nine different subperiods; each consecutive subperiod covered an additional quarter of observations.29 Each of the nine subperiods covered the period from the first available data point until the start of the quarter for which the optimal portfolio was to be calculated. As a result, a series of (conditional) forecasts of the variance-covariance matrix of exchange rate depreciations for the next three months resulted, that is, (Va,). The inverse (V-') was calculated and multiplied by the vector of forecasted covariances between exchange rate depreciations and changes in the zerms of trade, (V1V,,5).30 The r. Its for the optimal portfolio shares for Indonesia are shown in table 7-1, where the portfolios are scaled to sum to one and where a negative portfolio share implies that a country should invest its foreign currency assets in the currency to hedge terrns of trade risk. As can be observed, the relative shares of the currencies change quite a bit from quarter to quarter, and, as it turns out, the unscaled portfolios also change. Note, however, that the effective currency distribution of the portfolio does not change much through time once one accounts for the high correlation between the period-to-period changes of the European currencies over this period. The sums of the shares of the European currencies (DM, SwF, £, and Ff) are for each quarter (from the first quarter of 1986 through the first quarter of 1988): 10.9, 13.8, 7.4, 18, 34.4, 19.7, 25.8, 11.1, and 6.1 percent. The combined European share is Table 7-1 Optimal Portfolios for Indonesia Period AC DM SwF £ Ff US$ 1986.1 -0.005 0.307 -0.055 0.007 -0.154 0.900 1986.2 -0.022 0.320 -0.028 0.028 -0.182 0.884 1986.3 -0.001 0.164 -0.012 0.021 -0.100 0.928 1986.4 -0.027 0.384 0.019 0.027 -0.252 0.849 1987.1 -0.009 0.801 0.026 0.150 -0.632 0.665 1987.2 0.006 0.462 0.015 0.075 -0.354 0.797 1987.3 -0.033 0.703 -0.017 0.030 -0.479 0.777 1987.4 0.044 0.323 0.001 0.029 -0.243 0.847 1988.1 0.031 0.191 -0.005 0.014 -0.139 0.907 108 COMMODITY RISK MANAGEMENT AND FINANCE Table 7-2 Optimal Portfolios for Turkey Period y DM SwF £ Ff USS 1986.1 0.911 -0.311 -0.893 0.255 1.131 -0.093 1986.2 0.335 -0.677 -0.589 0.531 1.265 0.135 1986.3 0.799 -0.479 -0.833 0.718 1.019 -0.225 1986.4 0.548 -0.365 -0.974 0.932 0.867 -0.007 1987.1 0.390 -0.363 -1.022 0.857 1.086 0.052 1987.2 0.362 -0.159 -0.863 0.618 1.190 -0.147 1987.3 0.237 -0.123 -1.234 0.483 1.783 -0.146 1988.1 0.115 -0.086 -1.842 0.498 2.511 -0.197 thus significantly more stable than the individual shares, a reflection of the high correlation among the European currencies.3' The sum of the unscaled portfolio weights ranges between about 7 and 48, which suggests different absolute levels of borrowing. Similar analysis can be conducted to find the currency portfolios that hedge against changes in export prices, export values, import prices, or import values. Comparing these portfolios of terms of trade hedges with Indonesia's actual portfolio composition during this period suggests that a move toward the optimal portfolios could have resulted in a large reduction in the variance of Indonesia's net position, as the optimal portfolios differed substantially from their actual portfolios.32 It turns out that rolling forward optimal portfolios (calculating each portfolio using data to that point in time) for each quarter between early 1986 and early 1988 was effective in reducing the variance of the debt service relative to the country's terms of trade, when compared with rolling forward a portfolio that had the actual currency composition of Indonesia's debt at the end of 1985. Presumably, the movement in Indonesia's borrowing portfolio away from 4X to I JS$ resulted in increased stability of the country's debt service burden relative to the purchasing power of exports. The case for Turkey was analyzed similarly. Applying the strategy described above, table 7-2 presents the optimal portfolios for each quarter. Here, one notices the large changes in the optimal portfolio shares through time, unlike Indonesia where they were relatively stable. The sum of the unscaled portfolio weights ranged between about 0.9 and 2, suggesting, similar to the results for Indonesia, different absolute levels of borrowing. The sums of the shares of European currencies for the nine quarters were as follows: 18.2, 53, 42.6, 45.9, 55.8, 78.5, 90.9, 77.7, and 108 percent. The sums suggest a somewhat more stable weight IMPLICATIONS FOR EXTERNAL DEBT MANAGEMENT 109 Table 7-3 Optimal Portfolios, Shares Positive, for Turkey Period X DM SwF £ USS Surn 1986.2 0.075 0.000 0.000 0.337 0.349 0.239 0.554 1986.3 0.338 0.000 0.000 0.462 0.200 0.000 0.576 1986.4 0.117 0.000 0.000 0.677 0.067 0.138 0.705 1987.1 0.000 0.000 0.000 0.582 0.233 0.180 0.746 1987.2 0.020 0.000 0.000 0.436 0.544 0.000 0.759 1987.3 0.000 0.000 0.000 0.228 0.769 0.003 0.627 1987.4 0.037 0.000 0.000 0.251 0.712 0.000 0.663 1988.1 0.000 0.000 0.000 0.124 0.876 0.000 0.375 for the European currencies as a whole compared with the individual European currency weights. There is a relatively large difference between Turkey's actual debt portfolio (as of late 1988) and the calculated optimal debt portfolios, which suggests that there was room for considerable hedging by modi- fying the external debt portfolio. Application of a similar methodology, as was used for Indonesia, resulted in no significant variance reduction, however, most likely because of the large volatility in portfolio shares from period to period. Restricting the portfolio shares to be positive, that is, not ahiowing any investing in foreign currencies, resulted for the nine quarters in the portfolios for Turkey shown in table 7-3. Restricting the weights of the currencies to be positive led to less skewed and somewhat more stable portfolios. In addition, the sum of the unscaled portfolio amounts (the right-hand column of the table) was more stable. Overall, the results for Turkey need to be interpreted with extreme caution because the weights turn out to be very unstable over time. TFhis can most likely be explained by the fact that Turkey's economy has undergone significant structural changes in its export and import patterns during this period.33 As the structure of the underlying model is changing over time, it prevents the calculation of portfolios that can serve as effective hedges. Imposing more restrictions, while solving for the portfolio weights, and/or using different econometric techniques would therefore be unlikely to lead to more stable results. The results for both countries point up some general pitfalls in the empirics. One rests in the data for the terms of trade, which traditionally have been of poor quality for many developing countries. The major pitfall of the empirical applications, however, is most likely that the relationships between the terms of trade and exchange rates changes are not stable or sufficiently robust over time that the optimal portfolio for 110 CONMMODITY RISK MANAGEMENT AND FINANCE the next period can be determined with accuracy. Correlations between terms of trade and foreign exchange rates for both countries were relatively low. As for topics for further empirical research, several come to mind. One is to perform these types of analyses with a larger set of currencies. Another research topi, vould be to experiment with the use of an instrumental variable to forecast the developing country's currency changes and obtain the deviations from the expected exchange rate changes. This econometric technique might be necessary because many of the developing countries' exchange rates are not "market" rates and often do not follow the assumed random walk (in first differences). Other research extensions would be to account for the movements of the lender's interest rates in calculating the effective costs of foreign borrow- ings and to expand the set of possible liability instruments by including, for example, commodity-linked bonds. Conclusion This chapter has examined the issues involved in integrating commod- ity and exchange risk management. It has pointed to weaknesses in the currently accepted guidelines regarding derivation of the optimal cur- rency composition of a country's external liability and has presented a model that can be used to calculate the optimal debt portfolio for a country that wishes to hedge against exchange rate and commodity price fluctuations. The chapter has also summarized estimates of the optimal currency composition of Indonesia's and Turkey's external debt, derived on the basis of this model. The optimal portfolio calculated for Indonesia for a recent period was an effective hedge, reducing the variance of the costs of borrowing relative to Indonesia's terms of trade. The applica- tions of the theoretical model show that even though developing coun- tries might have only limited access to organized currency futures and commodity hedging markets, they can manage their external exposure effectively if they can at least structure their external debt in light of the relationships between exchange rates and commodity prices. It seems fair to conclude that there can be significant benefits from integrating currency risk management with commodity risk manage- ment, particularly as dollar/nondollar currency movements are likely to have offsetting effects on the relative level of the country's debt burden in the form of primary commodity price movements. Because many devel- oping countries depend heavily on exports earnings from primary commodities to service their external debt obligations, a certain amount of nondollar external debt obligations could be a good external liability policy. The optimal amount of nondollar obligations and the division IMPLICATIONS FOR EXTERNAL DEBT NMANAGEMENT 111 aniong the specific nondollar currencies will depend on the relationships between the commodity prices and exchange rates in question. Because these relationships might not be very strong and may be unstable over timne, care has to be taken in implementing the portfolio comnpositions r(:sulting from the empirical work. The policy guidelines discussed earlier might still be of use in verifying the properties of the portfolio compo- s Ltions. Notes 1. Dornbusch (1985), p. 335. 2. The World Bank, Anniual Report, 1987, p. 49. 3. The share of dollar-denominated external liabilities of all developing countries reporting to the World Bank Debt Reporting System (DRS) hovered around 63 percent in the early 1980s and then steadily declined from 66 percent to around 50 percent in 1987. The decline since 1985 has been in part due to the depreciation of the U.S. dollar and in part due to the relative retreat of U.S.-dollar-based lenders from sovereign lending. 4. For example, the. U.S.-dollar-rre sured level of external debt of all DRS-reporting developing countries was USS102.7 tillion. 5. In general, movements in import as well as export prices have affected the developing countries. *Vebb and Zia (1988) have performed some counterfactual scenarios in whicil they demonstrate that, assuming that the change in resource flows as a result of terms-of-trade changes was met by increased or decreased external debt buildup (using the actual volumes of exports and imports in the 1980s), for a number of developing countries, their external debt in 1986 would have been substantially less (as much as 25 percent of their gross domestic product) if the terms of trade for these countries had remained at their average level of the 1969-78 period. 6. For exampkc, weli -diversified financial institutions can transform an external liability denominated in one currency into a liability of another currency through a forward transaction at a cost that can be substantially below tb: opporrunity costs for a liability holder such as a developing country. 7. The conditions necessary to separate the hedging and speculative decision are well documented. See, for example, Breeden (1979). 8. The recent increase in commodity prices seems to confirm the inverse relationship between the dollar exchange rate and commodity prices. The slump in commodiry prices in the first years after the recent dollar depreciation can be, in part, explained by developing countries' needs to raise foreign exchange through the export of commodities whose demand was inelastic. Gilbert (1988) concluded that the long-run elasticiy of commodity price indices with respect to change in the value of the dollar-corrected for, among others, developing country debt servicing-wa-, approximately unity. This would imply that commnodity prices rise and fall inversely to dollar appreciation or depreciation and could have important implications for external liability management of a (primary) commodity exporting nation. He alsco concluded that there are suggestions that the interaction between dollar appreciation and the dollar-denominated debts has been responsible to a significant extent for the low primary commodity prices in the years during and immediately after the dollar appreciation. Dornbusch (1985) found an elasticity of the real commodity price on the real U.S. dollar exchange rate of approximately -0.82. Using lagged values for the real exchange rate, the elasticity became - 1.5. 112 COMMIODITY RISK MANAGEMENT AND FINANCE 9. See Giovannini (1985) and Dornbusch (1987) for their ideas and empirical work in this regard. 10. Lessard and Williamson (1985) is a good example of this literature. i1. Of course, whether or not purchasing power parity (PpP) holds plays an important factor in this matter. .f Prp held perfectly, currency tluctuations would presumably not affect real export earnings and costs of imprcts. For strong and conclusive rejections of nPp, see Frankel (1981) and Cumby and Obstfeld (1984). 12. For further information on the optimal currency basket literature, see Branson and Katseli (1982) and Lipschitz and Sund&rnrajan (1982). Williamson (1982) surveyed many of the issues on currency baskets. 13. Pagee (1981) reported that, in the late 1970s, approximately 55 percent of world exports were denominated in U.S. dollars. 14. For further analysis of this issue, see, for example, Dornbusch (1987), Giovannini (1985), Flood (1986), and Varangis and Duncan (1990). Dornbusch (1987) has a simple model in which the real dollar exchange rate enters in the commodity pricing function. 15. See Ahamed (1988) for a very useful discussion on optimal currency management, which is similar to the discussion here. Ahamed mentions real income as a potential underlying variable t-. niedge. A rule of thumb on currency management for countries with oil exports, for .xample, which has been popular during some periods, was that these countries should borrow British pounds or Norwegian kroner because these currencies were more likely to be correlated with the price (and export earnings) of oil. 16. 1 v-ante deviations from uncovered risk parity will be due, apart from transaction costs, to risk premia. As these risk premia will be largely determined in the developed capital markets that, compared with developing countries, have an advantage in carrying risk-because of factors like the wider portfolio choice in developed countries-it seems valid to argue that these risk premia will be relatively small :ompared with the risk- reducing benefits for the developing country involved. As long as the developing countries are more riskc adverse than what the developed countries' capital markets im.ply, transfer- ring risks from the developing to the developed countries can be a Pareto improvement. 17. This section is a brief summary of a restricted version of the model presented in Claessens (1988), which is also reported in Kroner and Claessens (1989). See the first paper for the general model and some further references. See Wells (1989) for similar work. 18. It is assumed that forward and futures markets for foreign exchange and commodity prices are insufficien0v available to allow the country to hedge these risks. 19. See Merton (1971) and Fischer (1975) for descriptions of the properties of Wiener processes ancI stochastic differential equations. The general equilibrium implications of these and other assumptions are not discussed here. 20. If one had assumed that foreign interest rates were not constant, the domestic currency return on a foreign bond would not necessarily have been perfectly correlated with the exchange rate, as foreign interest movements could have offset or increased cxchange rate movements. Short-term foreign currency deposits would still have a relative exposure (i.e., elasticity) of one with respect to exchange rates, but the exposure on the rcturns (or costs) of long-term fixed and/or floating instruments could have been different from one. Adler and Simon (1986), however, have shown that during the period from 1973 to 1980, the exposure on rcturns on foreign long-term bonds was essentiallv one with respect to their own currency and that exposure with respect to other currencies was essentially zero. This would imply that longer-term foreign, liabilities would present equal hedging potential against their own exchange rate changes as the short-term instruments used here. The verdict on the post-1986 period is still out and could very well be different because the interaction between interest rate changes and exchange rate changes has, if ai.ything, become more complex. INIPLICATIONIS FOR EXTERNAL DEBT MIANAGEIMENT 113 21. One m ist not assume that the law of one price holds necessarily for all goods (nor that ppp holdsi; that is, P(i) $ P' (i, j)e(j) necessarily for all i and i, where P(i, j) is the price of the traded ,ood i in terms of foreign currency j. Neither is it assumed that changes in the terms of trad, are perfectly correlated with the (weighted average of the) changes in the exchange rates. 22. The representative consumer technique is used hel? to mimic the sitiation in which the government acts perfectly in the interest of the indivildual citizen of the country and has instruments at its disposal to allocate (nondisrortionary) transfers to private citizens. Alternatively, the government can decide to hedge only the exposure of its own welfare or revenue and expenditures streams. Depending on, among other things, whether private citizens have access to foreign financial he ,,ing instruments, the two approaches can lead to different outcomes. 23. If the interest rates on the foLeign liabilities would not have been constant, then the excess return variance-covariance matrix could not have been replaced with the exchange rate covariance matrix nor the covariance of excess returns with prices with the covariance matrix of exchange rates with prices. 24. High risk aversion in developing countries and low risk premia (v n are compatible, provided the risk premium is largely determined in the lending counn..- and the level of risk is relatively low in lending countries. 25. The borrowing shares would apply to the country's net foreign liabilities, that is, the gross debt minus foreign exchange reserves and foreign exchange assets. The K prices should be interpreted as the prices nf goods that are importeci, relative to their opportunity cos n terms of domestic consumprton foregone (as export, have to be generated to pay for :mports). In other words, the K comr-qdiry prices are the relative terms of trade of the inldi;'!ddal K goods, zhat is, irdivieual import prices relative to the general level of export prices. Because the model does not deal with nontradable goods, it is not necessary to reflect in the relative price of goods the relative price of nontradables as well. 26. The use of one pnce variab!e-terms of trade-instead of K can be justified if the utility function to be maximized exhibits constant consumption shares. The covariances of the terms of trade with the exchange rates can then be written as a function of the covariances of the individual prices with the exchange rates. The empirical application later does not consider the use of foreign liabilities to hedge against domestic state variables or against nontradable assets. The only state variable is the terms of trade. 27. Empirical research on capital mobility has found that the extent of portfolio diversification, at least among developed countries, is too low to be explained by standard models of financially linked economies. Or, said differently, international as',et markets are not used extensively to facilitate the :ransfer of external risks. This has led a number of researchers (e.g., Cole and Obstfeld, 1988) to conjecture that real markets, such as international commodity trade, can make international asset trade redundant, as fluctua- tions in international terms of trade may play an important role in automatically pooling national economic risks. As strong restrictions on preferences and technologies are rc, iced to make international asset markets completely redundant (e.g., commodity market demands have to be unit elastic with respect to price), the analyses would indicate that international asset trade (e.g., external trade) can lead to welfare-increasing risk pooling arnong natinns-as a supplement and in addition to commodity trade. 28. This section summarizes work reported in more detail in Kroner and Claessens (1988). 29. The period covered was April 1, 1977 to March 31, 1988. The analysis itself was based on the logarithms of the exchange rates and the logarithms of the terms of trade, multiplied by 100. This is in harmony with the literature on exchange rates and gives the additional benefit of being able to interpret differenced logs as percentage change5 Recall 1.14 COMMODITY RISK MANAGEMENT AND FINANCE that the theoretical framework requires all the data to be differenced, so that one will deal with percentage changes. The five currencies chosen cover a currency share of approxi- mately 80 percent of all developing countries' external debt. 30. The forecasts of the covariances betwcen the exchange rate depreciations and the changes in the terms of trade turned out to be the unconditional covariances estimated over the respective period because the hypothesis that the covariances were not changing over time cou!d not be rejected. 31. The (simple) corr^lation coefficients among the Ff, SwF, and DM varied between 0.85 and 0.91 during 1981-88. The correlation between the £ and other European comriencies was somewhat weaker ant' varied around 0.63. '2. The actual portfolio composition of Indonesia's externa' debt for these periods is not reported here; however, it was roughly one-third yen, one-third dollars, and one-third European currencies. 33. For example, the share of Turkey's total exports :o the Middle East has varied between 20 ,nd 45 percent between 1980 and 1987. Similarly, exports to and imports from Organisation for Ecor 0. IMever has shown that when :he Is condition is satisfied, maxirnization of expected utility is equivalent to maximizing a preference function V(ua, oc) of the mean and standard deviation of profits. From the many properties of V(gA, uj that are discussed it. Meyer's paper, twvo are particularly inmportant for this analysis. First, the slope of a risk-averse producer's indifference curves in mean-standard deviation space is always positive: (8-4) S(,u, a) = - V'(A' a)/V/A,l, cr) > 0. Second, V(y, cr) is concave, so that indifference curves in mean-standard deviation space are convex to the origin. Beforc investigating the shape of the pioducc--r's opportuhIkty set, the fo!lowing impcrtanlt assumption is made. ASSUNMTION 1. Bond issuers Must F..1y bor-'holders a risk preiiiium to hold the boi ds, plw > (1 + r). T-his assur iprion says that the expected gross return on holding bonds is greater th in the gross rate of return on a riskless asset. Because conimodiy-iin.ked bonds are risky fnancial instruments, and the certain interest ra;e r s available to investors, this assumption simply states that there is the asual risklreturn tradeoff among assets. Nowv co%,ider the opportuinity set of a capital-constrained producer in mean-standard deviation space. The mean and standard deviation of profits are (8-5) / = (1 + r)[it'b - c(q)] + p(q- b); and (8-6) cr = iq -blop where: p = expected output price and op = standard aeviation of the output price. The shape 4 the producer's opportunity set in mean-standard deviation space is llustrated graphically in figure 8-1. The opportunity set can be derived in three steps using 8-S, 8-6, and assumption 1. First, suppose that the quantity produced is fixed at some level, and b is set equal to this production level. b - q. Substituting the equality into 8-5 and 8-6 gives ,u = (1 + r) [wq - c(q)] and ur = 0. TMis defines a point on the ;I axis that is in the opportunity set. (See 'igure 8-1.) Sccond, suppose that the quantity produced remains fixej at q and b is decreased below the point at which b = q. Then differentiating 8-S and 8-6 gives 118 COMMODITY RISK MANAGEMENT AND FINANCE Figure 8-1 Optimal Bond Issues under Cpital Constraints Panel (a) p gb=~~c(qlw b=q q Panel (b) A IO b=q Panel (c) P =C(/)w/ b=q . . . . . . . . . . . . . HEDGINCG WITH COMNIMODITY-LINKED BONDS 119 (8-7) dp = [(1 + r)w - F] db; and (8-8) dr= -rrp db. Dividing these cquations gives the slope of the opportunity set as b decreases: (8-9) d/do- = [p - (I + r)w]/o-p. This part of the opportunity set is indicated by the positively sloped ray moving out from the . axis in figure 8-1. Assumption I ensures that the slope is positive as b decreases. Ncvertheless, b cannot fall too far below q because of the capital constraint. That is, the opportunity set becomes truncated at the point at which the revenue raised by issuing bonds is just equal to the cost of producing the fixed output q. Any further reductions in b beyond this point are unfeasible because there would not be enough revenue available to purchase the inputs required to produce q. This truncation point is also illustrated in figure 8-1. Third, suppose that tiw nLuantity produced remains fixed at q and b is increased above the poi,:i . - vhich b = q. Then 8-8 becomes do- = c-pdp and the slope of the opp,.. nulity set is now (8-10) d,41d./r = -i - (1 + r)v]/o-p. This part of the opportunity set is indicated by the negatively sloped ray moving out from the 1i axis in figure 8-1. Assumption 1 ensures that the slope of the opportunity set is negative as b increases. In this case, however, there is no truncation point because mote and more revenue is being raised from bond issues. The opportunity set shown in figure 8-1 is for changes in bond issues, while the quantity produced is kept constant. Notice, however, that changes in q simply move this opportunity set up and down the ,u axis. Furthermore, because the producer prefers higher profit means to lower ones, and the slope of the opportunitv set does not depend on the quantity produced, then the optimal q maximizes the intercept of the opportunity set on the ,u axis. The optimal quantity produced therefore satisfies (8-11) c'(q) - w= 0. Thus, the optimal production level depends only on marginal costs and the bond price. This separation property is a familiar result from the literature on futures market hedging, where it has been found that the optimal quantity produced depends only on marginal costs and the futures price (Danthine, 1978; Holthausen, 1979; Meyer and Robison, 1988). Equation 8-l1 shows that a similar result holds in the case of a capital-constrained producer issuing commodity-linked bonds, except that the bond price, not the futures price, is the action certainty equivalent price for the producer's output decisionl. 120 COMMODITY RiSK MANAGENMENT AND FINANCE Having determined the optimal quantity produced, the next step is to characterize the optimal bond isoae graphically in mean-standard devia- tion space. Three possible cases are illustrated in figure 8-1. In each case, the negatively sloped portion of the opportunity set is irrelevant because indifference curves are convex and positively sloped. In panel (a) of figure 8-1, the optimum is defined by a -angency between the producer's indifference curve and the opportunity set. In this situation, the producer issues less bonds than the quantity being pro- duced, b < q. The revenue raised by issuing bonds, however, is greater than the cost of production, so the excess is invested at the known interest rate r. The payout the producer expects to make on the extra bonds is greater than the sure return from investing the excess revenue. Nevertheless, the extra bonds provide an output price hedge for the producer, and this is why they are issued. Panel (b) of figure 8-1 represents an optimum in which the slope of the producer's indifference curve is greater than the slope of the opportunity set. This is a corner solution in which the optimal bori issue equals the quantity produced, b = q, and the variance of profit is reduced to zero. It will occur when producers are very risk averse and want to eliminate all risk. Once again, the optimal hedge requires bond issues that raise revenue in excess of the amount required to finance production costs, and the excess is invested at the interest rate r. Finally, panel (c) of figure 8-1 illustrates a constrained optimum in which the slope of the producer's indifference curve is less than the slope of the opportunity set. In this case, the producer is not very risk averse and would like to issue less bonds for hedging purposes (remember that the producer must pay the bondholder a risk premium to invest in the bond). Bonds sufficient to cover production costs, however, must always be issued, and so the optimum occurs at the truncation point on the upward-sloping portion of the opportunity set. These results illustrate the effect of producer risk preferences on the optimal risk/return tradeoff from issuing commodity-linked bonds. The risk premium on the bonds causes mean profit to fall whenever the producer issues more bonds. The p;incipal payment on the bond, however, is positively correlated with the commodity output price. Thus, the bonds provide a hedge against output price risk. If the producer is very risk averse, then there will be a compiete hedge, b = q. If the producer is not very risk averse, then the bond issue will cover only production costs. If producer risk preferences lie between these two extremes, the revenue raised by bond issues will be greater than that required to finance production costs, but not great enough to provide a complete hedge and eliminate all risk. HEDGING WITII COMMODITY-LD.-KF.) BONDS 121 Hedging with Commodity-Linkecd Bo3nds and Conventional Loans Suppose that the producer of the previous section now has access to conventional loans at a known intcrest rat., r. Everythinig else remains as before, including the existence of a m;larket tor commodity-linked boncds. Th, availability of convenltional loans does not change the profit function °-1 because the producer has exactly the same revenues and costs as before. What docs change is the capital conlstrainit, 8-2. Because any amount can be borrowed or lent at the interest rate r, the producer is no longer constrained to issuc enoughi bonds to cover production costs-the money can always be borrowed instead. The effects that conventional loans hlave on optimal productiorn and bond issue decisions are easy to derive graphically. To begin, consider the shape of the producer's opportunity set when conventional loans are available. Given somtle fixed level of OUtplut, q, the opportunity set for changes in b is almost identical to the previous case (witlhout conven- tional loans). The only difference is that the positively sloped ray is no longer truncated at the point at which revenue from bond sales equals production costs. Because production costs can now be financed by conventional loans as well as bonds, bond issues can feasibly be reduced all the way to zero. The nonnegativity constraint, 8-3, however, contin- ues to hold so that truncation now occurs at b = 0. This opportunity set is illbstrated in figure 8-2. Optimal output and bond issue decisions are characterized by consid- eration of preference maximization, subject to remaining in this oppor- tunity set. Three different situations are illustrated in figure 8-2. In panel (a), the optimum is defined by a tangency between the producer's indifference curve and the opportunity set. This rnay occur where revenues raised from bond issues are greater than, less than, or equal to production costs. At this solution, bond sales are strictly positive and the optimal output level satisfies, 8-11. The producer is risk averse enough to hedge by issu;,,g bonds, but not risk averse enough to eliminate all risk by setting b = q. Panel (b) of figure 8-2 illustrates the corner solution when the producer is very risk averse and issues sufficient bonds to reduce the profit variance .o zero. Panel (c) shows the interesting case in which conventional loans dominant commodity-linked bonds, b = 0. This oc -urs when the slope of the indifference curve is smaller than the slope of the opportunity set at the optimum: (8-12) S(Ai, o-) < [p - (I + r)w]v/op. 122 COMMODITY RISK MANAGEMENT AND FINANCE 1-igure 8-2 Optimal Bond Issues with Conventional Loans Panel (a) b=o b=q < < Panel (b) b=O b=q q b>q Ll~~~~~~~~~~~~~~C Panel (c) i Z.Io b=q ~ ~ ~ ~ ~ = b=q C bq a5 HiEDGING wi ryH COMMNioMvrY-LINKED i7ONDS 123 Equation 8-12 has an intuitive econoilic incerpretation. The slope of th indifference curve represenrts the "cost" of producing unhedged output and bearing the full risk of outpult priLe uncertainty. The slope of the opportunity set represents the "cost" of the risk premium that producers must pay to bondholders to facilitate a transfer of risk. If this "cost" of producing unhedged output is less thaln the "cost" of paying the risk premiumii, all production Losts are financed with conventional loanis, and no bonds are issued. rFlc less risk averse are producers, the inore likely that conventional loanls will dominlate coltimodity-liniked bolnds. The final task is to deterimiine the optimal output level whenl b = 0. If no bonds are issued, then output is completely unlledged. TuLs, at an optimum, q Imlust satisfy (8-13) S(A, (r) = [p-(1 + r)c'(q)/luj,. The slope of the producer's indiffercnce curve in mean-standard devia- tion space equals the slope of an opportunity set defined by variations in q with bond issues fixed at b = 0. Conclusion This chapter examined the behavior of capital-constrained commodity producers managing output price risk with commodiq -linked bonds. The study w as motivated by the problems of heavily indebted developing countries that have exhausted conventional sources of credit, but still face commodity price risks. Futures markets are not available because many commodities produced by developing countries do not have futures mar- kets, and those that do exist are typicallv located in major international financial centers, where developing countries may face substantial basis risk. Results of the investigation indicate that commodity-linked bonds could have an important role to play in hedging commodity price risks. If producers are highly risk averse, and the risk premium in the bond price is "not too high," then the optimal bond issue will equal the quantity produced, and the producer will be fully hedged. As producers get less risk averse and the risk premium on the bonds gets bigger, the optimal bond issue declines. If the risk premium is high enough and producers are "not too risk averse," then no bonds will be issued provided conventional loans are available. If conventional loans are not available, only enough bonds to cover production costs will be issued. These results were derived using a graphical mean-standard deviation approach that is fully consistent with expected utility maximization. The graphical approach is more intuitive and leads to simple proofs for the various results. Financial Instruments for Consumption Smoothing by Commodity-Dependent Exporters Brian Wright a?zd Iavid Newbery Loans and other investn:-nt contracts are widely perceived as legally enforceable in lende~r ountries but not in debtor countries. In that context, this paper shows how novel financing arrangements using commodiry bonds with put options for the seller can be used to stabilize risks associated with export prices. Given the substant;a! inst,.bility in all primary commodity markets, one would expect countries that depend on a single primary export for most of their foreign earnings to experience especially sharp fluctuations in export earnings and their underlying wealth., To the extent that these fluctuations affect consumption, they are costly, and one would expect such countries to seek ways of managing these fluctuations, thereby reducing their costs. In many countries, the nature of the resource endowmrent and its comparative advantage rule out production diversification as a signific;nt near-term strategy, and it is not included here. In addition, diversification is ruled out via exchange of equity investments with foreigners. In this chapter, the cost of export risk is co-nsidered and commodity bonds are shown, in fact, to be capable of achieving efficient smoothing of i.i.d. export price disturbances in some cases and eventually complete smooth- ing in others-if that is what countries really want or need. What are commodity bonds? Commodity bonds are bonds whose principal repayment (and perhaps dividend payments) may be made in units of physical commodity (or the terminal value of some appropriate 124 COM.MODITY-DEPENDENT EXPORTERS 125 futures contract). Typically, the bond f -yer has the option to receive the nominal face value or the commodity bundle. In the finance literature, stucdies of the pricing cr commnodity bonds (Schwartz, 1982; Carr, 1987; and Priovolos, 1 987a) do not d-inguish bonds issued by foreign governments from priate corporate bond issLuCs. The literature on foreign borrowing, however, recognizes that the distinction is crucial. Sovereign Borroxving and Default Prevention T'he main distinction betwveen corporate and sov,'reign borrowilng, described in masterly fashion by Keynes (1924) and incorporated in the seminal work of Eaton and Gersovitz (1981), is that collateral is generally unavailabie to creditors of a sovereigin borrower because the assets of the latter are located within its borders. Onlv in exceptional cases c.an they be attached by lenders in the event of default. The absence of a final distribution of assets to creditors, as seen in domestic bankruptcy, also changes the nature of default. It arises in the context of a sequence of strategic moves by creditors and the sovereign debtor who retains (and, in fact, cannot credibly foreswvear) the power to make subsequent decisions that affect the interests of creditors. Here, the focus is on income-smoothing financial transactions between investors in developed countries and in developing countries, Nvhich are heavily dependeint on a single commodity subject to substantial revenue fluctuations. The default penialty is enforcement of debt seniority clauses in the courts of all potential borrower-lealder nations, so that a defaulte.'s foreign investments or servicing of newv debt would be subject to seizure. Default means permanent eliminaticin of foreign borrowing or lending opportunities. The Costs of Income Variability ,onsider a country that has economically unresponsive production (zero supply elasticity) and seeks to maximize the discounted expected utility of its representative consumer (9-1) V, = E (1 + 8) -'U (cd *=0 where E is the expectation operator, 8 is the discount rate, c, is consus-nption in period t, and u is felicity, it' > 0, u" < 0. There is no storage. Output and price are each subject to one discrete i.i.d. random disturbance per period. 126 COMMODITY RISK MANAGEMENT AND FINANCE To dramatize the issues, assume that exports from a single commodity account for 33 percent of GNP on average and suppose that the coefficient of variation (cv) of output and price of the commodity are both 30 percent and that the correlation betwveen output and price can be ignored. Suppose also that all other income is nonstochastic and that the country optimally shares risks intemnally. There is, however, no saving or borrowing or othe- intertemporal income smoothing. Using the standard formulas2 for the c, 'st of risk, if the coefficient of relative risk aversion is R (defined for one-period variations in consumpticn) and .f the cv of consumption is s, then the cost of risk, p, is defined implicitly by u(c - p) = Eu(c,) (where a bar over a variable indicates its expected value), and the relative cost, pIc, is approximately (exactly if utility is quadratic in income per period) Rs2/2. If consumption must be equal to income each year, then s -- 0.33e where e is the cv of export revenlue. If output and price are independently normally distributed, then e2 = 0.19 (and this will hold approximately, even if output and price are not normal). In this case, if R has the not-unreasonable value of 2, the cost of risk is approximately 2 percent of average income, the amount representative consumers would be wiliing to forego each year in return for a stabilized consumption stream of c. Consumption Smoothing by Borrowing and Lending Can a country optimally smooth consumption by borrowing and lending from overseas sources? If the utility function is quadratic, then 8 can be interpreted as the rate at which future consumption is discounted by the representative consumer; if this is equal to the rate of interest abroad, r, then the country has no motive for saving or bor;:owing other than to smooth cons- mption. This assumption is made here to focus on the consumption smuothirig aspect of international borrowing. It is assumed that the exports are subject to random i.i.d. price disturbances. Then the optimally "smooched" consumption of a borrower committed to borrowing and lending only for smoothing and to meeting its interest payment obligations is c, = E,(c,.1) = - rL,.3 Under this scheme, sccumulated debt, L, follows a discrete random walk with increment equal to the difference between income y, and its mean, y. For permanent smoothing, there must be no limit on L. In finite time, however, L will pass the value at which repudiation becomes more attractive than continued interest payments, even if all borrowing and lending opportu- nities are then cut off.4 Thus, competitive lenders will not make unlimited loans. Any feasible loans would offer, at best, only incomplete and/or impermanent smoothing. COI...-IODITY-DEPENDEN1 EXPORTERS 127 The nature of the evolution of general obliga.son loan contracts for sovereign borrowers is a currently active research area.5 At this stage, it seems clear that full consumption smoothing by sovere; ,n borrowers using conventional borrowing and lending is unfeasible if the contract is not renegotiated. If it is, then the quest for a better instrument makes sense. Commodity Bonds Issued by Sovereign Lenders To simplify the discussion, assume that the commodity bond under discussion is a zero-coupon bond wi. payment upon maturity consisting only of a completely specified commodity bundle. The issuer is Lc-uined to be competitive and the market risk-neutral with respect to this bond. (See O'Hara [1984] for an analysis of the demand side of the market for commodity bonds under other assumptions.) As above, assume initially that all contracts are always honored. Under these assumptions, if the country issues commodity bonds (which in this model need only be one-period bonds) and if these can be issued (and indefinitely reissued) at the present value of the expected price -L lazxt period, then their risk-reducing properties in the steady state are exactly the same as those of an optimal forward or futures hedge at the same price. Newbery and Stiglitz (1981)6 show that, in the case of stationary, uncorrelated output and price disturbances, the ratio of income variance withi and without optimal forward hedgir,-' is rouighly 1/(1 + k2), where k is the ratio o. the cvs of price and output. In the numerical example above, k equals 1. If there is no other means of consumption smoothing by lending and borrowing, then conmmodity bonds will halve the steady stave costs of the risk-to 1 percent of GNP in the example above. If the cv of income were the same, but only price were stochastic, then commodity bonds eliminate risk, worth 2 percent of GNP. Assume, henceforth, that no other borrowing is possible and that all inco.ne variation is due to price. Then, with credible commitment, complete smoothing is achieved by selling commodity bonds for the whole (deterministic) output. The count-y then has constant income and consumption and delivers all output of random value to the lender. In low-price states, the smoothing raises income, so there is no incentive at all to default. But in high-price states, delivery to the lender reduces current income, yt, by (Yt - y). This, plus the expected present value of autarkic future consumption, may, in some high-price states, exceed the maximum. expected present value of the consumption path, given default does not occur now. Then, those states will rationally default; a no-default commitment is not credible. 128 ( ,. tIMODITY RISK MANAGEMIENT AND FINANCE The credibility of a no-default commitment by a commodity bond issuer depends on the parameters of the model. Consider the simple case with a two-point probability de- ity for the multiplicative income disturbance that is i.i.d., u = tv, with probabilities of outcomes +v and -v equal to one-half. Assume mean income is unity and utility is quadratic over the consumnption range, I - v to 1 + tv. Then the anlual cost of risk in the stochastic steady state (and the value of access to commodity bonds) is in dhis case, with all uncertainty, due to price: p* = Rv2/2 and the present value is p*/5 = Rv2/28. Now consider the stochastic steady state, in which a fraction (1 - a) of output, 0 < a < 1, is delivered each period in payment for commodity bonds issued one period earlier, and all consumption is financed from current sales of commodity bonds and the uncovered fraction (a) of output. If the income draw is high at v, then default is the expected-utility-maximizing decisio:i if-and only if-the curren- -ooi? gain, v - av, exceeds the present value of the risk cost incurred. The change in per period risk cost is Rv2(1 - a2)/2. Default occurs if the one-shot gain exceeds the present value of the increased risk cost, that is, if 8 > Rv (1 + a)/2, so full coverage is feasible if and only if 8 c Rtv/2; some fractional coverage is feasible if and only if 5 < Rv. As the cv, v, the relative risk aversion, R, or the uncovered fraction a increases, the minimum 8 consistent with default rises. Default on full coverage is not a problem in this case if income is risky enough and/or risk aversion is high enough. Optimal D)ynamic Smoothing StraL'gies Default Constraint Nonbinding As noted earlier, the commodity bonds may be default-free in the stochastic steady state with an i.i.d. price disturbance in wliich consump- tion equals the mean value of output, discounted one period. If so, one description of the optimal infinite horizon smoothing plan for implemen- tation in period 0, given current income, yo (assumed tor this exposition to be entirely from export of one commodity at price p) and the discount rate equal to the interest rate is as follows: Invest 63yo, where ,3 - 1/(1 + r), overseas for a certain periodic rate of return of r, take out a commodity bond to cover all output, with current sale price ,B y, and consume r,ByO + #y; in each period 0, 1, 2.... Full efficient consumption smoothing is immediLtely achieved forever. (A short forward contract plus a loan on the anticipated proceeds could replicate the above contract.) The opportunities for overseas investment at the (certain) market COMCMODIlY-DEPENDENT EXPORTERS 129 interest rate and for sale of commr.dity bonds at unbiased prices are all the financial facilities needed for rhis plan. Furthericore, note that if the initial income, yo, is invested where it can be collateralized for the commodity bond loan (for example, in the lending country), the default constraint is relaxed relative to the comparative static analvsis above, which assumed all income %vas from sales of commodity bonds and none of the current income in cht period in wvhich commodity bonds were introduced was saved. So, even if full commodity bond coverage seemed infeasible in that analysis, the above strategy may work. Default Constraint Binding On the other '-and, wvhat if the default constraint binds? The immedi- ate transition to full c. nsumption snmoothing is precluded. Or.c asks what the optimal consumption smoothing contract is in suck cases, following the analysis of Worrall (1987) and Kletzer (1988), and then sees the extent to which it can be replicated by existing financial instruments. Suppose the export price in any period t can take one of S values corresponding to S states of the world, p,(s) = p(s) = p(l) < p(2) < ... p(S), and associated with these values, the income of the country, valued at the spot price, is y(s) = p(s) 4, s = 1, 2, . . . , S. The optimal contingent borrowing contract is a level of borrowing, b, and a schedule for repayment in tne next period, M,5 -- A(, - in,, p,+,(s) + 1(s)j contingent on the price realization p,; I(s) that maximnizes the borrower's utility subject -' the desire not to default. If the present value function is V, then V is the solution to the problem (9-2) V(yt - in,) = Max 4()', - in, + b,) + E[V(y(s) - M,s)]/(1 + r) where y, and mi, are the levels of income at current price p, and debt repaymen- in the ctirrent , -riod t, and consumption c, = y, + , - tn, This is to be maximized by cH-osing [b,, M,J subject to the constraint tha. the borrower does not wish to default in any state s and, thus, foregoes any future lending or borrowing oppor-unities: (9-3) V(y - M,.,) - u(y(s)) + E[u(y)3lr, s = 1, 2, . . . , S and subject to the zero profit constraint that, for risk-neutral lenders, is (9-4) - b, + /3E[M,4] = 0. From the envelope condition, u'(y, - m. + b,) = V vy, - in,), V(.) is strictly concave, implying the e):istence or a unique optimum. The first-order conditions from this constrained maximization problem are (9-5) u'Vc,) = (1 + uW)V'(y(s) - Al,,), s = 1, 2, . . . , S where 4, is proportional to the multiplier on the default constraint in state s, which will be zero if the constraint does not bind. Original page # 130 is missing. COMMODITY-DEPENCENT EXPORTERS 13.1 consumprior. is cl = yl + b+ - ml - c0. Consumption never falls; assumring the maxirnum price p(S) has positive prLbability, in finite timc (period zv), i: occurs, and c,+, < p(S) -q is constant for = 0, 1, Z, 3.... (A longer maturity ofers no additional advantages in this model.) In each period, an instrument that can a-hieve this is a zero-coupon, one-period commodity bond payable in dollars or in a specified commoditv bundle at the seller's option. This instrument contrasts with the typical com- moditv-cow"ercible or commodity-ii1.ked bond that contains a call option for the purchaser, rathcr than a put for the seller. When .hc default constrainc hirnds, this scheme is not fuily efficient in general (though it is for the mto-point disturbance distribution in the exar ipe above). It would be weakly dominzted by the scheme presented above in which pavments *vere fully state-contin,,ent for each of the high btates.8 (Here the repaymenr m, made by the borrower when the put is !.ot exer.ised does not vary with the s -ite.) Under either scheme the consuirmptior path exhibits the same distinctive qualitative features of upward ratchcting and eventua! complete smooth.ng of consumption, given i.d. disturbances. The difference in welfare effects of the two sch--mes 'n man! cases will rot be large, and the much greater simplicity of our commodity bonds over flli state contingency gives them a strong ernpirica! advantage. Before closing this section, rote that the thcory used here assumes that sovereign defaults are penalized by withdrawal of all lending and borrowing opporzunidies. The historical record, however, (Lindert and NMorton, 1987; Eichenlgreen, 198.7) does not clearly show the expected differentiation in availabiliry of loans and their terms bet-ween countries that have defaulted several :imes and those that have never done so. On the other hand, despite 1he apparent'y lenient treatment of sove, ign defaulters, the overall e' post rate of return has substantially exceeded the return on lending wyithin the creditor countries themselves. (See Liridert ar4d Morton, 1987.) )3orrn.wers o;ten appear to make net repayrr1ents in circumstances in whic-l i. is difficult to demonstrate that their efforts are in tneir own self inteiost, even where the latter is recognized as ex.cnding well beyond stabilization.9 Resolution of these puzLles ,s currently an active area of theorn ical and empirical investiga- tion. Conclusion ConsurnDtio1-smoothing cculd, in principle, be quite valuable to many countries in the absence of any other risk-reducing strategies. Commod- it) bonds can achieve consumption smoothing in the face of random 132 COMIMODITY RiSK MANAGEMENT AND FINANCE - poet prices for commodity-dependent developing countries that dom- inates smoothing using other international arrangements, such as inter- national buffer funds or attempts to create longer-term futures markets.'0 Dependinig on ;i.,ir;ai conditions, the smoothing may be immediately complete (and constrained Pareto optimal) and use a straight commodity bond, or it m.ght involve a nondecreasing consujmption path, which becomes constant if and wvnen the highest income level is attained. In the latter case, the bond could be constructed as a conventional loan with artached put for the seller; equivalently, it could be constructed as a bond with a nominal face value at maturity and an attached commodity value, delivery of either to be at the seller's option. rhis type of commodlitv bond contrasts with the observed forms, which generally offer the buyer a similar choice. The consumption-smoothing achieved reduces downside exposure of the seller, while leavinig the seller a sufficiently large share of high realizations so that there is no temnptation to default. Although thils has only been shown in the case of pure price uncertainty with i.i.d. disturbances (and, hence, no interperiod storage), availability of a constant risk -free ate of return and market risk neutrality of leniders, the results sugg:st furt&.er investigation of the smoothing possibilities of these instruments in more general circumstances. Whether such smooth- ing is what commodity exporters want or need is another question. ContinLued access to the benefit of income-smoothing, however, is often identified as a major inducement for honoring loan contra, inally motivated by other objectives such as economic developm aton, Gersovit.t, ancl Stiglitz, 1986), although the observed procyclical nature of much borrowving raises questions about the smoothing objective (Gersovitz, I Q85). (See also, Fishlow, 1987.) Integration of this analysis with the extensive literature on swaps, renegotiations, and -.Iated matters is an obvious extension of this approach. Notes 1. This chapter is a substantial revision of an invited paper for the 1988 Winter American Sc cial Sciences Association Meeting for the session, "Financial Risk Management Needs of Developing Countries," which was published under the same title in the American Journal of Agricultural Economics, vol. 71, no. 2 (Mlay 1988). We thank, with the usual caveat, Doug Christian for research assistance; Jim Vercammen, Ken Kletzer, and T;m Worral for pointing ( .i errors in a previous draft; and seminar participants at the UnivL'simy of California-Berkeley and Larry Karp, Ken Kletzer, Peter Linderr, and Barry Eichengreen for helpful discussions. 2. If consumption c is a random variable with a coefficient of variarion s, u(E(c) - p) = Eu(c). Expand both sides in a Taylor series: u(E(c)) - pu'(E(c)) u(E(c)) + 0.Ss2E(c)u'(E(c)) or PIE(c) - 0.Ss2R. 3. Newbery and Stiglitz (1981), pp 201-02. COMMODITY-DEPENDENT EXPORTERS 133 4. If only borrowing opportun'ries are losr, but the country may invest the payments it saves overseas at the same interest rate, it can actuially achieve exactly the same con- sumption stream for periods beyond t + k, as if it did not default (or never borrowed at all). See Bulow and Rogoff (1988). The partial smoothing is similar to that ichieved by commodity sterage. See Wright and Williams (1982). 5. Sec Eaton, Gersovitz, and Stiglirz f 1986) for a recent survey. Sce also Kletzer (1988) and Bulow and Rogoff (1987). Alternative instruments are reviewed in Lessard and Williamson (1985). 6. Newbery and Stiglirz 1981), p. 186. 7. Worrall (1987), pp. 5-6, Results 1-3. S. This difference was pojinted out by our colleague, Ken Kletzer; the issue was also mooted in a private communication by Tim Worrall. 9. There is a significant body of literature following the pioneering work of Feder and Just (1977) on estimation (as distinct from explanationi) of debt-service behavior. 10. See Finger and de Rosa (1980) for a cautionary analysis of the Compensatory Finance Facility of the IMF. Finger and de Rosa found that, on average, it did not even stabilize the annual export incomes of participants. 10 Securitizing Development Finance: The Role of Partial Guarantees and Commodity Contingency Ronald Anderson, Christopher Gilbert, and Andrew Powell Throughout tile 1980s, the scale of indebtedness of many developing countries has, in conjunction with high interest rates and adverse terms of trade, meant that very little new private finance has been .ivailable to them. The lack of finance for investment has been a major impediment to economic growth in these countries. At the same r e, the poor service record on much of this debt has created major balan:e sheet problems for credizor banks. The largest component of developing country debc in private hands is in the form of general obligation bank loans. It is widely acknowledged that these problems would be lessened if this general obligation debt could be, in whole or in part, securitized-that is, if it coiild be traded in more or less standard form on liquid secondary markets, in the same way as are developed country bonds. Securitization would provide market valuations of existing debt and would allow debtor countries to raise new finance on terms that reflect their repayment potential; it would also permit creditor banks to adjust their balance sheets at relatively low cost. A number of proposals aimed at securitization have been proposed during the p3st few years, but, to date, none has attained any marked degree of success. 134 PARTIAL GUARANTEES AND COMMODITY CONTINGENCY 135 The major difficulty standing in the way of securitization is that debts of developing country govermnents and their immediate agcncies bear sovereign risk. In circumstances in which private-sector debtors fail to honor contractual obligations, it is possible for the creditors to take enforcement action through the courts. This possibility is not open to creditors when the counterpart is a sovereign government. In such cases, debt service is, in an important sense, voluntary. Sovereign risk is therefore a major source of the illiquidiry of current developing country debt. A prospective purchaser of an existing obligation must make detailed enquiries into the debtor country's economic and political situation, its likely need for new finance (which will provide an incentive to service current obligations on schedule), and its other outstanding obligations. Obligations of different countries will trade on different terms even in situations in which the contractual conditions are identical. Different potential purchasers will put different valuations on the same debt depending on their differing abilities to obtain service. The sovereign risk problem has been seen as intractable; however, progress is possible through a two-pronged attack. First, it is necessary to separate the default (sovereign) risk component of .he risk associated with the debt. Then it is possible to associate this default risk wvith a third-party guarantee priced at an actuarially fair rate. This guaranteed debt could then either trade in the same way as obligations issued by developed country governments or could provide the collateral against which new securities would be issued. The insurance premia associated wvith these obligations may be so high as to make the provision of insurance appear unfeasible. The second component of the plan is to find means of reducing the likelihood of default risk and, therefore, the size of the default insurance premia as well. To analyze the likelihood of default, a formal model of the default- rescheduling process is required. Using an extensive form game, an expression for the rescheduled payments is derived; if rescheduling takes place and the conditions under which default will be threatened are chanlged, then rescheduling negotiations will follow. It is this latter condition that is crucial to the argument. It combines "willingness to pay" with "ability to pay." Throughout the 1980s, general obligation debt has carried the implication that developing countries' ability to pay has been negatively associated with their contractual obligations, and this has resulted in high default probabilities. Adjustment of contractual debt repayment terms to give a positive association between ability to pay and contractual obligations will result in significantly lower default proba- bilities and, therefore, in lower default insurance premia. An obvious mechanism for obtaining the required positive association is to introduce commodity price contingency into contractual debt 136 COMMODITY RISK MANAGEMENT AND FINANCE obligations. This proposal replaces standard interest payments with a mixture of interest payments and payments linked to primary commodity prices. Powell and Gilbert (1988) argued that this form of debt would be advantageous to developing countries that have high levels of commodity price dependence. Hcre, the argument may be generalized because it is possible to see any country as a portfolio of productive assets, many of which will be associated with the price of an internationally traded good. Consequently, countries can issue a portfolio of debt with the associated repayment characteristics, and each of these components of the overall portfolio can provide the basis for a secure obligation. The chapter is organized as follows. First, a model of sovereign debt is developed. Then, the general terms necessary for securitizing debt will be discussed, including a brief reference to the experience in securitizing mortgage debt. Next, the model developed initially is applied to the main problems faced in securitizing developing country obligations. Several different instrument designs are compared in an effort to determine those most suitable for securitization. Finally, the institutional framewvork in which these securities could be issued is examined. Sovereign Risk In standard financial applications, a default occurs when one of the parties to a contract fails to honor the terms of the contract. When the borrowing party is a country, the conditions that imply default are rather elastic; a default occurs whenever the lender declares that the borroWer has violated the terms of the ooligation. This approach emphasizes that the declaration of default is an option available to the lender that the lender may not wish to exercise. In a private financial contract, declaration of default will trigger legal actions that will give the lender all or part of the sums owed. These actions are not available if the borrower is a sovereign nation or its immediate agent. In the case of sovereign debt, the declaration of default may penalize the borrowing country by denying it subsequent access to international credit markets. Recourse to this action may be relatively infrequent for the reason that declaration of default removes the threat of sanctions and, therefore, reduces the prospect of recovering the sums owed. A simple framework for understanding sovereign risk is an adaptation of a model used by Eaton, Gersovitz, and Stiglitz (1986). The default decision is based on a comparison of the cost of honoring the contract terms with the penalties resulting from default. The borrowing country will choose to not honor the contract if its payments exceed the penalty. PARTIAL GUARANTEES AND CONMMODITY CONTINGENCY 137 Figure 10-1 7he Default Decision Borrower de h / R(-R, R) Lender Declares Reschedules deauX t (-PA4 P-L) (-Q, Q) This, in turn, will lead to a rescheduling decision on the part of the lender. This can be illustrated as the simple extensive form game in figure 10-1. Here, the amounts in parentheses are the flow payoffs to the borrower and the lender respectively. The borrowing cotuntry is scheduled to make a payment of R to the lender, but alternatively may threaten default. In that case, the lender may declare default, resulting in the borrowing country making some cash payment, P, as a penalty. In addition, the borrowing country will lose future access to capital markets. Thus, if A is the value of this access, the net payoff to the defaulting country is -P - A. The lender will receive an amr v- t P - L where L is the deadweight loss associated with declan.g default. On the other hand, if the lender faced with nonperformance does not declare default, the lender will enter into a negotiation to determine a payment, Q, of the rescheduled loan. The lender will choose negotiationi if Q > P - L. What will determine Q? Because by agreeing to reschedule, the dc3dweight loss L and the loss of access A are avoided, it appears that there is an incentive to bargain. The rescheduling negotiation can be represented by the Nash bargaining game depicted in figure 10-2. Any successful bargain must leave each side as well-off as in formal default. The outcome most favorable to the borrowing country is at ,B where Q = P - L. The best outcome for the lender is at a where Q = P + A. Thus, in figure 10-2, the bargaining set is confined to the segment of the 138 COMMODITY RISK MANAGEMENT AND FINANCE Figure 10-2 The Rescbeduling Subgame Lender's payoff \ L ~~~~~~~~~~L Borrower's -PA 0 payoff downward sloping 45 degree line to the northeast of the threat point (-P - A, P - L). Any point in this set would be a conceivable solution and can be represented by (10-1) Q=P+wA-(1-w)L for 0 < w < 1. For exaniple, setting w = 0.5 gives point y and constitutes the Nash bargaining solution to this game. This model implies that payment will be made according to schedule if R < Q. Using equation 10-1, one sees that this arises if A > [R - P + (1 - w)L]/w. That is, if for the borrowing country the value of future access to capital markets is sufficiently high, it will pay on schedule. Otherwise, it will threaten default. Taken strictly, the model implies that default will never occur because rescheduling will always offer a Paretian improvement; in practice, default threats by sovereign debtors typically do result in rescheduling. This model may seem to overstate the case for Walter Wriston's view that "countries don't go bust." In fact, when lenders deal iepeatedly with sovereign borrowers, there can be a role for formal declarations of default in that these may enhance the creditor's reputation as a tough PARTIAL GUARANTEES AND CONIMODITY CONTINGENCY 139 negotiator. This bargaining power would tend to translate into an expectation of favorable future bargains for the creditor (a high iv) and, thus, a high value of Q. The result would be to reduce the frequency of nonperformance. A full discussion of these reputational issues can be investigated in a repeated game extension of the model (Grossman and van Huyck, 1985). The approach to sovereign risk adopted here stresses the voluntary nature of both deb service payments and default declaration. This does not imply, how-ever, that contractual terms are irrelevant because, as noted here, the service obligation determines the set of circumstances in which default will be threatened and rescheduling will take place. Thus, although this approach is closer to the "villing to pay" model, "ability to pay" does play an important rcle. In particular, if the default penalty P and the value A of access to credit are treated as state dependent, the rescheduled payment is, (10-2) Q(s) = P(s) + wA(s) - (I - w)L. In favorable states for the borrower, resulting perhaps from strong demand or high prices for its exports, the borrower is likely to perceive a high value A(s) of future access and will be aware that the lender can extract a higher default penalty P(s). Consequently, if scheduled pay- ments, R, are not state dependent, the borrower is likely to pay on schedule. In adverse states, the opposite holds, and the country is likely to violate the schedule. Notice that the way in which "ability to pay" feeds into the borrower's and lender's decision process is very different to the often mechanistic relationships used in the "solvency" literature. This general formulation is compatible with a variety of specifications of penalties that have appeared in the literature. Cooper and Sachs (1985) and Sachs and Cohen (1982) assume that the penalty to default is proportional to income, Gersovitz (1983) introduces a penalty that is dependent on the importance to the debtor of the opportunity to trade, and Eaton and Gersovitz (1981) employ a penalty dependent on the country being excluded frorn the market for physical capital. Each is a special case of this formulation. Even a powerful creditor will not be able to assure performance if other '.-tors create a strong incentive to threaten default. That is, in the terminology of the model here, even if the creditor can bargain hard (achieve a high w), the '5orrower may still threaten default because the payment terms (R) are severe, the default recovery (P) is low, or the value of future access (A) is low. Clearly, the nature of these variables is crucial to the predictions of this model. The value of future access to credit markets (A) will reflect the developing country's perception of the likely future demand for its 140 COMMODITY RISK MANAGEMENT AND FINANCE products. This, in turn, will depend on the country's resources and capabilities, the level and mix of world prod:!ct demand, and the pattern of international trade barriers. There is little that can be said about these within the scope of this chapter. It is clear, however, that anything that is conducive to the prospects for fuzure development will tend to raise A and, as a result, to reduce the problem of sovereign risk. The creditor's loss of declaring defau!t (L) includes the direct costs of exacting a penalty from the borrower. More important than this, however, could be the indirect effects of a declared default. Banks may rnaintain nonperforming loans on their books at full value. Were they to declare a default on the loans, they would be forced to take a charge against the capital of the firm. This in turn could mean that they would not meet capital adequacy requirements, thus forcing them to shrink their entire balance sheet. Creditors in this situation may place a very high value on the loss of declaring default. The model used here suggests that this tends to enhance the probability of threatened default. However, if a creditor has made an effort to remove this constraint through the provision of loan loss reserves, L need not be so large. Our model shows that this tends to improve the renegotiated terms for the creditor with the effect of decreasin, the likelihood of default. The value or the payment (P) that can be extracted upon default will depend upon the legal means available to the creditor for enforcing the contract. In the most extreme form of sovereign risk, the creditor has no legal recourse (P = 0). Somewhat counter-intuitively, this apparent advantage for the debtor will mean that nonperformance will be v;.wed as relatively more likely, so that amounts that can be borrowed at given terms will be limited. A sovereign borrower can overcome this problem by precommitting to relatively severe penalties in case of default. The most obvious way that this can be done is by placing some significant asset as collateral in an entity that falls under some legal regime other than that controlled by the borrower. It may be that a pa ticular contract form may have a legal status that is relatively advantageous from this viewpoint. This point, as well as the possibility that payments schedules (R) can be written to minimize nonperformance, is addressed later in this chapter. Securitization A security is generally taken to be a financip! obligation whose terms are standardized so that the holders of a parcicular type of security will be treated equally. Standardization is important in determining whether PARTIA; GUARANTEES AND CO1MMODITY CONTINCr-r ^ 141 an instrument is traded successfully in a secondary market. When a secondary market is active, a holding in the security may be quite liquid in the sense that it could be sold quickly without a great effect on its price. Secondary trading is also promoted when a security's credit risk is readily assessed. If an issuer's credit standing is not well established, its securities may be very liquid if they have been guaranteed by a separate, credit- worthy institution. Typically, an elaborate and costly process is involved in the issuing of securities, including registration with regulators, legal drafting, and marketing. What are the merits of securitization that justify these costs? The principal advantage of issuing securities derives from the liquidity that can result. By making it possible to trade in and out of positions in a security, the range of investors wvho may be willing to hold . is expanded. Consequently, the supply of funds is increased, and the price paid for the funds is reduced. A further implication of active secondary trading is that the value of the security is established in the marketplace. By contrast, an existing bank loan that is held on the books of the originating banks is not typically valued in a market. Consequently, because of changing market conditions or the conditions of the borrower, variations in the value of that obligation are not typically reported, except in extreme cases such as nonperformance. In the terminology of principal-agent theory, the lending institution is h. principal, and the borrower is the agent. The observability of actions taken by the borrower will be enhanced because market prices aggregate information available to a wide group of agents. As a result, actions that tend to decrease the value of the securities will be discouraged. In this way, market valuation of securities provides an element of discipline for managers. Although these arguments are most often applied to private profit- making enterprises, they are equally valid in the context of sovereign borrowing. One of the major problems with the current structure of developing country debt is that it is bome most heavily by the sharehold- ers of the commercial banks in developed countries. Providing access to other sources of finance would be a major advantage for many develop- ing countries, and market valuation of these debts would provide reassurance to bank shareholders. Furthermore, the pri.e of existing securities will indicate the terms that developing countries will likely face on new issues, and this provides an incentive to maximize the value of these securities. The fact that a very large proportion of developing country borrowing has taken the form of general obligation bank loans despite the advan tages of securitization is testimony to the obstacle to securitization resulting from sovereign risk. It will not be possible to completely 142 COMMirODITY RIsK MANAGEMENT AN[) FINANCE eliminate these difficulties, but it may be possible to minimize their impact. This can be done, first, by iso!ating the sovereign risk from the other components of risk and, second, by adopting contract specifica- tions that reduce the former component at the expense of the latter. Secuiritizing Developing Co-try Obligations In considering expanding the scope of securities in development finance, interest has tended to focus on debt/equity swaps. The use of equity finance may have considerable potential in some development projects. Its use in the presence of sovereign risk, however, is likely to be restricted. The reason is that equity is a claim on a residual profit stream. The performance of the stock will depend upon the actions of the managers of the assets. VNYhen monitoring and control are difficult, there is Ar. agency probl mv. which means that the return to shareholder equity .an suffer. Such pioblems have the potential of becoming extreme in the presence of sovereign -:sk. Consequently, one would expect considerable investor reluctance to acquire the residual income claims against sover- eign borrowers. Banking relationships are widely recognized as means of overcoming problems of asymmetric information. This may explain the widespread reliance on general obligation bank loans for development finance in recent years. The performance of these loans in the 1980s has made it clear that even if such relations are advantageous from the point of view of information, the problem of sovereign risk can mean that bank loaxis may be de facto residual income claims. Recognition of this has meant that banks have been resistant to extending further general obligation country loans. Recent experience has shown that a number of activities that were previously thought of as the exclusi- 9. province of bank lending can be successfully given access to securities markets through appropriate instrument design. A prime example of this has been the development of the secondary mortgage market in the United States. The U.S. mortgage market is complex; however, most of the new securities used in this industry, referred to as mortgage-; acked securi:ies (NlBss), fall along rairly standard lines., In most cases, [he underlying assets in the security are individual mortgages that are, to some extent, standardized with respect to terms (e.g., maturity date, coupon rate, and so on). Typically, these underlying mortgages imply a certain risk that the property will default, in which case the mortgage holder receives the liquidation value of mortgaged property. Furthermore, property owners typically have the PARTIAL GUARANTEES AND COMMODITfY CONTINGENCY 143 option to prepay so that the mortgage holders are uncertain with respect to the duration of these obligations. The process of crealing an MBs can be viewed as the splitting of the risks containtd in a se t of mortgages. First, in most cases, an NIBS is endowed with a guarantee against default granted in return for an insurare^e premium. by some third part. The MIBS itself is a title to a proport'inate share of the total revenues from the underlying mortgages including interest, scheduied payments of principal, prepayments of principal, and default insurance claims.2 In effe~:t, the insuring body assumes and prices the default risk. The prepayment (i.e., duration) risk is red,iced through the efiect of the law of large numbers applied to a pool of mortgages. The remraining prepayment risk and the interest rate risk are left to be priced in che market for \tBss. The rapid developmen t of the U.S. sNBS market suggests tha- if it is possible to isolate and goarantee performance risk, the rer..aining components of risk may be assumed and priced by the market.3 Analogously, an important srep towsard facilitating the sec,iritization of developing country obligationls would be to find a means of channeling the sovereign risk component of these obligations into the hands of those who have a comparative advantage in bearing this risk.4 The vehicle for accomplishing this would be for the appropriate body to insure the performance of the developirg country loans in return for an insurance premium. In the case of ronperformance by the borrower, the insurer would pay the lender the s,.heduled paymniei and, in return, would assume the nonperforming loans as a portion of its portfolio. The insurer would then negotiate rescheduling with the nonperforming borrower against the threat of declarinl, the borrower in default. An important question is which agency or agencies should provide performance guarantees. Expe rience in the NIBS market indicates that the guarantees may originate from either the private or the public sector. 1hus, the Government Nationlal Mortgage Association (Ginnie Mae) is a *ub1ic-sector body, the Federal National M'ortgage Association (Fannie Vae) is a quoted corporation with agency status, and the Federal r'ome Loan Mortgage Corporation (Freddie Mac) is a private corporation also vith agency status (Thyge.-son, 1985). Ar agency will have a comparative advantage in tHis function if it can )ffer this insurance at a lower premium than other aL .ncies. From figure L0-1 and equation 10-2, one notes that, allowing for general contingent ayoffs, R(s), the insurarce premium will be 10-3) f (R(s) - Q(s))f(s) ds Original page # 144 is missing. PARrIAI GUARANTEES A OM.MODITY CONTINGENCY 145 The Design of Cormrnodit,-Contingent Instruments and Associated Guarantees !n principle, this franuwork implies a simple criterioii for determining those securities most appropriate for issue by developing countries. Securities with different payoff profiles, R(s), will generallv implv dif- feren- 'ike!ihoods of default and, consequently, different insurance premia. One erion for security* design is te minimize the insurance preimium, ubject to the constraint that the default-risk-free value of the securitics equals or exceeds the finance required.7 Gi-ren the functions, P(s) and A,s), this is a straightforward problem. In practice, the func.ions P'(s) and A(s) are not necessarily well known so that the issue o' optimal contract design u- Id r qrlire considerable investigation. Here some of the considerations that appear importalnt i light of recent experiences are noted. First, consider the general specifi- cation of a contingeent instrument, R(s). Note that in the 1980s, many cemnmodity-dependent Jeve!oping countries found chat repayments due, R(s), were higlh in those r.,es precisely when incomes were low. This negative associatiot. cf Qks) and R(:) makes threatened default and rescheduling a very likely outcome in states adverse for the borioN,.r. In contrast, wri 'ng contract terms so that R(s) is positively correlated with Q(s) V.'ould , the probability of default risk. Earlie,, it :uggested th?.t Q(s) is likely to be posirively correlated with current and anticipated future export earnings X(s). This suggests making the repaynments schedule state dependent through X(s) as R(X(s)). T-here are, howeve: twvo strong arguments against this proposa . Firsr, contingency on export revenuesu will introduce mora! hazard con.siderations through output and stock decisions. Second, this form of contingency would work against standardization-a contract issued against Zaire's export revenues wvould have different characteristics from a contrae: against Peru's export revenues, even though both countries are major copper exporters. P.-ovided that m-rkets are competitive, both difficui:ies can be circum-.xented by introducrng contingency through internationally cquoted prices and exchange rates.8 If the relevant price is C(s) and if the devek ping country's oblige-ons are contingent on the price, R(C(s))-, the country's scheduled net revenues in state s fot one unit9 of exports are, (10-4') Y(s) = C(s) - R(C(ss)). If the default penalty, P, and the value of future access, A, are functions of the price of the country's product, the condition to induce the borrower to respect the contract terms can be wA'ritttn as (i0-S) R(C(s)) < P(C(ss)) + E 4(C(ss)) - (I - w)L. 146 COMMODITY RISK MANAGEMENT AND FINANCE When the obligation is straighc debt, the nayment is a constant in all states, R(s) = R0. If for low values of the commodity price the penalty and v-.lue of access are low, then there will be a critical commodity piice CG below which the country will have an incentive to threaten default. That is, (10-6) Ro > ?(C(s)) + tvA(C(s)) - (1 - w)L for C < C*. This situation is broadly what has been demonstrated by the ex--rt-nce of many developing countries in thle 1M'3Os and providcs . L .ic mctivation for seeking to introduce some form of :Or.on. V.. cntin- gency in the payments of the de-'eloping countries. A basic way of i.5trvducing commodity contingency when a project faces co.nmodity price uncertainty is to protect against low commodity prices by hedging in forward or futures markets if they are available. e-v v speciically, by financing through a combination of straight debt and forward sales at a forward price F, the payment terms become, (10-7) R(C(s)) = Ro + C(s) - F. This will assure a constant income Y(s) -- F - Ro under the contracts, although this does not necessarily assure an incentive to fulfill the contract terms. For, under 10-7, the inequality 10-S may or may not be maintained in all states depending upon the precise way that P(C(s)) and A(C(s)) va7r with C. If P(C) = C and the hedgeab' value exceeds the fixed pay.rent, F> Ro, however, then 10-5 necessarily u 'l hold. In tact, one of the possible advantages of a commodity forwatd contract at a market falling outside of the borrower's legal jurisdiction may be precisely that, in case of default, the borrower's commodity deliveries in ,he marlket may be attached through legal means. Several considerations suggest that straight debt combined with for- % -rd sales may not be the best means of assuring that the problem of 'ign risk is reduced to the point that insu'rance would be feasible. l )roblem that arises with this combination is that generally creates two credit risks, not one. To illustrate how this Liuld have adverse effects, suppose that the ca,mmodity price is low. The borrower will simultaneously have an incentive to perform on the forward sale and yet to threaten default on the debt contract if the depressed commodity price reduces the -alue of access and if the penalty on the debt contract is low or nonexistent. One way around this is to make the forward contract itself part of the collateral for the debt contract. The alternative would be to combine the payment features of the debt plus forward sale into a single instrument-that, in effect, would become a commodity-contin- gent bond. Even if combining the characteristics of straight debt and a forward PARTIAL GUARANTEES AND COMMODITY CONTINGENCY 147 sale into a commodity bond can reduce the problems of rr iltiple credit risks, it does not necessarily assure that relation 10-S will hold in all states. In particular, because, under 10-7, the payment rises with the comr- *dity price, favorabie states might create an incentive to default if P and A do not rise to keep pace with the commodity price. It may well be that if a commodity producer can retain the profits of a commodity price boom, the value of future access to credit may not rise and may actually fail as C rises beyond a certain range. A package to circumvent this problem is a combination of straight debt, the sale of a commodity forward at F, and the purchase of a commodity call with a strike price K > F, which can be wri ten as, (10-8) R(s) = Ro + C(s) - F - max(0,C(s) - K) Thus, the m.ximum payment would be Ro + (K -F). So far, this discussion has ignored a number of constraints that rnay impinge on instrument design. For instance, the schedule outlined in equation 10-8 may imply zero or negative payments in some states if commodity prices fal1 below a critical level (i.e., if C(s) < F - Ro). This feature may be unacceptable to investors. A solution to this would be to design an instrument that possessed both a minimum and a maximum payoff. For example, straight debt combined with a call purchase and written call at a lower strike price results in (10-9) R(s) = Ro + max(0,C(s) - K,) - max(O,C(s) - K2), where K2 > KI. This double-call feature guarantees a minimum payment R(s) = Ro, it has a range of commodity prices in which payments increase as the commodity price rises, and it has a maximum payment of R(s) = Ro + K2 - K. If penalties from nonpayment fall when commodity prices fall bclow K1, this type of instrument will necessarily increase the insurance premium. This fcarure might be viewed as necessary to ensure that a sufficient volume of funds is forthcoming from investors. In this discussion, the institutionai structure that would be most effective in the process of securitization has not been specified. In fact, many arrangements might be effective. An interesting possibility is to consider the guarantee as a put option on the value of the loan. Thus, the holder of the guarantee pays a premium and obtains a put option covering a portion of the loan at a specified e cercise price. The holder of the put compares the value of that portion of the loan covered with the exercise price of the option and exercises the put if the value of the loan, for whatever reason, falls below the exercise price. On exercising the put, the holder receives the exercise price, and the put writer assumes tha- portion of the loan covered. Note that, if t}-. writer of the put has a comparative advantage in bearing aovereign risk, then there should be a 148 COMMODITY RISK MANAGEMENT AND FINANCE Figure 10-3 A Financing Structure Com t cInvestorso Commodity contingent securities Commodity contingen loans Developing country financial institution premium for the put that would be acceptable to the purchaser, but that would make put writing on average profitable. The flexibility of this arrangement is very great indeed. In particular, the maturity of the put option and the times within its life that it may be exercised (referred to as "exercise windows") can both be altered. Furthermore, the exercise price of the option can be fixed at particular levels and could, in principle, be made contingent on the commodity price. This flexibility can be used to design a guarantee that provides maximum insurance against sovereign risk elements at minimum cost. Figure 10-3 illustrates the concept of the put option guarantee for a given set of relations between various institutions. The developed country financial institution could be a commercial bank with exist .g loans to a particular developing country or might be a new type of lender entirely. The characteristic of this structure is that the lender offers commodity- contingent loans and issues commodity-backed securities to a wide class of investors. Attached to the commodizy-contingent loans are put options held by the developed country financial institution covering some portion of the loan to the developing country. These options will ensure a higher credit rating for securities backed by such -loans. The put option guarantee separates out significant elements of the sovereign risk from other types of risks-akin to the separation of different types of risks in the U.S. mortgage backed securities market discussed earlier. These instrument designs and potential lending strcictures are only intended to be illustrative of the implications of this discussion of sovereign risk. Considerable further research is required. Given more PARTIAL. GUARANTEES AND) CO.MMODI rY CONTINGENCY 149 precise information on the nature of default penalties and the value of access and investor preferences, it should be possible to design appropri- ate payment schedules and structure guarantees to suit. Conclusion It has been argued here that insured, contingent-payoff securities could replace much of the general-obligationi governmental borroNving as a source of developing country finance. Furthermore, for reasons of standardization and moral hazard, income (export revenue) contingenlcy is a less promising avenue than contingency on a publicly observable, nonmanipulatable variable such as competitive commcdity prices or exchange rates. A possible objection to this is that contingency on commodity prices and foreign exchanlge may be of limited relevance to many larger and more diversified developing countries, particularly those with substantial exports of manufactures. These problems are not insurmcuntable. A country may be viewed as a portfolio of productive assets, each having a value more or less linked to the price of its good(s) in world trade. Thus, the finance for a country would give rise to a corresponding array of commodity-contingent liabilities, plus some amount of noncontingent obligations for activities for which contingency is unfeasible. In effect, securing general developing country obligations can be viewed as creating a "strip" of commodity-contingent claims, each of which is isolated from country-specific sovereign risk. As in the case of many MBSS, by unbundling the risks this way, they can be sold to agents with comparative advantages in bearing these risks at advantageous prices so that their value is greater than when bundled. The strip concept reinforces the argument for standardization. Thus, given the appropriate third party insurance against default, countries such as Zaire and Peru would both have an interest in issuing standard, copper-contingent bonds (backed by thehi copper export revenues) with the same payoff profiles, R(s). These securities will appear identical to prospective purchasers, in the same way that the purchaser of a futures contract does not need to know the identity of the seller. Nevertheless, it should be recognized that the insuring body will view these as different risks because the values of future access, A(s), and the penalties, P(s), may be different. In this event, the inr,urance premia required would differ. Another possible objection to this proposal is that the developing country sovereign risk is not insurable bccause it will be highly correlated across countries. The one important reason for this degree of correlation is that developing countries are extremely dependent upon a relatively 150 COMMODITY RISK MANAGEMENT AND FINANCE small group of commodities for their export earnings. As a result, a general depression of commodities has an adverse impact on many countries. Because of this, there is yet further reason for commodity- contingent securities. Once commodity price exposure is split, developing country sovereign risk will be a residual that is more likely to be independent and thus more readily insurable. It is not only, and perhaps not mainly, governments who will be the issuers of these new insured, contingent securities. In fact, many arrange- ments appear possible. In many cases, countries may find it effective to decentralize the finance decision and allow specialized enterprises to obtain their own finance and issue liabilities whose contingency matches the enterprise's earnings profile. Alternatively, the borrower might be a private corporation whose ability to borrow is compromised by a perceived threat of nationalization or expropriation. Again, it could be a private commercial bank that would post as collateral a portfolio of (existing or new) developing country loans. What would be the market for the new securities? Once the sovereign risk insurance is arranged, the success of the issues is largely a function of the abilities of the financiers in designing the payoff profiles and in marketing. These skills have been well developed elsewhere, and there is every reason to think they are applicable here. In particular, commodity- contingent bonds may well behave much like equities of private com- modity producers. Consequently, combined with commodity futures and forwards, there may be ample scope for hedging and arbitrage with the consequence that the liquidity of the insured, contingent claims may be quite high. Finally, it is impossible to state here which institutions are best capable of offering the required sovereign risk insurance. This analysis shows that it is a matter of who can offer a given insurance at the smallest premium. This, in turn, will depend on which institution can extract the greatest penalties, have the biggest impact on future access to finance, and bargain hardest. There is a presumption that this would be a large, very creditworthy institution that has been a long-term participant in inter- national lending. It needs to be emphasized that the insurance described here would be self-financing along actuarial grounds. Consequently, the insuring body could be a private, profit-seeking organization. Most important, no matter whether the insuring body would be priva,: or governmental, the guarantee would not require access to governmental tax revenues. PARTIAL GUARANTEES AND COMMIODITY CONTINGENCY 151 Notes 1. In 1983, the outstanding valuc of ,oBS obligations was $278 billion (Seiders, 1985), a figure comparable to the approximately S249 billion of outstanding nonguaranteed developing country debt (short and long term) in private hands at that time. See the World Bank (1988), pp. 87-88. 2. This describes a "pass-through," such as a Ginnie Nae. Othcr forms of mhIBss strip out the interest and various tranches oi principal repayment. 3. In the context of lending to de% eloping country governments and their agencies, these risks would be associated with var.-bilhry in export earnings, exchange rates, and interest rates. 4. The concep. of comparative advantage in bearing divcrse typcs of risks is discussed in Lessard (1986). S. Later, the 'ontiactual payments R will also become state dependent. 6. In the United ..>ates, the cffect of guarantecing institutions requiring that mBss confornm to certain standard forms was to create a high degree of standardization, which aided the growth of active secondary trading. 7. This critcrion is appropriate for a risk-neutral borrower. Risk aversion or intertem- poral consumption smoothing may also bc a consideration affecting the supply of securities. Most of the literature on commodity contingency takes this to be the sole objective for contingency. This analysis shows that the facilitation cr sccuritization is another, possibly more significant, consideration in structuring payoffs. In effect, this deals wiiti the demand for securities. 8. If markets are noncompetitive, price-contingent cont-acts may alter the incentives borrowers face in their production decisions. In this case, the price-contingent contracts may be manipulatable. See Anderson and Sundaresan (1984) and Newbery (1984). More generally, price contingency may affect borrower's invcstment allocation decisions. See Besley and Powell (1988). 9. Here, the figure has been normalized to ;llow for a quantity of unity. This is a harmless simplification given that quantiry uncertiinty is being subtracted in this discussion. Conclusion Theophilos Priovolos and Ronald C. Duncan The collection of papers brought together in this volume was written to advance knowledge about the demand, pricing, and use of commodity- linked finance.' Fall extended the work of O'Hara on the demand for commodity bonds and showed that the demand function for commodity bonds has two components-a speculative component and a hedging component-and that the demand for commodity bonds is positive when the investor has a lower relative modified risk tolerance than the market, that is, a higher relative modified risk aversion. Rajan simplified the work of Schwartz on the pricing of commodity bonds by introducing the use of binomial pricing theory. Thompson and Myers extended the typical one-period, mean-variance framework for the computation of the opti- mal commodity hedge ratio by the use of vector autoregression; thus, they were able to capture variations in both export patterns and departures from random walks in commodity prices. Claessens extended the typical optimal hedge methodology to include exchange rate risk, in additioIn to commodity price risk. Ball and Myers further extended this optimal hedge methodology to a sovereign borrower without any existing debt. The Wright and Newbery paper quantifies the costs of export revenue variability and the potential for risk reduction through reserve manage- ment and commodity hedging and demonstrates the importance of risk management for consumption smoothing. Employing a model of default based on the tradeoff between the borrower's expected future consump- tion smoothing benefits from external finanr, and the cost of meeting its obligation, Wright and Newbery show that, with commodity bonds, the probability of default is reduced. Such contracts reveal the "permanent" level of income that the country could count on from its commodity exports. I52 CONCLUSION 153 Anderson, Gilbert, and Powell show that borrowers and lenders do not always have a comparative advantage in hedging all types of risks. They show that the probability of default risk reduces w'hen the contract terms of an obligation are written so that the repayments schedule dependls on income. Moral hazard and cost standardization concerns constitute two strong arguments against using "income" such as export earnings. Provided markets are competitive, both difficultics can be circumve:ited by introducing contingency through internationally quoted price and exchange rates. They show that, for low values of commodity prices, the default penalty and the value of future access to finance are low (if they are a function of commodity prices) and that, beyond a critical commod- ity price level, developing countries will have an incentive to default. A standard recommendation has been that when a project faces commodity price uncertainty, it should be protected against the risk of low commodity prices by hedging in fornvard markets or other similar markets (such as futures, options, swaps, etc.) if they are available. More specifically, by financing through a combination of straight debt and forward sales, this will assure a constant income for the borrower. This strategy does not necessarily assure the incentives to fulfill the contract terms, however. Anderson, Gilbert, and Powell find the likely conditions under which incentives will exist to ensure that the terms of the contract are fulfilled. Several considerations suggest that straight debt comrbined with forward sales may still not be the best means of assuring that the problem oi sovereign risk is substantially reduced. One problem that arises with this combination is that it generally creates two credit risks, not one. Anderson, Gilbert, and Powell point out that one way around this difficulty is to make the forward contract itself part of the collateral for the debt contract; another way is to combine the payment features of the debt and the forward sale into a single instru- ment. This would become a commodity-contingent bond. If the default penal.-y or the vaiue- of access does not keep pace with the commodity price, the commodity bond will not necessarily assure that the contract will not be circumvented. It may well be that if a commodity producer can retain the profits of a commodity pricc boom, the value of future access to credit may not increase and may actually fall as prices rise beyond a certain range. A package to circumvent this problem is a commodity bond that combines a straight debt, the sale of a commodity forward, and the purchase of a commodity call at a strike price higher than that for which it was sold forward. Clearly, such an instrumcnt could be marketed best by the institution providing insurance at the smallest p:emium for any residual sovereign risk. This, in turn, will depend on who can extract the greatest penalties, have the biggest impact on future access to nnance, and bargain hardest. 154 COMMODITY RISK MANAGENMENT AND FINANCE There is a presumption that this would be a large, very creditworthy institution, which has been a long-term participant in international lending. It needs to be emphasized that the insurance the three authors describe could be self-financing along actuarial grounds. Consequently, the body could be a profit-seeking organization. There is also the point that the residual guarantee will be significantly less than that required if securitization of straight debt is contemplated. In other words, the institution's capital would be able to finance a greater amount of loans (if they were structured in the commodity-linked form) with the same amount of risk it would have otherwise been willing to assume. Commodity-linked financings have impo'tant advantages in the exter- nal financing of developing counzries relative to the traditional alterna- tives of foreign currency denominated, general obligation borrowing, or direct foreign investment. They allow developing countries that are overe-posed to particular risks, relative to those in the world economy, to shitt these risks to world capital markets on an ex ante basis. By contrast, general obligation financing also shifts risk, but only on an ex post basis through nonperformance with its attendant deadweight pen- alties. In contrast with direct investment and other forms of finance that also shift risk on an ex an:te basis, commodity finance is linked to observable, exogenous outcomes and does not require the same degree of cost.y monitoring or intrusion of foreign forces into domestic decision making. Commodity price-linked finance is preferable to other forms of indexed finance because moral hazard and standardization consider- ations work against such other forn.-. To sum up, commodity-linked financings have expanded rapidly in the late 1980s, but they have been mainly confined to entities in industrial countries. Creditworthiness questions handicap the developing countries in their access to this type of financing. Unless their credit standing can be enhanced, maybe through a third-party guarantee, many developing countries will find it difficult to have independent access to international financial markets for such finance, and they may have to depend on bilateral and multilateral aid and development agencies for their external funding needs. It is clear that the insurance premium required for such third-party guarantees is minimized when the insuring body has a comparative advantage in bearing sovereign risk and when the contrac- tual terms are contingent on factors affecting the borrower's present and future earnings. Commodity-price-contingent instruments are shown to be the most suitable obligation for the developing country needs. To achieve better risk management in the commodity-dependent developing countries, the implications for the practices of international development agencies on the basis of the findings of the papers included here are: CONCLUSION 155 * To support, with technical assistance, enhancement of institutional and human resources capacity in developing countries in the area of finance, in particular, in commcdiay price risk management * To support better risk managemnent practices in project and program lending in developing countries through technical support and/or appropriately tailored lending o To support commercial cofinancing with the use of partial guaran- tees and to make their own loans commodity price-contingent * To support, in the context of restructuring of commodity-dependent developing countries' debt, the exchange of existing debt for appro- priately tailored commodity price-contingent debt * To institute methods to hedge appropriately the derivative commod- ity exposure in the financial markets by commodity price-linked financings. Note 1. We would like to thank Todd Petzel and Donald R. Lessard for their enlightened discussion of several of the contributions in this book wlien they were presented during the 1988 American Agricultural Economics Association meetings in New York. This chapter incorporates as best as possible their major comments. For riore details, see Petzel (1989) and Lessard (1989). Original page # 156 is missing. Adler, Michael, and David Simon. 1986. "Exchange Rate Surprises in Intema- tional Portfolios." The Journal of Portfolio Management vol. 12, no. 2 (Winter), pp. 44-53. Ahamed, Liaquat. 19I8. "Liability Management: I\ PortfoliG Manager's Point of View." Paper presented at Trends in Internatio ial Capital Markets: Implica- tions for Developing Countries, Oxford. Anderson, R. W., ed. 1984. The Industrial Organization of Futures Markets. Lexington, Mass.: Lexington Books. Anderson, R. W., and J. P. Danthine. 1983. "Hedger Diversity in Futures Markets." Economic Journal vol. 93 (June), pp. 37089. Anderson, R. W., and S. M. Sundaresan. 1984. "Futures Markets and Monop- oly." In R. W. Anderson, ed. The Industrial Organization of Futures Markets. Lexington, Mass.: Lexington Books. Benninga, S., Rafael Eldor, and Itzhak Zilcha. 1985. "Optimal International Hedging in Commodity and Currency Forward Markets." Journal of Interna- tional Money and Finance vol. 4, pp. 537-52. Besley, Timothy, and A. P. Powell. 1988. "The Role of Commodity Indexed Debt in International Lending." Institute of Economics and Statistics, Oxford University, Oxford; processed. Bindf.r, B. F., and T. W. F. Lindquist. 1982. "Asset/Liability and Funds M4.ingement at U.S. Commercial Banks." Bank Administration Institute, Rolling Meadows. Black, Fischer, and M. S. Scholes. 1972. "The Valuation of Option Contracts and a Test of Market Efficiency." Journal of Finance vol. 17, pp. 399-417. . 1973. "The Pricing of Options and Corporate Liabilities." Journal of Political Economy vol. 81, pp. 637-59. 157 158 COMMODITY RISK MANAGEMENT AND FINANCE Bollerslev, T. B. 1986. "Generalized Autoregressive Conditionai Heteroskedas- ticity." Journal of Econometrics vol. 31, pp. 307-27. .1987. "Modelling the Coherence in Short Run Nominal Exchange Rates: A Multivariate Generalized ARCH Model." Northwestern University, Chicago; processed. Br. :ison, W. H., and L. T. Katseli. 1982. "Currency Baskets and the Real Effective Excha.ige Rates." In M. Gersovitz, et al. The Theory and Experience of Economic Development. Essays in Honour of Sir W. Arthur Lervis. London: George Allen and Unwin. Breeden, D. f. 1979. "An l.,tertemporal Asset Pricing Model with Stochastic Consumption ;.nd Investment Opportunities." Journal of Financial Economics vol. 7, pp. 265-96. . 1980. "Consumption Risk in Futures Markets." Journal of Finance vol. 35, pp. 503-20. . 1981. "Some Common Misconceptions about Futures Trading." Teach- ing Notes. Stanford University, Palo Alto, Calif.; processed. . 1984. "Futures Markets and Commodity Options." Journal of Eco- nomic Theory vol. 32, no. 2, pp. 275-300. Brennan, M. J. 1958. "The Supply of Storage." American Econornic Review vol. 48, no. 1, pp. M)-72. . 1986. "The Cost of Convenience and the Pricing of Commodity Contingent Claims." Working Paper CsFNI-130. Columbia Business School, New York. Brennan, M. J., and E. S. Schwartz. 1980. "Ana'yzing Convertible Bonds." Journal of Financial and Quantitative Analysis vol. 25, pp. 907-29. Brown, S. L. 1985. "Reformulation of the Portfolio Model of Hedging." American Journal of Agricultural Economics vol. 67, pp. 508-12. Budd, Nicholas. 1983. "The Future of Commodity-Indexed Financing." Hanrard Business Review vol. 61, no. 4, pp. 44-50. Bulow, Jeremy, and Kenneth Rogo'rf 1987. "A Constant Recontracting Model of Sovereign Debt." Social Systems Research Institute, University of Wisconsin, ,.ladison; processed. . i988. "Sovereign Debt: Is to Forgive to Forget?" NBER Working Paper 2623. Cambridge, Mass.: National Bureau of Economic Research. Campbell, R. B., and S. J. Turnovsky. 1982. "Stabilizing and We.-are Properties of Futures Markets: A Simulation Approach." Working Paper 83. Australian National Jniversity, Faculty of Economics and Rebearch School of Social Sciences, pp. 1-41. . 1985. "Analysis of the Stabilizing and Welfare Effects of Intervention in Spot and Futures Markets." NBER Working P-er 1698. Cambridge, Mass.: National Bureau of Economic Research, pp. '. Original page # 159 is missing. 160 COMMODITY RIsK MANAGEMENT AND SINANCE Dreyfus, S. E. 1965. .)ynarzaic Progratting 7nd the Calculu(s o/ Variaticns. New York: Academic Press. Liunn, K. B., and J. J. McDonnell. 1981. "Valuation of GM .MA Mortgage-P,acked S:curities." Jousrnal of F.nance vol. 36, no. 2 pp. 471-434. Dusak, Katherine. 3973. "Futures Trading and Investor Returns- An Investig>- tion of Commodity Marke- Risk Pr:nrniums."Journal of Political Economny vol. pp. 1387-1406. laton, Jon3than, and Mark Gersovitz. 198 1. "Debt with Po0t al Repudiation: Thce^crical and Emnpirical A:'alysis." Reveiw of Economic Studies vol. 48, pp. '89-339. Eaton, Jonathan, Mark Gersovitz, -nd J. E_ Stiglitz. 1986. "The Pure Tlieory :f Country Risk." European Econmnic Revietv vol. 30. pp. 481-513. Eichengreen, Barrv. 1987. "Til Debt Do Us Part: The U.S. Capital MNarket and Foreign Lending: 1920-1955." YBER Work;ing -aper 2394. Cambridge, Mass.: National Bure?-J of E&-nomic Research. Eldor, Rafael, and David Piieu. ;98'. "De-ter-ainants of the Household Demand for Hedging fnstrurrents." Foerdtr Institute f'r Econnrmic Pe.3e :h, Working Paper 1-85, Tel Aviv Universiry, pr,. 1-26. Engle, R. F. 1982. "Auteregressive ConJitional Heter ;skedasticity with Esti- mates of the Variance of U.K Inflation." Econometrica vol. S), pp. 987-1008. Engle, R. F., and T. B. Bollerslev. 1986. "Modelling the Persistence of Condi- tional Variances." Econo,,ietric Reviews vol. 5, pp. 1-50. Ligle, R. F., and C. W. J. Granger. 1977. "Co-integration and Error Correction: Representation, Estimation, and Testing." Econometrica vol. 55, pp. 25 1-76. Evans, Pa-ul. 1988. "Arc Consumers Ricardian? Evidence for e United States." Jour,..l of Polit:cal Econwetv vol. 96, pp. 903--10u4. Evnine, JerCmy. 1983. "Three Essavs !n the Use of Optio. Pricing Theory." PhD. Thes,is. Uriversiry of Calitornia, Berkelev; processed. Fall, Ni. A. 19S6. "Commodity-lndexe'l Bonds." Maa.ers T' .sis. Sloan School of Management, MIT, Cambridge, Mass.; processed. Feder, Gcrshon, and R. E. Just. 1977. 'A Study of £ebr Servicing Capacity Apply;ng Logit Analysis." Jos.rnal of Developrment Eccnoriocs, vol. 4, ra. 1, pp. 25-32. Firiger.J. M., and C). A. de R..a. 1980. "'The Compensatory Finance Facility and Exrpert Instabii.- t." Journal of World Trade Law vol. 14, Fp. 14-22. Fischer. Stanley. 1' 73. ' The Demanri for index Z.onds." Journa' of Political Economy vol. 83, F1. 309-34. 1978. "Cal: (1 -io Pricing When Lhe Exercise Price Is l,ncertain and the Valuation of !nAex Bon&." Journal of Finance vol. 33, no. 1: pp. 169-76. BIBLIOGRAPHY 161 Fishlow, Albert. 1987. "Lessons of the 1880's for -he 1930's." Working Paper 8724. University of California, Berkeley, Department of Economics. Flood, Eugene, Jr. 1986. "An Empirical Analysis of the Effect of Exchange Rate Changes on Goods Prices." Graduate School of Business Administration, Stanford University, April; processed. Frankel, J. A. 1981. "Flexible Exchange Rates, Prices and the Role of 'News': Lessons from the 1970s." Journal of Political Economy vc' 89, pp. 665-705. 1983. "EsLumation of Portfolio-Balance Functions That Are Mean- Variance Optimizing." Eu' .ipean Economic Review vol. 23, pp. 315-27. Gemmill, G. T. 1980. "The Effew,tiveness oi Hedging and the Variance of Spot and Futures Prices." City Univ rsity Busincss School, London; processed. 1985. "Optimal Hedging on Futures Markets for Commodity-Exporting Nations." European Econom;c Reviciv v'l. 27, pp. 243-61. Gersovitz, Mark. 1983. "Trade, Capital MG,bility and Sovereign Immunity." Discussior. Paper 108. Research Program in Developmeiit Studies, Princeton University. . 1985. "Banks' Internatiu.-Il Lending Decisions: What We Know and Implications for Future Research." hi: Gordon W. Smith and John T. Cudding- ton, eds. International Debt and the leveloping Countries. Washington, D.C.: World Bank. Gilbert, C. L. 1988. "The Impact of Exchange Rates and Developing Country Debt on Commodity Prices." Economic journal vol. 99, pp. 773-84. Giovannini, Albezrto. 1985. "Exchange Rates and Traded Goods Prices." Grad- uate School of Business, Columbia University, New York; processed. Gordon-Ashworth, Fiona. 1984. !nternational Commodity Control: A Csntem- porary History and Appraisal. London: Croom Helm. Goss, B. A., and B. S. Yamey, eds. 1978. The Economics of Futures Trading. London: Macinii!an. Grossman, H. I., and J. B. van liuyck. 1985 -:Sovereign Debt as an Contingent Claim, Excusable Default, Repudiation ar . Reputation," NBER Working Paper 1673. Cambridge, Mass.: National Bureau of Economic Research. Hansen, L. P., and T. S. 1980. "Formulating and Estimating Dynamic Linear Rational Expect ions Models." Journal of Economic Dynamics and Control vcl. 2, pp. 7-46. Haslem, J. A. 1984. Bank Funds Management: Text and Readings. Reston, N.J.: Resto- Publishing Cornpany. Hazuka, T. B. 1984. "Consumption Betas and Backwardation in Commodity Markets." Journal of Finance vol. 39, pp. 647-55. Heifner, R. G. 1978. "Miinimum Risk Pre-Harvest Sales of Soybeans." National Economic Anaiysis Division, U.S. Department of Agriculture, Washington, D.C. 162 COMMODITY RISK MANAGEM{ENT AND FINANCE Holthausen, Duncan. 1979. "Hedging and the Competitive Firm Under Price Uncertainty." Amer.an Economic Reviewv vol. 69, pp. 989-95. Ingersoll, J. E., Jr. 1982. "The Pricing of Commodity-Linked Bonds, Discussion." Journal of Finance vol. 37, no. 2, pp. 540-41. Ito, Kiyoshi, and H. P. McKean. 1964. Diffusion Processes and Their Sample Paths. New York: -.ademic Press. Johnson, L. L. 1960. "The Theory of Hedging and Specularion in Commodity Futures." Review of Economic Studies vol. 27, pp. 139-St. Jones, Terry. 1984. "Growing World of Commodity Finance." Eurom( ney Trade Finance Report vol. 13, pp. 29-30. Joskow, P. L. 1977. "Commercial Impossibility: The Uranium Market and the Westingnouse Case." Journal of Legal Studies vol. 6, pp. 119-76. Kantor, L. G. 1986. "Inflation Uncertainty and Real Economic Activity: An Alternative Approach." Review of Economics and Statistics vol. 68, pp. 493-500. Karp, Larry. 1986. "Dynamic Hedging with Uncertain Production." Working Paper 371. University of California, Division of Agricultural Sciences, pp. 1-25. Keynes, J. M. 1924. "Foreign Investment and the National Advantage." The Nation and Athenaeum. Kinney, J. M., and R. T. Garrigan, eds. 1985. The Handbook of Mortgage Banking. Homewood, Ill.: Dow Jones-Irwin. Kletzer, K. M. 1988. "Sovereign Debt Renegotiation Under Asymmetric Infor- mation." Discussion Paper 555. Yale University Economic Growth Center, New Haven, Conn. Koppenhaver, G. D. 1984. "Variable-Rate Loan Commitments, Deposit With- drawal Risk, and Anticipator, Hedging." Federal Reserve Bank of Chicago, Staff Memoranda sm-85-6, pp. 1-26. Korsvik, W. J., and C. 0. Meiburg. 1986. The Loan Officer's Handbook. Homewood, Ill.: Dow Jones-Irwin. Kraft, D. F., and R. F. Eng!e. 1982. "Autoregressive Conditional Heteroskedas- ticity in Multiple Time Series Models." Discussion Paper 82-23. University of California, San Diego. Kroner, Kenneth, and Stiin Claessens. 1988. "Improving the Currency Compo- sition of External Debt: Applications in Indonesia and Turkey." PPR Working Paper 150. World Bank, Washington, D.C.; processed. Lessard, D. R. 1977a. "Commodity-Linked Bonds from Less-Developed Coun- tries: An Investment Opportunity." MIT, Cambridge, Mass.; processed. . 1977b. "Risk Efficient External Financing Strategies for Commodity Producing Countries." MIT, Cambridge, Mass.; processed. BIBLIOGRAPHY 163 1979. "Risk Efficient External Financing for Commodity Producing Developing Countries: A Progress Report." MIT, Cambridge, Mass.; proc- essed. . 1980. "Financial Mechanisms for Stabilizing Revenues of Commodity Producing Developing Countries: Narrative Report." Sloan School of Man- agemcnt, MIT, Cambridge, Mass.; pro:essed. . 1986. "The Management of International Trade Risks." The Geneva Papers on Risk and Insurancc vol. 11, pp. 255-64. . 1987. "Recapitalizing Third-World Debt: Toward a New Vision of Commercial Financing for Less-Developed Countries." Alidland Corporate Financz Journal vol. S, pp. 6-21. . 1989. "Financial Risk Management Needs of Developing Countries: Discussion." American Journal of Agricultuiral Economics vol. 71, no. 2 (May), pp. 534-35. Lessard. D. R., and John Williamson. 1985. Financial Intermediation Beyond the Debt Crisis. Washington, D.C.: Institute for International Economics. Leuthold, R. M., and P. A. Hartmann. 1979. "A Semi-Strong Form Evaluation of the Efficiency of the Hog Futures Market." American Journal of Agricultural Economics vol. 61, pp. 482-89. Lindert, P. H., and P. J. Morton. 1987. "Huw Sovereign Debt Has Worked." Macro Policy Working Paper Series 45. University of California-Davis, Insti- tute of Government Affairs Research Program in Applied Macroeconomics, Davis, Calif. Lipschitz, Leslie, and V. Sundararajan. 1982. "The Optimal Basket in a World of Generalized Floating." IMF S_ff Papers, pp. 80-100. Long, J. B. 1974. "Stock Prices, Inflation and the Tern Structure of Interest Rates." Journal of Financ- {. -conomics vol. 1, no. 2, pp. 131-70. Madura, Jeff, and Reiff Wallace. 1985. "Hedge Strategy for International Porfolios." Journa' of Portfolio Management vol. 12, pp. 70-74. Markham, J. W., and K. K. Bergin. 1985. "The Role of the Commodity Futures Trading Commission ir International Commodity Transactions." George Washington Journal of International Law and Economics vol. 18, pp. 581- 629. Markowitz, H. M. 1952. "Portfolio Selection." Journal of Finance vol. 7, pp. 77-91. Mason, S. P., and R. C. Merton. 1985. "The Role of Contingent Claims Analysis in Corporate Finance." In E. Altman and M. Subrahmanyam, eds. Recent Advances in Corporate Finance. Homewood, Ill.: R. D. Irwin. McCarthy, David and Robert Palache. 1986. "Eurobonds, Bells and Whistles: How Issues Were Structured." International Financial Law Review vol. 5, no. 6, pp. 27-32. 164* CONMM{ODITY RISK MANAGEMENT AND FINANCE McDonald, Robert, and Daniel Siegel. 1984. "Option Pricing When the Under- lying Asset Earns a Below-Equilibrium Rate of Renurn: A Note." Journal of Finance vol. 39, no. i, pp. 261-65. McFadden, R. T. 1984. "Energy Futures C tracts and the Uses in Cuuntertrade/ Barter Deals." Countertrade & Bo-'er Quarterly vol. 4, pp. 47-50. McKean, H. P. 196°. Stochastic Integral. New York: Academic Press. McKinney, G. W., and W. J. Brown. 1974. Mantagement of Commiercial Bank Funds. New York: American Institute of Banking. McKinr.on, R. 1. 1967. "Futures Markets, Buffer Stocks, and Incomle Stability for Pr-mary ProdL.ers." Journal of Political Economy vol. 75, pp. 844-61. Mt. vnch. 1978. The Merrill Lynch Guide :o Speculating in Commocdity .4re3. New York. 1L.. ,, R. C. 1969. "Lifetime Portfolio Selection Under Uncertainty: The C, ,tinuous-Time Case." Review of Economic Statistics vol. 51, no. 3, pp. 247-57. . 1971. "Optimum Consumption and Portfolio Rules in a e ontinuous Time Model." Journal of Economic Theory vol. 3, pp. 373-13. . 1973a. "An Intertemporal Capital Asset Pricing Model." Econometrics vol. 41, pp. 867-87. 1973b. "Theory of Rational Option Pricing." Bell Journal of Econom;cs and Management Science, vol. 4, pp. 141-83. Meyer, Jack. 1987. "Two-Moment Decision Models and Expected Utiliry Maximization." The American Economic Review vol. 77, pp. 421-30. Meyer, Jack, and L. J. Robison. 1988. "Hedging and Price Randomness." American Journal of Agricultural Economics vol. 70, pp. 268-80. Newvbery. D. M. G. 1984. "The Manipulation of Futures Markets by a Dominant Producer." In R. W. Anderson, ed., The Industrial Organization of Fututres Markets. Lexington, Mass.: Lexington Books. Newbery, D. M. G., and J. E. Stiglitz. 1981. "The Theory of Commodity Price Stabilization." Oxford: Oxford University Press. O'Hara, Maureen. 1984. "Commodity Bonds and Consu:mption Risks." Journal of Finance vol. 39, Pp. 193-206. Page, S. A. 1981. "The Choice of Invoicing Currencies in Merchandise Trade." Nat 'onal Institute Economic Review vol. 81, pp. 60-72. Peck, A. E. 1975. "Hedging and Income Stability: Concepts, Implications, and an Example." American Journal of Agricultural Economics vol. 57, pp. 410-19. Petzel, T. E. 1989. "Financial Risk Management Needs of Developing Countries: Discussion." American Journal of Agricultural Economics vcl. 71, no. 2 (May), pp. 531-33. BIBLIOGRAPHY 165 Pindvck, R. S. 1983. "Cartel and Oligopolistic Pricing." Lecture Notes, Sloan School of Management, MIT, Cambridgr. Mass.; processed. Powell, A. P., and C. L. Gilbert. 1988. "The Use of Commodity Contingent Contracts in the Management of Developing Country Debt Risk." In D. Currie and D. Vines, eds. Macroeconomic Interactions Bctween North and South. Cambridge: Cambridge University Press. Powers, M. J., and David Vogel. 1984. Inside the Financial Futures Markets. New York: John Wiley & Sons. Priovolos, Theophilos. 1987a. "Commodity Bonds: A Risk Managenment Instru- ment for Developing Countries." :ECCM Working Paper 1987-12. World Bank, Washington, D.C.; processed. . 1987b. "An Overview -f Commodity Bonds: A Balance Sheet Manage- ment Instrument." IECCM, World Bank, Washington, D.C.; processed. Richard, S. F., and S. M. Sundaresan. 1981. "A Continuous Time Equilibrium Model of Forward Prices and Futures Prices in a Mulfigood Economy." Journal of Financial Economics vol. 9, pp. 347-71. Rolfo, Jacques. 1980. "Optimal Hedging under Price and Quantity Uncertainty: The Case of a Cocoa Producer." Jeu.,rnal oi Political Economy vol. 88, pp. 100-16. Sachs, Jeffrey, and Daniel Cohen. 1982. "LDC Borrowing with Default Risk." NBER Working Paper 925. Cambrid',e, Mass.: National Bureau of Economic Research. Samuelson, P. A. 1985. "The Public Interest ar.d Commerical ' 4vantage of a Mechanism to Hedge against Inflation Risks." MIT, Cambridge, Mass.; processed. Sarris, A. H. 1984. "Speculative Storage, Futures Markets, and the Stability of Commodity Prices." Economic Inquiry vol. 22, pp. 80-97. Schwartz, E. S. 1982. "The Pricing of Commodiry Bonds." Journal of Finance vol. 37, pp. 525-39. Seiders, D. F. 1985. "Residential Mortgage and Capital Markets." In The Handbook of Mortgage Banking. Homewood, Ill.: Dow Jones-Irwin. Shapiro, A. C. 1984. "Currency Risk and Relative Price Risk." Journal of Financial and Quantitative Analysis vol. 19, pp. 365-73. Sharpe, W. F. 1964. "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk." Journal of Finance vol. 19, no. 3, pp. 425-42. . 1981. Investment. Englewood Cliffs, N.J.: Prentice-Hall. Sims, C. A. 1980. "Macroeconomics and Reality." Econometrica vol. 48, pp. 1-48. Smirlock, M. 1986. "Hedging Bank Borrowing Costs with Financial Futures." Federal Reserve Bank of Philadelphia, Business Review, pp. 13-23. 166 COMMODITY RISK MANAGEMENT AND FINANCE Smith, C. W. 1976. "Opticn Pricing: A Review." Journal of Financial Economics vol. 3, pp. 1-51. Smith, C. W. 1978a. "Commodity Instability and Market Failure: A Survey of Issues." In F. G. Adams and S. Klein, eds. Stabilizing World Commodity Markets. Lexington, Mass.: Lexington Books. . 1978b. Numerical Solutions of Partial Differential Equations. Oxford: Oxford University Press. Smith, C. W., and R. Al. 5tulz. 1985. "Determinants of Firms' Hedging Policies." Journal of Fina-.cial and Quantitative Analysis vol. 20, pp. 391-405. Srinivasan, Bobby, and Anant Negandhi. 198S. "Hedging in Currency Futures: A Singapore Dollar Case Study." Asia Pacific Journal of Managcmeent vol. 2, pp. 170-79. Stapleton, R. C., and M. G. Subrahmanyam. 1984. "The Valuation of Multi- variate Contingent Claims in Discrete Time Models." Journal of Finance vol. 39, no. 1, pp. 207-29. Stein, J. L. 1961. "The Simultaneous Determination of Spot and Futures Prices." American Economic Review vol. 51, pp. 1012-2S. Stone, R. 1989. "Financing COMINCO's Red Dog Project." Fifth Min.ral Econom- ics Symposium, Toronto, Ontario. Stulz, R. M. 1981. "A Model of Intemational Pricing." Journal -)f Financial Economics vol. 9, pp. 383-406. . 1982. "Options on the Minimum or the Maximum of Two Risky Assets." Jo.nal of Financial Economics vol. 10, no. 2, pp. 161-85. 1984. "Optimal Hedging Policies." Journal of Financial and Quantita- tive Analysis vol. 19, pp. 127-40. Svensson, L. E. 0. 1987. "Optimal Foreign Debt Composition." World Bank, Washington, D.C., December; processed. - -. 1988. "Portfolio Choice and Asset Pricing with Nontraded Assets." Institute for International Economics, University of Stockholm, July; proc- essed. Tesler, L. G. 1981. "Why There Are Organized Futures Markets." The Journal of Law and Economics. vol. 24, no. 1, pp. 1-22. Thygerson, K. J. 1985. "Federal Government-Related Mortgage Purchase.-s." In The Handbook of Mortgage Banking. Homewood, Ill.: Dow Jonec irwin. Van Horme, J. C. 1980. Financial Market Rates and Flows. EnSiewood Cliffs, N.J.: Prentice Hall Inc. Varangis, Panos, and R. C. Duncan. 1990. "The Response of Japanese and U.S. Steel Prices to Changes in the Yen-Dollar Exchange Rate." wps 367. World Bank, Washington, D.C.; processed. BI'SLIOGRAPHY 167 Wtbb, S. B., and H. S. Zia. 1989. "Borrowings, Resource Transfers, and External Shocks to Developing Countries: Historical ar.d Counterfactual." PPR Working Paper 235. World Bank, Washington, D.C.; processed. We!ls, R. 1989. "Optimal Diversification in International Borrowing." Depart- ment of Econo.nics, University of California, Berkeley, January; processed. Williamson, Jchn. 1982. "A Survey of (he Literature on the Optimal Peg." Journal of Development Economics vc.l. 11, pp. 39-62. Woodward, P. 1989. "Trends in Gold Lending to Gold Mining Companies." Fifth Mineral Economics Symposium, Toronto, Ontario. Working, Holbrook. 1953. "Futures Trading and Hedging." American Eco- nomic Review vol. 43, pp. 314-43. World Bank. 1984. Borrowing and Lending Technology: A World Bank Glossary. Washington, D.C. 1988a. Commodity Trade and Price Trends. Washington, D.C. 1988b. "Financial Flows to Developing Countries." IECDI. Washington, D.C.; processed. . 1988c. World Debt Tables 1987-88, First Supplement. Washington, D.C. Worrall, Tim. 1987. "Debt with Potential Repudiation: Short-Run and Long- Run Contracts." University of Reading Discussion Papers in Economics, Series A, no. 186. Wright, B. D., and J. C. Williams. 1982. "The Economic Role of Commodity Stotage." Economic Journal vol. 92, pp. 596-614. Original page # 168 is missing. (Page numbers in italics indicate material in tables.) Africa, dependence on commodity exports Caisse Nationale d'Energie, bond issued in, 1 by, 11 Algeria, trade shock in, 2 Call option, 12, IS, 33-34, 147 Aluminun-linked financing, 36 Canada, 12, 29-30, 37 Andersor., Ronald, 6, 153 Capital: hedging with commodity-linked Asia, dependence on commodity exports bonds and, 116-20, 123; hedging with in, 1 conventional loans and Asset returns (demand function analysis), commodity-linked bonds and, 121-23 40-42 Capital Asset Pricing Model (CAPM), 39, Australia, 12, 29 40 Autoregressive conditional Ca ; (commodity price), defined, 14; in hereroskedasticiry (ARCH), 106, 107 pricing model, 72-74, 7S Autoregressive moving average (ARMA), Carr, Peter, 61, 125 106 Central Bank (Taiwan), gold puirchase by, 29 Ball, Richard J., 6, 152 Certificates of deposit (CD), commodity Bananas, 2, 91, 93 indexed, 13 Beef, 2, 91 Citibank, loan underwriting by, 38 Belgium, use of gold bonds in, 16 Claessens, Stiin, 5, 97, 152 Binomial pricing model: assumptions Coffee, 2, 91, 93 about, 62-67; bivariate normal Cohen, Daniel, 139 distribution in, 79-81; caps in, 72-74, Collars (commodity price), defined, 14 75; compar-d with Schwartz model, Cominco Ltd., 37-38 70-78; commmodity bundle price in Commodity bundle price in pricing model, 63, 72; continuous time model in, 79; 63, 72 convenience yield in 63, 70, 75; coupon Commodity Convertible Bond (CCB), rate in 62, 70, 75: debt in, 63, 70, 72, defined, 61 75; extensions in, 70; firm value in, Commodity Futures Trading Commission 62-63, 65, 70-72, 74; interest rate in, (CFTC), 12 63, 70; parameter determination in, Commodity indexed certificates of deposit, 67-69; payouws in, 63, 70 13 Black, Fischer, 56 Commodity-linked bonds: Bollerslev, T. B., 106 capital-constrained producers and, Bond International Gold (mine), gold 11G-20, 123; conventional loans and, loans and, 16 121-23; estimation of optimal portfolio Bonds (see particular kind of bond) of, 89; external debt allocation model Breeden, D. T., 50, 51, 54, 104 and, 86-89, 93; external debt allocation Brennan, M. J., 56 model empirical application (Costa Budget equation (in demand function Rica) and, 90-93; historical analysis), 42-43 background on, 4-5, 11; issued by Bullion loans, 13 sovereign lenders, 125, 127-28; issuers 169 170 INDEX of, 12; kinds of, 11-12, 13-14, 61, Cox, J. C., 51, 56, 62 124-25. See also Demand; ;'ricing Crude-oil-linked financing, 31-37 commodity-linked securities Currency: commodity exporters and Commodity-linked financing: importers and, 95; debt composition aluminum-linked, 36; copper-linked, 36, and, 1-2; gold-linked financing and, 16, 37-38; developing countries and, 11, 30 145-49; gold-linked, 13, 14-30; Currency composition: altering, 97; nickel-linked, 36, 37; oil-linked, 31-37; commodity risk and exchange rate proliferation of, 11, 12-13; as risk management model and, 103-06; management program, 4; silver-linked, commodity risk and exchange rate 12, 30-31, 32; uncertain commodity management model application and, price and, 58, 59. See also particular 106-10; cross-currency movement and, kinds of bonds; Pricing of 95-97; external liability and, 98, 100, commodity-linked bonds 101; hedging and, 99-101; real risks in, Commodity price risk, 1, 155 101-02; speculative decisions and, Commodity prices: caps, floors, and 98-99, 102 collars on, 14; hedging instruments and Currency swaps, 97 uncertain, 96; pricing of commodity-linked securities and, 58, Danthine, J. P., 119 59, 62; relations between exchange rate Debt: Algerian, 2-3; commodity bond and, 99; risk and external debt pricing and, 61, 63, 79; commodity managemnent and, 97, 101-02; bond pricing model and senior, 70, 72, securirization and, 149, 150; volatility 75; composition of developing country, in, 95-96 1-2; crisis in Costa Rica, 2, 90-93; Commodity risk and exchange rate currency choice and external, 101, 102; management model, 103-06; empirical currency composition and, 100, 101; application of (in Indonesia and general obligation bank loans as, 146; Turkey), 106-10 hedging instruments anid external, Commodity variable-rate loans, 13 97-9g, 99; model for allocating optimal Consumption smoothing external, 86-89, 93; portfolio (commodity-dependent exporters), 152; estimation, 89; sovereign debt risk and, by borrowing and lending, 126-27; 135, 136-40, 141, 142, 143, 144, commodity bonds issued by sovereign 147-48, 149 lenders and, 127-28; default and, Debt service, 1, 85, 116, 123; in Costa 127-28; default constraint binding and, Rica, 2, 90; cross currency exchange 129-31; default constraint nonbinding rate risk and, 96; exports and, 96-97; and, 128-29; default prevention and, hedging policy and, 100-01; in 125; export risk and, 124; income Indonesia, 108, 110; securitization and, variability costs and, 125-26. 127, 128, 135; sovereign debt risk and, 139; in 129; interest rates and, 129; risk and, Turkey, 109, 110 128; sovereign borrowing and, 125 Default, 57, 152, 153; choice of Continunus time model, 39, 79 commodity-contingent instrument and, Convenience yield (commodity bond 146, 149; consumption smoothing pricing), 63, 70, 75 (commodity dependent exporters) and, Cooper, R. N., 139 127-31; loan insurance and, 144; Coomner, P. H., 40 mortgage market and, 143; risk and Copper-linked financing, 36, 37-38 pricing of co,nmodity-linked securities, Costa Rica, trade shock in, 2; optimal 58-60, 62, 73; sovereign borrowing external debt allocation analysis and, and prevention of, 125; sovereign debt 90-93 risk and, 135, 136-40 Coupon rate in pricing model, 62, 70, 75 Deficit (current account), 87 INDEX 171 Demand: continuous-time intertemporal Fall, M. A., 11, 152 model for, 39; determinants of, 48-SI; Federal Home Loan Mortgage functions, 45-48, 53-55, 152. See also Corporation (Freddie Mae), 143 Multigood case; One-consumption good Federal National Mortgage Association case model (Fannie Mae), 143 Developing countries: commodiry-linked Financing. See Aluminum-linked financing and, 11, 145-49, 154; financing; Commodity-linked financing; commodity pricc risk and, 1; debt Copper-linked financing; Gold-linked composition in, 1-2; exchange rate financing; Nickel-linked financing; hedging in, 96; secu inzation and, 135, Oil-linked financing; Silver-linked 142-44, 149-50 financing Deviation analysis (hedging with Firm value in pricing model, 62-63, 65, commodi:y-linked bonds), ilS, 117, 7R72, 74 120 Fishlow, Albert, 132 Dieffenbachl, B. C., .54 Floors (commodity price), 14, 61 Dive-sification, 97-98, 124 France, 11, 14-15 Eaton,'tonathan, 12.5, 132, 136, 139 Generalized Autoregressive Conditional Eaton lonthan 12S 132 136 139Heteroskedasticity (GARCH), 106, 107 Echo Bay Mines, Ltd., gold-linked security et eresticity G , an, '51 Germany, interest rates in 2, and, 15-16 Gersovitz, Mark, 125, 132, 136, 139 Eichengreen, Barry, 131 Gilbert, Christopher, 6, 136, 153 Electricity, bond indexed to price of, 11 Giscard bonds, 14-IS Engle, R. F., 106 Gold-linked financing, 13; convertible Euromarket, S, 12 issues in, 26-23; examples of, 14-15; Evnine, Jeremy, 62 length of loans in, 29; price of gold Exchange rate: commodity prices and, 99; and, 30; size of loans in, 16, 29; commodity risk and exchange rate warrant issues in 16, 17-25 management model and, 103-06; Gold repos 13 commodity risk and exchange rate Goverment National Mortgage management model, empirical Associati-'n (Ginnie Mae), 143 application, 106-10; cross-currency, Gross.-n.. 1-, 139 95-96, 99, 102 Exports, 85, 152; Algeria's commodity Hansen, L. P., 89 exposure and, 2-3; choice of Hedging: commodity-linked bonds and, commodity-contingent instrument and, 116-23; debt service and, 100-01; 145, 149, 150; consumption smoothing demand analysis and, 47, 49; and, 124-32; Costa Rica and, 2 , 91; diversification and, 97-98; exports and, debt-service-to-export ratio fluctuations 99, 100, 102; external debt allocation and, 96-97; dependence on commodity, and, 93; in forward markets, 153; 1; diversification and, 97; exchange rate imports and, 100; policy guidelines for, and, 99; external debt allocation model 99-101; portfolio (commodity risk and and, 86, 87, 89; fluctuations in earnings exchange rate management model), from, 124; nedging policy and, 99, 100, 103-06; portfolio example (empirical 102; sovereign debt risk and, 139 application of model), 106-10; risks of External debt allocation model: external debt position and, 85; application of in Costa Rica, 90-93; speculative activity versus, 98-99; estimation methods for operationalizing uncertain commodity prices and, 96 rules and, 89; rules for issuing Holthausen, Duncan, 119 commodity-linked bonds and, 86-89, Hong Kong, gold CDs :n, 13 93 Hirohito gold coin, 29 172 INDEX Imports: diversification and, 97; exchange Location and scale (LS) condition, 115, rate and, 99; external debt allocation 117 model and, 86, 87, 88; hedging policy Long, J. B., S5 and, 100 Inco, commodity-indexed bonds and, 37 McKean, H. P., 40 Income variability (consumption Magna, commodity-indexed bonds and, smoothing), 125-26, 127, 128, 129 38 Indonesia, 96, 108-10 Mlalaysia, palni oil prices in, 38 Ingersoll, J. E., S1 Maximization problem in deManum Insurance: loan, 143-44, 149; risk function analysis, 43-45 management programs and, 3-4; Merton, R. C., 39, Sl, 53, 56, 59 sovereign risk and, 150 Metallgesellschaft, commodity-indexed Interest rates: consumption smoothing bonds and, 38 analysis and, 129; copper-linked Mexican oil bonds (petrobonds), 33 financing and, 38; in Costa Rica, 93; Meyer, Jack, 1 15, 117, 1 '9 Giscard bonds and, 15; gold loans and, Mortgage market, 142-43, 149 29, hedging with conventional loans Morton, P. J., 131 a:id, 121; morgage market and, 143; Multigood case model (in demand option type bonds and, 12; pricing of function analysis): demand functions in, commodity-linked securi6es and, 56, 53-55; the model, 51-53 58-60, 61, 63, 70; replacing standard, Myers, Robert J., 5, 6, 152 136; risk, 58-60; shift in, 1-2; Nationalization, 11, 150 speculative rates and, 102; swaps and, Newbery, David, 6, 127, 152 14; variable rate loans and, 13 Newmont (mine), gold loans and, 16 Ito, Kiyoshi, 40, 41 Nickel-linked financing, 36, 37 Japan, interest rates in, 2; sourcing of O'Hara, Maureen, 5, 86, 127, 152 gold in, 29 Oil-linked financing: bond issues i.;, 34-35, 37; development of, 31, 33, 36 Keynes, J. M, 125 Oil shock, effect of, 2 Kraft, D. F, 106 One-consumption good case model Kroner, Kenneth, 97(demand functions analysis): asset returns in, 40-42; assumptions for, Latin America, dependence on commodity 39-40; budget equation, 42-43; exports in, 1 demand ofuntionsin, 48-SI; Lessard, D. R., 86 dtriavo h eadi,4-1 Lessard, D. R., 86 ~~maximization problem in, 43-45 Liability management, commodity bonds Opportu n s rtb(edging wit 4 and, 61 ~~~~~~Opportunity set (hedging with and, 61 commodity-linked bonds), 117, 119, Lindert, P. H., 131 120 Loans, 116; bullion, 13; commodity Outut price risk, 115, 120, 121, 123 variable-rate, 13; consunmption smoothing analysis and sovereign Papua New Guinea, copper investments lenders and, 125, 127-28; in, 38 crude-oil-linked financing and, 31-37; Payouts in pricing model, 63, 70 debt and gencial obligation bank, 134; Peru, 145, 149 gold-linked financing and, 14-30; Petro-Lewis Corporation, and oil-linked hedging with conventional, 121-23; notes, 33 insurance, 143-44, 149; securitization Phibro-Salomon Inc., and oil options, 36 and, 141; silver-linked financing and, Placer Dome (mine), gold loans and, 16 30-31, 32 Powell, Andrew, 6, 136, 153 INDEX 173 Prices. See Commodits prices; OutpUt and, 135, 142-44, 149-50; general price risk terms for, 140-42 Pricing commodiry-linked bonds: default Self-insurance instruments, 3, 4 risk and, 57, 58-60, 62, 73; interest Separation property, 119 rate risks and, 56, S8-60, 61, 63, 70; Sharp,, W./ F., 39 %harpe-Lintner Capital Asset N'odel for, Sharpe-Lintner Capital Asset Pricing _9. See also Binomial pricing mL iCl; Model (CAPM), 39 Schwartz pricing model Silver-linked financing, 12, 30-31, 32 Privolos, Theophilos, 5, 61, 125 Sohio Oil Company, oil bond issue by, 36 Put option, 12, 16, 33-34, 147, 148 Solomon Pacific Resources NL, gold loan repayrnents by, 29 Rajan, Raghuram, 5, 152 Sovereign debt risk, 135, 136-40, 141, Refinement Intemational Company, 142, 143, 144, 147-48, 149. See also gold-indexed bonds and, IS Debt Risk: commodity-linked securities pricing Sovereign lenders, 125, 127-28. See also and default, 57, 58, S9, 62, 73; Loan, commodity-linked securities pricing and Speculation: demand analysi, and, 47; interest rate, 56, 58-60, 61, 63, 70; external liability decisions and, 102; commodity price, 1, 62; demand hedging vs., 98-99 function analysis of assets and, 39, 55; Stiglitz, J. E., 127, 132, 136 export, 124; external debt allocation Strip (commodiry-contingent claims) model and, 93; external debt position ^ - nept, 149 and, 85; managemen1t cf commodity Stliz, R. M., 104 and exchange, 97-102; management Sunshine Mining Company, silver-linked programs, 3-4; mortgage .narket and, financirg by, 30-31 143, 149; output price, 115, 120, 121, Svensson, L. E. O., 104 123; securitization and credit, 141; Swaps, 14; curren,y, 97 sovereign debt, 13S, 136-40, 141, 142,B 143 14 14'48 i9; sverein' ' Taiwanese Central Bank, gold purchases 143, 144, 147-48, 149; sovereign b,2 lenders and, 128, 150 by, 29 Robison, L. J., 115, 119 Third party insurance instruments, 4, 154 Ross, S. A.,1, 56, 162 Thompson, Stanley R., 5, 152 Rubinstein, M., 62 Thygerson, K. J., 143 Trade shocks, 2, 90 Sachs,J. D., 139 Samuelson, P. A., 48 Uncertain commodity price version of Sargent, T. S., 99 Schwartz model, SS Scholes, M. t., 56 United Kingdom, interest rates in, 2 Schware, E. S., 5, 56, 59, 60, 61-62, 70 United States, 1, 4, 12, 13, 30-31, 33, 36, 71, 73, 125, 152 38, 143 Schwartz pricing model, 56-60; compared Value of firm (commodity bond pricing), with binomial pricing model, 70-78; 62, 63, 65, 72, 74 default risk version of, 58-60; interest van Huyck, J. B., 139 rate risk version of, 58-60; uncertain commodity price version of, 58 Warrants, 15-16, 17-2S, 'O, 37-38 Secondary rortgage market, 142-43, 149 Williamson, John, 86 Secondary trading of securities, 141 Worrall, Tim, 129 Securities and Exchange Corr .*_-^n Wright, Brian, 6, 152 (SEC), 12 Wriston, Walter, 138 Securitization. 147; debt obligations and, 134; developing country obligations Zaire, 145, 149