The Xorld Bank Development Research Depar tslent Discussion Papers No. 39 THE WIPUL.ATION ;?F FUTURES MARKETS BY A DOMINANT PRODUCER David M.Newbery September 1982 '9 .s NOTE; Discussion Papers=are preliminary m a t e r i a l s c i r c u l a t e d t o s t i m u l a t e d i s c u s s i c n and c r u i c a l comment. References i n publication t o Discussion PapersTshould be cleared w f t ~t h e authors t o p r o t e c t t h e t e n a t i v e c h a r a c t e r of these papers. The papers express the views o f t h e authors and should n o t be i n t e r p r e t e d t o r e f l e c t those or t h e World Bank. -- TRE ?MI?I'rULATIOB OF FUTURES W T S BY A DOXINAXT PROIIUCER - by David Y. Newbery World Bank September 1982 .* , L I Q Paper prepared f o r the Conference on the I n d u s t r i a l 0rganizat.ion of Futures Harkets sponsored by the Center f o r thg Study of Futures Y'arkets a t Columbia University, Nev York City, Novembeg 4-5, 1982. - -ri * B * I Views expressed a r e those of the author alone Znd do not n e c e s s a r i l y r e f l e c t those of the Xorld Bank. I an indebted t o Ron .haer:;on f o r useful discussions on t h i s t o p i c . The ?!ani?ulation of Futures Markets by a Doninant Producer by David H. Newberj The World %ank Abstract This paper studies the impact of a futures market on a cash market in which there is a doninant producer and a conpetiti.ve fringe of price- taking f i m s . It is shown that a futures market has t.~oeffects: it increases the productitn of the fringe producers because it enables then to reduce t h e i r r i s k , but it also enables the doninant producer t o manipulate futures narkets sales t o induce the fringe firms to produce less. Thus the dominant producer has an incentive to destroy futures markets, but, f a i l i n g t h a t , h i s a c t i v i t i e s nevertheless increase the efficiency of the futures market (reduce its b i a s ) , and reduce producer risk. I f fringe producers a r e (unreasonably) ~ i s kaverse, and cannot observe the dominant producer's current supply or storage decision, then he has a further incentive t o destabilize the cash market. David X. Newbery Yorld Bank Septeaber 1982 1. Introduction The r e c e n t developnent of f u t u r e s a a r k e t s i n crude o i l and o i l products raises i n a n a c u t e f o n the q u e s t i o n of how f u t u r e s markets o 2 e r a t e for- c o m o d i t i e s whose production is doninated by l a r g e producers or c a r t e l s . Does t h e presence of a f u t u r e s n a r k e t reduce o r i n c r e a s e t h e market power of the dominant producer? Should consumers encourage t h e development of such markets o r r e g u l a t e and r e s t r i c t t h e i r operation? Does the market power of the dominant producer i n t h e cash mrket: have any counterpart i n t h e f u t u r e s market? I n p a r t i c u l a r , does a dominant producer have an i n c e n t i v e t o nanipulate f u t u r e s markets? Clearly these and o t h e r questions t o do with tSe perfornance of f u t u r e s markets f o r imperfec t l y c o ~ p eitt i v e l y produced c o m o d i t ies r e q u i r e us t o go beyond t h e standard y e r f e c t l y competitive nodels. The t r a d i t i o n of t r e a t i n g primary commodities a s though they a r e produced and traded under conditions of p e r f e c t competition is s n r p r i s - i n g l y s t r o n g and needs questioning q u i t e a p a r t from the case of o i l . . I n 'tHe f i r s t p l a c e , aany governments, i n both developed and develop.Lng c o u n t r i e s , intervene i n a g r i c u l t u r a l markets, so t h a t t h e n a t u r a l u n i t of production is arzuably the country, r a t h e r than the i n d i v i d u a l fanner o r p l a n t a t i o n . These c o u n t r i e s o f t e n produce a s i g n i f i c a n t share of world b E production. For m i n e r a l s , t h e sane companies reappear-fa aany d i f h e r e n t c o u n t r i e s , and t h e l a r g e s t conpanies c o n t r o l a s i g n i f i c a n t f r a c t i o n of world production. Newbery, (1981) l i s t e d 8 comnodities f o r ,*li,ich s i n g l e c o u n t r i e s c o n t r o l l e d nore than 50 percent of world t r a d e , and a f u r t h e r 13 f o r which s i n g l e countries controlled between 25 and 50 percent (zveraged over 1977-79). I n t e r e s t i n g l y , Saudi Arabian o i l just qualified i n t h i s period with 26 percent (and a i g h t not on 1981-82 :data) whilst a r a z i l i a n coffee was excluded over t h i s period with on17 17 percent. Ln the second place, to the extent that prinary producers have long been concerned about both the s t a b l l i t y and l e v e l of commodity prices, there have been nzde repeated attempts t o e s t a b l i s h commodity c a r t e l degrees o . .. such c a r t e l s have been p a t e n t i a l l y large r e l a t i v e to the market, and well placed t o trade on the established futures m r k e t s . O fthe 21, commodities where country trade shares a r e above 25 percent, a t l e a s t 9 ha.ve futures xarkets and a r e l i s t e d i n Table 1 below. ( I n addition, bauxite was m e of the commodities, and there is 'a futures market i n aluminium.) Copper, coffee and cocoa, a l l with a c ~ l v efutures markets and moderate producer concentration, did not appear on the o r i g i n a l list '>ut a r e ineluded i n Table 1 for completeness. It therefore seems inpor:ant to try and model the behaviour of dominant conmodity ,prpducers confronted with the choice of trading on futures mrkeks. Apart from any other reason, there a r e powerful i n c e n t h e s , nentioned below, for producers to be d i s c r e t e about any + ' L attempt_ KO manipulate futures m r k e t s , and hence manipulation v i l l be - - d i f f i c a t unless the motives and s t r a t e g i e s of such agents can be B w c l a r i f i e d . Finally, there is evidence that the coffee c a r t e l engaged i n Table 1 Shares of Individual Countries i n World Trade of Commodities Traded on Futures Yarkets, Average 1977-79 Share Product (Percent) - USA ?lake Australia Wool (greasy) Rubber USA T i s USA Cotton. Saudi .L-abia O i l . Canada Barley Cuba Sugar Cocoa Copper B r a z i l Coffee - -- Sources: .- Commodity Trade and Price Trends, World Bank 1981, FA0 Trade Yearbook 1979. a 8 I e x t e c s i v e narket a n i p u l a t i o n j.n t h e period 1977-79, so that, t h e s u b j e c t is of more than academic interest. (See t h e f a s c i n a t i n g accounts i n Greenstone (1981) and E d ~ u n d s(1982)). The main conclusion of t h i s paper is t o show t h a t i f a l l agents have access t o t h e sane information, and can p r e d i c t t h e production and t r a d i n g s t r a t ? g y of t h e dominant producer, the doninant producer has an i n c e n t i v e t o a n i p u l n t e the f u t u r e s market i n order t o b e n e f i t h i s p o s i t i o n i n t h e cash market, but nevertheless his f u t u r e s trading a c t i v i t y reduces the b i a s i n t h a t market- Moreover, h i s market power i n t h e f u t u r e s s a r k e t diminishes t h e a o r e competitive s p e c u l a t o r s e n t e r t h e market, and the l e s s averse t o r i s k they a r e . The second r e s u l t is t h a t i f agents have t h e same information but cannot observe t h e pzoduction decision of the dominant producer, then he may have an incentive t o follow randomized production s t r a t e g y ( o r t o randomize h i s s t o r a g e decision.) However, unless f r i n g e producers are very r i s k averse, t h i s w i l l be a n u n a t t r a c t i v e s t r a t e g y . The paper is organized a s follows. The next s e c t i o n d i s c u s s e s the r o l e of i n f o m a t i o a and the inportance of specifying what t h e . , d i f f e r e n t market p a r t i c i p a n t s know when making t h e i r decisions. S e c t i o n 3 sets out the node1 of .the futures market and demonstraies chat, assuming '? 6 t h e duninant producer is l e s s r i s k averse than t h e f r i a g e producers, he - would b e n e f i t from the c o l l a p s e of t h e f u t u r e s market.? Seccion 4 d i s c u s s e s the i n c e n t i - ~ e sf o r manipulating :he f u t u r e s narket when agents have f u l l i n f o m a t i o n , f i r s t a s a l a r g e s p e c u l a t o r , :>en as a l a r g e producer. This denonstrates the aain r e s u l t t h a t he b e n e f i t s from I m n i p u l a t i o n a s a l a r g e ?reducer, no matter what the source of r i s k . R e f i n a l s e c t i o n discusses the extent t o which the dominant producer can b e n e f i t from varying h i s decisions from year t o year when h i s competitors - cannot observe the current decision, but can only p r e d i c t the average 2. The Role of I n f o m a t i o n i n the Yanipulation of Futures Yarkets - The simplest m d e l in which to examine the incentives for f u t u r e s market manipulation is one of a non- storable a g r i c u l t u r a l f i n a l consumption c o m o d i t y produced i n an annual cycle. A t the tine of p l a n t i n g the f u t u r e weather (and hence output) a r e uncertain, a s , consequently, is the post harvest market c l e a r i n g p r i c e , p. Since the commodity is not s t o r e d , nor f u r t h e r processed, the only agents concerned a r e the producers, consumers, and speculators. I shall assume that consumcrs have no incentive t o hedge, and so the only p a r t i c i p a n t s i n the futures m a r k ~ t w i l l be t h e producers and speculators. 1! h e futures narket opens a t the s t a r t of the crop season, and contract expires a f t e r the harvest is i n and the s i o t narket c l e a r i n g price has been established. Thus f a m e r s nake ,..%9. - -- t h e i r production decisions a t the same t i n e as choosing t h e i r f u t u r e s trades, and knowing the f u t u r e s price, pf . - .E -1/ If the commodity is f u r t h e r processed, then 2rocessors rill a l s o hedge, and experience d i f f e r e n t r i s k s than producers, as =illstock- holders f o r s t o r a b l e c o m o d i t i e s . Xodelling t h i s behaviour is important f o r some questions - notably vhether futures markets a r e biased - but a r e not obviously relevant f o r ~ w r k e tnani?ulation. See Stein (1979) and Anderson and Eanthine (1982) f o r aodels with processors and stockholders. Since we a r e interested i n nodelling mznipulation by a doninant producer, I s h a l l a s s m e t h a t there is one d o d n a n t producer ( t o be thought of as the marketing board of a large exporting country, o r its counterpart f o r a c a r t e l ) facing a fringe of competitive small producers - the farmers i n the r e s t of the world. The doninant producer is y e l l organised enough t o arrange adequate iacone insurance f o r its own f a r n e r s (via Oonestic price supports, d i r e c t transfers, etc.) and large enough t o secure adequate intertemporal income smoothing by borrowing and lending, s o t h a t it a c t s as a r i s k neutral agent. (See Newbery and S t i g l i t z , 1981, 14.3, pp. 201-204). The fringe farmers are risk averse. The f i r s t and c r u c i a l issue t o address i n discussing narket manipulation is what information the various participants have, and uhat use they nake of it i n choosing t h e i r strategies. It is convenient to distioguish three cases, with v e r j different inplications for market manipulability. A t one extreme, the dominant producer m y hold r a t i o n a l expectations about demand and supply conditions whilst the fringe producers nay follow some naive forecasting or d e c i s i o i rule. This 1 @ implies that the dominant producer knows what t h i s decision rule is and b - - can compute the fringe decisions given information available a t the s t a r t '9 i of the crop year, and, given h i s own decisions, can predict the joint * * * d i s t r i b u t i o n of h i s output and the aarket clearing price (a; a Sufficient I # s t a t i s t i c of the d i s t r i t u t i o n- I see Newbery and S t i g l i t z , Ch. 10, 11.) Clearly, the dominant 2roducer is well placed to nanipulate futures uarkets and. to exploit h i s superior infomation and forecasting a b i l i t y . a r t (1977) has studied this fora of mni?ulation, vhich relies on being able t o systematically d s l e a d the o t h e r agents and hence cause them t o make losses. It appears that the alleged coffee rzarket mmi?ulati~n described by Greenstone (1981) and Ednunds (1982) r e l i e d on t h i s s t r a t e g y , s i n c e i n 1977 the c a r t e l bought J u l y f u t u r e s heavily, and a l s o bought physical coffee t o prevent it reaching the market, t o squeeze t h e market. aad speculators possessed t h e same inforirltion a s the c a r t e l ( i n p a r t i c u l a r , the c a r t e l ' s plans) then t h i s mneuver would not have succeeded. A t the o t h e r extreme, a l l agents nay have access t o the sane infornation when making t h e i r decisions, and hold rationa:L expectations, . . i n t h e sense t h a t they know the model which describes the ( s t o c h a s t i c ) *.. determination of market equilibrium. Tnis would be the case i f agents knew tte objectives ( u t i l l t v functions), production functions, nature of denand, and the j o i n t probability d i s t r i b u t i o n describing the s t o c h a s t i c elements, and were a b l e t o compute t h e equilibrium choices of a l l agents. There is thus c2mplete synmetry of infornation. The t h i r d p o s s i b i l i t y l i e s between the two extremes, though i . t c l o s e r to the f u l l r a t i o n a l expectations equilibrium just described. Agents have f ~ l l ~ i n f o r a a t i oabout produczion and u t i l i t y functions, and n *% the nature of ri"sk, but cannot observe production decisions. In an * - unchanging v o r l e i n long run equilibrium agents could nak.e the same m production decisions each year, and chese would then be predicrable. Fringe agznts, being individually i n s i a n f f i c a n t , vould halve no Fzcentive not :o ma'- such predictable decisions, but the dominant producer na:j b e n e f i t f r c n randonizing h i s production about soce (ulcimately) - ( d . u A,. c d U-l 0 and hence reduces the dominant ?roducer8s profits. Since he gat.= no insurance benefits fron the futares market, he is unambiguously vorse cff w+.th the market than without. To e s t a b l i s h t h i s r e s u l t , we need t o nodel the production decisions of the f a m e t s and the futures trading decisions of f a m e r s and speculators. Following vell-established t r a d i t i o n , assume that agents have constant absolute risk aversion and that prices and quantities a r e j o i n t l y normally distributed. This allows us to use the mean-variance a r a l y s i s of the standard c a p i t a l a s s e t pricing model, and gives r i s e t o l i n e a r trading r u l e s which can be aggregated and solved i n closed form. - These admittedly strong assumptions can be defsnded as second order - approximations to a more complex r e a l i t y , and should nok p r w e c r i t i c a l i n - the analysis which follavs. Suppose that output, q, a f t e r the harvest de?ends c u l t i p l i c - a t i v e l y on the weather (z) and the level of inputs, x: N q = Bf(x), Z 0 = 1, Var 8 = a2. h - - I n the absence of a futures market, the farmer's income is 'i C -- L e- N y = pQ -.- ( 2 ) where the input ? r i c e is v , and the o u t p r price is , a randoa variable a t the t i a e of ?laa?r:ng. I f h is the coeffi.?ient of risk averston, and :he f a m e r chooses to aaxlmize ex?ected u t i l i t y , then his decision ~ r o b l e n is equivalent to maximizing U * Ey - 1/2d Vary (3 (e.g. see Newbery and S t i g l ~ t z ,1981, D. 85). Thus the faraer's choice of x s a t i s f i e s where - a = FY?e Af Var pe is the action certainty equivalent prfce (i.e., that price ~rhich, i n the absence of uncertainty, would lead the farmer to choose the sane a c t i o n , or level of input, x. If there is a futures marker. %e farmer can, i n addition, choose 9 t h i s ledel of futirres s a l e s , z, i n whtch case h i s lncone w i l : b be and h i s objective is to maximize E f o r ~ a r dpurchases which balance the f a n e r s ' forward s a l e ) i f p is below the expected future price. The normal backwardation provides the r i s k premitn which covers the cost of transferring r i s k from farners t o speculators. However, it is worth pointing out t h a t even i n t.his simple nodel i n which there a r e no processors o r stockholders whose hedging needs might conplement those of the i a n e r ' s , it is still possible for pf to equal o r exceed the expected future price. To see t h i s we need to 1-ok a t equilibrium i n the futures market, i n which net futures s a l e s aust be zero. I n the absence of any other agents t h i s implies that the sum of s a l e s of farners and speculators nuat be zero, o r , i f a l l agents share common b e l i e f s , and face the same risk, 9: - 1 1 0 = c(zS + cov ( P , P ~ ) z ) = P - P c ( x + - ) . Var p ''- Var p hS Let a measure the e f f e c t i v e degree of risk aversion of the market as a whole: - Tius i f there are n f a n e r s and m speculators, a l l equally r i s k averse, - a = X/(n + m) , whilst i f any 'bgent is r i s k neutral, then a = 0 and the 4 - market a c t s r i s k neutrally. average tota: production is then the bias i n the futures aarket,or the extent of coma1 Sackxardation, is and the e q u i l i b r i m f*-.tures s a l e by f a n e r s i is, fron (12) and (8) vhere, f o r farmer i - Bi-= I - - i 1 Z Q , O < B < 1 , i-i a_ is a measure of the extent to which the fanner is nore risk averse than 1 -i - ;Yerage ( A /a) and nore exposed to r i s k than average (q /Q). If a l l f a r n e r s a r e i d e n t i c a l and there a r e no speculators, 3 = 0, whilst i f there i s one r i s k neutral speculator, so a = 0, then $ = 1. I n between, i f there a r e n fanners and a speculators, a l l equally r i s k averse, then, for an average farmer The t e r n ,6 can a l s o be thought of as the extent t o which the farner is e able t o share the r i s k -41th other agents i n the economy. Tlne larger 'is I the nunber of speculators, the aore the farmer is able to transfer r i c k t o -- - then, and the nore heavily he is willing to be involve# i n the futures market. The l e s s r i s k averse speculators a r e , the snaTler w i l l e be c , and I I) the aore irilling they v i l l be to accept the Earners risk, and again, the nore the f a m e r v i l l be willtag to trade these risks i n the future I markets. I I f , a s assuned, ;, and 8 a r e j o i n t l y normally d i s t r i b ~ u t e d , Appendix X shows t h a t equation (13) can be w r i t t e n where a,a a r e r e s p e c t i v e l y , the c o e f f i c i e n t s of v a r i a t i o n of output and P p r i c e , and r is t h e c o r r e l a t i o n c o e f f i c i e n t between output and price. Clearly, t h i s expression can be negative, i n which case from equation (12) p w i l l exceed f and t h e f u t u r e s market w i l l e x h i b i t contango instead of backwardation. When the f a r n e r can hedge on a f u t u r e s n a r k e t , h i s a c t i c n c e r t a i n t y equivalent p r i c e , if , is, from (7) where z is the optimal f u t u r e s trade, s a t i s f y i n g (8) o r (13). Suppose now t h a t a f u t u r e s market is introduced i n t o an otherwise unstabilized n a r k e t , and t h a t it has no e f f e c t on the b e l i e f s or information about f u t u r e L prices. I f it had no e f f e c t on the post narket p r i c e d i s t r i b u t i o n , then from (5) and (15) s u b s t i t u t i n g from (13). I n t h i s case the futures market *lnanbiguously increases the a c t i o n certainty eqvivalent p r i c e , r h i c h , other things equal, w i l l induce a supply response, and thus lower the average spot price. The dominaiit producer derives no insurance benefit i r o n the futures market, since he is r i s k neutral, but is c l e a r l y harmed by the increase i n fringe supply, and hence v i l l be h o s t i l e t o the introduction of futures markets, and w i l l have an incentive t o destroy them. He would, i n p a r t i c u l a r , have an incentive t o play on the populist sentiments of regulators by encouraging then to believe t h a t futures clarkets can be manipulated t o the disadvantage of producers, i f he thought t h i s might provoke moves t o r e s t r i c t or close future markets. H e would h,ave an incentive to convince other potential participants i n the m a r k e t h a t the ?eTL Q market was nanipulated, or rigged, and hence the game unfair and not worth playing. There is some evidence that futures markets known t o be dominated by government marketing agencies a r e unpopular, and consequently t h i n (Gray, 1960). Since the dominant producer c e r t a i n l y has an incentive to mislead other agents, i t should not be d i f f i c u l t t o so con.vince these agents, and there is the consolation t h a t if an attempted squleeze or other manipulation f a i l s i n its primary purpose, it may succeed by d i s c r e d i t i n g * the market. The remedy f o r t h i s kind of behaviour is to provide as nuch - - public information a s possible about the actions of t5e dominant p-qducer, ' * - i n order t o broaden the market and increase the nmber of tga.ders. Fron (17), the fringe suppl:~response increases with 3 , i.e. frm ( ! 4 ) , w i t h : the nunber of speculators, n. 4. Incentives f o r Yanipulating Futures Harkets with F u l l I n f o r n a t i o n I f f u t u r e s n a r k e t s a r e , however, s u c c e s s f u l l y introduced and u a i n t a i n e d , they w i l l a f f e c t the t r a d i n g e n v i r o m e n t of the dominant producer, and he w i l l have an i n c e n t i v e t o manipulate t h e f u t u r e s n a r k e t even i f a l l p a r t i c i p a n t s know what s t r a t e g y he is pursuing. A t t h i s point, it is perhaps worth defining nanipulation. The Commodicies Trading Commission defined it thus i n 1977: "... conduct i n t e n t i o n a l l y engaged i n r e s u l t i n g i n an a r t i f i c i a l p r i c e t h a t does not r e f l e c t t h e b a s i c f o r c e s of supply and demand. . . A f i n d i n g of manipulation i n v i o l a t i o n of t h e (Commodicies Exchange) A c t r e q u i r e s a f i n d i n g t h a t th,e p a r t y engaged i n conduct v i t h the I n t e n t i o n of a f f e c t i n g the market p r i c e of a c o m o d i t y (a? d e t e n i n e d by t h e f o r c e s of supply and demand) and as a r e s u l t of such conduct o r course of a c t i o n an a r t i f i c i a l p r i c e was created. ( a t 21, 477, CFTC Dkt No.75-4, Feb. 18, 197'7 [1975-77 T r a n s f e r Binder] CCH Comm. Fut. L. Rep. 120, 271., c i t e d by Greenstone, 1981, p. 11.) This seems acceptable i f w e i n t e r p r e t " a r t i f i c i a l p1:ice1' as a p r i c e d i f f e r i n g from t h e c o a p e t i t i v e p r i c e . Clearly, a l a r g e producer w i l l knw t h a t h i s a c t i o n s w i l l a f f e c t t h e p r i c e - t h e question is , r whether he takes advantage of t h i s power. The competit'ive equi1ib:iun i n f - the f u t u r e s market with a r i s k n e u t r a l agent is one i n which p - = p and -5 t h e market is unbiased. Any trading s t r a t e g y r h i c h f a i l s t o y i e l d t h i s * outcome is, i n gur f u l l i n f o m a t i o n nodel, evidence of a a n i p u l a t i o n . - b dominant prciiucer has two d i f f e r e n t motives for ~ a n i ? u l a c i n g the f u t u r e s market. First., a s l a r g e agent, he may be able t o e x e r c i s e market power i n t h e f u t u r e s mrket q u i t e independently of h i s a c t i v i t t e s on a proriucer. This he does by influencing :he spread bet-;@en the f u t u r e s price pf and the expected cash price 5 , both d i r e c t l y 5y trading on :he futures r e and hence affecting p f , and i n d i r e c t l y , by changing pf he -f, can change the action c e r t a i n t y equivalent price, p and hence induce a - supply response which a f f e c t s the cash price, p. The second way i n which the dominant producer can advantageously m n i p u l a t e the futures market is to change the futures price, and hence, via a change i n the a c t i o n certainty equivalent price, induce a supply response by the fringe which increases the dominant producer's p r o f i t s . I f , f o r example; he can lower the futures price t h i s w i l l reduce fringe supply and increase h i s sales price. However, t h i s is not costless, as he may lose on h i s futures trading a c t i v i t i e s , and the extent to which t h i s strategy is profitable requires a careful cost- benefit analysis. The next two sections consider each of t5ese motives separately i n special cases, chosen t o yield a quanttfiable escinate of the importance of such manipulation. The f i r s t simplifying assuaption is that both demand and ex- ante supply schedules a r e linear. If the prod-lction function of a representative f a m e r is * vhere k is sone constant chosen to yield a sensible £ o m for f ( x ) for low .E * - * levels of output, then, assuming the i i p u t price of x is unity, ? l a m e d output vill be Wlth pure denand r i s k , it is t r u e q u i t e generally t h a t the a c t i o n c e r t a i n t y equivalent p r i c e is t h e f u t u r e s price (Danthine, 1978). The argument goes a s follows. Let U(y)be the u t i l i t y of incone y , then Earners choose inputs x aL1d f u t - ~ r e ssales z t o ! The f i r s t order conditions a r e I *.. f' EU'p = w EU' ElJ'p = pf EU' hence f a f p f ' ( x ) = v , p - p . (23) . t e 4.2 P e r f e c t l y Correlated Supply U s k If Earners experience perfectly correlated supply risk, so that I t h e i r o;tput is I i i 2 q = 3 f (I<), E8 = 1, Var 8 = a A then t h e i r a c t i o n c e r t a i n t y equivalent price, p , is, from (16) and (8); - - f - cov (P,& A - p = Epe ~ { ~p0a rcovVar 2(?,?@) } - ( $ - P Var pl For p e r f e c t l y c o r r e l a t e d pure supply r i s k , the c o r r e l a t i o n bet:veen p r i c e and output is r = -1, and a = a . From Appendix X P - a2 - -2 2 Var p0 = p 7((1- E ) +~2 a2 1 - p a ( 1 - E)2 . . E: E 4 so, ignoring t e r n i n a If producers experience additive r i s k , however, so t h a t then p is again p , as cac be seen fron the f i r s t order conditions f o r f expected u t i l i t y naximization: *.. -- - W N $ki- 0 4 u V ) . '4 u w c aJ aJ c a 0, P a m k t aJ Y u 0 k PC aJ 3 a h P 0 0 4 U (d l-i 7 a. 4 C 2 U 3 2. $ I 0, Q) k 3 U 1 f 4 elasticity of supply were the producer to behave competitively. K is an arbitrary constant vhich does not affect the equilibrium output.) Since it is by no neans obvious that the doninant producer will benefit from futures mrket nanipulatioc as a producer (and not just as a risk-neutral agent) it is inportant to consider different types of risk specification. - 4.5 Pure Demand a s k Fringe supply is riskless and equal to If the doninant producer produces q and sells S futures, equilibrium in the futures narket requires (cf 27): which, substuting for Q, gives Z q u i l i b r i m i n t h e cash market r e q u i r e s the average p r i c e t o s a t i s f y ~ h i c h ,with (40), g i v e s The dominant producer's expected p r o f l t s a r e which, frcm (38), can be w r i t t e n Since f r m (42) Q is l i n e a r i n q and S, so is s. C o ~ s e q u e n t l yexpression (43) c o n t a i n s terns i n Sq, and hence t h e . t optimizing choice of S w i l l depend on q, azd vice versa. ~ h e r e f d r etSe - producer's choice of futuse t r a d e s , S, w i l l depend cn h i s choice of output, q, and v i c e verqd! - To q u a n t i f y t h i s interdependence, maxiaire y - i n (43) with r e s p e c t t o - where f r a (41) a ; / a ~= - I/. This can be solved t o y i e l d Note t h a t when p = 1, q = 0, SO that there is no doninant producer, the r e s u l t collapses i n t o t h e previous case of a large speculator,, for vhom s - ' The expected profi: maximizing choice of input, x, s a t i s f i e s where the t e r n i n braces is the dominant producer's action certainty equivalent narginal revenue, 4IR. Subst-Ltuting for5 and i$/aq t h i s can be w r i t t e n whilst fron (36) . ~ h & etwo equatiorts can be solved to yield where . . O = 1 + p(=vll+ l l / ~ ) Equations (45) and (46) can be solved f o r S and q, but one conclusion is inmediate; S i n c r e a s e s -with q. I n t h e previous s e c t i o n w e saw t h a t a l a r g e s p e c u l a t o r would still be a n e t f u t u r e s buyer, so S would be negative. If he is also a producer, then he buys fewer futures. The e f f e c t s of t h f s , from (421, is t o reduce Q and hence i n c r e a s e h i s market power i n t h e cash market. 4.5.1 The Consequences of Excluding t h e Doninant Producer from t h e Futures Yarket I f t h e dominant producer is somehow excluded from t h e f u t u r e s market, then t h e market equilibrium can be found from (46) and (42) by s e t t i n g S = 0. The dominant producer z c t s r a t h e r l i k e another competitive s p e c u l a t o r (so f a r as a r b i t r a g i n g p r i c e s ) provided S < 0. I f , on t h e o t h e r hand, S > 0 the dominant p-ioducer vould be a n p l i f y t n g the b i a s i n t h e f u t u r e s market, t o the disadvantage of consunei-s and possibly l/producers. I n such a case, banning rhe doninant pr3ducer from t r a d i n g may improve matters. kowever, it can be !shown - 2/ t h a t it is never d e s i r a b l e f o r the producer t o be a net f u t u r e s s e l l e r , - - and so, perhaps s u r p r i s i n g l y , allowing the dominant producer t o t r a d e on .* L t h e f u t u r e s market always re-!uces the degree of b i a s of the a a r k e t i n t h i s = a Jlr - I model. There is another o r a d d i t i o n a l way of reducing t h e b i a s , and t h a t - I / As shorn above, reducing the bias reduces producer r i s k but m y , v i a the supply response, reduce t h e i r income and l o ~ e ru t i l i t y . See Appendix B. - 2/ See Appendix C. al 5 c w 5 1 M G rl TJ k U E! Li (W aw U c w 3 w Ll a (A 4 Ll w u a3 ' - t Ll a U c cd c 4 P 0 a w 5 '44 $4 (cf. (38).) Eliminate betveen (47) and (48) to give The average cash market clearing price satisfies The dominant producer again wishes to maxisize expected profit n i s can be vritten, using ( 4 8 ) , as ?! I ..sin, since 5 and Q a r e l i n e a r i n and S from (L9) and (50), p cont.ains terms i n {S , and hence the p r o f i t maximizing choice of futureis s a l e s , S, depends on planned production, q , and vice versa. Thus che cloninant - producer does not a c t just as a large speculator, b ~ chooses h i s t speculative position t o benefit h i s r o l e a s a producer. It is clear that t h i s a r g u e n t is robust, for it merely require a y / ? q a ~t o be non-zero, 2 which, given t h a t incone is b i l i n e a r i n prices and q u a n t i t i e s , and t h a t prices depend on q u a n t i t i e s , is v i r t u a l l y guaranteed as the only point t o check is that a l l the t e r n s do not cancel. Since they do not cancel i n the simplest l i n e a r examples, i n which any cancelling is nost l i k e l y t o occur, ve can conclude that the futures and cash narkets positions of the dominant producer a r e interdependent. The next question t o resolve is whether the dominanit producer's interventions reduce o r increases the Sias i n the futures marlset. The simplest t e s t of h i s position is t o ask i n which direction he wishes t o move s t a r t i n g with zero futures s a l e s , i.e. what is the sign of from (52). From (50) After some nanipulation t h i s can be written wtLch has the sign of - (1 - E). It follovs from (48) that the doninant producer is on the opposite s i d e of the futurzs narket t o the hedging elenent of the fringe fa-mers - i.e. i f the famers are hedging by s e l l i n g futures, which they w i l l i f the market is i n e l a s t i c E < 1 then the dominant producer w i l l be buying futures, and vice . . versa ( i f E > 1). Thus the e f f e c t of the d o n i ~ i n tproducer i s again t o further a r b i t r a g e prices, and, assuming t h i s t o be desirable, h i s presence is welcome (provided, of course, that everyone shares the same information and knows his objectives). ?!oreover, a s equations ( 4 9 ) , (50), (52) and (54) show, as the futures market becomes more e f f i c i e n t (as i t s r i s k aversion, a, tends to zero), t o the nanipulative power of the dominant producer i n the futures narket goes t o zero (see especially (54), where * S = 0 i f a = 0.) , I 4 - - 4.7 Conclusions - .5 C * Even #he\? a l l agents share the same i n f o m a t Lon and 'Ence can C predict h i s strategy, the dominant prodr~cers t i l l has an incentTve t o manipulate the futures a.ar!cet, beyond the ?oint he would choose Lf he were merely a large speculator. Nevertheless, h i s intervention .,lways has the -1/ - For bounded price, a s q I-, c > 1. e f f e c t of reducing the bias on the futures narket (though not as nuch a s i f he r i t h e r acted competitively, or a s large speculator), and hence exluding hi31 from the futures market, would on the a s s u p t i o n here of f u l l - infornation, reduce the efficiency of the futures inarket. Finally, h i s market power i n the futures market dininishes v i t h the r i s k aversion of that m r k e t (i.e. a s the number of speculators increases, andfor t h e i r r i s k aversion decreases). 5. Incentives for Destabilizing Yar'xets I f dominant producers can predict planned fringe supply (or can . do so a s well as the fringe farmers can), but fringe farmers cannot observe the doninant producer's current production plans, but only h i s , average planned production, then the dominant producer might have an incentive t o randonize h i s supply. This incentive is easiest to study i n the absence of futures markets and storage, but the argument c a r r i e s over t o these nore complex cases. For zxanple, where the dominant producer stores, he may have an incentive to randomize h i s stcrage decision, and L where there i s a futures market, he nay benefit fron further destabilizing the cash market. In a l l cases, the notive i s the sane - i n s t a b i l i t y is c o s t l y to fringe producers who w i l l respond by reducing t h e i r supply to - the benefit of the dominant producer. . However, it is also cc~stlyt o the I dominant producer and w i l l not necessariiy be worthwhile ( i n contrast to futures aarket nanipulation discussed above, which is always worthwhile). Ye s h a l l exanine a nodel v i t h demand r i s k , and no futures market, i n which the doninant producer can ctloose h i s average out?ut, q , and the uagnirude of t5e variation about t h i s , 9, measured by its The t o t a l price variance is, from (21), v = Var u i s2/E , 2 n variance, sL. on the (reasonable) assunption that demand and supply r i s k a r e - uncorrelated. Dernand and (certain) fringe supply can be written where the action c e r t a i n t y equivalent price is .. a 2 - p = Ep - X Q Var p, Var p = a2 + s2/E = v . Thus 4 1 - (1 + - ( 1 - f - E - q ) } ( l + pwA) - ( 1 11) - P a 1 + PVA + PT/E ( 5 6 ) '3 - .z * - e 0 w The dominant producer chooses q (or more correctly, Zx, average i>?ut) and s2 (deternined by the variance of input) t? aaxinize expec~edprofi;: 7 = Ep (q - t 0) 9v?r - 2 9 = W - 2a - E - E w h e ~ ofrom ( 3 6 ) , if, as assumed, wa 1 The key question is whether destabilizing behaviour is profitable, i.e., whether Now, from (56) which, if risk is mall, has p - 1,and 1-q- p, so Hence, a necessary co-ndition for profitable destabilization is - ;%us i f f r i n g e producers a r e s u f f i c i e n t l y r i s k averse, then it v i i l be d e s i r a b l e f o r t h e doninant producer t o e x p l o i t t h i s r i s k averion by I I d e s t a b i l i z i n g t h e a a r k e t . Since X is not dimensionless, it is b e s t I replaced by R = -XI,where II is f r i n g e incone, approximately p/2 near Q =p, p = 1 , and P is the c o e f f i c i e n t of r e l a t i v e r i s k aversion. Then t h e condition beccmes b4... Taking the r a t h e r favorable ( f o r d e s t a b i l i z a t i o n ) parameters used b e f o r e , p = 1/2, E =q = 1, A = 1, m = 3 / 4 , v = 1/10, then t h e i n i t i a l v a l u e of R is 9.107, which is very high (empirical estimates cluster around -~aluesof 1-2. See Newbery and S t i g l i t z , 1981, Ch. 7). 5.1 Conclusions About Destabilizing Markets For d e s t a b i l i z a t o n t o be p r o f i t a b l e , f r i n g e producers nust be . L e more r i s k averse than some c r i t i c a l l e v e l , which, i n the: absence of - s t o r a g e , is (implausi3lp) high. I n t h e presence of a f u t u r e s s a r k e t , - d e s t a b i l t z a t t o n is l i k e l y to be even l e s s '&tractive a s f r i n g e producers - I a r e p a r t i a l l y insured, and t h e coscs t o th& doainant producer a r e of the I m saae magnitude a s before. Similarly, d e s t a b i l i z i n g storage is, a t t h e nargin, presumably as c o s t l y a s d e s t a b i l i z i n g f u t u r e supply ( s i n c e :hey are, a t the m ~ r g i n ,substitutes). Hence t h i s forn of m E which inplies from (B. 1) that - - which is k p o s s i b l e, therefore S< 0. (The same argunent: hold vith I! a greater force i f it is assumed t h a t S > 0).