The risk premium in commodity markets

Scott, Ernest Maurice

doi:10.14288/1.0093760

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UBC Theses and Dissertations

The risk premium in commodity markets Scott, Ernest Maurice 1976

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Title	The risk premium in commodity markets
Creator	Scott, Ernest Maurice
Publisher	University of British Columbia
Date Issued	1976
Description	The economic function of commodity futures markets is generally acknowledged to be that of affording the commodity handler the opportunity to reduce his risk per unit of the commodity by shifting that risk to an economic unit which is better able, or more willing, to accept it, with attendant long run benefit to the ultimate consumer. In the literature related to the theory of hedging and speculative activity conflicting views have evolved and remain unresolved concerning the process of price determination and the related question of the nature of the risk premium, which represents the return for acceptance of the price risk. Some authors have argued in a manner consistent with the concept that a risk premium is built into the structure of futures prices. This view conforms with the basic tenet of the theory of finance and of economics to the effect that investors are fundamentally risk averse and that their behaviour reflects an attitude of risk aversion throughout. However, a challenge to the assumption of risk averse behaviour has been a recurring theme throughout the literature of commodity markets. Several authors have contended that the services of risk reduction afforded to hedgers are available at no cost. If the latter view is confirmed to be valid it implies, at the very least, that commodity markets are a unique type of financial market. Utilizing theoretical, descriptive, and particularly empirical analysis, the primary objective of this study is to examine an aspect of the theory of commodity markets: the nature and magnitude of the risk premiums, if any, which are received by speculators from hedgers; and the significance of hedging activity relative to the payment of .any such risk premiums. Based on the theory of risk aversion and the implications of wealth effects, a theory of hedging and speculation is suggested. The risk premium is then assumed to be determined by the set of simultaneous relationships which comprise the supp1y-demand model for futures contracts. In the empirical analysis, linear regression techniques are employed to test the demand function of the model and to examine certain other characteristics of commodity markets. Using market data for the nominal period 1961-70, the three commodities studied are among the most heavily traded on United States commodity exchanges, namely; wheat, corn, and soybeans. As expected, the mean semi-monthly holding period realized risk premium is not found to be significantly different from zero. Also, in the context of the capital asset pricing model, the systematic risk measure for each of the three commodities is found to be not significantly different from zero These conclusions are consistent with those of previous authors. Concerning the significance of hedging activity, it is concluded that the realized risk premium is positively related to the change in net short hedging consistent with the theory suggested. However, contrary to expectations and to the theory of financial markets, the speculative demand function for futures contracts is found to be very highly if not infinitely elastic. Finally, a test of the characteristics of commodity markets concludes that such markets conform with the efficient markets hypothesis.
Genre	Thesis/Dissertation
Type	Text
Language	eng
Date Available	2010-02-12
Provider	Vancouver : University of British Columbia Library
Rights	For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
DOI	10.14288/1.0093760
URI	http://hdl.handle.net/2429/20182
Degree	Doctor of Philosophy - PhD
Program	Business Administration
Affiliation	Business, Sauder School of
Degree Grantor	University of British Columbia
Campus	UBCV
Scholarly Level	Graduate
AggregatedSourceRepository	DSpace

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THE R I S K P R E M I U M IN COMMODITY M A R K E T S by E R N E S T M A U R I C E S C O T T B . S c . E . E . , U n i v e r s i t y o f M a n i t o b a , 1 9 ^ 6 M . B . A . , U n i v e r s i t y o f W a s h i n g t o n , 1969 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T OF THE R E Q U I R E M E N T S FOR THE D E G R E E OF DOCTOR OF PH I L O S O P H Y i n THE F A C U L T Y OF COMMERCE AND B U S I N E S S A D M I N I S T R A T I O N We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE U N I V E R S I T Y OF B R I T I S H C O L U M B I A A u g u s t , 1976 © E r n e s t M a u r i c e S c o t t , 1976 In presenting th is thesis in par t ia l fu l f i lment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shal l make i t f reely avai lable for reference and study. I further agree that permission for extensive copying of th is thesis for scholar ly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publ icat ion of th is thesis for f inanc ia l gain shal l not be allowed without my written permission. Faculty of Commerce Department of Finance  The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 D a t ; e September 9 , 1976 i i ABSTRACT The economic f u n c t i o n of commodity f u t u r e s m a r k e t s i s g e n e r a l l y acknowledged to be t h a t of a f f o r d i n g the commodity h a n d l e r the o p p o r t u n i t y to reduce h i s r i s k per u n i t of the commodity by s h i f t i n g t h a t r i s k to an economic u n i t wh ich i s b e t t e r a b l e , or more w i l l i n g , to a c c e p t i t , w i t h a t t e n -dant long run b e n e f i t to the u l t i m a t e consumer . In the l i t e r a t u r e r e l a t e d to the t h e o r y of hedg ing and s p e c u l a t i v e a c t i v i t y c o n f l i c t i n g v iews have e v o l v e d and remain u n r e s o l v e d c o n c e r n i n g the p r o c e s s of p r i c e d e t e r m i n a t i o n and the r e -l a t e d q u e s t i o n of the n a t u r e of the r i s k p remium, wh ich r e p r e s e n t s the r e t u r n f o r a c c e p t a n c e of the p r i c e r i s k . Some a u t h o r s have argued i n a manner c o n s i s t e n t w i t h the c o n c e p t t h a t a r i s k premium i s b u i l t i n t o the s t r u c t u r e q.fv f u t u r e s p r i c e s . T h i s v iew conforms w i t h the b a s i c t e n e t of the t h e o r y of f i n a n c e and of economics to the e f f e c t t h a t i n v e s t o r s a r e f u n d a m e n t a l l y r i s k a v e r s e and t h a t t h e i r b e h a v i o u r r e f l e c t s an a t t i t u d e of r i s k a v e r s i o n t h r o u g h o u t . However , a c h a l l e n g e to the a s s u m p t i o n of r i s k a v e r s e b e h a v i o u r has been a r e c u r r i n g theme t h r o u g h o u t the l i t e r a -t u r e of commodity m a r k e t s . S e v e r a l a u t h o r s have contended t h a t the s e r v i c e s of r i s k r e d u c t i o n . a f f o r d e d to h e d g e r s a r e a v a i l -a b l e a t no c o s t . If the l a t t e r v iew i s c o n f i r m e d to be v a l i d i t i m p l i e s , a t the v e r y l e a s t , t h a t commodity m a r k e t s a re a un ique type of f i n a n c i a l m a r k e t . i i i U t i l i z i n g t h e o r e t i c a l , d e s c r i p t i v e , and p a r t i c u l a r l y e m p i r i c a l a n a l y s i s , the p r i m a r y o b j e c t i v e of t h i s s tudy i s to examine an a s p e c t of the t h e o r y of commodity m a r k e t s : the n a t u r e and magn i tude of the r i s k p remiums, i f a n y , wh ich a r e r e c e i v e d by s p e c u l a t o r s from h e d g e r s ; and the s i g n i f i c a n c e of hedg ing a c t i v i t y r e l a t i v e to the payment of .any such r i s k p rem i urns . Based on the t h e o r y of r i s k a v e r s i o n and the i m p l i -c a t i o n s of w e a l t h e f f e c t s , a t h e o r y of hedg ing and s p e c u l a t i o n i s s u g g e s t e d . The r i s k premium i s then assumed to be d e t e r -mined by the se t of s i m u l t a n e o u s r e l a t i o n s h i p s wh ich c o m p r i s e the supp1y-demand model f o r f u t u r e s c o n t r a c t s . In the e m p i r i c a l a n a l y s i s , l i n e a r r e g r e s s i o n t e c h n i q u e s a r e employed to t e s t the demand f u n c t i o n of the model and to examine c e r t a i n o t h e r c h a r a c t e r i s t i c s o f commodity m a r k e t s . Us ing market d a t a f o r the nominal p e r i o d 1 9 6 1 - 7 0 , the t h r e e c o m m o d i t i e s s t u d i e d a re among the most h e a v i l y t r a d e d on U n i t e d S t a t e s commodity e x c h a n g e s , n a m e l y ; w h e a t , c o r n , and s o y b e a n s . As e x p e c t e d , the mean s e m i - m o n t h l y h o l d i n g p e r i o d r e a l i z e d r i s k premium i s not found to be s i g n i f i c a n t l y d i f f e r e n t f rom z e r o . A l s o , in the c o n t e x t of the c a p i t a l a s s e t p r i c i n g m o d e l , the s y s t e m a t i c r i s k measure f o r each of the t h r e e c o m m o d i t i e s i s found to be not s i g n i f i c a n t l y d i f f e r e n t f rom z e r o These c o n c l u s i o n s a r e c o n s i s t e n t w i t h those of p r e v i o u s a u t h o r s . i v C o n c e r n i n g the s i g n i f i c a n c e of hedg ing a c t i v i t y , i t i s c o n c l u d e d t h a t the r e a l i z e d r i s k premium i s p o s i t i v e l y r e l a t e d to the change in net s h o r t hedg ing c o n s i s t e n t w i t h the t h e o r y s u g g e s t e d . However, c o n t r a r y to e x p e c t a t i o n s and to the t h e o r y of f i n a n c i a l m a r k e t s , the s p e c u l a t i v e demand f u n c t i o n f o r f u t u r e s c o n t r a c t s i s found to be very h i g h l y i f not i n f i n i -t e l y e l a s t i c . F i n a l l y , a t e s t of the c h a r a c t e r i s t i c s of commodity markets c o n c l u d e s t h a t such markets c o n f o r m w i t h the e f f i c i e n t markets h y p o t h e s i s . V T A B L E OF C O N T E N T S P a g e C H A P T E R I I n t r o d u c t i o n 1 T h e F u n c t i o n o f C o m m o d i t y M a r k e t s 1 S t a t e m e n t o f t h e P r o b l e m 4 I m p o r t a n c e t o F i n a n c e ^ O u t l i n e o f R e m a i n d e r o f D i s s e r t a t i o n 7 C H A P T E R I I T r a d i n g i n C o m m o d i t y M a r k e t s 10 H e d g i n g a n d S p e c u l a t i o n 22 D e f i n i t i o n o f t h e R i s k P r e m i u m 28 E a r l i e r T h e o r i e s o f t h e R i s k P r e m i u m 30 E m p i r i c a l R e s e a r c h 3 9 C H A P T E R I I I A T h e o r y o f t h e R i s k P r e m i u m 51 L i n e a r F o r m o f t h e M o d e l 5 9 E m p i r i c a l A n a l y s i s 59 M a j o r H y p o t h e s e s t o b e T e s t e d M e a s u r e m e n t o f t h e R e a l i z e d R i s k P r e m i u m 70 C H A P T E R IV D a t a a n d S o u r c e s 7^ T e s t P r o c e d u r e 77 E m p i r i c a l R e s u l t s 78 v i Page CHAPTER V Summary and C o n c l u s i o n s 118 FOOTNOTES 12^ BIBLIOGRAPHY 130 V I I LI ST OF TABLES F u t u r e s C o n t r a c t M a t u r i t y Months . R e g r e s s i o n of the S e m i - M o n t h 1 y h o l d i n g P e r i o d R e a l i z e d R i s k Premium on Comparable R e t u r n s on the S&P 5 0 0 S e c u r i t y P r i c e Index R e g r e s s i o n of the S e m i - M o n t h l y H o l d i n g P e r i o d R e a l i z e d R i s k Premium on the Change i n Net Hedg i n g . R e g r e s s i o n of the S e m i - M o n t h l y H o l d i n g P e r i o d R e a l i z e d R i s k Premium on the L e v e l of Net H e d g i n g . C o c h r a n e - O r c u t t I t e r a t i v e T e c h n i q u e A p p l i e d t o t h e R e g r e s s i o n of the S e m i - M o n t h l y H o l d i n g P e r i o d R e a l i z e d R i s k Premium on the Change in Net Hedging and the Leve l of Net H e d g i n g . C o r r e l a t i o n M a t r i x A p p l i c a b l e to J u l y Soybeans F u t u r e s C o n t r a c t ( 1 9 6 1 - 7 0 ) R e g r e s s i o n of the S e m i - M o n t h l y H o l d i n g P e r i o d R e a l i z e d R i s k Premium on the Lagged Change in Net H e d g i n g . R e g r e s s i o n of the S e m i - M o n t h l y H o l d i n g P e r i o d R e a l i z e d R i s k Premium on the Subsequent P e r i o d Change in Net Hedging LIST OF FIGURES Graph of Expected U t i l i t y of F i n a l Wea l th v s . R i s k y A s s e t s He ld as a P r o p o r t i o n of I n i t i a l Wea l th v i i i ACKNOWLEDGEMENT I w i s h to e x p r e s s my g r a t e f u l a p p r e c i a t i o n to the members of my T h e s i s C o m m i t t e e ; to James D. MacBeth and to Rober t W. Whi te f o r t h e i r many h e l p f u l comments and c r i t i c i s m s a n d , p a r t i c u l a r l y , to M i c h a e l J . B r e n n a n , whose k n o w l e d g e , d i r e c t i o n , and a s s i s t a n c e were g i v e n u n s t i n t i n g l y and have proven to be i n v a l u a b l e from the o u t s e t . To John G. Cragg and M a u r i c e D. Lev i f o r t h e i r g u i d a n c e both in and out of the c l a s s r o o m , I a l s o e x t e n d my s i n c e r e thanks . CHAPTER I INTRODUCTI ON A r e c u r r i n g and u n r e s o l v e d c o n t r o v e r s y in the l i t e r a t u r e of commodity f u t u r e s m a r k e t s c o n c e r n s the n a t u r e and the m a g n i -tude of the r i s k premiums wh ich a r e embodied in f u t u r e s p r i c e s and which r e p r e s e n t the p r i c e of i n s u r a n c e wh ich hedgers pay to s p e c u l a t o r s f o r the s e r v i c e s of r i s k r e d u c t i o n wh ich a r e a f f o r d e d the hedgers th rough the medium of f u t u r e s c o n t r a c t s . One body of o p i n i o n a s s e r t s t h a t the r i s k premium i s p o s i t i v e and of s i g n i f i c a n t magn i tude w h i l e the c o n t r a r y o p i n i o n c o n t e n d s t h a t the r i s k premium i s z e r o or even n e g a t i v e . U t i l i z i n g t h e o r e t i c a l , d e s c r i p t i v e , and p a r t i c u l a r l y e m p i r i c a l a n a l y s i s , t h i s d i s s e r t a t i o n examines the n a t u r e and magn i tude o f the r i s k premium, and the s i g n i f i c a n c e of h e d g i n g a c t i v i t y r e l a t i v e t o the payment of such r i s k p remiums, as a p p l i c a b l e to c e r t a i n of the c o m m o d i t i e s wh ich a re h e a v i l y t r a d e d in commodity f u t u r e s m a r k e t s in the U n i t e d S t a t e s . THE FUNCTION OF COMMODITY MARKETS The economic f u n c t i o n of commodity f u t u r e s markets may be i d e n t i f i e d as t h a t of a f f o r d i n g the commodity h a n d l e r the o p p o r -t u n i t y to reduce h i s r i s k per u n i t o f the commodity by s h i f t i n g t h a t r i s k of u n d e s i r a b l e p r i c e movements to an economic u n i t wh ich i s b e t t e r a b l e , or more w i l l i n g , to a c c e p t i t , w i t h a t t e n d a n t long run b e n e f i t to the u l t i m a t e consumer . T h i s means t h a t the merchant i s a b l e to borrow funds from f i n a n c i a l i n s t i t u t i o n s more r e a d i l y and at more a t t r a c t i v e terms than would o t h e r w i s e be the c a s e . -2-In the U n i t e d S t a t e s , the i n d i v i d u a l commodity exchanges a r e s u b j e c t to l e g i s l a t i o n of Congress and a r e r e g u l a t e d by the Commodity Exchange A u t h o r i t y of the Department of A g r i c u l t u r e . Each commodity e x c h a n g e , such as the C h i c a g o Board of T r a d e , i s i n d e p e n d e n t o f i t s s i s t e r e x c h a n g e s , but each exchange d e f i n e s as i t s o b j e c t i v e the m a i n t e n a n c e and r e g u l a t i o n of a commodity market w h e r e i n exchange members, commodity h a n d l e r s , and the p u b l i c may t r a d e in f u t u r e s c o n t r a c t s . The body of i n d i v i d u a l s and f i r m s whose d e f i n e d b u s i n e s s i n v o l v e s t r a n s a c t i o n s in a spot commodity a re c l a s s i f i e d as h a n d l e r s of the commodi ty . Dependent upon h i s p a r t i c u l a r o b -j e c t i v e s , a h a n d l e r may h o l d e i t h e r a long or a s h o r t p o s i t i o n i n the a c t u a l commodi ty . I f h i s o b j e c t i v e i s to a c q u i r e c u r r e n t i n v e n t o r y in the commodity wh ich he s t o r e s f o r l a t e r s a l e then he w i l l , ove r most or a l l of the y e a r , h o l d a long p o s i t i o n . Other h a n d l e r s may c o n t r a c t to d e l i v e r the n a t u r a l or a p r o c e s s e d form of the commodity but not a c t u a l l y h o l d i n v e n t o r y at the t ime of e n t e r i n g i n t o the commitment . Such h a n d l e r s h o l d a s h o r t p o s i t i o n in the a c t u a l commodi ty . In the absence of commodity f u t u r e s m a r k e t s , and a s i d e f rom the o t h e r c o s t s i n h e r e n t t o h i s b u s i n e s s , t h e h a n d l e r must bear t h e r i s k of p r i c e changes wh ich move a g a i n s t h i s commit ted p o s i t i o n in the a c t u a l commodi ty . In the case of the h a n d l e r who i s l o n g , s h o u l d p r i c e s move down subsequent to h i s a c q u i -s i t i o n of i n v e n t o r y , he w i l l e x p e r i e n c e e i t h e r an o p p o r t u n i t y -3-l o s s or an a c t u a l l o s s dependent upon the t i m i n g o f such p r i c e movements and the t i m i n g of the s a l e of h i s i n v e n t o r y . The h a n d l e r who i s s h o r t the a c t u a l commodity w i l l e x p e r i e n c e c o m p a r a b l e l o s s e s s h o u l d p r i c e s move upwards subsequent to h i s commitment of a c o n t r a c t u a l p o s i t i o n . Commodity f u t u r e s markets a f f o r d an o p p o r t u n i t y to the h a n d l e r to reduce the r i s k of such u n d e s i r a b l e p r i c e movements. That i s , whereas p r e v i o u s l y the h a n d l e r h e l d an open -ended p o s i t i o n in the a c t u a l commodity he i s now a b l e to " c o v e r " h i s p o s i t i o n by t a k i n g an o p p o s i t e p o s i t i o n in commodity f u t u r e s . In the case of the long h a n d l e r he can hedge h i s p o s i t i o n by e n t e r i n g upon the s h o r t s i d e of a f u t u r e s c o n t r a c t where the o t h e r p a r t y to the c o n t r a c t i s e i t h e r a s h o r t h a n d l e r or a s p e c u l a t o r . S i m i l a r l y , a s h o r t h a n d l e r may e n t e r upon the long s i d e of a f u t u r e s c o n t r a c t . The p a r t i e s to any p a r t i c u l a r f u t u r e s c o n t r a c t may be h e d g e r -h e d g e r , s p e c u 1 a t o r - s p e c u 1 a t o r , or h e d g e r - s p e c u 1 a t o r . It i s the l a s t c a t e g o r y wh ich i s of p r i m a r y i n t e r e s t however s i n c e i t i d e n t i f i e s the net s p e c u l a t i v e p a r t i c i p a t i o n i n v o l v e d in a b s o r b i n g the f u t u r e s c o n t r a c t s o f f e r e d by h e d g e r s . By h i s p a r t i c i p a t i o n , the s p e c u l a t o r r e l i e v e s the h a n d l e r o f ' ' h i s open -ended p o s i t i o n in a c t u a l s and t h e r e b y assumes the r i s k a s s o c i a t e d w i t h subsequent p r i c e f l u c t u a t i o n s . The i n c e n t i v e to the s p e c u l a t o r to a c c e p t t h i s r i s k i s p resumably the e x -p e c t a t i o n of a p o s i t i v e r e t u r n on h i s i n v e s t m e n t , a r e t u r n wh ich may be r e a l i z e d o n l y i f p r i c e changes prove to be f a v o r a b l e to h i s p o s i t i o n . - it -STATEMENT OF THE PROBLEM In the p e r f o r m a n c e of t h e i r economic f u n c t i o n , commodity f u t u r e s m a r k e t s a r e g e n e r a l l y acknowledged to have p l a y e d a s i g n i f i c a n t r o l e in the d e t e r m i n a t i o n of commodity spot p r i c e s and in the tempora l d i s t r i b u t i o n of those c o m m o d i t i e s which a re t r a d e d in such m a r k e t s . In the l i t e r a t u r e r e l a t e d to the t h e o r y of h e d g i n g and s p e c u l a t i v e a c t i v i t y in commodity m a r k e t s , c o n f l i c t i n g v iews have e v o l v e d and remain u n r e s o l v e d c o n c e r n i n g a s p e c t s o f the p r o c e s s of p r i c e d e t e r m i n a t i o n and the r e l a t e d q u e s t i o n of the n a t u r e of the r i s k p remiums, i f a n y , wh ich a r e p a i d by hedgers to s p e c u l a t o r s . It i s t h e r e f o r e the o b j e c t i v e of t h i s work to examine the c o m p e t i n g t h e o r i e s and to conduct an e m p i r i c a l a n a l y s i s of the r i s k premiums a p p l i c a b l e to c e r t a i n s e l e c t e d c o m m o d i t i e s wh ich a r e h e a v i l y t r a d e d in commodity f u t u r e s m a r k e t s . IMPORTANCE TO FINANCE It i s both i n t e r e s t i n g and i n s t r u c t i v e to draw c e r t a i n c o m p a r i s o n s between f i n a n c i a l markets and commodity m a r k e t s . In f i a n c i a l m a r k e t s , the c l a i m o f a s s e t h o l d e r s on the i s s u e r s of f i n a n c i a l i n s t r u m e n t s t a k e s the form of cash f l o w s t reams c o m p r i s e d of d i v i d e n d s , i n t e r e s t p a y m e n t s , r e t u r n of p r i n c i p a l , e t c e t e r a , dependent upon the p a r t i c u l a r form o f i n s t r u m e n t . The i s s u a n c e of f i n a n c i a l i n s t r u m e n t s p r o v i d e s f i n a n c i n g f o r the i s s u e r but i t a l s o s i m u l t a n e o u s l y p r o v i d e s an o p p o r t u n i t y f o r c e r t a i n economic u n i t s , the u l t i m a t e s a v e r s , to p a r t i c i p a t e in the u n d e r t a k i n g s o f the b u s i n e s s and government s e c t o r s of of the economy. Commodity m a r k e t s a r e in f a c t a type of f i n a n c i a l market w h e r e i n the i n s t r u m e n t t a k e s the form of a f u t u r e s c o n -t r a c t and w h e r e i n the c l a i m to cash f l o w s i s r e p l a c e d w i t h a c l a i m on the c o m m o d i t i e s i n v o l v e d . In commodity m a r k e t s , the c o m p a r i s o n to the p o s i t i o n s of the i s s u e r of a f i n a n c i a l i n -s t r u m e n t and t h a t of an a s s e t h o l d e r in f i n a n c i a l markets can most r e a d i l y be d e p i c t e d under a s t a t e of net s h o r t h e d g i n g . The h e d g e r , who has i n v e s t e d in and h o l d s i n v e n t o r y in a commodi t y , " i s s u e s " a f u t u r e s c o n t r a c t under w h i c h he assumes a l i a b i l i t y to d e l i v e r the commodity i f the c o n t r a c t i s not c l o s e d out p r i o r t o m a t u r i t y . For h i s p a r t , the s p e c u l a t o r a c q u i r e s a c l a i m on the commodity and may t a k e d e l i v e r y in l i e u of c l o s i n g out the c o n t r a c t . As in the case of pure f i n a n c i a l i n s t r u m e n t s , the c r e a t i o n of a f u t u r e s c o n t r a c t p r o v i d e s an o p p o r t u n i t y f o r c e r t a i n economic u n i t s to p a r t i c i p a t e in an u n d e r t a k i n g of the b u s i n e s s s e c t o r . C o i n c i d e n t a 1 1 y , a n d ' o f some i m p o r t a n c e , the i n v e s t m e n t in f u t u r e s c o n t r a c t s a l s o commits a p o r t i o n of t o t a l w e a l t h wh ich might o t h e r w i s e seek an a l t e r n a t e , and c o m p e t i n g use in the economy. W h i l e f u t u r e s c o n t r a c t s do not p r o v i d e f i n a n c i n g d i r e c t l y f o r the commodity h a n d l e r they d o , i n d i r e c t l y , f a c i l i t a t e such f i n a n c i n g . That the r i s k per d o l l a r o f i n v e s t m e n t in hedged i n v e n t o r i e s i s l e s s than in unhedged i n v e n t o r i e s i s r e a d i l y r e f l e c t e d , f o r e x a m p l e , in the a v a i l a b i l i t y and terms of commerc ia l bank loans to h a n d l e r s . - 6 -A f u r t h e r c o m p a r a t i v e c h a r a c t e r i s t i c of f i n a n c i a l markets and commodity m a r k e t s r e l a t e s to the c o n c e p t of e f f i c i e n t m a r k e t s . In the case of t h o s e h e a v i l y t r a d e d c o m m o d i t i e s w h i c h a r e s t u d i e d i n t h i s a n a l y s i s , the work of o t h e r s has e v i d e n c e d t h a t commodity exchanges d i s p l a y the a t t r i b u t e s of e f f i c i e n c y . Only in i n s t a n c e s of p o o r l y d e v e l o p e d or t h i n m a r k e t s , where the c o m m o d i t i e s i n v o l v e d are i n f r e q u e n t l y t r a d e d , have s i g n i f i c a n t q u e s t i o n s been r a i s e d to the c o n t r a r y . ' A b a s i c t e n e t of the t h e o r y of f i n a n c i a l economics i s t h a t i n v e s t o r s a re f u n d a m e n t a l l y r i s k a v e r s e . In f a c t , the a s s u m p t i o n of r i s k a v e r s i o n and of the e x i s t e n c e of a r i s k premium p r o v i d e s the f o u n d a t i o n f o r numerous f i n a n c i a l m o d e l s . 2 T h i s i s the c a s e in M a r k o w i t z " p o r t f o l i o t h e o r y and in 3 S h a r p e ' s c a p i t a l a s s e t p r i c i n g m o d e l . The a s s u m p t i o n of r i s k a v e r s i o n has been shown by Arrow t o be a n e c e s s a r y c o n d i t i o n f o r e q u i l i b r i u m in f i n a n c i a l m a r k e t s . V a r i o u s o t h e r 5 6 7 a u t h o r s , i n c l u d i n g Fama , L i n t n e r .and J e n s e n , have s t r u c t u r e d c e r t a i n of t h e i r work on the a s s u m p t i o n t h a t the economic u n i t i s r i s k a v e r s e . The p o t e n t i a l f o r d e p a r t u r e from the a n a l o g y w i t h f i n a n c i a l markets i s perhaps most p o i g n a n t w i t h r e s p e c t to the a s s u m p t i o n of r i s k a v e r s i o n . A p r i o r i , i t appears r e a s o n a b l e to assume t h a t the - p a r t i e s to f u t u r e s c o n t r a c t s would ^ d i s p l a y r i s k a v e r s i o n in a manner c o m p a r a b l e to t h a t assumed in o t h e r f i n a n c i a l m a r k e t s . Under t h i s a s s u m p t i o n hedgers would be e n v i s a g e d as b e i n g w i l l i n g to o f f e r . a r e t u r n to s p e c u l a t o r s commensurate w i t h the r e d u c t i o n in p r i c e r i s k . S i m i l a r l y , s p e c u l a t o r s would be e x p e c t e d to demand a r e t u r n c o m p a t i b l e w i t h the p e r c e i v e d r i s k to wh ich they are e x p o s e d . However , a c h a l l e n g e to the a s s u m p t i o n of r i s k a v e r s e b e h a v i o u r has been a r e c u r r i n g theme t h r o u g h o u t the l i t e r a t u r e of commodity f u t u r e s m a r k e t s . Some a u t h o r s have argued in a manner c o n s i s t e n t w i t h the concept t h a t a r i s k premium i s b u i l t i n t o the s t r u c t u r e of f u t u r e s p r i c e s . T h i s p o s i t i o n i s , however , by no means u n i v e r s a l . The c o n c e p t has been c h a l l e n g e d by those who have contended t h a t the s e r v i c e s of r i s k r e d u c t i o n a f f o r d e d to hedgers by f u t u r e s t r a d i n g are a v a i l a b l e at no c o s t to the h e d g e r s . Such a c o n t e n t i o n , i f v a l i d , would indeed be of i m p o r t a n c e to f i n a n c e . At the v e r y l e a s t , i t would imply the e x i s t e n c e of a un ique f i n a n c i a l m a r k e t . At m o s t , i t would c a l l i n t o q u e s t i o n the a s s u m p t i o n of r i s k a v e r s i o n u n d e r l y i n g an e x t e n s i v e body of the t h e o r y of f i n a n c e . OUTLINE OF REMAINDER OF DISSERTATION The main body of the d i s s e r t a t i o n i s d i v i d e d i n t o f o u r c h a p t e r s . In Chapte r I I , the e s s e n t i a l i n s t i t u t i o n a l and p r o -c e d u r a l a s p e c t s of t r a d i n g in commodity f u t u r e s markets a r e f i r s t d e s c r i b e d . The economic r o l e of f u t u r e s m a r k e t s i s then i d e n t i f i e d and the t h e o r y of hedg ing and of s p e c u l a t i o n i s d i s c u s s e d . F o l l o w i n g a c l a r i f i c a t i o n of the a l t e r n a t i v e forms of d e f i n i t i o n of the r i s k premium, the b a s i c c o m p e t i n g t h e o r i e s of the r i s k premium are r e v i e w e d s t a r t i n g w i t h the c o n f l i c t i n g 8 9 p o s i t i o n s of Hardy and Keynes . The m o d i f i c a t i o n s and e x t e n -s i o n s of the t h e o r y by Cootner ' and T e l s e r " a r e then e l a b o r a t e d wh ich l e a d s to a summary of the e m p i r i c a l r e s e a r c h wh ich has been c o n d u c t e d . In Chapte r I I I , a t h e o r y of the r i s k premium i s s u g g e s t e d and the l i n e a r form of the supp1y-demand model f o r f u t u r e s c o n -t r a c t s i s s t a t e d f o l l o w e d by a c o n s i d e r a t i o n of the q u e s t i o n s which a r i s e in the e m p i r i c a l a n a l y s i s of the model and in the a p p l i c a t i o n of l e a s t s q u a r e s r e g r e s s i o n to the demand f u n c t i o n . The major h y p o t h e s e s to be t e s t e d in an a t t e m p t to i s o l a t e the r i s k premium and to d e t e r m i n e i t s r e l a t i o n s h i p to h e d g i n g a c t i v i t y a re e x p r e s s e d and the b a s i s o f measurement of the r e a l i z e d r i s k premium i s then d e t a i l e d . The r e p o r t of the e m p i r i c a l a n a l y s i s i s embodied in Chapter IV. R e f e r e n c e i s f i r s t made to the d a t a and t h e i r s o u r c e s . A comment i s i n c l u d e d on the t e s t p r o c e d u r e s f o l l o w e d and an a n a l y t i c a l r e p o r t and assessment of the s e v e r a l t e s t s c o n d u c t e d then c o m p r i s e s the main body of the c h a p t e r . More p a r t i c u l a r l y , the r e l a t i o n s h i p d i s c e r n e d between the s e m i -month l y h o l d i n g p e r i o d r e a l i z e d r i s k premium and each of the net hedg ing l e v e l , the change in net h e d g i n g and the r e t u r n s on a s e c u r i t y market i n d e x , f o r each of w h e a t , c o r n , and s o y -beans f u t u r e s c o n t r a c t s , i s r e p o r t e d and d i s c u s s e d . The r e s u l t s of a t e s t o f the e f f i c i e n t market c h a r a c t e r i s t i c s of t r a d i n g in soybeans f u t u r e s c o n t r a c t s a r e a l s o r e p o r t e d . Chapter V summarizes the f i n d i n g s and c o n c l u s i o n s of the s tudy and o f f e r s s u g g e s t i o n s f o r f u r t h e r r e s e a r c h w h i c h might p r o v i d e a d d i t i o n a l i n s i g h t i n t o the c h a r a c t e r i s t i c s and r e l a t i o n s h i p s wh ich t y p i f y t r a d i n g in commodity f u t u r e s marke CHAPTER I I TRADING IN COMMODITY MARKETS 1 2 In Nor th A m e r i c a , the i n s t i t u t i o n of commodity f u t u r e s t r a d i n g d a t e s back to the m i d - n i n e t e e n t h c e n t u r y . Throughout most of i t s l i f e , i t has been s u r r o u n d e d by v a r y i n g degrees of c o n t r o v e r s y and l a c k of u n d e r s t a n d i n g . In the U n i t e d S t a t e s , as w e l l as in o t h e r c o u n t r i e s where f u t u r e s t r a d i n g has been and/or i s c o n d u c t e d , h o t l y c o n t e s t e d l e g i s l a t i o n has not i n -f r e q u e n t l y been b e f o r e the p u b l i c e y e . In the l a t t e r p a r t o f the 1 9 t h c e n t u r y , v a r i o u s s t a t e l e g i s l a t u r e s passed b i l l s l i m i t i n g f u t u r e s t r a d i n g and the f i r s t n a t i o n a l U .S . l a w , wh ich was s u b s e q u e n t l y d e c l a r e d u n c o n s t i t u t i o n a l , was passed in 1 9 2 1 . The G r a i n F u t u r e s Act f o l l o w e d in 1 9 2 2 and was l a t e r changed and renamed the Commodity Exchange Act in 1 9 3 6 . F r e -quent amendments have e n s u e d . I n d i c a t i v e of the i n t e n s i t y of the f e e l i n g s toward f u t u r e s t r a d i n g wh ich have been h e l d by some i s the f a c t t h a t hundreds of b i l l s have been i n t r o d u c e d to Congress w i t h the o b j e c t i v e of p r o h i b i t i n g such t r a d i n g . In t u r n , c e r t a i n of the s p i r i t of the l e g i s l a t i o n may be e v i d e n c e d by q u o t i n g from the Commodity Exchange A c t . " . . . t h e t r a n s a c t i o n s and p r i c e s of c o m m o d i t i e s on such boards of t r a d e a r e s u s c e p t i b l e to s p e c u -l a t i o n , m a n i p u l a t i o n , and c o n t r o l , and sudden or u n r e a s o n a b l e f l u c t u a t i o n s i n the p r i c e s t h e r e o f f r e q u e n t l y o c c u r as the r e s u l t o f such s p e c u l a t i o n , m a n i p u l a t i o n , or c o n t r o l , wh ich a re d e t r i m e n t a l to the p r o d u c e r or the consumer and the p e r s o n s - 1 1 -h a n d l i n g c o m m o d i t i e s and t h e p r o d u c t s and by p r o d u c t s t h e r e o f i n i n t e r s t a t e c o m m e r c e . . . " T h e r e a p p a r e n t l y i s s u b s t a n c e t o t h i s s t a t e m e n t . P r i o r t o t h e e n a c t m e n t o f s t a t e and s u b s e q u e n t l y f e d e r a l l e g i s l a t i o n t h e r e w e r e n u m e r o u s e x a m p l e s o f c o r n e r s and m a r k e t m a n i p u l a t i o n . The y e a r 1868 w o u l d seem t o h a v e been p a r t i c u l a r l y n o t a b l e f o r s u c h s p e c u l a t i v e a c t i v i t y w i t h a c o r n e r a month r e p o r t e d t o h a v e o c c u r r e d among t h e c o m m o d i t i e s t r a d e d on t h e C h i c a g o B o a r d o f T r a d e a l o n e . Even up t o t h e p r e s e n t t i m e some a b u s e s , a l b e i t o f a r e l a t i v e l y m i n o r n a t u r e , do o c c u r b u t d i s c i p l i n e o f t h e o f f e n d e r s i s m e t e d o u t , p r i m a r i l y by t h e c o m m o d i t y e x c h a n g e s t h e m s e l v e s . W h i l e s u c h e v e n t s a r e c o l o r f u l , i t i s more i n s t r u c t i v e t o t u r n t o a d i s c u s s i o n o f t h e n a t u r e o f f u t u r e s t r a d i n g and t h e p a r t i c i p a n t s a n d t h e i r o b j e c t i v e s . The C h i c a g o B o a r d o f T r a d e i s t h e o l d e s t c o m m o d i t y e x c h a n g e i n t h e U n i t e d S t a t e s . H a v i n g s t a r t e d a s a s p o t m a r k e t i n 1848, i t r e c e i v e d i t s c h a r t e r i n 1859, and commenced f u t u r e s t r a d i n g i n 1865. T o d a y , as m e a s u r e d by t h e p r o p o r t i o n o f t o t a l t r a d i n g , i t c o n t i n u e s as t h e l a r g e s t s i n g l e c o m m o d i t y e x c h a n g e on t h i s c o n t i n e n t . W h i l e i n d e p e n d e n t o f i t s s i s t e r e x c h a n g e s , e a c h s u c h e x c h a n g e i d e n t i f i e s as i t s b a s i c o b j e c t i v e t h e m a i n t e n a n c e and r e g u l a t i o n o f a c o m m o d i t y m a r k e t w h e r e i n e x c h a n g e m e m b e r s , c o m m o d i t y h a n d l e r s , and t h e p u b l i c may t r a d e i n f u t u r e s c o n t r a c t s . E a c h e x c h a n g e n o t o n l y e s t a b l i s h e s s t a n d a r d s and p r o c e d u r e s f o r t h e a c t i v i t y o f t r a d i n g and t h e c o n d u c t o f i t s members b u t a l s o e s t a b l i s h e s c o n t r a c t u a l s t i p u l a t i o n s p e r t a i n i n g t o t h e - 12 -q u a l i t y and s i z e of c o n t r a c t of each commodity wh ich i s to be t r a d e d . Wheat i s a pr ime example of a commodity wh ich i s h e a v i l y t r a d e d on the C h i c a g o Board of T r a d e . The u n i t wh ich i s t r a d e d i s a " c o n t r a c t " of 5,000 b u s h e l s and both the q u a l i t y and the p o i n t of d e l i v e r y a r e s p e c i f i e d to e n s u r e u n i f o r m i t y . C o n t r a c t s a re d e f i n e d f o r d e l i v e r y in J u l y , September , December, M a r c h , and May. A f u t u r e s c o n t r a c t , t h e n , i s an agreement to l a t e r buy and s e l l a commodi ty . The i n i t i a t i o n of such a c o n -t r a c t does not i n v o l v e the exchange of c a s h or the change of t i t l e t o the commodity between the p a r t i e s to the c o n t r a c t . R a t h e r , such c o n t r a c t s c a l l f o r d e f e r r e d p e r f o r m a n c e and e x -change of t i t l e . P r o v i s i o n i s i n c o r p o r a t e d f o r the c o n t r a c t to mature and f o r the d e f e r r e d commitments to be consumated b u t , in f a c t , t y p i c a l l y l e s s than two per c e n t of the c o n t r a c t s eve r m a t u r e . It i s w e l l to draw the d i s t i n c t i o n between f u t u r e s c o n -t r a c t s and f o r w a r d c o n t r a c t s . Forward c o n t r a c t s were o r i g i n a l l y made between c o u n t r y m e r c h a n t s and t e r m i n a l r e c e i v e r s w i t h the e x p l i c i t i n t e n t i o n of the p a r t i e s to the c o n t r a c t to make and t a k e d e l i v e r y . Such c o n t r a c t s a r e not t r a d e d on the o r g a n i z e d commodity exchanges but r a t h e r a r e n e g o t i a t e d in i n f o r m a l m a r k e t s . One may v iew f u t u r e s m a r k e t s and f u t u r e s t r a d i n g as an o u t g r o w t h of the o r i g i n a l t i m e or f o r w a r d c o n t r a c t s . Both c o n t r i b u t e to the p r o c e s s of p r i c e d e t e r m i n a t i o n and each c o n -t r i b u t e s m e a n i n g f u l l y to the market p r o c e s s . However, our i n t e r e s t s a r e d i r e c t e d to the purposes and p r o c e s s e s of f u t u r e s t r a d i n g in o r g a n i z e d commodity exchanges and h e n c e f o r t h a l l r e f e r e n c e s to c o n t r a c t s and to t r a d i n g w i l l p e r t a i n s p e c i f i c a l l y to f u t u r e s c o n t r a c t s u n l e s s o t h e r w i s e d e s i g n a t e d . A s i d e from the exchange members and t h e i r r e p r e s e n t a t i v e s on the t r a d i n g f l o o r , the p a r t i c i p a n t s i n commodity f u t u r e s mar -k e t s may be c l a s s i f i e d e i t h e r as hedgers or as s p e c u l a t o r s . The hedgers a r e , a l m o s t by d e f i n i t i o n , the h a n d l e r s of the commodity and may be i d e n t i f i e d as b e i n g in one of two c a t e g o r i e s . The f i r s t c a t e g o r y i n c l u d e s , in the c a s e of g r a i n , the f a r m e r s , e l e v a t o r o p e r a t o r s , g r a i n m e r c h a n t s , and e x p o r t e r s who, a t v a r i o u s t imes t h r o u g h o u t the year or c o n t i n u o u s l y t h r o u g h o u t the y e a r , o h o Id a long cash ( i . e . i n v e n t o r y ) p o s i t i o n in the commodi ty . The second c a t e g o r y i s c o m p r i s e d of p r o c e s s o r s of the commodity and i n c l u d e s such as m i l l e r s , p r o c e s s o r s , and feed m a n u f a c t u r e r s . The commodity p o s i t i o n of the v a r i o u s p r o c e s s o r s i s d i v e r s e and tends to be un ique to the p a r t i c u l a r p r o d u c t s w i t h which they a r e i n v o l v e d . In g e n e r a l , however , the p a t t e r n a p p l i c a b l e to the p r o c e s s o r s i s d i s s i m i l a r to t h a t o f the h a n d l e r s in the f i r s t c a t e g o r y . F l o u r m i l l e r s o f f e r a good e x a m p l e . At the t ime of the h a r v e s t , they tend t o be long new c rop cash but as b a k e r s p l a c e o r d e r s and the f l o u r b u y i n g season g e t s underway they a r e s h o r t cash f l o u r . Each of the h a n d l e r s may hedge by t a k i n g a p o s i t i o n in f u t u r e s o p p o s i t e to h i s e x i s t i n g c a s h p o s i t i o n . From the d e v e l o p m e n t o f h e d g i n g p r a c t i c e s i n t h e 1 8 7 0 1 s and 1 8 8 0 1 s t h e p r o c e s s o f c o v e r i n g a c a s h p o s i t i o n i n t h e f u t u r e s m a r k e t has been v i e w e d as one o f s h i f t i n g t h e r i s k o f o w n e r s h i p f r o m t h e h a n d l e r t o some o t h e r p a r t y who i s p r e p a r e d t o c a r r y t h i s r i s k . In t u r n , t h e r i s k i n v o l v e d was r e c o g n i z e d as a r i s i n g o u t o f t h e c o m b i n a t i o n o f o w n e r s h i p o f p o s i t i v e o r n e g a t i v e i n v e n t o r i e s and o f v a r i a b l e and u n c e r t a i n p r i c e s w h i c h may a d h e r e i n t h e f u t u r e . The h e d g e r i s e n g a g e d i n t h e m o v e m e n t , m a r k e t i n g , a n d / o r p r o c e s s i n g o f a c o m m o d i t y s u c h as w h e a t . H i s p r i m a r y b u s i n e s s d o e s n o t e n t a i l s p e c u l a t i n g on t h e f u t u r e p r i c e s o f w h e a t and i t i s t h e r e f o r e f u n d a m e n t a l t h a t he s e e k t o a b s t r a c t f r o m t h o s e r i s k s w h i c h may p r o v e t o be f a t a l t o h i s b a s i c b u s i n e s s e n t e r p r i s e . In t h e c a s e o f s u c h as a g r a i n m e r c h a n t , h i s n e e d f o r c a p i t a l t o c o v e r h i s i n v e s t m e n t i n i n v e n t o r y i s o f s i g n i f i c a n t p r o p o r t i o n s . The r e l a t i v e l y f a v o r a b l e t e r m s o f c r e d i t e x t e n d e d by c o m m e r c i a l b a n k s t o s u c h a m e r c h a n t who has c o v e r e d h i s l o n g c a s h p o s i t i o n i n t h e f u t u r e s m a r k e t , as c o m -p a r e d t o t h e t e r m s o f c r e d i t t o a m e r c h a n t who i s n o t s o c o v e r e d , i s b u t one r e f l e c t i o n o f t h e m e r i t a t t a c h e d t o t h e r i s k s h i f t i n g p r o c e s s . I n c i d e n t a l l y , w h i l e t h e d i s c u s s i o n o f f e r e d h e r e m i g h t be i n t e r p r e t e d t o i m p l y t h a t a h a n d l e r a l w a y s c o v e r s h i s c a s h p o s i t i o n by an e q u a l and o p p o s i t e p o s i t i o n i n t h e f u t u r e s m a r k e t t h i s , o f c o u r s e , i s n o t n e c e s s a r i l y t h e c a s e i n p r a c t i c e . H a n d l e r s may and s o m e t i m e s do c h o o s e t o s p e c u l a t e on p r i c e m o v e m e n t s and do n o t n e c e s s a r i l c o m p l e t e l y or even p a r t i a l l y c o v e r t h e i r cash commodity p o s i t i o n W h i l e the two p a r t i e s to a f u t u r e s c o n t r a c t may be a s h o r t and a long h e d g e r , more t y p i c a l l y the o p p o s i t e s i d e of the hedg ing t r a n s a c t i o n in the f u t u r e s market i s o c c u p i e d by a s p e c u l a t o r . Nobly e x p r e s s e d i t may be s a i d t h a t s p e c u l a t o r s come f o r w a r d to a c c e p t the o p p o r t u n i t y o f f e r e d by the hedgers to c a r r y c e r t a i n of the r i s k i n h e r e n t to the commodity h a n d l e r ' s b u s i n e s s a n d , by so d o i n g , the s p e c u l a t o r p r o v i d e s or f a c i l i -t a t e s the p r o v i s i o n of c a p i t a l and m i n i m i z e s r i s k as d e s i r e d by the h e d g e r s . Less n o b l y e x p r e s s e d , the s p e c u l a t o r u n -d o u b t e d l y e n t e r s the market by reason of the a t t r a c t i o n of p o t e n t i a l l y h i g h r a t e s of r e t u r n to be r e a l i z e d on h i s c a p i t a l . Adam S m i t h ' s i n v i s i b l e hand may u n k n o w i n g l y be g u i d i n g the s p e c u l a t o r s ' a c t i o n b u t , to the degree t h a t the s a t i s f a c t o r y f u n c t i o n i n g of f u t u r e s t r a d i n g in commodity markets c o n t r i b u t e s to the economic p r o c e s s e s i n v o l v e d , the e s s e n t i a l c h a r a c t e r -i s t i c i s t h a t s p e c u l a t o r s p e r f o r m t h e i r n e c e s s a r y and v a l u a b l e r o l e . I n c i d e n t a l l y , and p a r a l l e l to the c l o s i n g comment above c o n c e r n i n g h a n d l e r s , i t i s not to be i m p l i e d from t h e s e remarks t h a t s p e c u l a t o r s a lways and o n l y t a k e f u t u r e s c o n t r a c t p o s i t i o n s o p p o s i t e to h e d g e r s . Such a s t a t e c o u l d o n l y adhere i f the e n t i r e p o p u l a t i o n of s p e c u l a t o r s h e l d but one e x p e c -t a t i o n c o n c e r n i n g the d i r e c t i o n of subsequent movement of p r i c e s . . . a h i g h l y u n l i k e l y e v e n t . In f a c t , d i v e r s e v iews c o n c e r n i n g the f u t u r e movement of p r i c e s i s."v i r tua 1 1 y a lways the p r e v a l e n t s t a t e w i t h the r e s u l t t h a t s p e c u l a t o r s may be on o p p o s i t e s i d e s of a f u t u r e s c o n t r a c t c o i n c i d e n t w i t h i d e n -t i c a l c o n t r a c t s w h e r e i n the p a r t i e s i n v o l v e d are c o m p r i s e d of s p e c u l a t o r s and h e d g e r s . E x t e n s i v e d e t a i l i n g of the mechan ics of f u t u r e s t r a d i n g i s not w a r r a n t e d f o r pu rposes of t h i s d i s s e r t a t i o n but an o v e r -v iew of c e r t a i n f a c t s i s germane to l a t e r d i s c u s s i o n . The t y p i c a l U .S . commodity exchange l i m i t s the number of exchange members a n d , f u r t h e r , l i m i t s membership to i n d i v i d u a l s . Membership e n t i t l e s the i n d i v i d u a l to engage in t r a d i n g on the f l o o r of the e x c h a n g e . In t u r n , the i n d i v i d u a l s r e p r e s e n t v i r t u a l l y eve ry f a c e t of the a c t i v i t y r a n g i n g from p r o d u c e r s th rough b r o k e r s to i n d i v i d u a l l a r g e s p e c u l a t o r s . In many i n s t a n c e s , the i n d i v i d u a l m e m b e r . i s f i n a n c e d by , i s an employee o f , or i s o t h e r w i s e e f f e c t i v e l y c o n t r o l l e d by a f i r m whose b u s i n e s s i n v o l v e s f u t u r e s t r a d i n g . The example of a non-member s e e k i n g to p a r t i c i p a t e in t r a d i n g and u t i l i z i n g the s e r v i c e s of a commiss ion merchant or commiss ion house w i l l s e r v e to o u t l i n e b r i e f l y the p r o c e s s i n v o l v e d . Throughout h i s b ranch o f f i c e s , the c o m m i s s i o n merchant m a i n t a i n s a h i g h l y e f f i c i e n t . a n d e x t e n s i v e communi -c a t i o n system such t h a t he i s a b l e to a d v i s e p r i c e q u o t a t i o n s v i r t u a l l y s i m u l t a n e o u s l y w i t h t r a d i n g a c t i o n on the exchange f l o o r and i s a b l e to e x e c u t e market o r d e r s a l m o s t as q u i c k l y . Some c o m m i s s i o n houses i n d i r e c t l y own exchange memberships w h i l e o t h e r s u t i l i z e the s e r v i c e s of a b r o k e r who i s an e x -change member. In any e v e n t , when an i n d i v i d u a l i n v e s t o r p l a c e s a buy or s e l l o r d e r , i t i s communicated t o the b r o k e r on the t r a d i n g f l o o r who seeks to e x e c u t e the o r d e r . In a d d i t i o n to the c o m p e t i n g b r o k e r s on the t r a d i n g f l o o r , t h e r e a r e a l s o s e v e r a l o t h e r c a t e g o r i e s of member p a r t i c i p a n t s . " S c a l p e r s b r i d g e s h o r t t ime gaps in the f l o w of o r d e r s " and add l i q u i d i t y to the market by s t a n d i n g ready to buy j u s t below the l a s t t r a d e d p r i c e or to s e l l j u s t above the l a s t t r a d e d p r i c e . " P i t t r a d e r s " m a i n t a i n no o v e r n i g h t p o s i t i o n but seek to p r o f i t from i n t r a d a y p r i c e c h a n g e s . Compared to the s c a l p e r s , the p i t t r a d e r s b r i d g e b i g g e r t ime gaps in the f l o w . o f o r d e r s . They a t t e m p t to sense the d i r -e c t i o n of p r i c e movement and to buy when they b e l i e v e the p r i c e i s r i s i n g and to s e l l when they b e l i e v e the p r i c e i s f a l l i n g . As opposed to the l a s t two c a t e g o r i e s , the " f l o o r t r a d e r " i s more f l e x i b l e in h i s p e r f o r m a n c e and w i l l commonly t r a d e in more than one commodi ty . By c o m p a r i s o n w i t h the s c a l p e r s and p i t t r a d e r s , whose r e s p o n s e i s ve ry l a r g e l y r e l a t e d to t e c h -n i c a l c o n s i d e r a t i o n s , the f l o o r t r a d e r t y p i c a l l y i s r e s p o n d i n g to a b r o a d e r range of f a c t o r s , both t e c h n i c a l and fundamenta l in n a t u r e . I t i s i n t o t h i s mix of t r a d e r s , each v y i n g one w i t h the o t h e r , t h a t the i n d i v i d u a l ' s o r d e r a p p e a r s . The o r d e r p l a c e d may be one of s e v e r a l k i n d s , most of wh ich a r e s y n o n y -mous w i t h o r d e r s of the same name in the s e c u r i t i e s ' m a r k e t . A " m a r k e t " o r d e r i s one to be e x e c u t e d at the b e s t p r i c e the - 1 8 -b r o k e r can o b t a i n . " L i m i t " o r d e r s a r e to buy or s e l l but s u b j e c t to a s p e c i f i e d maximum or minimum p r i c e r e s p e c t i v e l y . " S t o p " o r d e r s a r e a l s o o r d e r s to buy or s e l l but become a p p l i c a b l e o n l y when the p r i c e s r i s e or f a l l to a p r e s c r i b e d l e v e l . " S t o p l i m i t " o r d e r s combine the f e a t u r e s of s top and l i m i t o r d e r s . C e r t a i n o t h e r t ypes of o r d e r s a r e more p a r t i c u -l a r l y a p p l i c a b l e to commodity m a r k e t s . For e x a m p l e , a " t r a i l i n g s t o p " o r d e r i n v o l v e s a v a r i a b l e r a t h e r than a d e f i n e d s t o p p r i c e such an o r d e r might c a l l f o r a s a l e i f the p r i c e s h o u l d f a l l by , s a y , t h r e e c e n t s f rom the h i g h e s t l e v e l a t t a i n e d . "Sea 1e" - o r d e r s i n v o l v e e x t e n d e d buy or s e l l o r d e r s w i t h , f o r e x a m p l e , one c o n t r a c t to be s o l d on a s c a l e down at each of s e v e r a l s p e c i f i e d p r i c e s u n t i l a r e q u i r e d number of c o n t r a c t s have been s o l d . " C o n t i n g e n t " o r d e r s c a l l f o r a c t i o n to be taken in one d e l i v e r y month when the p r i c e a t t a i n s a s p e c i f i e d l e v e l in a n o t h e r d e l i v e r y month. " S p r e a d s " i n v o l v e s i m u l t a n e o u s buy and s e l l o r d e r s in d e f i n e d months and w i t h a s p e c i f i e d p r i c e s p r e a d . For e x a m p l e , a s p r e a d may be p l a c e d t o s e l l one c o n t r a c t in December wheat and buy one c o n t r a c t in J u l y wheat at a 10 cent d i f f e r e n t i a l or more , premium J u l y . Other forms o f o r d e r s i n v o l v i n g a r b i t r a g e a c r o s s more than one exchange t r a d i n g i n the same-commodity ( e . g . C h i c a g o and Kansas wheat) or a c r o s s d i f f e r e n t or r e l a t e d p r o d u c t s ( e . g . soybeans and soybean meal ) a r e a l s o among the a l t e r n a t i v e s open to the t r a d e r . As p r e v i o u s l y n o t e d , t r a d i n g i s in the form of " c o n t r a c t s " o f s p e c i f i e d s i z e and q u a l i t y o f t h e c o m m o d i t y w i t h e a c h c o n -t r a c t i n a g i v e n c o m m o d i t y b e i n g i d e n t i c a l t o a l l o t h e r s u c h c o n t r a c t s e x c e p t as t o t h e s t i p u l a t i o n o f t h e d e l i v e r y m o n t h . F o r e a c h t r a d e , someone i s l o n g and someone i s s h o r t . In t h e p r i c e m o v e m e n t s w h i c h o c c u r f o l l o w i n g t h e t r a d e , one p a r t y g a i n s and t h e o t h e r p a r t y l o s e s . E x c l u d i n g c o m m i s s i o n c h a r g e s , f u t u r e s t r a d i n g i s a z e r o sum game w i t h g a i n s and l o s s e s a l w a y s summing t o z e r o . H a v i n g t a k e n a p o s i t i o n i n t h e f u t u r e s m a r k e t and a s s u m i n g , as i s u s u a l l y t h e c a s e , t h a t t h e i n d i v i d u a l d o e s n o t i n t e n d t o e f f e c t o r t o a c c e p t d e l i v e r y u n d e r t h e c o n -t r a c t , t h e n t h e i n d i v i d u a l m u s t i n s t r u c t h i s c o m m i s s i o n h o u s e , a t some t i m e p r i o r t o t h e m a t u r a t i o n o f t h e c o n t r a c t , t o t a k e t h e o p p o s i t e a c t i o n w h i c h w i l l c l o s e o u t h i s n e t l o n g o r s h o r t p o s i t i o n . F o r e x a m p l e , i f a s p e c u l a t o r has gone l o n g 5 0 0 0 b u s h e l s o f D e c e m b e r w h e a t by p u r c h a s i n g one c o n t r a c t i n , s a y , A u g u s t , t h e n he m u s t " r e v e r s e " h i s p o s i t i o n by s e l l i n g one D e c e m b e r w h e a t c o n t r a c t p r e f e r a b l y p r i o r t o t h e f i r s t d a y o f t h e d e l i v e r y m o n t h . S i m i l a r l y i f he had e n t e r e d i n t o a s p r e a d p o s i t i o n as d e s c r i b e d a b o v e , he m u s t s u b s e q u e n t l y t a k e a r e v e r s e s p r e a d a c t i o n t o undo h i s c o m m i t m e n t . W h i l e two p a r t i c u l a r p a r t i e s a r e n e c e s s a r y t o e n t e r i n t o a g i v e n c o n t r a c t i t d o e s n o t f o l l o w t h a t t h e c o n t r a c t i s b i n d i n g upon t h o s e p a r t i e s u n t i l t h e y j o i n t l y a r r i v e a t a m u t u a l l y a g r e e a b l e t i m e and c o m m o d i t y p r i c e a t w h i c h t o r e v e r s e t h e i r p o s i t i o n s . Each i n d i v i d u a l may r e v e r s e h i s o r i g i n a l p o s i t i o n a t any t i m e s u b j e c t , o f c o u r s e , t o a d e q u a t e -20-l i q u i d i t y c h a r a c t e r i s t i c s of the m a r k e t . Such a r r i v a l and d e -p a r t u r e of p a r t i e s to c o n t r a c t s in a n y . g i v e n f u t u r e s month r e s u l t s in a c o n t i n u a l l y v a r i a b l e number of "open c o n t r a c t s " f o r t h a t d e l i v e r y month . By d e f i n i t i o n , an open c o n t r a c t i s an o u t s t a n d i n g c o n t r a c t agreement wh ich has been n e i t h e r s e t t l e d by d e l i v e r y nor o f f s e t by r e v e r s e a c t i o n . One open c o n t r a c t i n v o l v e s someone who i s long and someone who i s s h o r t . The summation of such c o n t r a c t s r e p r e s e n t s the "open i n t e r e s t " and t h i s i n f o r m a t i o n i s c o m p i l e d d a i l y by the exchanges as w e l l as by the Commodity Exchange A u t h o r i t y in the case of r e g u l a t e d commod i t i e s . One o t h e r a s p e c t of the b a s i c t r a d i n g p r o c e d u r e s w a r r a n t s r e f e r e n c e . When a t r a d e t a k e s p l a c e and a c o n t r a c t in f u t u r e s i s e n t e r e d i n t o , no money changes hands between the two t r a d e r s i n v o l v e d . The agreement i s a f u t u r e s c o n t r a c t and c a l l s f o r s e t t l e m e n t not on the d a t e i t i s e n t e r e d i n t o but r a t h e r in the d e1 i v e r y -month d e s i g n a t e d by the c o n t r a c t and under r u l e s and p r o c e d u r e s d e s i g n a t e d by the e x c h a n g e . How-e v e r , t h i s does not mean t h a t an i n d i v i d u a l can commence t r a d i n g t h r o u g h a c o m m i s s i o n house w i t h o u t p r e v i o u s l y meet ing c e r t a i n f i n a n c i a l s t i p u l a t i o n s . Each commodity exchange s t i p u l a t e s minimum marg in r e q u i r e m e n t s wh ich the t r a d e r must d e p o s i t w i t h the c o m m i s s i o n house b e f o r e an o r d e r can be a c c e p t e d . W h i l e n o r m a l l y s t i p u l a t e d as an amount per u n i t of the commodity i n v o l v e d , the marg in w i l l t y p i c a l l y be of the o r d e r of 10 per cent or l e s s of the c o n t r a c t v a l u e . The marg in r e q u i r e m e n t - 2 1 -w h i c h , under c e r t a i n c i r c u m s t a n c e s , may take the form of non -cash c o l l a t e r a l , i s i n t e n d e d to g u a r a n t e e c o n t r a c t p e r f o r m a n c e and is h e l d on d e p o s i t by the c o m m i s s i o n house and may not be used f o r any o t h e r p u r p o s e . i n t e r e s t i s n e i t h e r p a i d on the marg in so d e p o s i t e d nor i s i t cha rged on the b a l a n c e of the c o n t r a c t v a l u e . With the marg in r e p r e s e n t i n g such a s m a l l p e r c e n t a g e of the commodity f u t u r e s p r i c e i t i s e v i d e n t t h a t r e l a t i v e l y s m a l l movements in t h a t p r i c e can r e f l e c t as a s i g n i f i c a n t p r o p o r t i o n of the m a r g i n . Shou ld the p r i c e move-ment be in a d i r e c t i o n u n f a v o r a b l e to the i n d i v i d u a l 's c o n -t r a c t p o s i t i o n the r e s u l t may be t h a t h i s marg in i s eroded and he becomes s u b j e c t to a m a i n t e n a n c e marg in c a l l . The i n d i v i d u a l must then i m m e d i a t e l y r e e s t a b l i s h the r e q u i r e d marg in t h r o u g h a d d i t i o n a l payments to the c o m m i s s i o n house or h i s p o s i t i o n under the c o n t r a c t w i l l be e l i m i n a t e d so as to p r o t e c t the c o m m i s s i o n h o u s e . T h i s i s a p r i m a r y reason why such houses may r e q u i r e g r e a t e r than the exchange minimum marg in r e q u i r e m e n t b e f o r e they w i l l a c c e p t a p r o s p e c t i v e c l i e n t . U n l i k e b r o k e r a g e c h a r g e s i n v o l v e d in the t r a d i n g in s e c u r i t i e s , t r a n s a c t i o n c h a r g e s f o r commodity t r a d e s a re not e x p l i c i t l y e x p r e s s e d as a p e r c e n t a g e of the c o n t r a c t v a l u e . R a t h e r , t r a n s a c t i o n f e e s a re l e v i e d in a c c o r d a n c e w i t h a s c h e d u l e e s t a b l i s h e d by the exchange i n v o l v e d . F u r t h e r , the s p e c i f i e d f e e i n c l u d e s both the o p e n i n g and c l o s i n g t r a n s a c t i o n s a round t u r n and i s p a y a b l e o n l y when the c o n t r a c t p o s i t i o n i s c l o s e d o u t . - 22 -HEDGING AND SPECULATION i The s u p p l y - d e m a n d model f o r hedg ing c o n t r a c t s i s se t out f o r m a l l y in Chapte r I I I . However, p r i o r to an e x a m i n a t i o n of the l i t e r a t u r e r e l a t e d to the r i s k premium in commodity f u t u r e s mar -k e t s , i t i s d e s i r a b l e to d i s c u s s t h o s e f a c t o r s wh ich i t i s b e -l i e v e d c o n t r i b u t e to the d e c i s i o n of the hedger and the s p e c u -l a t o r c o n c e r n i n g f u t u r e s c o n t r a c t s . That s p e c u l a t o r s a c c e p t an e lement of r i s k a s s o c i a t e d w i t h p r i c e movements and t h a t hedgers r e c e i v e a degree of p r i c e i n s u r a n c e t h r o u g h the medium of f u t u r e s c o n t r a c t s i s u n i v e r s a l l y a c c e p t e d . That i s , the economic r o l e of commodity markets in s h i f t i n g r i s k to economic u n i t s who are b e t t e r a b l e or more w i l l i n g to a c c e p t t h a t r i s k i s not in q u e s t i o n . What i s in q u e s t i o n i s the t h e o r y as i t r e l a t e s to whether or not hedgers a re r e q u i r e d to pay f o r the s e r v i c e s a f f o r d e d by s p e c u l a t o r s a n d , i f s o , the r e l a t i o n s h i p of the magn i tude of t h a t r i s k premium to the magn i tude or volume of the s e r v i c e s p r o v i d e d . C o n s i d e r f i r s t the t h e o r y of h e d g i n g . A h a n d l e r who s u b s t i t u t e s an unhedged p o s i t i o n f o r one w h e r e i n h i s p o s i t i o n in the spot or a c t u a l commodity i s o f f s e t by a p o s i t i o n in f u t u r e s i s one who s u b s t i t u t e s h i s e x p o s u r e to the r i s k of commodity spot p r i c e movements f o r the r i s k of movements i n the b a s i s the b a s i s i s d e f i n e d as the d i f f e r e n c e between the c u r r e n t spot p r i c e and the c u r r e n t f u t u r e s p r i c e . That i s , i f an i n d i v i d u a l such as a g r a i n merchant h o l d s -23-i n v e n t o r y in a commodity he may e i t h e r s e l l the commodity at the e x i s t i n g spot p r i c e or he may c o n t i n u e t o h o l d the i n v e n t o r y f o r l a t e r s a l e . If he a n t i c i p a t e s t h a t the f u t u r e spot p r i c e w i l l r i s e s u f f i c i e n t l y above the c u r r e n t spot p r i c e to reward him a d e q u a t e l y f o r m a i n t a i n i n g h i s i n v e s t m e n t in the i n v e n t o r y , he w i l l do s o . Assuming he chooses to m a i n t a i n h i s long p o s i t i o n in the a c t u a l commodi ty , the merchant must then d e c i d e whether to h o l d the i n v e n t o r y unhedged or to e n t e r upon the s h o r t s i d e of a f u t u r e s c o n t r a c t whose m a t u r i t y i s r e l a t e d to the t ime he a n t i c i p a t e s l i q u i d a t i n g t h a t i n v e n t o r y . By e n t e r i n g i n t o the f u t u r e s c o n t r a c t , the merchant may f i x the g r o s s r e t u r n on h i s i n v e n t o r y because he may d e l i v e r h i s h o l d i n g a g a i n s t the s h o r t f u t u r e s c o n t r a c t . However, the d e c i s i o n to e n t e r i n t o a f u t u r e s c o n t r a c t i n v o l v e s more d e t a i l e d c o n s i d e r a t i o n s . If subsequent to e n t e r i n g i n t o the f u t u r e s c o n t r a c t , both the c u r r e n t spot p r i c e and the f u t u r e s p r i c e change by the same amount then the h e d g e r ' s p o s i t i o n i s u n a f f e c t e d s i n c e , s h o u l d he at any t ime d i s p o s e of the i n v e n t o r y and c o v e r h i s f u t u r e s c o n t r a c t p o s i t i o n , the g a i n or l o s s on the s a l e of i n v e n t o r y w i l l be equated to h i s l o s s or g a i n , r e s p e c t i v e l y , on the f u t u r e s c o n t r a c t . However, i f , subsequent to e n t e r i n g i n t o the f u t u r e s c o n t r a c t , the spot p r i c e and the f u t u r e s p r i c e do not change by the same amount then a change in the b a s i s magn i tude i s e x p e r i e n c e d . The m e r c h a n t ' s p o s i t i o n w i l l be more or l e s s f a v o r a b l y a f f e c t e d dependent upon the d i r e c t i o n of t h i s c h a n g e . In t u r n , any such change in b a s i s magn i tude -24-may be shown t o be a f u n c t i o n o f t h e v o l u m e o f c o m m e r c i a l s t o c k s e x i s t i n g a t any t i m e . 1 3 H o u t h a k k e r o b s e r v e d t h a t t h e l e v e l o f c o m m e r c i a l s t o c k s i s r e f l e c t e d b o t h i n t h e b a s i s m a g n i t u d e and i n t h e c o r r e l a t i o n b e t w e e n c h a n g e s i n t h e s p o t p r i c e and c h a n g e s i n t h e f u t u r e s p r i c e . As t h e c r o p i s h a r v e s t e d and moves i n t o c o m m e r c i a l h a n d s t h e s p o t p r i c e t e n d s t o f a l l r e l a t i v e t o t h e f u t u r e s p r i c e . The f a r t h e r t h e s p o t p r i c e f a l l s b e l o w t h e f u t u r e s p r i c e t h e g r e a t e r i s t h e b a s i s m a g n i t u d e i n a d i r e c t i o n f a v o r a b l e t o t h e s h o r t h e d g e r . In t h e m i d d l e o f t h e c r o p y e a r t h e s p o t p r i c e t e n d s t o r i s e r e l a t i v e t o t h e f u t u r e s p r i c e w i t h a r e s u l t i n g movement i n t h e b a s i s w h i c h i s l e s s f a v o r a b l e t o t h e l o n g h e d g e r . The c o r r e l a t i o n e f f e c t i s n o t u n i f o r m l y c o m p l e m e n t a r y t o t h e b a s i s e f f e c t . H o u t h a k k e r o b s e r v e s t h a t " c h a n g e s i n t h e s p o t p r i c e a r e c l o s e l y c o r r e l a t e d w i t h c h a n g e s i n t h e f u t u r e s 1 h p r i c e i f f u t u r e s a r e a c l o s e s u b s t i t u t e f o r a c t u a l s . " T h i s i s t h e s i t u a t i o n w h i c h p r e v a i l s when c o m m e r c i a l s t o c k s a r e l a r g e . When s t o c k s a r e s m a l l , f u t u r e s and a c t u a l s a r e no l o n g e r a s c l o s e s u b s t i t u t e s . T h a t i s , t h e a c t u a l s " a r e s p e c i f i c as r e g a r d s gt7ad;e and l o c a t i o n , w h e r e a s f u t u r e s c o n -t r a c t s can be s a t i s f i e d w i t h a more o r l e s s w i d e r a n g e o f g r a d e s and l o c a t i o n s c h o s e n a t t h e s e l l e r ' s o p t i o n . " ^ T h e r e -f o r e , c o r r e l a t i o n w i l l be h i g h i n t h e p o s t h a r v e s t p e r i o d b u t w i l l d e c r e a s e as c o m m e r c i a l s t o c k s a r e p r o g r e s s i v e l y d e p l e t e d - 2 5 -t h r o u g h o u t the c rop y e a r . Hence, c o r r e l a t i o n c o n s i d e r a t i o n s f a v o r both long and s h o r t hedg ing in the m i d d l e of the c r o p y e a r when s t o c k s a r e l a r g e but w i l l be a d e t e r r e n t to both long and s h o r t h e d g i n g in the p r e h a r v e s t p e r i o d and in the post h a r v e s t p e r i o d when c o m m e r c i a l s t o c k s a r e b e i n g r e p l e n i s h e d . Hence, both the b a s i s magn i tude and the c o r r e l a t i o n e f f e c t f a v o r s h o r t hedg ing when c o m m e r c i a l s t o c k s a r e l a r g e but not when they are s m a l l . In the case of long h e d g i n g , the c o r r e l a t i o n e f f e c t i s f a v o r a b l e when c o m m e r c i a l s t o c k s a r e l a r g e but the b a s i s i s n o t . The o p p o s i t e a p p l i e s when commerc ia l s t o c k s are s m a l l . Assuming p r i c e u n c e r t a i n t y per u n i t t ime i s s t a t i o n a r y , the l e v e l of c o m m e r c i a l s t o c k s i s a l s o a measure of the t o t a l i n v e s t m e n t in a g i v e n commodity and hence d e t e r m i n e s the t o t a l r i s k r e q u i r e d to be borne by those who h o l d t i t l e to a g i v e n 1 6 commodi ty . As n o t e d , the h a n d l e r f a c e s the a l t e r n a t i v e of a c c e p t i n g the t o t a l p r i c e r i s k and h o l d i n g h i s s t o c k s of the commodity unhedged , or of a l l o c a t i n g some p o r t i o n of h i s t o t a l i n v e s t m e n t to a l e s s r i s k y a s s e t in the form of hedg ing c o n t r a c t s . G iven the h a n d l e r ' s w i l l i n g n e s s to bear r i s k h i s d e c i s i o n to e n t e r i n t o f u t u r e s c o n t r a c t s w i l l be a f u n c t i o n of h i s t o t a l i n v e s t m e n t in a c t u a l s . C o l l e c t i v e l y , the d e c i s i o n of a l l h a n d l e r s to reduce t h e i r t o t a l r i s k w i l l be r e l a t e d to the l e v e l of commerc ia l s t o c k s p r e v a i l i n g at any t i m e . It i s f u r t h e r s u g g e s t e d in Chapter II I t h a t the h a n d l e r i s i n f l u e n c e d in h i s d e c i s i o n to hedge by c o n s i d e r a t i o n of w e a l t h e f f e c t s . A g a i n r e f e r r i n g to the g r a i n merchant as - 2 6 -an e x a m p l e , he makes an i n i t i a l d e c i s i o n to a l l o c a t e a p o r t i o n of h i s w e a l t h in the form o f i n v e s t m e n t in the r i s k y a s s e t r e p r e s e n t e d by the commodi ty . S h o u l d the spot p r i c e of the commodity s u b s e q u e n t l y r i s e the h a n d l e r w i l l seek to a l l o c a t e some p o r t i o n of h i s r e s u l t i n g w e a l t h inc rement to a l e s s r i s k y a s s e t f o r m . S h o r t hedg ing c o n t r a c t s r e p r e s e n t such an o p p o r -t u n i t y and the l e v e l of s h o r t hedg ing would be e x p e c t e d to i n c r e a s e w i t h an i n c r e a s e in spot p r i c e s . By the same t o k e n , w e a l t h e f f e c t s would be e x p e c t e d to be r e f l e c t e d by a d e c r e a s e in the l e v e l o f s h o r t hedg ing in the f a c e of d e c r e a s e d spot p r i c e s . U n l i k e the h e d g e r , the s p e c u l a t o r ' s p o s i t i o n in a f u t u r e s c o n t r a c t i s not o f f s e t or a f f e c t e d by a p o s i t i o n in the a c t u a l commodi ty . The r e t u r n wh ich the s p e c u l a t o r r e a l i z e s on h i s i n v e s t m e n t in a f u t u r e s c o n t r a c t i s dependent upon the d i r e c t i o n of movement of the f u t u r e s p r i c e subsequent to the i n i t i a t i o n of the f u t u r e s c o n t r a c t . As d i s c u s s e d l a t e r , one v iew contends t h a t , in a f u t u r e s market where net s h o r t hedg ing p r e v a i l s , i t w i l l be n e c e s s a r y f o r the hedger to d e p r e s s the f u t u r e s p r i c e below the e x p e c t e d f u t u r e spot p r i c e in o r d e r to induce the s p e c u l a t o r to e n t e r upon the long s i d e of the c o n t r a c t . Only i f the f u t u r e s p r i c e i s below t h a t wh ich i s e x p e c t e d to p r e v a i l a t c o n t r a c t m a t u r i t y can the s p e c u l a t o r e x p e c t a p o s i t i v e r e t u r n . ^ The o p p o s i t e would a p p l y in a f u t u r e s market dominated by net l ong h e d g i n g . Assuming t h i s v iew to be v a l i d , the h a n d l e r ' s d e c i s i o n to hedge i s a f u n c t i o n -27-of the magn i tude of the inducement he i s r e q u i r e d to o f f e r the s p e c u l a t o r in o r d e r to e n t e r the f u t u r e s c o n t r a c t . For e x a m p l e , the g r a i n m e r c h a n t ' s s u p p l y of s h o r t hedg ing c o n t r a c t s w i l l be a f u n c t i o n of the magn i tude of the r i s k premium he i s r e q u i r e d to o f f e r r e l a t i v e to the p e r c e i v e d v a l u e of the p r i c e i n s u r a n c e h e a c q u i r e s . The c o n s i d e r a t i o n s d e t e r m i n i n g the s p e c u l a t o r ' s demand f o r f u t u r e s c o n t r a c t s a r e l e s s c o m p l e x . As p r e v i o u s l y o b s e r v e d , the s p e c u l a t o r ' s p o s i t i o n in a f u t u r e s c o n t r a c t i s not o f f s e t by a p o s i t i o n in the a c t u a l commodi ty . Hence he i s c o n c e r n e d o n l y w i t h the d i r e c t i o n of movement of the f u t u r e s p r i c e s u b -sequent to i n i t i a t i o n of the c o n t r a c t . In p a r t i c u l a r the long s p e c u l a t o r ' s demand f o r f u t u r e s c o n t r a c t s w i l l i n c r e a s e as a f u n c t i o n of the amount by wh ich the c u r r e n t f u t u r e s p r i c e i s d e p r e s s e d below t h a t w h i c h he e x p e c t s to p r e v a i l at a l a t e r d a t e . That i s , the s p e c u l a t o r ' s d e c i s i o n to e n t e r i n t o a f u t u r e s c o n t r a c t i s dependent o n l y upon the magni tude of the r i s k premium which he p e r c e i v e s i s i n c o r p o r a t e d in the c u r r e n t f u t u r e s p r i c e . / Any c o n s i d e r a t i o n of w e a l t h e f f e c t s as they a f f e c t the s p e c u l a t o r n e c e s s a r i l y r e l a t e to the l e v e l o f h i s i n v e s t m e n t in r i s k y f u t u r e s c o n t r a c t s . No doubt such con s i dp'ra t i ons do i n f l u e n c e the i n d i v i d u a l s p e c u l a t o r in a manner p a r a l l e l to the h a n d l e r . However , i t i s the demand f u n c t i o n of the com-p o s i t e s p e c u l a t i v e p o p u l a t i o n wh ich i s of i n t e r e s t . Viewed in t h i s c o n t e x t , the f r a c t i o n of t o t a l w e a l t h i n v e s t e d by -28-s p e c u l a t o r s in commodity f u t u r e s c o n t r a c t s s u f f i c i e n t l y s m a l l t h a t any w e a l t h e f f e c t s i g n o r e d . DEFINITION OF THE RISK PREMIUM The term " r i s k premium" r e p r e s e n t s a s o u r c e of p o t e n -t i a l m i s u n d e r s t a n d i n g and c o n f u s i o n in any s tudy of commodity m a r k e t s . T h i s p o s s i b i l i t y i s enhanced i f one a t t e m p t s to b u i l d upon or r e l a t e to h i s knowledge of the l i t e r a t u r e of f i n a n c e and e c o n o m i c s . In e x a m i n i n g , f o r e x a m p l e , the c h a r a c t e r i s t i c s of a p a r t i c u l a r i n v e s t m e n t , modern f i n a n c e l i t e r a t u r e seeks to i d e n t i f y 1 as a measure of r i s k the e x t e n t to which an i n v e s t m e n t may t u r n out to be b e t t e r or worse than e x p e c t e d . In p a r t i c u l a the m a t h e m a t i c a l e x p e c t a t i o n of the p r o b a b i l i t y d i s t r i b u t i o n of p o s s i b l e outcomes i s d e f i n e d as the e x p e c t e d v a l u e of the i n v e s t m e n t and the second s t a t i s t i c a l moment about the mean of the p r o b a b i l i t y d i s t r i b u t i o n ( v a r i a n c e , or s t a n d a r d d e v i a t i o n ) may, under f a m i l i a r a s s u m p t i o n s , be taken as the measure of d i s p e r s i o n of the outcome, or r i s k , of the i n v e s t m e n t p o r t f o l i o A s i d e from the p r a c t i c a l d i f f i c u l t i e s of d e t e r m i n i n g the ex ante p r o b a b i l i t y d i s t r i b u t i o n s of outcomes wh ich may be in the mind of the t r a d e r of commodity f u t u r e s , the a d o p t i o n of the term " r i s k premium" in the l i t e r a t u r e of commodity m a r k e t s p r e - d a t e s the q u a n t i f i c a t i o n of r i s k in modern f i n a n c e l i t e r a t u r e . To the e a r l i e r w r i t e r s in the s u b j e c t of commodity m a r k e t s , the r i s k premium d e f i n i t i o n r e l a t e d o n l y i n d i r e c t l y to the v a r i a b i l i t y of p r i c e s . R a t h e r , i t had an e x p l i c i t meaning i s assumed to be can be s a f e l y -29-which i s un ique to commodity m a r k e t s . It was the d i f f e r e n c e between the e x p e c t e d f u t u r e spot p r i c e and the c u r r e n t f u t u r e s p r i c e . The measure c l e a r l y embodies an e x p e c t a t i o n , however d e t e r m i n e d , of f u t u r e spot p r i c e s . But t h i s i s not the a s p e c t of g r e a t e s t i m p o r t a n c e . What i s i m p o r t a n t i s t h a t t h e s e w r i t e r s employed a d e f i n i t i o n of r i s k premium c o m p a t i b l e w i t h t h e i r i n t e r e s t in whether hedgers a re r e q u i r e d t o i n c o r p o r a t e a premium in the c u r r e n t f u t u r e s p r i c e in o r d e r to induce s p e c u -l a t i v e a c t i v i t y . If they a r e , then the c u r r e n t f u t u r e s p r i c e i s a b i a s e d e s t i m a t e of the e x p e c t e d f u t u r e spot p r i c e and the r i s k premium, as d e f i n e d , t a k e s on a f i n i t e v a l u e . In the more r e c e n t l i t e r a t u r e the same t e r m , r i s k premium, has been used in a d i f f e r e n t c o n t e x t . Recent w r i t e r s have sought to c a s t the s tudy of commodity m a r k e t s more c l o s e l y in the mold of modern f i n a n c e l i t e r a t u r e and have e x p r e s s e d ex pos t r a t e s of r e t u r n above the r i s k f r e e r a t e per p e r i o d on f u t u r e s c o n t r a c t s as a measure of the r e t u r n to r i s k , in a manner comparab le to t h a t employed when t r e a t i n g of s e c u r i t i e s and o t h e r r i s k y i n v e s t m e n t s . The p o t e n t i a l m i s u n d e r s t a n d i n g t h e r e f o r e a r i s e s not o n l y because r i s k in commodity m a r k e t s i s u n l i k e t h a t n o r m a l l y u n d e r s t o o d in modern f i n a n c e but a l s o because the term " r i s k premium" has not been c o n s i s t e n t l y a p p l i e d . F u r t h e r , s i n c e the " c l a s s i c " r i s k premium i s e x p r e s s e d as a f i n i t e ( d o l l a r ) v a l u e w h i l e the " m o d e r n " r i s k premium i s e x p r e s s e d as a r a t e of r e t u r n , the two a r e not d i r e c t l y c o m p a r a b l e . In the e x a m i n a t i o n -30-of the l i t e r a t u r e wh ich f o l l o w s i t i s t h e r e f o r e n e c e s s a r y to be c o g n i z a n t of the a p p l i c a b l e meaning of the a u t h o r i n v o l v e d . Carehas been t a k e n in the w r i t i n g to e n s u r e t h a t m i s u n d e r -s t a n d i n g s do not a r i s e . EARLIER THEORIES OF THE RISK PREMIUM 1 8 Three a l t e r n a t i v e t h e o r i e s have been o f f e r e d to e x p l a i n the p r o c e s s of p r i c e d e t e r m i n a t i o n wh ich f o l l o w s in the wake of the i n t e r a c t i o n of hedg ing and s p e c u l a t i v e a c t i v i t y i n f u t u r e s m a r k e t s . Hardy c o n s i d e r e d f u t u r e s m a r k e t s in c o m m o d i t i e s as 19 d i s p l a y i n g many of the a t t r i b u t e s of a g a m b l i n g c a s i n o . Of the c l a s s of s p e c u l a t o r s who come to gamble in t h i s s o c i a l l y a c c e p t a b l e f o r m , by f a r the m a j o r i t y a r e i n d i v i d u a l s who d e r i v e s a t i s f a c t i o n f rom and a r e w i l l i n g to pay f o r r i s k b e a r i n g . In o t h e r w o r d s , s p e c u l a t o r s in commodity markets a r e c o m p r i s e d of a s u b s e t of i n v e s t o r s who can be u n i q u e l y i d e n t i f i e d as r i s k l o v e r s . A c k n o w l e d g i n g t h a t the m a j o r i t y of s p e c u l a t o r s l o s e money, Hardy c o n t e n d s t h a t as l o s s e s d e p l e t e t h e i r r a n k s , o t h e r amateur s p e c u l a t o r s s t a n d ready to r e p l a c e them. Hardy b e l i e v e d t h a t the l a r g e p r o f e s s i o n a l s p e c u l a t o r s r e p r e s e n t the v e r y few s u r v i v o r s of the e x p o s u r e to t h i s p r o c e s s and t h a t , on b a l a n c e , the c o m p e n s a t i o n r e c e i v e d by s p e c u l a t o r s i s z e r o or even n e g a t i v e . E x p r e s s e d a l t e r n a t e l y , Hardy con tends t h a t s p e c u -l a t o r s p r o v i d e i n s u r a n c e a g a i n s t the r i s k o f u n d e s i r a b l e p r i c e a b e r r a t i o n s a t no c o s t , or even at some n e g a t i v e c o s t , to the - 3 1 -hedger who seeks t h i s s e r v i c e . H a r d y ' s v iews i n v i t e c h a l l e n g e . A c k n o w l e d g i n g t h a t some gamblers do d i s p l a y u t i l i t y c h a r a c t e r i s t i c s toward r i s k a k i n to t h o s e Hardy a s c r i b e s to s p e c u l a t o r s , i t i s a l s o r e a d i l y c o n c e i v a b l e t h a t some gamble rs a r e numbered among the t r a n s i e n t component of the s p e c u l a t i v e p o p u l a t i o n . However , the n o t i o n t h a t the s p e c u l a t i v e p o p u l a t i o n i s c o m p r i s e d s o l e l y of gamblers who seek no r i s k premium o f f e n d s the a s s u m p t i o n of r i s k a v e r s i o n in f i n a n c i a l m a r k e t s w h e r e i n the r a t e of r e t u r n demanded would be c o m p a t i b l e w i t h the p e r c e i v e d r i s k . The f u r t h e r n o t i o n t h a t the s p e c u l a t i v e p o p u l a t i o n w i l l pay hedgers f o r the o p p o r t u n i t y of g a m b l i n g appears to be even more v u l -n e r a b l e . I f some such s u b s e t of i n v e s t o r s s h o u l d e x i s t , i t would p r o v i d e an o p p o r t u n i t y f o r o t h e r p e r c e p t i v e r a t i o n a l s p e c u l a t o r s to r e a l i z e r e t u r n s d i s p r o p o r t i o n a t e to the r i s k s i n v o l v e d by e n t e r i n g on the o t h e r s i d e of the m a r k e t . The long s t a n d i n g f o r e c a s t i n g t h e o r y , wh ich has been 20 c i t e d by R o c k w e l l and o t h e r s , c o n s i d e r s t h a t any p o s i t i v e r e t u r n wh ich may be r e a l i z e d by s p e c u l a t o r s i s due e x c l u s i v e l y to t h e i r a b i l i t y to f o r e c a s t p r i c e s a c c u r a t e l y and in com-p e t i t i o n w i t h h e d g e r s . That i s , o n l y t h o s e s p e c u l a t o r s who a r e s u p e r i o r a n a l y s t s r e a l i z e p o s i t i v e r e t u r n s . There i s l i t t l e wh ich can or need be s a i d c o n c e r n i n g t h i s t h e o r y , in the l i g h t of our p r e s e n t p u r p o s e s , s i n c e i t does not g i v e e x p l i c i t c o n s i d e r a t i o n to the q u e s t i o n of whether "32-s p e c u l a t i v e r e t u r n s a r e o r a r e n o t d i r e c t l y l i n k e d t o t h e b e a r i n g o f r i s k . To t h e d e g r e e t h a t t h e K e y n e s - H i c k s - C o o t n e r t h e o r y c i t e d b e l o w e m b o d i e s t r a d e r f o r e c a s t i n g a b i l i t y , t h e f o r e c a s t i n g t h e o r y , p e r s e , i s n o t m u t u a l l y e x c l u s i v e . W i t h o u t d o u b t t h e t h e o r y w h i c h has r e c e i v e d t h e g r e a t e s t a t t e n t i o n i n t h e l i t e r a t u r e and w h i c h has r e c e i v e d r e n e w e d a t t e n t i o n r e c e n t l y i s t h a t o r i g i n a l l y o f f e r e d by 2 tl' K e y n e s . The p o s i t i o n t a k e n by K e y n e s was e n t i r e l y d i f f e r e n t f r o m t h a t o f H a r d y . K e y n e s c o n t e n d e d t h a t t h e s p e c u l a t i v e e x c e s s demand f u n c t i o n f o r f u t u r e s c o n t r a c t s i s l e s s t h a n p e r f e c t l y e l a s t i c and t h a t h e d g e r s a r e r e q u i r e d t o pay s p e c u -l a t o r s a r i s k p r e m i u m i n o r d e r t o i n d u c e them t o a c c e p t t h e p r i c e r i s k . H i s t h e o r y o f n o r m a l b a c k w a r d a t i o n e m b r a c e d t h e c o n c e p t t h a t f u t u r e s p r i c e s a r e downward b i a s e d e s t i m a t e s o f e x p e c t e d f u t u r e s p o t p r i c e s . K e y n e s t h e r e f o r e b e l i e v e d t h a t , on a v e r a g e , t h e s p e c u l a t o r can r e a p s u b s t a n t i a l p r o f i t s by t a k i n g l o n g f u t u r e s c o n t r a c t p o s i t i o n s and r i d i n g up t h e d i f f e r e n t i a l b e t w e e n t h e f u t u r e s p r i c e and t h e e x p e c t e d f u t u r e s p o t p r i c e . K e y n e s c i t e d t h r e e s i t u a t i o n s i n s e t t i n g o u t h i s t h e o r y . When c o m m o d i t y s t o c k s a r e n o r m a l and e x p e c t e d t o r e m a i n s o ( i . e . f u t u r e s p o t p r i c e e x p e c t e d t o be t h e same as t h e c u r r e n t s p o t p r i c e ) , t h e c u r r e n t s p o t p r i c e must e x c e e d t h e c u r r e n t f u t u r e s p r i c e by t h e amount o f t h e r i s k p r e m i u m . When c o m m o d i t y s t o c k s a r e low t h e c u r r e n t s p o t p r i c e e x c e e d s t h e c u r r e n t f u t u r e s -33-p r i c e by an amount g r e a t e r than t h a t d e t e r m i n e d by the r i s k premium but not by an e x a c t l y d e f i n a b l e amount s i n c e the spot p r i c e depends upon the w i l l i n g n e s s of the buyer to pay f o r c u r r e n t c o n s u m p t i o n . F i n a l l y , when commodi ty s t o c k s a re l a r g e , the c u r r e n t f u t u r e s p r i c e exceeds the c u r r e n t - spot p r i c e (a c o n d i t i o n termed a contango) but the f u t u r e s p r i c e must s t i l l be l e s s than the e x p e c t e d f u t u r e spot p r i c e by the amount of the normal b a c k w a r d a t i o n . A major d e f i c i e n c y in the K e y n e s i a n f o r m u l a t i o n was t h a t i t f a i l e d to comprehend the i m p l i c a t i o n s of a h a r v e s t commodity where s t o c k s a re b u i l t up r a p i d l y over a s h o r t p e r i o d and then a r e consumed g r a d u a l l y over an e x t e n d e d p e r i o d . That i s , by c l a i m i n g t h a t c u r r e n t f u t u r e s p r i c e s must a lways be downward b i a s e d e s t i m a t e s of e x p e c t e d f u t u r e spot p r i c e s Keynes o v e r l o o k e d the p r i c e r e l a t i o n s h i p s which may adhere when the f u t u r e s c o n t r a c t b r i d g e s a h a r v e s t p e r i o d . In f a c t , i t was the r e c o g n i t i o n of t h i s i n f l u e n c e wh ich was p r i m a r i l y r e s p o n -s i b l e f o r C o o t n e r ' s subsequent s u g g e s t e d m o d i f i c a t i o n to Keynes 1 t h e o r y . T e s t s wh ich have been c o n d u c t e d by v a r i o u s a u t h o r s have shown the o r i g i n a l form of Keynes 1 t h e o r y to be i n v a l i d . The t h r u s t of the body of l i t e r a t u r e wh ich has ensued has been p r i m a r i l y d i r e c t e d to an a t t e m p t to v e r i f y and/or m o d i f y one or more of the above t h e o r i e s . In p a r t i c u l a r , a t t e n t i o n has been f o c u s s e d on Keynes 1 b a c k w a r d a t i o n t h e o r y and H a r d y ' s g a m b l i n g t h e o r y . -34-As s t a t e d , Keynes 1 p o s i t i o n d i d not r e q u i r e the s p e c u -l a t o r to e x e r c i s e e x p l i c i t judgement c o n c e r n i n g the d i r e c t i o n of f u t u r e p r i c e movements in o r d e r t o r e a l i z e a p o s i t i v e r e t u r n on h i s i n v e s t m e n t over the long run t h a t i s , the s p e c u l a t o r need o n l y take long f u t u r e s c o n t r a c t p o s i t i o n s and r i d e up the d i f f e r e n t i a l between the f u t u r e s p r i c e and the e x p e c t e d f u t u r e 2 2 spot p r i c e . H i c k s g e n e r a l l y agreed w i t h K e y n e s ' b a c k w a r d a t i o n t h e o r y but acknowledged t h a t s p e c u l a t o r s d i s p l a y e x p l i c i t p r i c e e x p e c t a t i o n s . " F u t u r e s p r i c e s a re t h e r e f o r e n e a r l y a l w a y s made p a r t l y by s p e c u l a t o r s , who seek a p r o f i t by b u y i n g f u t u r e s when the f u t u r e s p r i c e i s below the spot p r i c e they e x p e c t to r u l e 2 3 on the c o r r e s p o n d i n g d a t e . " 2 4. L i k e H i c k s , Cootner a c c e p t e d t h a t the s p e c u l a t o r e x -e r c i s e s p r i c e f o r e c a s t i n g a b i l i t y . More p a r t i c u l a r l y , Cootner drew a t t e n t i o n to the s e a s o n a l n a t u r e of the hedg ing a c t i v i t y a s s o c i a t e d w i t h a " h a r v e s t " commodi t y , a c h a r a c t e r i s t i c wh ich Keynes had not s t r e s s e d . Immedia te l y p r i o r to the h a r v e s t , when s t o c k s a re low, s h o r t h e d g i n g w i l l t y p i c a l l y be l i g h t . Indeed , the h e d g i n g p o s i t i o n may be net l o n g . Cootner argued t h a t , f o l l o w i n g the h a r v e s t , s h o r t hedg ing i n c r e a s e s and the r e q u i s i t e long s p e c u l a t i o n i s a t t r a c t e d o n l y i f the f u t u r e s p r i c e , f o r any g i v e n m a t u r i t y , i s p r o g r e s s i v e l y lowered as the volume of h e d g i n g c o n t r a c t s o f f e r e d i s i n c r e a s e d . T h i s p r o c e s s i s v iewed as c o n t i n u i n g u n t i l s h o r t hedg ing r e a c h e s a peak . From t h a t p o i n t u n t i l the next h a r v e s t p e r i o d hedge l i f t i n g r e s u l t s in f u t u r e s p r i c e s s l o w l y r i s i n g . " . . . w e would e x p e c t - 3 5 -the p r i c e to f a l l u n t i l hedged i n v e n t o r i e s reached a peak - a t the peak of the h a r v e s t - and r i s e o n l y a f t e r h e d g e - 1 i f t i n g began to exceed new h e d g i n g . " 2 5 " Hence , Cootner e v i d e n t l y a s s o c i a t e d changes in f u t u r e s p r i c e s w i t h changes in the l e v e l of hedg ing and t h e r e f o r e e x p e c t e d " n o t t h a t f u t u r e s p r i c e s s h o u l d r i s e over the l i f e of the ( f u t u r e s ) c o n t r a c t but t h a t they s h o u l d r i s e a f t e r the peak of hedg ing has p a s s e d . " 2 6 Each of Keynes , H i c k s and Cootner a c c e p t e d t h a t a r i s k premium i s " p a i d " by hedgers to s p e c u l a t o r s v i a the mechanism of the f u t u r e s p r i c e b e i n g a downward b i a s e d e s t i m a t e of the e x p e c t e d f u t u r e spot p r i c e . However , whereas Keynes i m p l i e d t h a t the f u t u r e s p r i c e t r e n d s upward on a v e r a g e t h r o u g h o u t the l i f e of the c o n t r a c t becoming c o i n c i d e n t w i t h spot p r i c e at c o n t r a c t m a t u r i t y , Cootner i n t r o d u c e d a d i s t i n c t m o d i f i c a t i o n or c l a r i f i c a t i o n . A g i v e n f u t u r e s c o n t r a c t i s not n e c e s s a r i l y c o i n c i d e n t w i t h the nominal c rop y e a r . Indeed , t r a d i n g in c e r t a i n f u t u r e s c o n t r a c t s commences p r i o r to and the c o n t r a c t matures subsequent to the h a r v e s t p e r i o d . Hence, the span of the l i f e of a f u t u r e s c o n t r a c t may o v e r l a p a h a r v e s t p e r i o d . Cootner t h e r e f o r e d i d not a s s o c i a t e the r e l a t i o n s h i p between spot and f u t u r e s p r i c e s d i r e c t l y w i t h s u p p l y and demand of the commodi ty , as had Keynes . R a t h e r , Cootner e n v i s a g e d the deman f o r s p e c u l a t i v e s e r v i c e s , as e v i d e n c e d by the l e v e l of hedg ing c o n t r a c t s o f f e r e d , as b e i n g the o p e r a t i v e v a r i a b l e . S i n c e he b e l i e v e d the s p e c u l a t i v e e x c e s s demand f u n c t i o n f o r hedg ing c o n t r a c t s to be l e s s than p e r f e c t l y e l a s t i c Cootner e x p e c t e d -36-f u t u r e s p r i c e s to be i n v e r s e l y r e l a t e d to hedg ing a c t i v i t y and hence the r i s k premium to be d i r e c t l y r e l a t e d to the volume of hedg ing c o n t r a c t s . E x p r e s s e d a l t e r n a t e l y , Cootner i n t r o d u c e d a hedg ing p r e s s u r e h y p o t h e s i s as b e i n g fundamenta l to the d e t e r m i n a t i o n of p o s i t i v e r i s k premiums i n commodity m a r k e t s . At t h i s j u n c t u r e i t must be o b s e r v e d t h a t t h e r e i s a seeming l a c k of c l a r i t y as to the h e d g i n g v a r i a b l e s Cootner deemed t o be of p r i m a r y i m p o r t a n c e . Cootner b e l i e v e d t h a t s p e c u l a t o r s t a k e i n t o a c c o u n t the a l t e r n a t i v e r a t e of r e t u r n per p e r i o d wh ich can be e x p e c t e d e l s e w h e r e ( i . e . when a s s e s s i n g the c u r r e n t f u t u r e s p r i c e r e l a t i o n s h i p to the e x p e c t e d f u t u r e spot p r i c e ) and he b e l i e v e d t h a t the s p e c u l a t o r e x c e s s demand s c h e d u l e f o r h e d g i n g c o n t r a c t s i s l e s s than p e r f e c t l y e l a s t i c so t h a t f u t u r e s p r i c e s v a r y i n v e r s e l y w i t h the l e v e l of net 2 7 s h o r t hedg ing commitments . Yet h i s hedg ing p r e s s u r e t h e o r y , wh ich e n v i s a g e d f u t u r e s p r i c e s as p r o g r e s s i v e l y f a l l i n g as net s h o r t h e d g i n g i n c r e a s e s , and r i s i n g as net s h o r t hedg ing d e c r e a s e s , seems to r e l a t e changes in f u t u r e s p r i c e s to changes in the l e v e l o f net s h o r t h e d g i n g . Some y e a r s l a t e r , Coo tner s e t out a c l a r i f i c a t i o n of h i s hedg ing p r e s s u r e t h e o r y as e x p r e s s e d a b o v e . The key e lement of the c l a r i f i c a t i o n was the r e c o g n i t i o n t h a t no r a t i o n a l s p e c u -l a t o r would buy f u t u r e s c o n t r a c t s u n l e s s h i s e x p e c t e d r e t u r n at l e a s t e q u a l l e d h i s d e s i r e d r e t u r n w h i c h , in most i n s t a n c e s , means t h a t "he w i l l not buy because the p r i c e i s low r e l a t i v e to 2 8 e x p e c t a t i o n s , i f he e x p e c t s i t to become s t i l l lower f i r s t ; - 3 7 -2 q T h e r e f o r e , except f o r e r r o r s of judgement or l ong term c a p i t a l g a i n p r o b l e m s ^ each f u t u r e s h o u l d be e x p e c t e d to r i s e from the t i m e hedg ing in the f u t u r e becomes net s h o r t s h o r t hedg ing p r e s s u r e s h o u l d not be e x p e c t e d to d e p r e s s p r i c e s d u r i n g h a r v e s t . Only i f the h a r v e s t hedg ing g r a d u a l l y s h i f t s f rom 1 i q u i d a t i o n of long hedges to s h o r t hedg ing s h o u l d f u t u r e s 3 1 p r i c e s be e x p e c t e d t o d e c l i n e d u r i n g the h a r v e s t . " W h i l e Cootner contended t h a t h i s e a r l i e r s t a t e m e n t of the t h e o r y had been c o r r e c t , the above c l a r i f i c a t i o n would appear to have i n t r o d u c e d a v e r y d i s t i n c t m o d i f i c a t i o n . The l a t e r v e r s i o n of the t h e o r y r e j e c t s the n o t i o n t h a t hedg ing p r e s s u r e w i l l r e s u l t i n , s a y , p r o g r e s s i v e l y i n c r e a s i n g m a g n i -tudes o f net s h o r t h e d g i n g in a g i v e n f u t u r e s c o n t r a c t c a u s i n g p r o g r e s s i v e l y lower c u r r e n t f u t u r e s p r i c e s in t h a t c o n t r a c t . I n s t e a d , the l a t e r v e r s i o n of the t h e o r y a c k n o w l e d g e s t h a t , under c o n d i t i o n s of net s h o r t h e d g i n g , f u t u r e s p r i c e s w i l l n o r m a l l y r i s e o v e r t i m e . In t u r n , the r a t e of i n c r e a s e in the f u t u r e s p r i c e w i l l depend on the r a t e of d e c r e a s e in the l e v e l o f net s h o r t h e d g i n g . Thus C o o t n e r 1 s l a t e r t h e o r y i s c o n s i s t e n t w i t h the e x i s t e n c e of r a t i o n a l s p e c u l a t o r s , whereas h i s e a r l i e r t h e o r y r e q u i r e d i r r a t i o n a l s p e c u l a t o r s to be long in f u t u r e s 32 w h i l e f u t u r e s p r i c e s were f a l l i n g . The m o d i f i c a t i o n a l s o made c l e a r t h a t Cootner r e l a t e d changes in f u t u r e s p r i c e s to the l e v e l o f net s h o r t h e d g i n g and t h a t i t was the l a t t e r wh ich he v iewed as the c r i t i c a l hedg ing v a r i a b l e . - 3 8 -ln summary, H a r d y ' s c o n t e n t i o n t h a t the e x p e c t e d r i s k premium i s z e r o or even n e g a t i v e i s i n c o m p a t i b l e w i t h the a s s u m p t i o n of r i s k a v e r s i o n in f i n a n c i a l m a r k e t s . N e i t h e r is*, the K e y n e s - H i c k s t h e o r y , wh ich con tends t h a t the f u t u r e s p r i c e i s a downward b i a s e d e s t i m a t e of the f u t u r e e x p e c t e d spot p r i c e such t h a t the e x p e c t e d r i s k premium i s p o s i t i v e , a c c e p t a b l e as s t a t e d s i n c e i t d i s r e g a r d s the i m p l i c a t i o n s of h a r v e s t c o m m o d i t i e s and does not comprehend the s t a t e when the h e d g i n g p o s i t i o n i s net l o n g . The e a r l i e r v e r s i o n of C o o t n e r ' s t h e o r y s u p p o r t e d the b a s i c K e y n e s - H i c k s p o s i t i o n but drew a t t e n t i o n to the i m p l i c a t i o n s o f h a r v e s t c o m m o d i t i e s on the movements of f u t u r e s p r i c e s . In p a r t i c u l a r , Cootner a rgued t h a t the s p e c u l a t i v e demand f u n c t i o n i s l e s s than p e r f e c t l y e l a s t i c and t h a t the r i s k premium i s a f u n c t i o n of the change in net s h o r t h e d g i n g . The t h e o r y o f f e r e d in t h i s t h e s i s a l s o s u g g e s t s t h a t the r i s k premium may be r e l a t e d t o the change in net s h o r t h e d g i n g but in manner q u i t e u n l i k e t h a t s u g g e s t e d by C o o t n e r . In the l a t e r v e r s i o n of h i s t h e o r y , C o o t n e r m o d i f i e d h i s p o s i t i o n a n d , w h i l e m a i n t a i n i n g t h a t the s p e c u l a t i v e demand f u n c t i o n i s l e s s than p e r f e c t l y e l a s t i c , s u g g e s t e d t h a t the r a t e of r e t u r n i s a f u n c t i o n of the l e v e l  of net s h o r t h e d g i n g . T h i s l a t t e r p o s i t i o n i s c o m p a t i b l e w i t h the e x i s t e n c e of r a t i o n a l , r i s k a v e r s e s p e c u l a t o r s . - 3 9 ; -EMPIRICAL RESEARCH In the p r e v i o u s s e c t i o n the term " r i s k premium" was c o n s i s t e n t l y employed in a c c o r d a n c e w i t h i t s " c l a s s i c " d e f i n i -t i o n t h a t i s , e x p e c t e d f u t u r e spot p r i c e minus c u r r e n t f u t u r e s p r i c e . However, in c o n t r i b u t i n g to the body of em-p i r i c a l r e s e a r c h , a l l of the a u t h o r s have not found i t a p p r o p r i a t e to c o n f o r m to t h i s c l a s s i c d e f i n i t i o n . In p a r -t i c u l a r , Cootner and T e l s e r have employed the c l a s s i c d e f i n i -t i o n w h i l e Dusak has used the " m o d e r n " d e f i n i t i o n w h e r e i n r i s k premium means the r a t e of r e t u r n per p e r i o d above the r i s k f r e e r a t e . To e n s u r e c l a r i t y in t h i s s e c t i o n the terms " c l a s s i c r i s k premium" and "modern r i s k premium" a r e used to the degree n e c e s s a r y to a v o i d m i s u n d e r s t a n d i n g . Except in the case of s o - c a l l e d l o p s i d e d m a r k e t s , e m p i r i c a l r e s e a r c h to date has not e s t a b l i s h e d c o n c l u s i v e l y whether or not hedgers a re r e q u i r e d to pay s p e c u l a t o r s f o r the s e r v i c e s of r e d u c t i o n in the p r i c e r i s k wh ich they p r o v i d e . 3 3 T e l s e r ; was one of the r e s e a r c h e r s who sought to t e s t the b a s i c K e y n e s i a n p o s i t i o n t h a t t h e r e i s an upward t r e n d in f u t u r e s p r i c e s as the f u t u r e s c o n t r a c t approaches m a t u r i t y . In o r d e r to a t t e m p t to a b s t r a c t f rom any u n d e r l y i n g p r i c e t r e n d s , he s u b d i v i d e d the 1 9 2 6 - 5 4 p e r i o d i n t o s u b p e r i o d s c o m p r i s i n g y e a r s of i ) r i s i n g p r i c e s , i i ) s t a b l e p r i c e s , and i i i ) f a l l i n g p r i c e s . He then r e c o r d e d the s i g n of m o n t h - t o - m o n t h f u t u r e s p r i c e changes and sought to d e t e r m i n e i f t h e r e was e v i d e n c e of - A O -s u p p o r t f o r the K e y n e s - H i c k s t h e o r y . He found no such s u p p o r t and hence a c c e p t e d the h y p o t h e s i s of no t r e n d in f u t u r e s p r i c e s . R e c o g n i z i n g the p a r t i c u l a r t h e o r y which T e l s e r w i s h e d to c o n s i d e r , h i s c o n c l u s i o n c o n c e r n i n g the r e s u l t s of the t e s t of the n u l l h y p o t h e s i s of no t r e n d in f u t u r e s p r i c e s as they approach t h e i r m a t u r i t y da tes was v a l i d . However , l i m i t a t i o n s of the t e s t must a l s o be r e c o g n i z e d . That i s , w h i l e the t e s t p r o v i d e d e v i d e n c e damaging to the o r i g i n a l Keynes 1 p o s i t i o n , i t d i d not e x p l i c i t l y examine the q u e s t i o n of the p r e s e n c e or absence of a r i s k premium.. For e x a m p l e , had a comparab le t e s t been a p p l i e d to c u r r e n t s p o t p r i c e c h a n g e s , f o r the sample of s t a b l e p r i c e y e a r s , the r e s u l t s would v e r y l i k e l y have s u g g e s t e d t h a t a h y p o t h e s i s of no t r e n d in s p o t p r i c e s c o u l d not be r e -j e c t e d . But c l e a r l y such a t e s t does not imply t h a t the long h a n d l e r i s not compensated f o r h i s s u p p l y of s t o r a g e and h a n d l i n g of the commodi ty . N e v e r t h e l e s s , T e l s e r appeared to a c c e p t such an i m p l i c a t i o n c o n c e r n i n g the r i s k premium in h i s f u r t h e r a n a l y s i s . -T e l s e r b e l i e v e d t h a t the number of s p e c u l a t o r s e n t e r i n g a f u t u r e s market was s u f f i c i e n t to b i d away any d i f f e r e n c e between the e x p e c t e d spot p r i c e and the c u r r e n t f u t u r e s p r i c e w i t h the r e s u l t t h a t the c l a s s i c r i s k premium i s z e r o and s p e c u -l a t i v e s e r v i c e s a r e a v a i l a b l e to hedgers at no c o s t . In o t h e r w o r d s , T e l s e r b e l i e v e d t h a t the s p e c u l a t o r s ' e x c e s s demand c u r v e f o r f u t u r e s c o n t r a c t s i s h i g h l y e l a s t i c such t h a t the c u r r e n t f u t u r e s p r i c e tends to equa l the spot p r i c e r e a l i z e d at m a t u r i t y of the f u t u r e s c o n t r a c t . - 4 i : -ln the absence of f u t u r e s t r a d i n g , T e l s e r argued t h a t the f i r m " h o l d s an amount of s t o c k s such t h a t the net m a r g i n a l c o s t of h o l d i n g t h e s e s t o c k s e q u a l s the e x p e c t e d change in t h e i r p r i c e d u r i n g the t ime they a r e h e l d " where the net m a r g i n a l c o s t i s equa l to the m a r g i n a l c o s t of s t o r a g e l e s s 3 5 the m a r g i n a l c o n v e n i e n c e y i e l d . In the p r e s e n c e of f u t u r e s t r a d i n g , i f the e x p e c t e d spot p r i c e e q u a l s the c u r r e n t f u t u r e s p r i c e t h e n , T e l s e r s u g g e s t e d , the f i r m ' s s t o c k h o l d i n g s c h e d u l e i s r e l a t e d , not to the e x p e c t e d p r i c e change per s e , but to the d i f f e r e n c e s in p r i c e s of f u t u r e s c o n t r a c t s of s u c c e s s i v e matu r i t i e s . Hence, f o r e x a m p l e , the h i g h e r the f u t u r e s p r i c e r e l a -t i v e to the c u r r e n t spot p r i c e , the g r e a t e r the amount of commo-d i t y s t o c k s the long h a n d l e r w i l l be induced to h o l d and hence the g r e a t e r the number of s h o r t hedg ing c o n t r a c t s he w i l l seek to e n t e r i n t o to p r o t e c t h i m s e l f a g a i n s t the p r i c e r i s k . For the s h o r t h a n d l e r the h i g h e r the f u t u r e s p r i c e r e l a t i v e t o the c u r r e n t spot p r i c e the l e s s a t t r a c t i v e i s a long hedge and the s m a l l e r the number of such f u t u r e s c o n t r a c t s he w i l l buy . "The e x c e s s s u p p l y of f u t u r e s c o n t r a c t s , b e i n g the o f f e r s of f u t u r e s by the s h o r t hedgers l e s s the demand f o r c o n t r a c t s by the long h e d g e r s , has a p o s i t i v e s l o p e because an i n c r e a s e in the f u t u r e s p r i c e i n c r e a s e s the net o f f e r s of f u t u r e s c o n t r a c t s by the h a n d l e r s . " 3 6 Us ing d a t a f o r c o t t o n and w h e a t , T e l s e r r e g r e s s e d a f u n c t i o n of the d i f f e r e n c e between f u t u r e s p r i c e s of s u c c e s s i v e - im-m a t u r i t i e s on the l o g a r i t h m of each of commodity s t o c k s and c o n s u m p t i o n , and on the f r a c t i o n of t o t a l s t o c k s h e l d by the government under p r i c e s u p p o r t p r o g r a m s . W i t h the e x c e p t i o n of one of the wheat e q u a t i o n s , the c o e f f i c i e n t of the commodity s t o c k v a r i a b l e was p o s i t i v e and T e l s e r c o n -c l u d e d s u p p o r t f o r the h y p o t h e s i s t h a t the s l o p e of the e x c e s s s u p p l y f u n c t i o n f o r f u t u r e s c o n t r a c t s i s p o s i t i v e . In summary, T e l s e r c o n c l u d e d t h a t s i n c e h i s t e s t s showed t h a t f u t u r e s p r i c e s d i s p l a y no upward t r e n d as they approach m a t u r i t y , f u t u r e s p r i c e s t h e r e f o r e equa l the e x p e c t e d spot p r i c e and hedgers can reduce p r i c e r i s k s at l i t t l e or no c o s t , a t l e a s t in those f u t u r e s markets where t h e r e i s adequate s p e c u l a t i v e p a r t i c i p a t i o n . Hav ing c o n c l u d e d t h a t the e x p e c t e d p r i c e changes equa l the d i f f e r e n c e in f u t u r e s p r i c e s of s u c c e s s i v e m a t u r i t i e s , T e l s e r i n t e r p r e t e d t h a t the r e g r e s s i o n e q u a t i o n s r e l a t i n g s t o c k s to f u t u r e s p r i c e s o f f e r e d s u p p o r t f o r the m a r g i n a l c o n v e n i e n c e y i e l d t h e o r y . Cootner c h a l l e n g e d T e l s e r on both t h e o r e t i c a l and em-3 7 p i r i c a l g r o u n d s . By a d o p t i n g an e x c e s s demand f u n c t i o n wh ich was h i g h l y , indeed i n f i n i t e l y , e l a s t i c T e l s e r had assumed t h a t s p e c u l a t o r s were w i l l i n g to p l a y f o r the l o v e of the game, t h e r e b y e l i m i n a t i n g any p o s s i b i l i t y of p o s i t i v e r e t u r n s to the -43-s p e c u l a t o r s and e n s u r i n g e q u a l i t y of the f u t u r e s p r i c e and the e x p e c t e d spot p r i c e . I f , i n s t e a d , i t i s assumed t h a t s p e c u -l a t o r s r e q u i r e a f i n i t e r e t u r n per p e r i o d t h e n , Cootner s u g g e s t e d , the demand f u n c t i o n f o r f u t u r e s c o n t r a c t s i s l e s s than p e r f e c t l y e l a s t i c and the f u t u r e s p r i c e i s not n e c e s s a r i l y equa l to the e x p e c t e d s p o t p r i c e . In the case of a h a r v e s t commodi ty , the volume of s t o c k s and hence the volume of s h o r t hedg ing c o n t r a c t s o f f e r e d grows r a p i d l y f o l l o w i n g a h a r v e s t . If the demand f o r f u t u r e s c o n t r a c t s i s l e s s than p e r f e c t l y e l a s t i c , i t may then be n e c e s s a r y to d e p r e s s f u t u r e s p r i c e s i n o r d e r to induce the r e q u i r e d s p e c u l a t i v e p a r t i c i p a t i o n . As s t a t e d p r e v i o u s l y , Cootner t h e r e f o r e e x p e c t e d " t h e p r i c e to f a l l u n t i l hedged i n v e n t o r i e s reached a peak and r i s e o n l y a f t e r hedge - 1 i f t i n g j 0,0 began to exceed new hedg J rig'.' '*' Hence, i t was not n e c e s s a r y t h a t f u t u r e s p r i c e s s h o u l d r i s e over the l i f e of the c o n t r a c t , as s t a t e d by Keynes and t e s t e d by T e l s e r , " b u t t h a t they s h o u l d 3 Q r i s e a f t e r the peak of hedg ing has p a s s e d . " J J C o n t r a r y to the T e l s e r p o s i t i o n , C o o t n e r ' s f o r m u l a t i o n p e r m i t s the p o s s i b i l i t y of p o s i t i v e r a t e s of r e t u r n b e i n g r e a l i z e d by s p e c u l a t o r s . In h i s e m p i r i c a l w o r k , Cootner sought to t e s t the v a l i d i t y of h i s hedg ing p r e s s u r e t h e o r y of f u t u r e s p r i c e movements. S i n c e h i s purpose was to d e t e r m i n e not whether s p e c u l a t o r s do make money but r a t h e r whether f u t u r e s p r i c e movements a re such t h a t s p e c u l a t o r s can make money, C o o t n e r ' s t e s t e n t a i l e d assuming t h a t a s p e c u l a t o r e s t a b l i s h e d a p o s i t i o n in wheat f u t u r e s in May and c a r r i e d t h a t p o s i t i o n th rough to the f o l l o w i n g A p r i l . Us ing the same group of " s t a b l e p r i c e y e a r s " which T e l s e r had p r e v i o u s l y s e l e c t e d , Cootner found t h a t , on the a v e r a g e , f u t u r e s p r i c e s f e l l f rom May to O c t o b e r -November, and rose f rom then u n t i l the f o l l o w i n g May. He t h e r e f o r e c o n c l u d e d t h a t i n c r e a s e d net s h o r t hedg ing in the p o s t h a r v e s t p e r i o d i s accompanied by d e c r e a s e d f u t u r e s p r i c e s and t h a t , as i n v e n t o r i e s are consumed and hedges a r e l i f t e d , the f u t u r e s p r i c e s r i s e . Cootner d i d not e x p l i c i t l y i n c l u d e the magni tude of the net h e d g i n g p o s i t i o n in h i s a n a l y s i s but he d i d o b s e r v e t h a t i f " v i s i b l e s u p p l i e s " (a measure of c o m m e r c i a l s t o c k s of the commodity) had been c o n s i d e r e d r a t h e r than s i m p l y c o n s t r u c t i n g an average month l y p r i c e index of wheat f u t u r e s f o r r e f e r e n c e as he had done , the s e a s o n a l p a t t e r n was even more a p p a r e n t . In the e n s u i n g exchange between the two a u t h o r s , T e l s e r acknowledged the p o s s i b i l i t y of an upward t r e n d in f u t u r e s p r i c e s and hence of a f i n i t e c l a s s i c r i s k premium. However , he found l i t t l e s u p p o r t f o r C o o t n e r 1 s hedg ing p r e s s u r e h y p o t h e s i s . C o o t n e r 1 s p o s i t i o n remained b a s i c a l l y u n a l t e r e d . In commenting on C o o t n e r 1 s w o r k , Gray p o i n t e d out t h a t in f o u r of the ten s t a b l e p r i c e y e a r s s t u d i e d , the May f u t u r e s p r i c e a c t u a l l y d e c l i n e d over the D e c e m b e r - A p r i1 p e r i o d r a t h e r than r i s i n g as the o v e r a l l ave rage c i t e d by C o o t n e r . Indeed, ' Gray s u g g e s t e d t h a t C o o t n e r ' s p r i c e i n d e x , t o g e t h e r w i t h the p a r t i c u l a r c o m b i n a t i o n of p r i c e s wh ich had p r e v a i l e d as a t -ks-November 30 in the s t a b l e y e a r s s t u d i e d , had combined to i n -t r o d u c e a l a r g e b i a s i n t o the r e s u l t s . F u r t h e r , and o t h e r than "a rough c o r r e s p o n d e n c e in the t i m i n g of the peak of hedg ing and the p r i c e t r o u g h " , Gray r e p o r t e d l i t t l e c o r r e s p o n d e n c e between changes i n v i s i b l e s u p p l i e s o f the commodity and changes in C o o t n e r ' s p r i c e i n d e x . L i k e C o o t n e r , Gray e x p r e s s e d r e s e r -v a t i o n c o n c e r n i n g T e l s e r ' s i s o l a t i o n of and c o n c e n t r a t i o n on the s t a b l e p r i c e y e a r s and e x p r e s s e d s u p p o r t of a l o n g e r sample p e r i o d . To r e i t e r a t e , in h i s o r i g i n a l p r e s e n t a t i o n of the h e d g i n g p r e s s u r e t h e o r y , Coo tner had s t a t e d t h a t he e x p e c t e d f u t u r e s p r i c e s to f a l l as net s h o r t hedg ing i n c r e a s e d and then to r i s e as the h e d g i n g " p r e s s u r e " was l i f t e d . At a l a t e r d a t e , however , Cootner acknowledged t h a t such an e x p e c t a t i o n c o n c e r n i n the movement of f u t u r e s p r i c e s i s i n c o n s i s t e n t w i t h r a t i o n a l b e -h a v i o u r on the p a r t of s p e c u l a t o r s . That i s , no r a t i o n a l s p e c u l a t o r w i l l buy a f u t u r e s c o n t r a c t , r e g a r d l e s s of the p r e s e n t f u t u r e s p r i c e , i f he e x p e c t s t h a t p r i c e to f a l l s t i l l f u r t h e r r e l a t i v e to the e x p e c t e d f u t u r e s p o t p r i c e . Hence e x c e p t , f o r e x a m p l e , as s p e c u l a t o r s might e r r o n e o u s l y judge the l e v e l to wh ich net s h o r t hedg ing w i l l r i s e in the pos t h a r v e s t p e r i o d and t h e r e f o r e the f u t u r e s p r i c e wh ich w i l l be r e q u i r e d to c l e a r the m a r k e t , i t i s not w a r r a n t e d to e x p e c t a phenomenon of hedg ing p r e s s u r e in the form Cootner had o r i g i n -a l l y s u g g e s t e d . T h e r e f o r e , e x c e p t as a g r a d u a l s h i f t f rom net long to net s h o r t h e d g i n g may cause a d e c l i n e d u r i n g the h a r v e s t -46-p e r i o d , f u t u r e s p r i c e s must r i s e from the t ime t h a t hedg ing in the f u t u r e s c o n t r a c t becomes net s h o r t . A l s o i n a more r e c e n t p a p e r , T e l s e r r e p o r t e d on a d d i t i o n a l work , two a s p e c t s of wh ich a r e d i r e c t l y r e l a t e d to the p r e s e n t s t u d y . In a f u r t h e r e x a m i n a t i o n of the o r i g i n a l Keynes 1 p o s i t i o n , T e l s e r examined whether f u t u r e s p r i c e s tend to r i s e over the l i f e of a f u t u r e s c o n t r a c t by s t u d y i n g the movement of a s e a s o n a l p r i c e index over the 1952-62 p e r i o d of c o m p a r a t i v e l y s t a b l e g e n e r a l p r i c e l e v e l s . Of the t h r e e c o m m o d i t i e s s t u d i e d , soybean f u t u r e s d i s p l a y e d an upward s e a s o n a l and c o r n f u t u r e s a downward s e a s o n a l w h i l e the s e v e r a l wheat f u t u r e s c o n t r a c t s d i s p l a y e d mixed r e s u l t s . T e l s e r i n -t e r p r e t e d these r e s u l t s , wh ich e x p l i c i t l y d i s r e g a r d e d h a r v e s t e f f e c t s on hedg ing a c t i v i t y , as e v i d e n c e a g a i n s t the Keynes 1 h y p o t h e s i s . As in h i s o r i g i n a l p a p e r , he f u r t h e r c o n c l u d e d on the b a s i s of t h i s t e s t t h a t f u t u r e s p r i c e s can be r e g a r d e d as the market e x p e c t a t i o n of subsequent spot p r i c e s , a c o n c l u s i o n w h i c h , as noted p r e v i o u s l y , does not appear to be w a r r a n t e d by the n a t u r e of the t e s t . S e c o n d l y , T e l s e r sought to d e t e r m i n e whether an i n c r e a s e i n s h o r t h e d g i n g d e p r e s s e s f u t u r e s p r i c e s by r e l a t i n g the s e a s o n a l p a t t e r n of hedg ing commitments to the s e a s o n a l of f u t u r e s p r i c e s . In an a t t e m p t to remove " y e a r e f f e c t s " , T e l s e r d e f l a t e d f u t u r e s p r i c e s and h e d g i n g commitments by t h e i r r e s -p e c t i v e a v e r a g e s over the l i f e of the r e l a t e d c o n t r a c t and - 4 7-o b t a i n e d the s e a s o n a l index f o r each quote as the a v e r a g e of the d e f l a t e d quotes over the y e a r s in the s a m p l e . C o n t r a r y to the e x p e c t a t i o n s of the h e d g i n g p r e s s u r e t h e o r y , the r e -g r e s s i o n of the s e a s o n a l p r i c e index on the s e a s o n a l hedg ing i n d i c e s d i s p l a y e d a p o s i t i v e s h o r t hedg ing c o e f f i c i e n t and a n e g a t i v e long hedg ing c o e f f i c i e n t . T e l s e r i n t e r p r e t e d t h e s e f i n d i n g s as b e i n g i n c o n s i s t e n t w i t h the h e d g i n g p r e s s u r e h y p o t h e s i s but c o n s i s t e n t w i t h the h y p o t h e s i s t h a t s p e c u -l a t o r s " p r e f e r r i s k and a r e w i l l i n g to pay f o r i n c u r r i n g r i s k " • and w i t h the h y p o t h e s i s t h a t " s h o r t hedgers i n c r e a s e the amount of s h o r t hedg ing the l a r g e r t h e i r e x p e c t e d r e t u r n from s h o r t h e d g i n g . 1 " As in h i s e a r l i e r s t u d i e s , T e l s e r c o n c l u d e d t h a t " t h e f u t u r e s p r i c e can be c o n s i d e r e d as an u n b i a s e d p r e d i c t o r of the subsequent spot p r i c e . In d e s i g n i n g h i s s e a s o n a l p r i c e i n d e x , T e l s e r s t a t e d t h a t i t "ought to a c c o u n t f o r changes of the annual a v e r a g e p r i c e ( i . e . of the p a r t i c u l a r f u t u r e s c o n t r a c t ) and ought not to be too much o b s c u r e d by the i r r e g u l a r q u o t e - t o - q u o t e p r i c e 46 c h a n g e s " " wh ich t y p i c a l l y o c c u r . In s e e k i n g to e l i m i n a t e the i n f l u e n c e of year e f f e c t s i t i s not a p p a r e n t to what degree d i s t o r t i o n s may have been i n t r o d u c e d in the r e g r e s s i o n r e -l a t i o n s h i p s . Indeed , p a r t i c u l a r l y i f the modern r i s k premium d e f i n i t i o n i s e m p l o y e d , i t would appear to be p r e f e r a b l e to employ the raw d a t a s e r i e s d i r e c t l y as i s done in the p r e s e n t s t u d y . By so d o i n g , r e g r e s s i o n a n a l y s i s p e r m i t s d i r e c t assessment of s e m i - m o n t h l y r e a l i z e d r a t e s of r e t u r n as a -48-f u n c t i o n o f h e d g i n g l e v e l s o r c h a n g e s i n h e d g i n g l e v e l s . 47 More r e c e n t l y D u s a k , u s i n g t h e m o d e r n r i s k p r e m i u m d e f i n i t i o n , a d o p t e d a d i f f e r e n t a n a l y t i c a l a p p r o a c h i n an a t t e m p t t o r e s o l v e t h e c o n f l i c t . R e a s o n i n g t h a t f u t u r e s m a r k e t s a r e no d i f f e r e n t i n p r i n c i p l e f r o m m a r k e t s f o r o t h e r r i s k y a s s e t s , Dusak e m p l o y e d a f o r m o f t h e c a p i t a l a s s e t p r i c i n g m o d e l w h e r e i n s e m i - m o n t h l y h o l d i n g p e r i o d r i s k p r e m i u m s f o r e a c h o f w h e a t , c o r n and s o y b e a n s w e r e r e g r e s s e d on s e m i - m o n t h l y r e t u r n s o f a m a r k e t i n d e x o f t o t a l w e a l t h . In t h i s m o d e l , t h e S&P 500 I n d e x was u s e d a s a p r o x y f o r t o t a l w e a l t h . Dusak f o u n d t h a t , f o r t h e p e r i o d 1952-67, t h e a v e r a g e s e m i - m o n t h l y h o l d i n g p e r i o d r e t u r n f o r e a c h o f t h e t h r e e c o m m o d i t i e s was c l o s e t o z e r o o r n e g a t i v e . In t h e r e s u l t s o b t a i n e d f r o m t h e c a p i t a l a s s e t p r i c i n g m o d e l , t h e a and g v a l u e s f o r e a c h o f t h e c o m m o d i t i e s w e r e f o u n d n o t t o be s t a t i s t i c a l l y d i f f e r e n t f r o m z e r o . Dusak c o n s i d e r e d h e r f i n d i n g s p a r t i c u l a r l y d a m a g i n g t o t h e K e y n e s i a n t h e o r y . S i n c e t h e s y s t e m a t i c r i s k m e a s u r e s w e r e f o u n d t o be v e r y c l o s e t o z e r o and " s i n c e t h e mean r e t u r n s ( w h i c h a r e a c t u a l l y r i s k p r e m i u m s ) a r e a l s o v e r y c l o s e t o z e r o , we may c o n c l u d e t h a t t h e d a t a on c o m m o d i t y f u t u r e r e t u r n s d u r i n g o u r s a m p l e p e r i o d c o n f o r m b e t t e r t o t h e c a p i t a l m a r k e t s mode l t h a n t o t h e K e y n e s i a n m o d e l . In f a c t , t h e c o n t e s t i s n o t e v e n c l o s e . " -us-D u s a k 1 s f i n d i n g t h a t the ave rage s e m i - m o n t h l y h o l d i n g p e r i o d r e t u r n s ove r a long t ime p e r i o d a re not s i g n i f i c a n t l y d i f f e r e n t from z e r o o f f e r s e v i d e n c e a g a i n s t Keynes 1 t h e o r y but i t does not a d d r e s s the Cootner v e r s i o n of Keynes 1 t h e o r y . The f i n d i n g t h a t the s y s t e m a t i c r i s k of i n d i v i d u a l c o m m o d i t i e s r e l a t i v e to the S&P Index i s z e r o does p r o v i d e a new p e r s p e c t i v e . However , one would not c o n t e n d t h a t the S&P Index i s n e c e s s a r i l y a s a t i s f a c t o r y index f o r t o t a l w e a l t h . A l s o , the f a c t t h a t the p r i c e movements of i n d i v i d u a l c o m m o d i t i e s a r e u n c o r r e l a t e d w i t h an index of s t o c k p r i c e movements does not r e s o l v e the r i s k premium q u e s t i o n or the r e l a t e d q u e s t i o n of whether commodity f u t u r e s market s p e c u -l a t o r s a r e or a re not r i s k a v e r s e . What can be s a i d i s t h a t f i n d i n g t h a t c e r t a i n commodity f u t u r e s c o n t r a c t s d i s p l a y z e r o b e t a c o e f f i c i e n t s i d e n t i f i e s them as a p a r t i c u l a r t ype of r i s k y a s s e t wh ich i s a v a i l a b l e f o r i n c l u s i o n in a p o r t f o l i o o t h e r w i s e c o m p r i s e d of r i s k y s e c u r i t i e s . In summary, i t i s g e n e r a l l y agreed t h a t commodity f u t u r e s markets s e r v e the economic f u n c t i o n of s h i f t i n g an e lement of r i s k , f rom the commodity h a n d l e r s to an economic u n i t , the s p e c u l a t o r s , wh ich i s b e t t e r a b l e or more w i l l i n g to a c c e p t t h a t r i s k . The answer to the q u e s t i o n o f whether hedgers a r e r e q u i r e d to pay s p e c u l a t o r s f o r the s e r v i c e s of r e d u c t i o n in the p r i c e r i s k remains u n r e s o l v e d . E x p r e s s e d a l t e r n a t e l y , the q u e s t i o n as to whether the commodity f u t u r e s r -50 • market s p e c u l a t i v e p o p u l a t i o n i s c o m p r i s e d of gamble rs such t h a t the e x c e s s demand f u n c t i o n f o r f u t u r e s c o n t r a c t s i s p e r -f e c t l y e l a s t i c , or whether t h a t s p e c u l a t i v e p o p u l a t i o n d i s p l a y s r i s k a v e r s e c h a r a c t e r i s t i c s such t h a t the e x c e s s demand f u n c t i o n i s 1 e s s - t h a n - p e r f e c t 1 y e l a s t i c , remains unanswered . It i s not s u f f i c i e n t to a s c e r t a i n t h a t the average r i s k premium., how-ever d e f i n e d , over an e x t e n d e d t ime p e r i o d , i s not s i g n i f i c a n t l y d i f f e r e n t f rom z e r o . For w h i l e such a f i n d i n g does negate a c c e p t a n c e of the t h e o r y of normal b a c k w a r d a t i o n as o r i g i n a l l y p r e s e n t e d by Keynes , a c c e p t a n c e of the n u l l h y p o t h e s i s to the e f f e c t t h a t s p e c u l a t o r s earn no r i s k premium i s w a r r a n t e d o n l y i f the s t a t e m e n t i s v a l i d a f t e r c o n s i d e r a t i o n has been g i v e n to the t i m i n g and volume of the net hedg ing p o s i t i o n . CHAPTER I I I 49 A THEORY OF THE RISK PREMIUM" The p r i m a r y o b j e c t i v e of t h i s s t u d y i s to examine an a s p e c t of the t h e o r y of commodity m a r k e t s : the n a t u r e and magni tude of the r i s k premiums, i f a n y , wh ich a r e r e c e i v e d by s p e c u l a t o r s f rom h e d g e r s ; and the s i g n i f i c a n c e of hedg ing a c t i v i t y r e l a t i v e to the payment of any such r i s k premiums. T h i s o b j e c t i v e i n v o l v e s the t e s t of a t h e o r y of the demand f u n c t i o n f o r f u t u r e s c o n t r a c t s . However, s i n c e the r i s k premium i s d e t e r m i n e d by both the s u p p l y and demand f o r f u t u r e s c o n t r a c t s , i t i s n e c e s s a r y a l s o to c o n s i d e r the s p e c i -f i c a t i o n of the s u p p l y f u n c t i o n . S p e c i f i c a l l y , the r i s k premium i s assumed to be d e t e r m i n e d by the f o l l o w i n g s e t of s i m u l t a n -i «. • u • 50 eous r e l a t i o n s h i p s : Q_s = f { I , P $ , E (RP) } H e d g e r s 1 Supp l y F u n c t i o n . = f { E ( R P ) } S p e c u l a t o r s ' Demand F u n c t i o n . where Qg = net s u p p l y of f u t u r e s c o n t r a c t s by commodity h a n d l e r s . = net demand f o r f u t u r e s c o n t r a c t s by s p e c u l a t o r s . I = c o m m e r c i a l s t o c k s of the commodi ty . P<> = c u r r e n t spot p r i c e of the commodi ty . E(RP) = e x p e c t e d r i s k premium. In e q u i l i b r i u m , net s u p p l y and net demand f o r f u t u r e s c o n t r a c t s i s equa l ( i . e . Q<. = Q n ) • -52-The h e d g e r s 1 s u p p l y of f u t u r e s c o n t r a c t s i s assumed to be a f u n c t i o n of t h r e e v a r i a b l e s : ' ' ' i ) the l e v e l of commerc ia l s t o c k s of a commodity i s a d e t e r m i n a n t o f the t o t a l r i s k r e q u i r e d to be borne by someone. When a h a n d l e r a c q u i r e s i n v e n t o r y in a commodi ty , he must d e c i d e whether to assume the t o t a l p r i c e r i s k and h o l d the i n v e n t o r y unhedged, or to hedge p a r t o f h i s commodity s t o c k s t h r o u g h the medium of f u t u r e s c o n t r a c t s . G iven the h a n d l e r ' s w i l l i n g n e s s to bear r i s k , some p r o p o r t i o n of h i s s t o c k s w i l l be hedged f o r any p a r t i c u l a r spot p r i c e and r i s k p rem i um. i i ) the spot p r i c e v a r i a b l e i s i n t r o d u c e d to comprehend the w e a l t h e f f e c t as r e f l e c t e d in the h a n d l e r ' s ut i 1 i ty f u n c t i on . Some p o r t i o n of the w e a l t h of r i s k a v e r s e i n d i v i d u a l s w i l l be h e l d in the form of r i s k y a s s e t s so long as the e x p e c t e d 52 r a t e of r e t u r n i s g r e a t e r than the r i s k f r e e r a t e . If A = i n i t i a l i n v e s t m e n t in i n v e n t o r y by the h a n d l e r a = unhedged p o r t i o n of t h a t i n v e n t o r y S = s u p p l y of f u t u r e s c o n t r a c t s by the h a n d l e r then S = A - a where each of the terms i s e x p r e s s e d in monetary u n i t s . - 5 3 -5 3 For the i n d i v i d u a l commodity h a n d l e r , l e t y = A + aX where y = f i n a l w e a l t h X = r a t e of r e t u r n on r i s k y a s s e t s (a random v a r i a b l e ) Then, E{U(y)} = E{U(.A + aX)} E W ( a ) , 0<a<A _(3 . 1 ) The h a n d l e r , in the a l l o c a t i o n of h i s i n i t i a l i n v e s t m e n t among r i s k y (unhedged) and s e c u r e (hedged) a s s e t s , w i l l seek to max imize E{UCy)}. The f i r s t and second d e r i v a t i v e s of E q u a t i o n ( 3 . 1 ) w i t h r e s p e c t to " a " a r e : W (a) = E{U' (y)X} (.3.2) W"Ca) = E{U"Cy)X2} (.3-31 For the r i s k a v e r s e i n v e s t o r , U " (y) < 0 f ° r a 1 1 Y a n d hence W"(a)<0 f o r a l l " a " . W' (a ) i s t h e r e f o r e a l w a y s d e c r e a s i n g and the graph of W(a) must t h e r e f o r e have one of the t h r e e forms shown in F i g u r e 3 - 1 . For the commodity h a n d l e r to whom F i g u r e 3 . 1 a a p p l i e s , W(a) has i t s maximum at a = 0 . Such a r h a n d l e r w i l l m a i n t a i n h i s i n v e s t m e n t i n i n v e n t o r y f u l l y hedged at a l l t imes and hence w i l l not c o n t r i b u t e to a change in the s u p p l y of hedg ing c o n t r a c t s in r e s p o n s e to a change in the spot p r i c e of the commodi ty , as d i s c u s s e d b e l o w . The case of F i g u r e 3 . 1 b , where the h a n d l e r a c c e p t s the t o t a l p r i c e r i s k and r e t a i n s a l l of h i s i n v e n t o r y i n v e s t m e n t in r i s k y (unhedged) form i s , as Arrow s u g g e s t s , " l e s s -5h-A F i g u r e 3 • 1 a W F i g u r e 3 . 1 b W A F i g u r e 3 . 1 c - 5 5 -i n t e r e s t i n g " , s i n c e he never c o n t r i b u t e s to the s u p p l y of hedg i ng cont rac t s . The case of p a r t i c u l a r i n t e r e s t i s t h a t d e p i c t e d in F i g u r e 3 - l c where t h e r e i s an i n t e r i o r maximum at wh ich W'(a) = E { U ' C Y ) X } = 0 ( 3 . 4 ) At t h a t i n t e r i o r maximum, a* i s the measure of the s t o c k s which w i l l be h e l d i n unhedged form w h i l e A - a * i s the amount of the i n v e s t m e n t in i n v e n t o r y to be hedged in f u t u r e s m a r k e t s . In h i s a n a l y s i s of the t h e o r y o f r i s k a v e r s i o n , Arrow c o n c l u d e d t h a t " i t f o l l o w s from the h y p o t h e s i s of i n c r e a s i n g r e l a t i v e r i s k a v e r s i o n t h a t the w e a l t h e l a s t i c i t y of demand 5 5 f o r cash b a l a n c e s i s a t l e a s t 1". Arrow d e f i n e s as a measure of a b s o l u t e r i s k a v e r s i o n ; R A(Y) = " U " ( Y ) ( 3 . 5 ) U ' ( Y ) and as a measure of r e l a t i v e r i s k a v e r s i o n : R R(y) = - Y U " ( Y ) ( 3 . 6 ) U ' (y) where U ' ( y ) = m a r g i n a l u t i l i t y of w e a l t h U " ( Y ) = r a t e of change of m a r g i n a l u t i l i t y w i t h r e s p e c t to w e a l t h (second d e r i v a t i v e of t o t a l ut i 1i t y ) -56-To o b s e r v e t h e r e l a t i o n s h i p b e t w e e n " a " and " A " , d i f f e r e n t i a t e E q u a t i o n C3•2) w i t h r e s p e c t t o " A " as f o l l o w s : d E { U ' (y ) X } = 0 dA E { U " C Y ) X C1 + X da) } = 0 dA E { U " C Y ) X } + E { U " ( Y ) X 2 } d a _ = 0 dA da = - E { U " ( Y ) X } C3.7) dA E { U " ( Y ) X 2 } As s t a t e d p r e v i o u s l y , f o r t h e r i s k a v e r s e i n v e s t o r , U " ( Y)<0 f o r a l l Y a n d h e n c e W"(a)<0 f o r a l l " a " . H e n c e , s i n c e t h e s i g n o f t h e d e n o m i n a t o r i n E q u a t i o n (3-7) i s n e g a t i v e , t h e s i g n o f d_a_ i s t h e same as t h a t o f t h e n u m e r a t o r . D e c r e a s i n g dA a b s o l u t e r i s k a v e r s i o n w h i c h , as A r r o w o b s e r v e s , n o r m a l l y a p p l i e s , r e q u i r e s t h a t R ^ ( Y ) ' s a d e c r e a s i n g f u n c t i o n o f y, and i t c a n be shown t h a t t h e amount o f r i s k y a s s e t s h e l d i n c r e a s e s w i t h i n c r e a s e s i n w e a l t h . . As s t a t e d a b o v e , A r r o w c o n c l u d e d t h a t t h e h y p o t h e s i s o f i n c r e a s i n g r e l a t i v e r i s k a v e r s i o n i m p l i e s t h a t t h e w e a l t h e l a s t i c i t y o f demand f o r c a s h b a l a n c e s ( i . e . s e c u r e a s s e t s ) i s a t l e a s t 1 . I t f o l l o w s t h a t da < 1 . dA As a p p l i e d t o c o m m o d i t y f u t u r e s m a r k e t s , t h e w e a l t h e f f e c t i m p l i e s t h a t i n c r e a s e s i n t h e s p o t p r i c e w i l l r e s u l t i n an i n c r e a s e i n t h e v o l u m e o f s h o r t h e d g i n g c o n t r a c t s o f f e r e d by h a n d l e r s . I f , f o l l o w i n g h i s i n i t i a l d e c i s i o n c o n c e r n i n g t h e p r o p o r t i o n o f h i s i n v e s t m e n t i n c o m m o d i t y s t o c k s t o be h e d g e d , t h e r e i s an i n c r e a s e i n t h e s p o t p r i c e , t h e h a n d l e r w i l l -57-e x p e r i e n c e an i n c r e a s e in w e a l t h by reason of t h a t p o r t i o n of h i s i n v e n t o r y h e l d unhedged. By c o m p a r i s o n w i t h the a l l o c a t i o n of h i s i n i t i a l w e a l t h among r i s k y and s e c u r e a s s e t s , the i n c r e a s e d spot p r i c e r e s u l t s in the unhedged s t o c k s r e p r e s e n t i n g a g r e a t e r p r o p o r t i o n o f the h a n d l e r ' s t o t a l w e a l t h . Assuming e i t h e r c o n s t a n t or i n c r e a s i n g r e l a t i v e r i s k a v e r s i o n , the h a n d l e r w i l l need to a l l o c a t e a p o r t i o n of the p o s i t i v e w e a l t h inc rement to a s e c u r e a s s e t f o r m . Hence , an i n c r e a s e in the spot p r i c e may r e s u l t in some l i q u i d a t i o n of i n v e n t o r i e s . However , spot p r i c e s and f u t u r e s p r i c e s b e i n g p o s i t i v e l y c o r r e l a t e d , the f u t u r e s market a f f o r d s the h a n d l e r the a l t e r n a t i v e of a l l o c a t i n g a p o r t i o n of h i s w e a l t h i n c r e m e n t to f u t u r e s c o n t r a c t s . It would t h e r e f o r e be e x p e c t e d t h a t , c e t e r i s p a r i b u s , an i n c r e a s e in the spot p r i c e of a commodity w i l l be accompanied by an i n c r e a s e in the s u p p l y of s h o r t hedg ing c o n t r a c t s . S i m i l a r l y , when the commodity spot p r i c e d e c r e a s e s , the r e l a t i v e r i s k a v e r s i o n h y p o t h e s i s i m p l i e s t h a t the long h a n d l e r reduces the number of s h o r t hedg ing c o n -t r a c t s o f f e r e d . An e x p e c t a t i o n a r i s i n g from t h i s a n a l y s i s i s t h a t changes in net s h o r t h e d g i n g w i l l be p o s i t i v e l y c o r r e l a t e d w i t h changes i n f u t u r e s p r i c e s and hence w i t h r e a l i z e d r i s k premiums. i i i ) f i n a l l y , the d e c i s i o n to hedge Is i n f l u e n c e d by the magn i tude of the e x p e c t e d modern r i s k premium the h a n d l e r i s r e q u i r e d to o f f e r in o r d e r to market the f u t u r e s c o n t r a c t to a n o t h e r market p a r t i c i p a n t . -58- . T h i s e x p e c t e d r i s k premium has been en 1 i kened to the c o s t of i n s u r a n c e . The h a n d l e r who h o l d s a c o n t r a c t u a l p o s i t i o n i n the a c t u a l commodity i s exposed to the r i s k of p r i c e changes wh ich move a g a i n s t h i s i n v e n t o r y p o s i t i o n . The m e r i t of hedg ing in f u t u r e s m a r k e t s i s t h a t the h a n d l e r s u b s t i -t u t e s h i s open -ended p o s i t i o n f o r one where h i s i n v e n t o r y p o s i t i o n i s t i e d to the f u t u r e s p r i c e e s t a b l i s h e d by the f u t u r e s c o n t r a c t , t h e r e b y a c q u i r i n g a degree of i n s u r a n c e . The measurement of the r i s k premium i s d i s c u s s e d e l s e w h e r e . It i s s u f f i c i e n t to o b s e r v e here t h a t , c e t e r i s p a r i b u s , the s m a l l e r the e x p e c t e d r i s k premium, the l a r g e r w i l l be the number of f u t u r e s c o n t r a c t s o f f e r e d by the commodity h a n d l e r . U n l i k e the h e d g e r , the s p e c u l a t o r ' s p o s i t i o n in a f u t u r e s c o n t r a c t i s not o f f s e t or a f f e c t e d by a p o s i t i o n in the a c t u a l commodi ty . Hence , the i n v e n t o r y of commerc ia l s t o c k s does not impinge upon the s p e c u l a t o r ' s demand f u n c t i o n . A l s o , i t i s assumed t h a t the p r o p o r t i o n of t o t a l s p e c u l a t i v e w e a l t h t h a t i s i n v e s t e d in commodity f u t u r e s i s s u f f i c i e n t l y s m a l l t h a t w e a l t h e f f e c t s can be i g n o r e d . T h e r e f o r e , the s p e c u l a t o r s ' demand f u n c t i o n f o r f u t u r e s c o n t r a c t s i s a f u n c t i o n s o l e l y of the r i s k premium which s p e c u l a t o r s e x p e c t to r e c e i v e from hedgers f o r a c c e p t i n g the open -ended r i s k of p r i c e changes wh ich move a g a i n s t the s p e c u l a t o r s ' f u t u r e s c o n t r a c t p o s i t i o n . Arrow has shown t h a t w i t h d e c r e a s i n g a b s o l u t e r i s k a v e r s i o n the demand f o r r i s k y a s s e t s i n c r e a s e s as the e x p e c t e d r e t u r n on such a s s e t s i n c r e a s e s . C o n s i s t e n t w i t h A r r o w , the s p e c u l a t o r s ' - 5 9 -demand f o r f u t u r e s c o n t r a c t s i s e x p e c t e d t o be p o s i t i v e l y r e l a t e d t o t h e r i s k p r e m i u m . LI NEAR FORM OF THE MODEL The s e t o f s i m u l t a n e o u s e q u a t i o n s w h i c h c o m p r i s e t h e d e m a n d - s u p p 1 y mode l may be e x p r e s s e d i n l i n e a r f o r m as f o l l o w s : Q s = a Q + c ^ l + a 2 P $ + a 3 E ( R P ) + ua ( 3 - 8 ) Q-D = B Q + 3 3 E ( R P ) + y g ( 3 . 9 ) The v a r i a b l e s (and Q ^ ) a n d E ( R P ) a r e e n d o g e n o u s and I and P^ a r e e x o g e n o u s . C o n s i s t e n t w i t h t h e p r e v i o u s d i s c u s s i o n t h e t h e o r e t i c a l v a l u e s o f t h e c o e f f i c i e n t s a r e a j>0,>0,a^<0 and $^>0. T ime s u b s c r i p t s h a v e been o m i t t e d . In t h e e m p i r i c a l w o r k , r e g r e s s i o n a n a l y s i s t e c h n i q u e s a r e a p p l i e d t o t h e demand f u n c t i o n o f t h e m o d e l . In s o d o i n g , c e r t a i n e c o n o m e t r i c p r o b l e m s a r i s e as do q u e s t i o n s o f m e a s u r e -ment a s s o c i a t e d w i t h t h e r i s k p r e m i u m . B o t h o f t h e s e w a r r a n t e x p l i c i t a t t e n t i o n and a r e c o n s i d e r e d i n t h e f o l l o w i n g s e c t i o n . E M P I R I C A L A N A L Y S I S In t h e e m p i r i c a l a n a l y s i s o f t h e d e m a n d - s u p p 1 y m o d e l , c e r t a i n q u e s t i o n s a r i s e i n v o l v i n g : i ) i d e n t i f i c a t i o n o f t h e demand f u n c t i o n , and i i ) u n b i a s e d and c o n s i s t e n t p r o p e r t i e s o f t h e o r d i n a r y l e a s t s q u a r e s e s t i m a t o r s The o r d e r c o n d i t i o n s f o r i d e n t i f i c a t i o n r e q u i r e t h a t , f o r an e q u a t i o n t o be e x a c t l y i d e n t i f i e d , t h e number o f e x o -g e n o u s v a r i a b l e s e x c l u d e d f r o m t h e e q u a t i o n must be e q u a l t o - 6 0 -t h e number o f e n d o g e n o u s v a r i a b l e s i n c l u d e d i n t h e r i g h t hand s i d e o f t h e e q u a t i o n . E x p r e s s e d a l t e r n a t e l y , an e q u a t i o n i s e x a c t l y i d e n t i f i e d i f and o n l y i f u n i q u e v a l u e s o f t h e s t r u c -t u r a l p a r a m e t e r s may be f o u n d f r o m a k n o w l e d g e o f t h e r e d u c e d f o r m p a r a m e t e r s . As i s t y p i c a l i n s i m u l t a n e o u s s y s t e m s o f t h e f o r m o f t h e d e m a n d - s u p p 1 y m o d e l r e p r e s e n t e d by E q u a t i o n s ( 3 - 8 ) and ( 3 - 9 ) , t h e s u p p l y f u n c t i o n i s t h e r e f o r e u n i d e n t i f i e d ( i . e . u n d e r i d e n t i f i e d ) and t h e demand e q u a t i o n i s o v e r i d e n t i f i e d . Under t h e s e c o n d i t i o n s , t h e a p p l i c a t i o n o f o r d i n a r y l e a s t s q u a r e s t o t h e demand f u n c t i o n w i l l , i n g e n e r a l , r e s u l t i n 57 p a r a m e t e r e s t i m a t e s w h i c h a r e b i a s e d and i n c o n s i s t e n t . Even w h e r e t h e m e t h o d o f o r d i n a r y l e a s t s q u a r e s i s a p p l i e d t o an e q u a t i o n i n a s e t o f s i m u l t a n e o u s r e l a t i o n s h i p s w h i c h i s e x a c t l y i d e n t i f i e d , i n c o n s i s t e n t e s t i m a t e s may r e s u l t due t o t h e s i m u l t a n e o u s n a t u r e o f t h e e n d o g e n o u s v a r i a b l e s . In e s t i m a t i n g t h e o v e r i d e n t i f i e d demand e q u a t i o n , two s t a g e l e a s t s q u a r e s i s a s i n g l e e q u a t i o n m e t h o d w h i c h l e a d s t o c o n s i s t e n t e s t i m a t i o n . U n f o r t u n a t e l y , d a t a i s n o t a v a i l a b l e f o r t h e e x o g e n o u s v a r i a b l e s as r e q u i r e d by t h i s m e t h o d . I t t h e r e f o r e i s n e c e s s a r y t o c o n s i d e r t h e p r o p e r t i e s o f t h e e s t i -m a t o r s w h i c h w i l l d e r i v e f r o m t h e a p p l i c a t i o n o f o r d i n a r y l e a s t s q u a r e s t o t h e demand f u n c t i o n . To e x a m i n e t h e p r o b l e m o f b i a s and i n c o n s i s t e n c y , f i r s t e q u a t e t h e r i g h t hand s i d e o f E q u a t i o n s ( 3 . 8 ) and ( 3 - 9 ) , u n d e r t h e c o n d i t i o n o f m a r k e t e q u i l i b r i u m , and o b t a i n t h e r e d u c e d •61 form e q u a t i o n f o r E ( R P ) : a 0 + c i j l + a 2 P $ + a 3 E ( R P ) + y a = 3 Q + 3 3 E(RP) + y g ( a 2 - 3 3 ) E ( R P ) - P ( J - 0 ( J - a , I - - y a E(RP) = 3 Q - a Q " a , I. - « 2 ? s + y 3 " y a a 3 " ^3 a 3 " ^3 a 3 " B 3 ' a 3 " ^3 (3.10) To o b t a i n the reduced form e q u a t i o n f o r Q, s o l v e each of E q u a t i o n s (3-8) and (3-9) f o r E ( R P ) . From ( 3 . 8 ) , E(RP) = - a Q - a , 1 ~ a 2 PS + 1 QS " 1 y a (3-11) and f rom (3-9) , E ( R P > " " ^ + 1 Q D - 1 y3 (3.12) 3, 3~ 3~ 3 3 Under market e q u i l i b r i u m , = 0_n so t h a t the s u b s c r i p t on the q u a n t i t y v a r i a b l e may be dropped and the r i g h t hand s i d e of E q u a t i o n s (3.11) and (3.12) may be e q u a t e d . * !i + ]_ Q " ]_ Vl = " % - ^ 1 1 " ^2 PS + ]_ Q " ]_ y a 3^ 3^ 3^ V - ^ i I " «z PS + i_ y3 ' ]_ y a 3^ 3^ 3^ l a 3 ' 3 3 } °- = a 3 3 0 ' a 0 3 3 ' ' " a_2 PS + i_ y3 " l^a a^3 3 a 3 ^ 3 a 3 a 3 ^3 a 3 - 6 2 -a 3 e Q - a Q 3 3 _1 « 2 1 1 - a 3 1 - a 3 p s + 3 3 y 8 " a 3 y a a 3 - g 3 a 3 ~ 8 3 a 3 ~ 8 3 a 3 - 8 3 a 3 - e 3 a 3 3 3 a 3 8 3 a 3 3 3 a 3 8 3 a 3 8 3 a 3 8 Q - a Q 8 3 • - a ] 8 3 . *1 ' " a 2 3 3 p s + a 3 U 8 -a 3 - 8 3 a 3 ~ 8 3 a 3 ~ 8 3 a 3 - 6 3 a 3 - 8 3 In t h i s s t u d y , the demand f u n c t i o n r e g r e s s i o n e q u a t i o n s a re run w i t h ECRP) d e f i n e d as the dependent v a r i a b l e and w i t h Q as the independent v a r i a b l e . The a s s u m p t i o n s of the o r d i n a r y l i n e a r r e g r e s s i o n model r e q u i r e t h a t , i f o r d i n a r y l e a s t s q u a r e s e s t i m a t o r s a re to be u n b i a s e d and c o n s i s t e n t , the independent v a r i a b l e , Q_, be u n c o r r e l a t e d w i t h the random e r r o r term of the r e g r e s s i o n e q u a t i o n . The reduced form e q u a t i o n ( .Equation ( 3 - 1 3 ) ) i n d i c a t e s t h a t Q_ i s c o r r e l a t e d w i t h the e r r o r term of the demand f u n c t i o n (u 0 ) t such t h a t i n c o n s i s t e n t e s t i m a t e s w i l l , in g e n e r a l , d e r i v e from the a p p l i c a t i o n of o r d i n a r y l e a s t s q u a r e s . However , p r o c e e d i n g to examine the p r o p e r t i e s of the e s t i m a t o r s in the l i g h t of the form of the n u l l h y p o t h e s i s b e i n g t e s t e d ; H^: The e l a s t i c i t y of demand f o r f u t u r e s c o n t r a c t s i s i n f i n i t e . H j : The e l a s t i c i t y of demand f o r f u t u r e s c o n t r a c t s i s l e s s than i n f i n i t e , i t i s e v i d e n t t h a t , s i n c e under the n u l l h y p o t h e s i s 8 3 i s i n f i n i t e and s i n c e by a s s u m p t i o n .a^ .- < 0 , the c o e f f i c i e n t of u f t in E q u a t i o n ( 3 - 1 3 ) i s z e r o and Q i s u n c o r r e l a t e d w i t h the - 6 3 -e r r o r t e r m . Hence , under the n u l l h y p o t h e s i s , the e s t i m a t e s d e r i v e d from the a p p l i c a t i o n of o r d i n a r y l e a s t squares to the demand e q u a t i o n w i l l be c o n s i s t e n t and u n b i a s e d . Under the a l t e r n a t i v e h y p o t h e s i s , 8^ i s f i n i t e . Under t h e s e c o n d i t i o n s , E q u a t i o n ( 3 . 1 3 ) would s u g g e s t t h a t the independent v a r i a b l e i s p o s i t i v e l y c o r r e l a t e d w i t h the e r r o r term of the demand e q u a t i o n , i m p l y i n g t h a t the e s t i m a t e d v a l u e s w i l l be h i g h e r than the t r u e va1ue s . The above a n a l y s i s i s d i r e c t e d to t h o s e i n s t a n c e s where the l e v e l of net h e d g i n g i s the s o l e independent v a r i a b l e . C e r t a i n of the r e g r e s s i o n e q u a t i o n s run in the c o u r s e of the s tudy i n c l u d e v a r i a b l e s such as the change in net h e d g i n g , e i t h e r in a s i m p l e r e g r e s s i o n e q u a t i o n or in a m u l t i p l e r e -g r e s s i o n e q u a t i o n w i t h the l e v e l of net hedg ing as a second independent v a r i a b l e . Under a c o m p a r a b l e n u l l h y p o t h e s i s , the same c o n c l u s i o n as o b t a i n e d above would a p p l y where such as the change in net hedg ing v a r i a b l e i s i n c l u d e d . In those i n s t a n c e s where the t r u e c o e f f i c i e n t ( e q u i v a l e n t to j ) of the independent v a r i a b l e i s n o n - z e r o , the p a r a m e t e r e s t i m a t e s would appear to be b i a s e d . S i n c e the ex a n t e r i s k premium cannot be o b s e r v e d , i t i s n e c e s s a r y to employ the ex p o s t r i s k premium as an e s t i m a t e . However, s i n c e the r i s k premium appears o n l y as a dependent v a r i a b l e in the e q u a t i o n s to be e s t i m a t e d , and i t i s assumed t h a t the mean of any o b s e r v a t i o n e r r o r i s z e r o , the p r e s e n c e of - 6 4 -such an o b s e r v a t i o n e r r o r causes no b i a s in the e s t i m a t e d c o e f f i c i e n t s . MAJOR HYPOTHESES TO BE TESTED  H y p o t h e s i s #1 In D u s a k 1 s e x a m i n a t i o n of the b e h a v i o u r of f u t u r e s p r i c e s , the concept of the c a p i t a l a s s e t p r i c i n g model was a d o p t e d , an index of s e c u r i t y p r i c e s b e i n g employed as a proxy f o r t o t a l w e a l t h . Dusak found t h a t the mean s e m i - m o n t h l y h o l d i n g p e r i o d r e t u r n s and the measure of s y s t e m a t i c r i s k were both v e r y c l o s e to z e r o . As p r e v i o u s l y d i s c u s s e d , the f i n d i n g t h a t the mean r i s k premium i s not s i g n i f i c a n t l y d i f f e r e n t f rom z e r o does not negate the Cootner v e r s i o n of K e y n e s ' t h e o r y . Such a f i n d i n g does imply t h a t , on a v e r a g e , the c u r r e n t f u t u r e s p r i c e i s an u n b i a s e d e s t i m a t e of the f u t u r e spot p r i c e . The f u r t h e r f i n d i n g c o n c e r n i n g the s y s t e m a t i c r i s k i m p l i e s t h a t the r e t u r n on i n v e s t m e n t in f u t u r e s c o n t r a c t s i s i n d e p e n d e n t of the r e t u r n on a l l r i s k y a s s e t s t a k e n t o g e t h e r . As a p r e l i m i n a r y t e s t , the i n i t i a l h y p o t h e s i s i s d e s i g n e d 58 to v e r i f y D u s a k ' s f i n d i n g s : HQ : F u t u r e s c o n t r a c t s e m i - m o n t h l y h o l d i n g p e r i o d r e a l i z e d r i s k premiums are independent of comparab le h o l d i n g p e r i o d r e t u r n s on a s e c u r i t y market index an have a mean v a l u e of z e r o . H^: S e m i - m o n t h l y h o l d i n g p e r i o d r e a l i z e d r i s k premiums on f u t u r e s c o n t r a c t s a r e f u n c t i o n a l l y r e l a t e d to c o m p a r a b l e h o l d i n g p e r i o d r e t u r n s on a s e c u r i t y ma r k e t i ndex . -65-The t e s t e q u a t i o n i s : R P t = Y 0 + ? ! R mt + e t where the S & P 500 index s e r v e s as a proxy f o r a w e a l t h index in the c o m p u t a t i o n of market r e t u r n s and e - i s the (unobserved) random d i s t u r b a n c e t e r m . i ) If n e i t h e r RP nor y^  a r e s i g n i f i c a n t l y d i f f e r e n t f rom z e r o , the n u l l h y p o t h e s i s i s a c c e p t e d . The sample i n c l u d e d i n t h i s s t u d y r e f l e c t s q u a n t i t a t i - v e r e s u l t s c o m p a t i b l e w i t h t h o s e o b t a i n e d by Dusak. i i ) I f RP i s not s i g n i f i c a n t l y d i f f e r e n t f rom z e r o and i s s i g n i f i c a n t l y d i f f e r e n t f rom z e r o , the n u l l h y p o t h e s i s i s not a c c e p t e d . W h i l e d i s p l a y i n g a mean v a l u e of z e r o , f u t u r e s c o n t r a c t s e m i - m o n t h l y h o l d i n g p e r i o d r i s k premiums a r e not i ndependent of c o m p a r a b l e h o l d i n g p e r i o d r e t u r n s on a s e c u r i t y market i n d e x , i i i ) I f RP i s s i g n i f i c a n t l y g r e a t e r than z e r o and y -,. i s not s i g n i f i c a n t l y d i f f e r e n t f rom z e r o , the n u l l h y p o t h e s i s i s not a c c e p t e d . W h i l e the measure of s y s t e m a t i c r i s k i s not s i g n i f i c a n t l y d i f f e r e n t f rom z e r o , the f i n i t e r i s k premium i m p l i e s s u p p o r t f o r K e y n e s ' t h e o r y . H y p o t h e s i s #2 Both Keynes and H i c k s b e l i e v e d t h a t c u r r e n t f u t u r e s p r i c e s were downward b i a s e d e s t i m a t e s of f u t u r e spot p r i c e s and t h a t the s p e c u l a t o r need o n l y c o n t i n u o u s l y m a i n t a i n a long f u t u r e s c o n t r a c t p o s i t i o n t o be a s s u r e d of p o s i t i v e r e t u r n s . In the e a r l i e r v e r s i o n of h i s t h e o r y , Cootner sought to m o d i f y - 6 6 -the K e y n e s - H i c k s t h e o r y by r e l a t i n g the payment of a r i s k premium by hedgers to the change • i n net h e d g i n g . C o n t r a r y to T e l s e r , Cootner b e l i e v e d the s p e c u l a t i v e demand f u n c t i o n to be l e s s than p e r f e c t l y e l a s t i c and s u g g e s t e d t h a t f u t u r e s p r i c e s would f a l l as net s h o r t hedg ing i n c r e a s e d and r i s e as the hedg ing " p r e s s u r e " was l i f t e d . That i s , Cootner h y p o t h e s i z e d a reduced form e q u a t i o n t h u s : RP = a Q + a ] AN H where the c o e f f i c i e n t of the change in net s h o r t hedg ing v a r i a b l e (ANH) i s n e g a t i v e ( i . e . < 0). By c o m p a r i s o n , c o n s i d e r the l i n e a r form of the h e d g e r s 1 s u p p l y f u n c t i o n , E q u a t i o n (3.8); Q s = a Q + a, I + a 2 P<. + E ( R p ) C 3 _ 8 ) where the random e r r o r term i s o m i t t e d . For a change in the net s u p p l y of f u t u r e s c o n t r a c t s by commodity h a n d l e r s , E q u a t i o n (3-8) becomes : AQ $ = a Q + a] Al + c t 2 A P $ + a^A E(RP) If the s p e c u l a t i v e e x c e s s demand f u n c t i o n i s assumed to be i n f i n i t e l y e l a s t i c such t h a t 3^ = °° ( E q u a t i o n (3.12)), then AE(RP) = 0. As d i s c u s s e d p r e v i o u s l y , t h e - h y p o t h e s i s of i n c r e a s i n g r e l a t i v e r i s k a v e r s i o n i m p l i e s t h a t an i n c r e a s e in the spot p r i c e of a commodity wh ich e f f e c t s an i n c r e a s e in the w e a l t h of the h a n d l e r w i t h a l o n g , unhedged i n v e n t o r y p o s i t i o n , w i l l r e s u l t in an i n c r e a s e in the volume of hedg ing c o n t r a c t s o f f e r e d to s p e c u -l a t o r s . The t h e o r y would t h e r e f o r e s u g g e s t t h a t changes in the -67-volume of net s h o r t h e d g i n g and changes in the spot p r i c e a r e p o s i t i v e l y c o r r e l a t e d . I f , f u r t h e r , changes in the spot p r i c e and in the f u t u r e s p r i c e a re p o s i t i v e l y c o r r e l a t e d as o b s e r v e d 59 by Houthakker and o t h e r s , i t f o l l o w s t h a t changes in the volume of net s h o r t h e d g i n g c o u l d a l s o be p o s i t i v e l y c o r r e -l a t e d w i t h the r e a l i z e d r i s k premium. Hence the p o s i t i o n t a k e n by Cootner c o n c e r n i n g the r e l a t i o n s h i p between the r e a l i z e d r i s k premium and the change in net s h o r t hedg ing i s c o n t r a r y to t h a t s u g g e s t e d by the t h e o r y of the r i s k premium based on a c o n s i d e r a t i o n of w e a l t h e f f e c t s . These c o m p e t i n g a l t e r n a t i v e s a re encompassed in the h y p o t h e s i s : HQ : The s e m i - m o n t h l y h o l d i n g p e r i o d r e a l i z e d r i s k premium i s p o s i t i v e l y r e l a t e d to the change in net s h o r t hedg i ng . Hj : The s e m i - m o n t h l y h o l d i n g p e r i o d r e a l i z e d r i s k premium i s n e g a t i v e l y r e l a t e d to the change in net s h o r t h e d g i n g . The e q u a t i o n to be t e s t e d i s of the f o r m : R P t = Y 0 + Y2 A N H + e t where ANH i s the change in the l e v e l or volume of net s h o r t hedg ing c o n t r a c t s over the s e m i - m o n t h l y h o l d i n g p e r i o d . i ) If Y 2 i s s i g n i f i c a n t l y g r e a t e r than z e r o , the n u l l h y p o t h e s i s i s a c c e p t e d . Such a f i n d i n g would be c o m p a t i b l e w i t h the t h e o r y of the r i s k premium p r e s e n t e d h e r e i n but i s c o n t r a r y to t h e e a r l i e r v e r s i o n of C o o t n e r 1 s t h e o r y . -68-i i ) If y*2 ' s s i g n i f i c a n t l y l e s s than z e r o , a c c e p t a n c e of the a l t e r n a t i v e h y p o t h e s i s i s i n d i c a t e d . Suppor t i s i n d i c a t e d f o r the e a r l i e r v e r s i o n of C o o t n e r ' s t h e o r y but the f i n d i n g i s i n c o m p a t i b l e w i t h the i m p l i c a t i o n s of the i n c r e a s i n g r e l a t i v e r i s k a v e r s i o n hypothes i s . H y p o t h e s i s #3 In the l a t e r v e r s i o n of h i s t h e o r y , Cootner acknowledged t h a t the hedg ing p r e s s u r e t h e o r y was i n v a l i d in the sense t h a t no r a t i o n a l s p e c u l a t o r would buy a f u t u r e s c o n t r a c t i f he e x -p e c t e d the f u t u r e s p r i c e to become lower than i t s p r e s e n t l e v e l . He t h e r e f o r e c o n c l u d e d t h a t f u t u r e s p r i c e s s h o u l d r i s e from the t ime t h a t h e d g i n g in the f u t u r e s c o n t r a c t becomes net s h o r t . Only i f , d u r i n g the h a r v e s t p e r i o d , net hedg ing s h i f t e d from long to s h o r t d i d Cootner b e l i e v e f u t u r e s p r i c e s would d e c l i n e . Cootner t h e r e f o r e e v i d e n t l y e n v i s a g e d t h r e e " s t a g e s " wh ich might o c c u r over the l i f e of a f u t u r e s c o n t r a c t wh ich b r i d g e s a h a r v e s t p e r i o d ; a) t r a n s i t i o n of net h e d g i n g from long to s h o r t ( d u r i n g h a r v e s t ) accompanied by f a l l i n g f u t u r e s p r i c e s , b) i n c r e a s i n g l e v e l s of net s h o r t h e d g i n g ( immedia te pos t h a r v e s t ) accompanied by s t a b l e or r i s i n g f u t u res p r i c e s , c ) d e c r e a s i n g l e v e l s of net s h o r t hedg ing accompanied by r i s i n g f u t u r e s p r i c e s . -69-W h i l e a c k n o w l e d g i n g t h a t " t h e r e need be no ' u n i v e r s a l 60 t r u t h ' about s p e c u l a t i v e r e t u r n s " , i t was C o o t n e r ' s b a s i c c o n t e n t i o n t h a t r i s k a v e r s e s p e c u l a t o r s would e x h i b i t a l e s s than p e r f e c t l y e l a s t i c demand c u r v e and t h a t such a s p e c u l a t o r " w i l l o n l y buy f u t u r e s c o n t r a c t s at p r i c e s below those e x p e c t e d at the e x p i r a t i o n of the c o n t r a c t s . " ^ ' F u r t h e r m o r e , the h i g h e r the l e v e l of net s h o r t h e d g i n g , the l a r g e r the r i s k premium r e q u i r e d by the s p e c u l a t o r . A h y p o t h e s i s c o n c e r n i n g the s p e c u l a t i v e demand f u n c t i o n i s as f o l l o w s : H Q : The e l a s t i c i t y of demandf-f'or f u t u r e s c o n t r a c t s i s i n f i n i t e . Hj : The e l a s t i c i t y of demand f o r f u t u r e s c o n t r a c t s i s l e s s than i n f i n i t e . The e q u a t i o n to be t e s t e d i s a s i m p l e l i n e a r r e g r e s s i o n mode 1 of the f o r m : R P t = Y Q + Y 3 NH t + e t • where N H i s d e f i n e d as the volume of net s h o r t hedg ing c o n t r a c t s and i s e q u i v a l e n t to the q u a n t i t y v a r i a b l e of the s p e c u l a t i v e e x c e s s demand f u n c t i o n . i ) I f n e i t h e r Y Q N O R Y ^ a r e s i g n i f i c a n t l y d i f f e r e n t f rom z e r o , the n u l l h y p o t h e s i s i s a c c e p t e d . The r e a l i z e d r i s k premium i s independent of the volume of net s h o r t hedg ing c o n t r a c t s . Such a f i n d i n g i s i n c o m p a t i b l e w i t h the Cootner p o s i t i o n and a c c e p t a n c e of a s u b s t i -t u t i o n h y p o t h e s i s i s i n d i c a t e d . -70-i i ) I f ' s s i g n i f i c a n t l y g r e a t e r t h a n z e r o , t h e a l t e r -n a t i v e h y p o t h e s i s i s a c c e p t e d . S p e c u l a t o r s e a r n a r i s k p r e m i u m w h i c h i s d e p e n d e n t upon t h e l e v e l o f n e t s h o r t h e d g i n g , c o n s i s t e n t w i t h C o o t n e r ' s pos i t i o n . The a b o v e t e s t e q u a t i o n i s c o m p a t i b l e w i t h t h e l i n e a r f o r m o f t h e s p e c u l a t i v e e x c e s s demand f u n c t i o n as e x p r e s s e d i n E q u a t i o n ( 3 . 1 2 ) b u t w h e r e t h e r e a l i z e d r i s k p r e m i u m i s e m p l o y e d i n l i e u o f t h e e x p e c t e d r i s k p r e m i u m . In t e r m s o f E q u a t i o n ( 3 . 1 2 ) , a c c e p t a n c e o f H y p o t h e s i s # 3 i s e q u i v a l e n t t o a c c e p t i n g t h a t 3^ = °°. The f o r e g o i n g d i s c u s s i o n has d e l i n e a t e d t h e t h r e e b a s i c h y p o t h e s e s t e s t e d i n t h i s s t u d y . D e t a i l s o f t h e t e s t p r o c e d u r e s , c o m p u t a t i o n m e t h o d s , v a r i a t i o n s i n t h e t e s t e q u a t i o n s w h i c h w e r e e x a m i n e d , and o t h e r r e l e v a n t i n f o r m a t i o n a r e d i s c u s s e d i n C h a p t e r TV. MEASUREMENT OF THE R E A L I Z E D R I S K PREMIUM In t h e c a l c u l a t i o n o f t h e r e a l i z e d r i s k p r e m i u m , t h e c h a n g e i n p r i c e o f t h e a p p l i c a b l e f u t u r e s c o n t r a c t o v e r t h e s e m i - m o n t h l y h o l d i n g p e r i o d i s a m e a s u r e o f t h e t r a d e r ' s g r o s s r e t u r n f o r t h a t p e r i o d . H o w e v e r , a q u e s t i o n a r i s e s as t o t h e s t i p u l a t i o n o f t h e i n v e s t m e n t b a s e on w h i c h t h e d e s i r e d p e r c e n t a g e r a t e s o f r e t u r n a r e t o be c a l c u l a t e d . As n o t e d p r e v i o u s l y , t h e m a r g i n r e q u i r e d t o be p l a c e d on d e p o s i t , and w h i c h r e p r e s e n t s t h e t r a d e r ' s i n i t i a l i n v e s t m e n t , - 7 1 -i s t y p i c a l l y equa l to somewhat l e s s than 10% of the f u t u r e s c o n t r a c t market v a l u e at the t ime of i n c e p t i o n of the c o n t r a c t . W h i l e m a i n t e n a n c e marg in c a l l s may s u b s e q u e n t l y o c c u r , a 10% f i g u r e t h e r e f o r e makes a nomina l a l l o w a n c e f o r the e f f e c t of t h e s e marg in c a l l s on the t r a d e r ' s a v e r a g e i n v e s t m e n t over t i m e . As s u c h , i t i s more r e p r e s e n t a t i v e of the t r a d e r ' s a c t u a l i n v e s t m e n t than i s e i t h e r the d o l l a r amount of the f u t u r e s c o n t r a c t market v a l u e or the d o l l a r amount of the m a r g i n . The i n v e s t m e n t base i s t h e r e f o r e d e f i n e d as 10% of the f u t u r e s c o n t r a c t p r i c e f o r the commodity at the i n c e p t i o n of the a p p l i -c a b l e s e m i - m o n t h l y h o l d i n g p e r i o d . above the p r e v a i l i n g r i s k f r e e r a t e i t i s a l s o n e c e s s a r y to s p e c i f y the i n t e r e s t r a t e d a t a s e r i e s to be employed f o r t h i s p u r p o s e . It was d e c i d e d to use the e f f e c t i v e y i e l d s of 90 day U .S . T r e a s u r y b i l l s to r e p r e s e n t the r i s k f r e e r a t e . As s t a t e d a b o v e , the i n v e s t o r ' s i n i t i a l i n v e s t m e n t i s r e p r e s e n t e d as 10 p e r c e n t of the commodity f u t u r e s p r i c e at the b e g i n n i n g of the s e m i - m o n t h l y h o l d i n g p e r i o d , say p e r i o d t . Hence h i s f i n a l w e a l t h at the end o f the p e r i o d i s S i n c e the r i s k premium i s d e f i n e d as the r a t e of r e t u r n F i n a l w e a l t h = . 1 OP f , t (1 + P f , t + 1 - P f , t ) ( 3 . 1 4 ) . 1 OP f , t where = f u t u r e s p r i c e ( d a i l y , c l o s e ) a t the commencement of the s e m i - m o n t h l y p e r i o d . 72-P"f t + j = f u t u r e s p r i c e ( d a i l y c l o s e ) at the end of the s e m i - m o n t h l y p e r i o d . The i n v e s t o r ' s g r o s s r a t e of r e t u r n f o r the s e m i - m o n t h l y h o l d i n g per i od i s Gross r a t e of r e t u r n = F i n a l w e a l t h - I n i t i a l i n v e s t m e n t I n i t i a l i nvestment = - 1 0 P f , t ( 1 + P f , t + 1 - P f , t ) " - 1 0 P f , t - 1 0 P f , t  • , 0 P f , t P f , t + 1 " P f , t ( 3 . 1 5 ) • 1 0 P f , t S u b t r a c t i n g the s e m i - m o n t h l y r i s k f r e e r a t e of r e t u r n t o o b t a i n the r e a l i z e d r i s k premium, R P t = P f , t + 1 " P f , t " R F t ( 3 . 1 6 ) . 1 0 P f Tk~~ ' > t whe r e RP = R e a l i z e d r i s k premium f o r the s e m i - m o n t h l y h o l d i n g p e r i o d . RF = U .S . 90 day T r e a s u r y b i l l r a t e ( e f f e c t i v e annual r a t e ) . E q u a t i o n ( 3 . 1 6 ) i s a p p l i c a b l e where the i n v e s t o r s a t i s -f i e s the marg in r e q u i r e m e n t by a cash d e p o s i t w i t h the c o m m i s s i o n m e r c h a n t . W i t h i n the f ramework of the p r a c t i c e s s t i p u l a t e d by most U .S . Commodity E x c h a n g e s , some v a r i a t i o n f rom the p o s t i n g of cash c o l l a t e r a l may be p e r m i t t e d by c e r t a i n b r o k e r s . For e x a m p l e , some b r o k e r s a c c e p t U .S . T r e a s u r y B i l l s as c o l l a t e r a l s u b j e c t to a s p e c i f i e d minimum. In such i n s t a n c e s , the c l i e n t - 7 3 -may or may not be charged i n t e r e s t on the amount of the m a r g i n . The b r o k e r , however , must make cash d e p o s i t s w i t h the c l e a r i n g house equa l to the commodity e x c h a n g e ' s s p e c i f i e d marg in f o r the net of the long and s h o r t p o s i t i o n s of the b r o k e r ' s c l i e n t s . Hence , the tendency i s f o r the b r o k e r to encourage cash c o l l a -t e r a l or to c h a r g e i n t e r e s t where n o n - c a s h c o l l a t e r a l i s a c c e p t e d . W h i l e t h e s e c o n s i d e r a t i o n s r e f l e c t m a r k e t i n g s t r a -t e g i e s on the p a r t of the b r o k e r , i t i s e v i d e n t t h a t , where n o n -cash c o l l a t e r a l i s a c c e p t e d and no i n t e r e s t c h a r g e s a r e imposed , f u t u r e s c o n t r a c t s may be e n t e r e d i n t o w i t h o u t any i n v e s t m e n t per s e . In any e v e n t , the c o m p u t a t i o n of the r i s k premium h e r e i n i s s p e c i f i c a l l y e x p r e s s e d as the h o l d i n g p e r i o d r a t e of r e t u r n on the marg in r e q u i r e m e n t l e s s the r i s k f r e e r a t e per p e r i o d , where the marg in r e q u i r e m e n t i s d e f i n e d as 10% of the f u t u r e s p r i c e at the t ime of i n i t i a t i o n of the c o n t r a c t , as embodied in E q u a t i o n ( 3 . 1 6 ) . CHAPTER IV DATA AND SOURCES W h e a t , c o r n and s o y b e a n s a r e t h e t h r e e c o m m o d i t e s i n -c l u d e d i n t h i s s t u d y . Of t h e U . S . f u t u r e s m a r k e t s w h e r e t h e s e c o m m o d i t i e s a r e h e a v i l y t r a d e d , t h e C h i c a g o B o a r d o f T r a d e r e c o r d s t h e h i g h e s t v o l u m e o f t r a n s a c t i o n s and a s s u m e d l y m o s t s t r o n g l y d i s p l a y s t h e a t t r i b u t e s o f an e f f i c i e n t m a r k e t . T r a d i n g d a t a f o r t h e n o m i n a l t e n y e a r p e r i o d o f a n a l y s i s has b e e n d r a w n f r o m t h a t s o u r c e . F o r e a c h o f w h e a t and c o r n , t h e r e a r e f i v e f u t u r e s c o n -t r a c t s p e r y e a r w h i c h a r e t r a d e d . A t t h e o u t s e t o f t h e p e r i o d o f s t u d y , i n 1 9 6 1 , t h e r e w e r e s i x f u t u r e s c o n t r a c t s p e r y e a r f o r s o y b e a n s . H o w e v e r , c o m m e n c i n g i n 19 6 2 , a s e v e n t h c o n t r a c t was a d d e d . The m a t u r i t y m o n t h s f o r t h e f u t u r e s c o n t r a c t s i n e a c h o f t h e c o m m o d i t i e s a r e shown i n T a b l e I. TABLE I FUTURES CONTRACT MATURITY MONTHS Wheat C o r n S o y b e a n s J a n u a r y F e b r u a r y M a r c h A p r i l May J u n e J u l y A u g u s t S e p t e m b e r Oc t o b e r November December x x X X X X X X X X' X : T r a d i n g i n i t i a t e d w i t h t h e A u g u s t , 1 9 6 2 f u t u r e s c o n t r a c t " 7 5 -For each of the t h r e e c o m m o d i t i e s , the s t u d y i n i t i a t e s w i t h the J u l y , 1961 f u t u r e s c o n t r a c t and t e r m i n a t e s w i t h the May, 1972 f u t u r e s c o n t r a c t . Hence , w i t h the e x c e p t i o n of August s o y b e a n s , t h e r e a re ten c o n t r a c t s of each m a t u r i t y c o v e r e d by the d a t a . The l i f e of any i n d i v i d u a l c o n t r a c t i s somewhat v a r i a b l e but i s t y p i c a l l y between ten and t w e l v e months . In t u r n , t h i s means t h a t f o r any p a r t i c u l a r c o n t r a c t m a t u r i t y , t h e r e a r e t y p i c a l l y about 22 s e m i - m o n t h l y h o l d i n g p e r i o d s and t h a t , f o r the ten year s t u d y p e r i o d , t h e r e a r e about 220 s e m i - m o n t h l y h o l d i n g p e r i o d s f o r any c o n t r a c t m a t u r i t y month . In p a r t of the s t u d y p e r i o d , some i n s t a n c e s o c c u r r e d where t r a d i n g in the e x p i r i n g c o n t r a c t o v e r l a p p e d w i t h t r a d i n g in the new c o n t r a c t . For e x a m p l e , t r a d i n g in the September , 1 969 wheat c o n t r a c t commenced in A u g u s t , 1968 even though the September , 1968 c o n t r a c t d i d not e x p i r e u n t i l the f o l l o w i n g month . Where t h i s o c c u r r e d , i t was assumed t h a t the t r a d e r s w i t c h e d to the new c o n t r a c t when t r a d i n g in i t was i n i t i a t e d . A g a i n , in the m i d - 1 9 6 0 ' s , and s p e c i f i c a l l y in the case of w h e a t , t h e r e were c e r t a i n i n s t a n c e s where the commodity exchange e v i d e n t l y e x p e r i m e n t e d w i t h c o n c u r r e n t t r a d i n g in both o l d c rop and new c r o p f u t u r e s c o n t r a c t s f o r p a r t i c u l a r m a t u r i t i e s . Where t h i s was done , t r a d i n g in the new c r o p c o n t r a c t was c o n -t i n u e d f o r o n l y a v e r y l i m i t e d p e r i o d . For e x a m p l e , w h i l e t r a d i n g was c o n d u c t e d i n the o l d c r o p S e p t e m b e r , 1964 c o n t r a c t ove r the normal t ime s p a n , t r a d i n g in a new c rop September , -76-1 9 6 4 c o n t r a c t began in A p r i l , 1 9 6 4 and c o n t i n u e d u n t i l c o n -t r a c t m a t u r i t y in September of t h a t y e a r . P r i c e movements in the o l d and new c r o p c o n t r a c t s were t y p i c a l l y v e r y h i g h l y c o r r e l a t e d a n d , f o r purposes of the s t u d y , t h e s e new c r o p c o n t r a c t s a r e d i s r e g a r d e d . Data s e r i e s r e p o r t i n g the volume of open c o n t r a c t s in each of w h e a t , c o r n , and soybeans a r e p u b l i s h e d f o r the commodi ty , but a re not s e g r e g a t e d by f u t u r e s c o n t r a c t , by the Commodity Exchange A u t h o r i t y of the U .S . Department of A g r i -c u l t u r e . In a d d i t i o n , t r a d e r s whose p o s i t i o n in a f u t u r e s , c o n t r a c t e q u a l s or exceeds an amount s p e c i f i e d by the S e c r e t a r y of A g r i c u l t u r e a re r e q u i r e d to r e p o r t t h e i r p o s i t i o n s d a i l y and to c l a s s i f y them as s p e c u l a t i v e or h e d g i n g . The net s h o r t hedg ing d a t a s e r i e s employed in the s tudy a re o b t a i n e d by s u b t r a c t i n g the long c o n t r a c t s f rom the s h o r t c o n t r a c t s of the r e p o r t e d l a r g e t r a d e r hedg ing a c t i v i t y . The s p e c i f i c s o u r c e s f rom which the v a r i o u s s e m i -month ly d a t a s e r i e s were c o m p i l e d i s as f o l l o w s : Data Source 1. F u t u r e s p r i c e and t r a d i n g d a t a Commodity F u t u r e s S t a t i s -t i c s , U .S . Department of A g r i c u l t u r e , Commodity Exchange A u t h o r i t y . 2 . S&P 5 0 0 d a i l y c l o s i n g index S e c u r i t y P r i c e Index Record ( 1 9 7 4 ) , S t a n d a r d & P o o r ' s T rade and S e c u r i t i e s S t a t i s t i c s . 3 . 9 0 day U .S . T r e a s u r y B i l l F e d e r a l Reserve Bank of r a t e s (new i s s u e s ) S t . L o u i s . - 7 7" TEST PROCEDURE As p r e v i o u s l y d i s c u s s e d , l i n e a r r e g r e s s i o n a n a l y s i s a p p l i e d t o the s p e c u l a t i v e demand f u n c t i o n w i t h t h e r i s k premium d e f i n e d as the dependent v a r i a b l e . The r i s k . p r e m i u m i s computed in a c c o r d a n c e w i t h E q u a t i o n ( 3 - 1 6 ) , n a m e l y : R P t = P f , t + 1 ~ P f , t " R F t ( 3 . 1 6 ) . 1 OP , 2 ¥ ~ ' > t The r e t u r n on the SSP 5 0 0 s e c u r i t y p r i c e index i s computed a s ; R mt = S P t + l " S P t ( Z , - ] ) S P t where SP = S&P 5 0 0 s e c u r i t y p r i c e index at the commence-ment of the s e m i - m o n t h l y h o l d i n g p e r i o d . SP j •= S&P 5 0 0 s e c u r i t y p r i c e index at the end of the s e m i - m o n t h l y h o l d i n g p e r i o d . In each of the r e g r e s s i o n s the f i r s t s e m i - m o n t h l y h o l d i n g p e r i o d i s assumed to commence c o i n c i d e n t w i t h the f i r s t r e p o r t e d s e m i - m o n t h l y c l o s i n g p r i c e f o r the s u b j e c t f u t u r e s c o n t r a c t . The f i n a l h o l d i n g p e r i o d i s assumed to t e r m i n a t e w i t h the l a s t r e p o r t e d s e m i - m o n t h l y c l o s i n g p r i c e Each f u t u r e s c o n t r a c t ( e . g . May c o r n ) i s of f i n i t e d u r a t i o n and embraces a range of f rom 19 to 2 3 s e m i - m o n t h l y h o l d i n g p e r i o d s . W h i l e r e g r e s s i o n e q u a t i o n s were run f o r each such " a n n u a l " c o n t r a c t the e s t i m a t e d p a r a m e t e r s o b t a i n e d are not -78-deemed t o be n e c e s s a r i l y r e p r e s e n t a t i v e o f l o n g run m a r k e t c h a r a c t e r i s t i c s and a r e n o t r e p o r t e d . R a t h e r , t h e f i n d i n g s a r e r e p o r t e d f o r t h e 10 y e a r r e g r e s s i o n e q u a t i o n s and f o r e a c h o f t h e two c o n s e c u t i v e 5 y e a r p e r i o d s o f t h e s a m p l e . Where d e s i r e a b l e , Chow s t a t i s t i c s a r e c o m p u t e d f o r t h e 2-5 y e a r p e r i o d s . C o r r e l a t i o n m a t r i c e s and o t h e r i n f o r m a t i o n a r e a l s o p r e s e n t e d . E M P I R I C A L RESULTS The t e s t n u m b e r i n g i s c o m p a t i b l e w i t h t h a t o f t h e h y p o t h e s e s as s e t o u t i n C h a p t e r I I I . In a l l i n s t a n c e s , t h e n e t s h o r t h e d g i n g v a r i a b l e i s d e f i n e d w i t h a p o s i t i v e s i g n . H e n c e , w h e r e t h e a c t u a l h e d g i n g p o s i t i o n i s n e t l o n g , t h e v a r i a b l e q u a n t i t y w o u l d e n t e r t h e r e g r e s s i o n e q u a t i o n w i t h a n e g a t i v e s i g n . T e s t #1 R e g r e s s i o n m o d e l : RP = Y + Y , R + e t o 1 1 mt t T a b l e II s u m m a r i z e s t h e e m p i r i c a l r e s u l t s o f t h i s p r e l i m i n a r y t e s t . F o r e a c h o f t h e t h r e e c o m m o d i t i e s e x a m i n e d , w i t h t h e s i n g l e e x c e p t i o n o f t h e November s o y b e a n s f u t u r e s c o n t r a c t mean r i s k p r e m i u m , n e i t h e r t h e e s t i m a t e d c o e f f i c i e n t s o f t h e m a r k e t r e t u r n v a r i a b l e n o r t h e mean r i s k p r e m i u m s p r o v e d t o be s i g n i f i c a n t l y d i f f e r e n t f r o m z e r o a t t h e 5% s i g n i f i c a n c e l e v e l . H e n c e t h e n u l l h y p o t h e s i s i s a c c e p t e d and i t i s c o n c l u d e d t h a t f u t u r e s c o n t r a c t s e m i - m o n t h l y h o l d i n g -79-p e r i o d r i s k p r e m i u m s a r e i n d e p e n d e n t o f c o m p a r a b l e h o l d i n g p e r i o d r e t u r n s on a s e c u r i t y m a r k e t i n d e x and t h a t t h e mean v a l u e o f t h e r i s k p r e m i u m s i s e q u a l t o o r v e r y c l o s e t o z e r o . In t h e c a s e o f w h e a t , t h e 10 y e a r mean r i s k p r e m i u m f o r a l l f i v e f u t u r e s c o n t r a c t s c a r r i e s a n e g a t i v e s i g n . By c o m p a r i s o n , a l l s e v e n s o y b e a n f u t u r e s c o n t r a c t s d i s p l a y a p o s i t i v e mean r i s k p r e m i u m . The r e s u l t s f o r c o r n a r e m i x e d . T h r e e o f t h e c o r n f u t u r e s c o n t r a c t s h a v e a n e g a t i v e mean r i s k p r e m i u m w h i l e t h e r e m a i n i n g two f u t u r e s c o n t r a c t s h a v e a p o s i t i v e mean r i s k p r e m i u m . H o w e v e r , c o m p u t a t i o n o f t h e t -s t a t i s t i c s e v i d e n c e s t h a t n o n e o f t h e mean r i s k p r e m i u m s f o r w h e a t o r c o r n i s s i g n i f i c a n t a t t h e 5% l e v e l and o n l y one o f t h e s e v e n 10 y e a r mean r i s k p r e m i u m s f o r s o y b e a n s ( i . e . November f u t u r e s c o n t r a c t ) i s s i g n i f i c a n t l y d i f f e r e n t f r o m z e r o . Even i n t h i s i n s t a n c e , t h e mean r i s k p r e m i u m i s n o t s i g n i f i c a n t a t t h e \% l e v e l and i t i s c o n c l u d e d t h a t , as e x p e c t e d , t h e mean r i s k p r e m i u m f o r t h e c o m m o d i t i e s s t u d i e d i s n o t s i g n i f i c a n t l y d i f f e r e n t f r o m z e r o . As an a s i d e , i t may be n o t e d t h a t t h i s i s t r u e n o t w i t h s t a n d i n g t h e f a c t t h a t e x p l i c i t a t t e m p t was made t o r e s t r i c t t h e s a m p l e t o a p e r i o d t h a t w o u l d q u a l i f y a s " s t a b l e " p r i c e y e a r s . The o b s e r v a t i o n t h a t t h e mean r i s k p r e m i u m i s n o t s t a t i s t i c a l l y d i f f e r e n t f r o m z e r o , w h i l e n o t s u r p r i s i n g , d o e s add w e i g h t t o t h e r e j e c t i o n by o t h e r s o f t h e K e y n e s - H i c k s t h e o r y . T h a t i s , t h e s p e c u l a t o r c a n n o t r e a l i z e p o s i t i v e - 8 0 -r e t u r n s by c o n t i n u o u s l y m a i n t a i n i n g a long f u t u r e s c o n t r a c t p o s i t i o n . The r e l a t i o n s h i p , i f any , between hedg ing a c t i v i t y and the payment of any r i s k premium i s , of c o u r s e , not c o n -s i d e r e d by t h i s t e s t . An i m p l i c a t i o n of the f i n d i n g t h a t the measure of s y s t e m a t i c r i s k f o r each of the t h r e e c o m m o d i t i e s i s equa l to or v e r y c l o s e to z e r o i s t h a t the r i s k i n h e r e n t in f u t u r e s c o n t r a c t s i s independent of the r i s k of a l l a s s e t s c o n s i d e r e d c o l l e c t i v e l y and hence can be d i v e r s i f i e d away. T h i s b e i n g s o , i n v e s t o r s w i l l not be compensated f o r the r i s k t h a t i s un ique to f u t u r e s c o n t r a c t s . As noted by Dusak and as d i s -c u s s e d in Chapte r I I , such an i n t e r p r e t a t i o n must be q u a l i f i e d by r e c o g n i z i n g t h a t the S & P 5 0 0 i ndex from which the market r e t u r n v a r i a b l e i s d e t e r m i n e d i s an i m p e r f e c t p roxy f o r t o t a l w e a l t h . That i s , b e i n g c o m p r i s e d p u r e l y of common s t o c k s , the S & P 5 0 0 i ndex does not embody the e f f e c t of r e t u r n s on such as b o n d s , r e a l p r o p e r t y , and commodity f u t u r e s c o n t r a c t s . TABLE I I : R e g r e s s i o n o f t h e S e m i - M o n t h 1 y H o l d i n g P e r i o d R e a l i z e d R i s k P r e m i u m on C o m p a r a b l e R e t u r n s on t h e S&P 500 S e c u r i t y P r i c e I n d e x . t o ' 1 mt t C o m m o d i t y : WHEAT F u t u r e s C o n t r a c t S a m p l e P e r i od ( t RP v a l u e ) ( t A v a l u e ) ( t A T l v a l u e ) R 2 D u r b i n -Wa t s o n No . o f O b s e r v a J u l y 1961-65 _ .0169 _ .0166 . 081 5 . 0001 1.61 1 0 8 (-1 . 128) (-1 .083) ( - • 1 1 9 ) 1966-70 - . 0 1 9 2 - . 0 1 9 2 . 2767 . 0 0 0 8 1 .63 1 1 1 ( - .749 ) ( - • 747) ( . 2 9 1 ) 1961-70 - .0181 - .oi;-84 1 £39 3 . 0002 1 .63 2 1 9 (-1 .2.1 2)1 .226 ) ( .232 ) S e p t . 1961-65 - .0084 - .0088 . 0902 . 000 1 1 .60 1 1 1 c- • 525) (" .536 ) ( • 1 1 9 ) 1966-70 - . 0010 - . 0010 • 7 9 1 9 . 0 0 7 0 1 . 5 1 1 1 2 ( - .039) (" .040) ( .884) 1961-70 - . 0047 - .0059 .5309 .0036 1 .54 223 ( - .308 ) ( - • 388) ( .888 ) Dec . 1961-65 .0004 - .001 2 .4418 .0026 1 .70 1 1 0 ( .024) (" .067) ( • 531) 1966-70 - .0182 - . 01 82 • 5267 .0030 1 .59 1 1 1 ( - .746) (" .677) ( .577 ) 1961-70 - .0089 - .0099 • 5209 . 0032 1 .64 221 ( - .558 ) (" .615) ( . 836 ) TAB LE I I : (cont i nued) Commodity : WHEAT A F u t u r e s Sample RP Y o C o n t r a c t P e r i o d (t va1ue) (t va1ue) March 1962-66 _ . 0004 . 0033 (- .023) ( - • 190) 1967-71 - . 0072 - .0070 (- .273) (- .266) 1 9 6 2 - 7 1 - .0038 - . 0049 (- .238) (- .308) May 1962-66 .0059 .0003 ( .277) ( .018) 1967-71 - . 0230 - .0235 . 8 7 3 (- .886) 1962-71 - .0087 - .01 06 (- .546) ( - . 661) (t v a l u e ) D u r b i n -Watson No. of O b s e r v a t i o n s 1 .2288 .0210 1 • 74 1 08 ( 1 .507) . 8 1 6 2 .0075 1 . 6 5 1 1 1 ( • 908) .9599 .0111 1 .67 21 9 ( 1 . 5 6 2 ) 1 .2382 .0185 1 • 92 1 1 0 ( 1 . 4 2 8 ) . 2443 .0006 1 • 9 1 1 1 2 ( .266) «• .5997 . 0040 1 .92 222 • 941) TABLE I I : (cont i nued) Commodity : CORN A F u t u r e s Sample RP Y o C o n t r a c t P e r i o d (t v a l u e ) (t va 1 ue J u l y 1961-65 _ . 0050 _ . 0046 (- • 339) (- . 308) 1966-70 - .0070 - . 0070 (- • 381) (- • 380) 196 1-70 - .0060 - . 0058 • 510) .489) S e p t . 1961-65 - .0059 _ .0083 (- .381) (- .522) 1 9 6 6 - 7 0 .0061 .0062 ( • 2 5 5 ) ( .258) 1961-70 . 0002 - . 0006 ( .014) .041) Dec. 1961-65 _ . 00 1 0 _ . 0008 (- .063) (- • 053) 1966-70 .0112 .0113 ( .404) ( • 405) 1961-70 .0052 .0050 ( .326) ( • 310) Y l (t v a l u e ) Du rb i n -Wa t s on No. of O b s e r v a t i o n s - . 1 0 2 4 . 0002 1 .89 1 09 ( - . 1 5 6 ) - . 1 4 5 5 . 0 0 0 4 1 • 52 1 1 1 ( - . 2 1 4 ) - . 1 2 4 6 .0003 1 .66 220 ( - . 2 6 4 ) .4988 . 0042 1 • 50 1 0 8 ( .667) . 3081 .001 3 1 • 57 1 1 1 ( .372) • 3449 .0017 1 • 54 2 1 9 ( .612) - . 0 3 3 5 . 0000 1 .48 1 1 0 ( - . 0 4 4 ) . 2080 . 0004 1 .49 1 1 1 ( .220) . 1 094 . 0001 1 .49 22 1 ( .175) TABLE I I : (cont i nued) Commodity : CORN A F u t u r e s Sample RP Y o C o n t r a c t P e r i o d (t v a l u e ) ( t v a l u e ) March 1 9 6 2 - 6 6 - . 0 0 7 5 - . 0 0 8 1 ( - . 4 9 1 ) ( - . 5 2 3 ) 1 9 6 7 - 7 1 . 0020 .0020 ( . 0 7 6 ) ( . 0 7 7 ) 1 9 6 2 - 7 1 - . 0027 - . 0 0 2 8 ( - . 1 7 6 ) ( - . 1 8 2 ) May 1962-66 . 0006 . 0 0 2 3 ( .044) ( . 1 6 2 ) 1967-71 . 0001 . 0 0 0 7 ( .004) ( .026) 1962-71 . 0004 .001 4 ..('.'0 2-6'); ( . 0 9 1 ) M R D u r b i n - No. of (t v a l u e ) Watson Obse rva t i on s . 2 0 9 6 . 0 0 0 8 1 . 7 1 1 1 0 ( .289) - .0359 . 0000 1 . 5 5 1 1 3 ( - . 0 4 0 ) .0412 .0000 1 .58 223 ( .070) - . 3 7 6 1 . 0 0 2 8 1 .83 1 1 0 ( T . 5 5 3 ) - . 3 1 5 7 .001 0 1 . 5 3 1 12 ( - . 3 2 9 ) - . 3 3 4 1 .001 3 1 . 7 6 222 ( - . 5 4 0 ) TABLE I I : (cont i nued) Commodity : SOYBEANS F u t u r e s Sample RP Y o Y l R 2 Durb i n - No. of C o n t r a c t Per i od (t va1ue) ( t va1ue) (t v a l u e ) Wa t son O b s e r v a t i o n s J u l y 1961-65 .0258 . 0 1 9 9 1.4806 .0113 1 -75 1 06 ( .847) ( .644) ( 1 . 0 8 8 ) 1966-70 • 0 2 5 3 . 0 2 5 3 - - . 1 3 2 9 . 0003 1 .96 1 1 1 (1 .289) (1 .284) ( - . 1 8 2 ) 1961 -70 . 0256 .0246 .5015 . 0023 1 . 8 0 217 (1 . 4 3 0 (1 .368) ( . 6 9 8 ) August 1962-65 - . 0029 - .0031 .0737 .0001 2 . 23 88 (- .134) (- .140) ( .077) 1966-70 .0330 .0324 - . 3 8 2 2 . 0022 1 .86 1 10 (1 .563) (1 • 527) ( - . 4 9 0 ) 1962-70 .0170 . 0 1 7 2 - . 2 7 2 7 . 001 1 1 . 9 8 1 98 (1 .112) (1 .126) ( - . 4 5 5 ) S e p t . 1961-65 . 0226 . 0 2 0 8 .3784 .0012 1 .87 1 06 (1 .023) ( . 9 1 7 ) ( . 3 5 7 ) 1966-70 .0255 .0253 - .921 1 . 0 1 8 6 1 .68 1 1 1 (1 .363) (1 .363) (-.1 . 4 3 8 ) 1961-70 .0241 .0252 - . 4 9 2 9 .0035 1 .76 2 1 7 (1 .679) (1 .744) ( - . 8 7 4 ) Nov. 1961-65 .0349 . 0 3 4 8 .0355 . 0000 1 . 6 3 1 1 1 (2 . 0 6 5 ) * (2 . 0 1 4 ) * ( .045) 1966-70 .0237 . 0 2 3 4 - . 5 0 2 5 .0059 1 .62 1 1 1 (1 • 307) ( 1 . 2 8 9 ) ( - . 8 0 7 ) 1961-70 . 0 2 9 3 . 0 2 9 8 - . 2 9 2 9 .0017 1.61 222 (2 . 3 6 6 ) * (2 . 4 0 4 ) * ( - . 6 0 7 ) TABLE I I : ( c o n t i nued) Commodity : SOYBEANS A F u t u r e s Sample RP Y o C o n t r a c t P e r i o d (t v a l u e ) (t va1ue) J a n . 1 9 6 2 - 6 6 .0339 .0351 (1 .777) (1 .810) 1 9 6 7 - 7 1 .01 74 . 01 84 ( • 940) ( .993) 1 9 6 2 - 7 1 . 0256 . 0 2 6 9 (1 • 932) (2 . 0 2 4 ) " March 1962-66 . 0299 .0286 (1 .452) (1 . 3 7 5 ) 1967-71 .0115 .0114 ( .655) ( .649) 1962-71 .0206 . 0 2 0 8 (1 .528) (1 .541) May 1962-66 . 0 2 5 7 .0255 (1 . 228) (1 .185) 1 9 6 7 - 7 1 .0077 .0095 ( .440) ( .544) 1 9 6 2 - 7 1 .01 66 .0185 (1 . 220) (1 .351) Y l (t v a l u e ) Durb i n -Wa t s on No. of O b s e r v a t i o n s - . 3422 . 0 0 1 3 1 . 7 2 1 1 0 (- . 3 7 7 ) - . 6 9 4 6 . 0 1 0 5 1 . 6 3 1 1 2 ( -1 . 0 7 9 ) - . 5 5 7 7 . 0 0 5 1 1 . 6 7 2 2 2 (-1 . 0 6 2 ) . 4 9 9 5 . 0024 2 . 0 8 1 1 0 ( • 5 1 0 ) - . 5 8 4 8 . 0 0 8 6 1 . 7 2 1 1 2 (- . 9 7 5 ) - . 1 9 7 7 . 0 0 0 6 1 . 9 2 2 2 2 (- . 3 7 4 ) . 0 3 8 8 . 0 0 0 0 2 . 0 6 1 1 0 ( . 0 3 7 ) - . 9 2 8 7 . 0 2 1 0 1 . 6 2 1 1 2 ( -1 . 5 3 6 ) - • 5 9 0 2 . 0 0 5 3 2 . 0 3 2 2 2 (-1 . 0 8 3 ) -87-Test #2 R e g r e s s i o n M o d e l : R P t = YQ + Y 2 A N H T + E T T a b l e III summarizes the r e s u l t s of the t e s t s u t i l i z i n g the above r e g r e s s i o n m o d e l . P a r t i c u l a r l y in the case of both c o r n and s o y b e a n s , and to a somewhat l e s s e r degree in the case of w h e a t , the s t r i k i n g r e s u l t of t h i s t e s t i s t h a t the c o e f f i -c i e n t of the change i n net hedg ing v a r i a b l e i s not o n l y s i g n i f i -c a n t but c a r r i e s a p o s i t i v e s i g n . That i s , the r i s k premium i s r e l a t e d , and p o s i t i v e l y s o , to the change in net s h o r t h e d g i n g . In both c o r n and s o y b e a n s , the r e s u l t s a r e u n i f o r m l y c o n s i s t e n t w i t h the e x c e p t i o n of one of the soybean 5 yea r s i m p l e r e g r e s s i o n e q u a t i o n s where the c o e f f i c i e n t , w h i l e p o s i -t i v e , i s not s i g n i f i c a n t at the 5% l e v e l . The f i n d i n g s f o r wheat a r e l e s s c o n c l u s i v e . For the 10 y e a r p e r i o d , the c o e f f i c i e n t of the change in net hedg ing v a r i a b l e i s u n i f o r m l y p o s i t i v e , but in o n l y f o u r of the f i v e f u t u r e s c o n t r a c t s , the September f u t u r e s c o n t r a c t b e i n g the e x c e p t i o n , i s the e s t i -mated c o e f f i c i e n t s i g n i f i c a n t l y d i f f e r e n t f rom z e r o . The r e s u l t s of the 5 yea r e q u a t i o n s a r e l e s s u n i f o r m . A s i d e from the f o u r c o e f f i c i e n t s which a r e both p o s i t i v e and s i g n i f i c a n t , the r e m a i n i n g e s t i m a t e d c o e f f i c i e n t s a r e n e i t h e r s i g n i f i c a n t l y d i f f e r e n t f rom z e r o nor u n i f o r m o f s i g n . H y p o t h e s i s #2 was c o n c e r n e d w i t h the r e l a t i o n s h i p between the r i s k premium and the change in net hedg ing v a r i a b l e , n a m e l y : - 8 8 -H^: The s e m i - m o n t h l y h o l d i n g p e r i o d r e a l i z e d r i s k premium i s p o s i t i v e l y r e l a t e d to the change in net s h o r t hedg i ng. H^: The s e m i - m o n t h l y h o l d i n g p e r i o d r e a l i z e d r i s k premium i s n e g a t i v e l y r e l a t e d t o the change in net s h o r t h e d g i n g . The t e s t r e s u l t s f a i l e d to r e j e c t the n u l l h y p o t h e s i s . As s u c h , t h e s e f i n d i n g s r u l e out C o o t n e r ' s e a r l i e r hedg ing p r e s s u r e t h e o r y . R a t h e r , i t has been found t h a t changes in f u t u r e s p r i c e s and changes in net s h o r t hedg ing a re p o s i t i v e l y c o r r e l a t e d such t h a t the r e a l i z e d r i s k premium i s p o s i t i v e l y r e l a t e d to changes in net s h o r t h e d g i n g . S i n c e C o o t n e r ' s hedg ing p r e s s u r e t h e o r y i s i n v a l i d , the r e l a t i o n s h i p o b s e r v e d i s e v i d e n t l y due to w e a l t h e f f e c t s . At any g i v e n p r i c e , the commodity h a n d l e r a l l o c a t e s a p r o p o r t i o n of h i s i n v e s t m e n t in i n v e n t o r y to a more s e c u r e a s s e t form ( v i a f u t u r e s c o n t r a c t s ) in a c c o r d a n c e w i t h h i s u t i l i t y c h a r a c t e r i s t i c Shou ld an i n c r e a s e in spot p r i c e s s u b s e q u e n t l y o c c u r the h a n d l e r w i l l e x p e r i e n c e an i n c r e a s e in w e a l t h by reason of t h a t p o r t i o n of h i s i n v e n t o r y wh ich was unhedged. Assuming he d i s p l a y s c o n -s t a n t or i n c r e a s i n g r e l a t i v e r i s k a v e r s i o n t h e n , c e t e r i s p a r i b u s i t i s o p t i m a l f o r the h a n d l e r to hedge a p o r t i o n of the p r e v i -o u s l y unhedged component of h i s i n v e n t o r y i n v e s t m e n t . Changes in spot p r i c e s and changes in f u t u r e s p r i c e s b e i n g p o s i t i v e l y c o r r e l a t e d , an i n c r e a s e in the spot p r i c e i s n o r m a l l y accompanie - 8 9 -by an i n c r e a s e in the f u t u r e s p r i c e . Hence an i n c r e a s e in the spot p r i c e wh ich r e s u l t s in an i n c r e a s e in s h o r t hedg ing due to w e a l t h e f f e c t s a l s o i m p l i e s the p o s i t i v e r e l a t i o n s h i p b e -tween the r e a l i z e d r i s k premium and changes in net s h o r t h e d g i n g . The same c o n c l u s i o n h o l d s , and f o r c o m p a r a b l e r e a s o n s , s h o u l d a d e c r e a s e in the spot p r i c e be e x p e r i e n c e d . TABLE I I I : R e g r e s s i o n of the S e m i - M o n t h l y H o l d i n g P e r i o d R e a l i z e d R i s k Premium on the Change in Net Hedg i ng . RP^ = Y Q + Y 2 ANH t + e t Commod i t y : WHEAT F u t u r e s Sample RP Y o Y 2 R 2 Du rb i n- No . of C o n t r a c t P e r i o d (t v a l u e ) (t v a l u e ) (t v a l u e ) Watson O b s e r v a t i o n s J u l y 1 9 6 1 - 6 5 - . 0 1 6 9 _ . 0 1 7 9 . - P . 40222 . 0061 1 . 6 2 1 0 8 ( f - K 1 2 8 ) ( - 1 . 1 9 0 ) ( - . 8 0 8 ) 1 9 6 6 - 7 0 - . 0 1 9 2 - . 0 0 9 1 1 1 . 2 1 2 7 . 1 5 3 9 1 . 6 3 1 1 1 ( - . 7 4 9 ) (- . 3 8 4 ) ( 4 . 4 5 2 ) * 1 9 6 1 - 7 0 - . 0 1 8 1 - . 0 1 3 7 5 . 5 2 6 2 . 0 5 1 5 1 . 6 2 2 1 9 ( - 1 . 2 1 2 ) \ ( - • 9 3 7 ) ( 3 . 4 3 D * S e p t . 1 9 6 1 - 6 5 - - . 0 0 8 4 _ . 0 0 8 4 - . 0 8 5 4 . 0 0 0 0 1 . 6 0 1 1 1 ( - . 5 2 5 ) (- . 5 2 2 ) ( - . 0 5 0 ) 1 9 6 6 - 7 0 - . 0 0 1 0 - . 0 0 1 3 4 . 6 4 3 9 . 0 3 3 5 1 . 4 4 1 1 2 ( - . 0 3 9 ) (- . 0 5 0 ) (1 . 9 5 2 ) 1 9 6 1 - 7 0 - . 0047 - . 0 0 5 0 2 . 5 8 9 5 . 0 1 3 4 1 • 5 2 2 2 3 ( - . 3 0 8 ) (- . 3 2 8 ) (1 . 7 3 0 Dec . 1961-65 +.0004 . 0 0 1 1 - 1 . 1 3 1 0 . 0 0 3 7 1 . 7 1 1 1 0 ( .024) ( . 0 6 4 ) ( - . 6 3 7 ) 1 9 6 6 - 7 0 - . 0 1 8 2 - .0161 6 . 4 9 7 7 . 0 6 6 7 1 . 5 0 1 1 1 ( - . 7 4 6 ) (- . 6 1 9 ) ( 2 . 7 9 1 ) * 1 9 6 1 - 7 0 - . 0 0 8 9 - . 0 0 9 5 3 . 1965 . 0 2 0 2 1 . 6 2 2 2 1 ( - . 5 5 8 ) (- • 5 9 8 ) ( 2 . 1 2 6 ) * TABLE I I I : (cont i nued) Commodity : WHEAT A Fu t u r e s Sample RP Y o C o n t r a c t P e r i o d ( t va1ue) (t v a l u e ) March 1 9 6 2 - 6 6 _ .0004 _ . 0 0 0 1 (- . 0 2 3 ) (- . 0 1 2 ) 1 9 6 7 - 7 1 - . 0 0 7 2 - . 0 0 5 9 (- . 2 7 3 ) (- . 2 3 2 ) 1 9 6 2 - 7 1 - . 0 0 3 8 - . 0042 (- . 2 3 8 ) (- . 2 7 0 ) May 1 9 6 2 - 6 6 . 0 0 5 9 . 0 0 5 9 ( • 2 7 7 ) ( . 3 3 4 ) 1 9 6 7 - 7 1 - . 0 2 3 0 - . 0 1 7 9 (- . 8 7 3 ) (- . 7 1 4 ) 1 9 6 2 - 7 1 - . 0 0 8 7 - . 0 0 6 7 (- .546) (- . 4 3 0 ) Y 2 R 2 Durb i n- No. of (t v a l u e ) Wa t son Observa t ions -.4084 . 0005 1 -77 1 0 8 (-.235) 7.2026 . 0809 1 .55 1 1 1 ( 3 . 0 9 7 ) * 3.7553 .0285 1 .65 219 ( 2 . 5 2 2 ) " .0951 .0000 1 . 94 110 1 (.053) vp 8.1287 . 10 2 5 1 .77 112 ( 3 . 5 4 5 ) " 4.5418 . 0404 1 . 88 222 ( 3 . 0 4 3 ) * T A B L E I I I : ( c o n t i n u e d ) C o m m o d i t y : CORN F u t u r e s S a m p l e RB V C o n t r a c t P e r i od ( t v a 1 u e ) ( t v a l u e ) J u l y 1 9 6 1 - 6 5 _ . 0 0 5 0 _ . 0 0 8 0 •OS • 3 3 9 ) ( " . 5 7 8 ) 1 9 6 6 - 7 0 - . 0 0 7 0 - . 0 2 0 3 ( - . 3 8 1 ) ( - 1 . 6 5 8 ) 1 9 6 1 - 7 0 - . 0 0 6 0 - . 01 42 ( - • 5 1 0 ) ( - 1 . 5 3 3 ) S e p t . 1 9 6 1 - 6 5 - . 0 0 5 9 - . 0 0 2 5 ( - . 3 8 1 ) ( - . 1 7 4 ) 1 9 6 6 - 7 0 . 0 0 6 1 - . 0 2 0 1 ( . 2 5 5 ) . 2 9 9 ) 1 9 6 1 - 7 0 . 0 0 0 2 - . 0 0 9 4 ( . 0 1 4 ) ( - . 8 7 8 ) D e c . 1 9 6 1 - 6 5 - . 0 0 1 0 . 0 0 1 6 ( - . 0 6 3 ) ( . 1 1 6 ) 1 9 6 6 - 7 0 . 0 1 1 2 . 0 0 4 7 ( . 4 0 4 ) ( • 2 5 4 ) 1 9 6 1 - 7 0 . 0 0 5 2 . 0 0 3 8 ( . 3 2 6 ) ( . 3 3 2 ) Y 2 R 2 D u r b i n - N o . o f ( t v a l u e ) Wa t s o n O b s e r v a t i o n s 5 - 5 0 8 5 . 1 2 6 6 1 - 7 2 1 0 9 ( 3 - 9 3 7 ) * 8 . 4 4 6 4 . 5 6 3 5 1 . 5 7 1 1 1 ( 1 1 . 8 6 2 ) * 7 . 7 0 8 9 . 3 8 5 1 1 . 5 9 2 2 0 ( 1 1 . 6 8 5 ) * 5 . 8 7 0 5 . 1 4 3 8 1 . 4 2 1 0 8 ( 4 . 2 2 0 ) * 9 . 8 0 5 9 . 5 9 2 0 1 . 7 6 1 1 1 ( 1 2 . 5 7 6 ) * 8 . 9 1 7 8 . 4 4 9 3 1 • 5 7 2 1 9 ( 1 3 . 3 0 5 ) * 7 . 5 0 8 7 . 2 7 6 8 1 . 6 0 1 1 0 ( 6 . 4 3 0 ) * 1 0 . 9 3 4 3 . 5 5 5 3 1 . 7 8 1 1 1 ( 1 1 . 6 6 8 ) * 1 0 . 0 6 5 3 . 4 7 7 2 1 . 7 1 2 2 1 ( 1 4 . 1 3 9 ) * TABLE I I I : (cont i nued) Commodity : CORN F u t u r e s Sample RP A Y o A Y 2 R 2 Du rb i n- No. of C o n t r a c t Pe r i od (t v a l u e ) ( t v a l u e ) (t v a l u e ) Wa t s o n O b s e r v a t i o n s March 1962-66 - . 0 0 7 5 - . 0 1 0 2 6 . 6 0 9 3 . 2 2 9 0 1 . 72 1 1 0 ( - . 4 9 1 ) ( - . 7 5 4 ) ( 5 . 6 6 3 ) * 1967-71 .0020 . 0020 1 0 . 7 1 3 0 . 5 7 4 9 1 .91 113 (v0'76).} ( .118) ( 1 2 . 2 5 1 ) * 1 9 6 2 - 7 1 S T O 0 2 7 - . 0 0 4 6 9 . 6 8 3 4 .4748 1 .76 223 ( - . 1 7 6 ) C - . 4 1 2 ) ( 1 4 . 1 3 5 ) * May 1 9 6 2 - 6 6 . 0 0 0 6 - . 0 0 4 7 5 . 2 9 1 0 . 1 6 8 7 1 • 73 110 , ( . 0 4 4 ) ( - . 3 7 3 ) ( 4 . 6 8 2 ) * 1967-71 .000 1 . 0 0 3 6 1 0 . 9 5 8 0 . 6 1 3 6 1 . 70 112 Y ( .004) ( . 2 1 0 ) ( 1 3 . 2 1 6 ) * 1 9 6 2 - 7 1 .0004 - . 0 0 2 9 9 . 6 8 9 5 . 4 9 7 2 1 .71 222 ( . 0 2 6 ) ( - . 2 6 5 ) ( 1 4 . 7 5 1 ) * TABLE I I I : (cont i nued) Commodity : SOYBEANS A F u t u r e s Sample RP Y o C o n t r a c t P e r i o d (t va1ue) (t v a l u e ) J u l y 1 9 6 1 - 6 5 . 0 2 5 8 . 0 2 7 7 ( • 8 4 7 ) (1 . 0 0 6 ) 1 9 6 6 - 7 0 . 0 2 5 3 . 0 1 9 8 (1 . 2 8 9 ) (1 . 0 3 4 ) 1 9 6 1 - 7 0 . 0 2 5 6 . 0 2 1 5 (1 . 4 3 1 ) (1 . 2 8 6 ) ^ Aug . 1 9 6 2 - 6 5 - . 0 0 2 9 . 0 0 2 8 (- • 1 3 4 ) ( . 1 4 6 ) - • " 70 1 9 6 6 - 7 0 . 0 3 3 0 . 0 2 9 1 (1 . 5 6 3 ) (1 . 3 8 6 ) 1 9 6 2 - 7 0 . 0 1 7 0 . 1 0 5 4 (1 . 1 1 2 ) (1 . 0 6 8 ) S e p t . 1 9 6 1 - 6 5 . 0 2 2 6 . 0 5 9 0 (1 . 0 2 3 ) (2 • 7 9 2 ) * 1 9 6 6 - 7 0 • 0 2 5 5 . 0 2 3 6 (1 • 3 6 3 ) (1 • 2 9 2 ) 1 9 6 1 - 7 0 . 0 2 4 1 . 0 3 3 3 (1 . 6 7 9 ) ( 2 . 4 2 2 ) * Nov . 1 9 6 1 - 6 5 . 0 3 4 9 . 0 3 7 1 (2 . 0 6 5 ) * (2 • 3 9 0 ) * 1 9 6 6 - 7 0 . 0 2 3 7 . 0 2 2 8 (1 • 3 0 7 ) (1 . 3 5 2 ) 1 9 6 1 - 7 0 . 0 2 9 3 . 0 3 0 1 (2 . 3 6 6 ) * ( 2 . 6 3 3 ) * Y 2 R 2 Du rb i n - No. of (t v a l u e ) Watson O b s e r v a t i o n s 9 . 7 2 9 6 . 1 9 1 7 1 . 7 6 1 0 6 ( 4 . 9 6 6 ) * 4 . 3 5 2 1 . 0 6 6 9 1 . 9 3 1 1 1 ( 2 . 7 9 5 ) * 7 . 3 2 6 0 . 1 3 4 4 1 . 8 1 2 1 7 ( 5 - 7 7 7 ) * 7 . 0 9 1 6 . 2 3 7 4 2 . 3 7 8 8 ( 5 . 1 7 5 ) * 3 . 2 7 0 2 . 0 3 3 5 1 . 7 9 1 10 (1 - 9 3 5 ) 5 . 2 6 6 5 . 1 0 4 5 1 . 9 3 1 9 8 ( 4 . 7 8 2 ) * 1 0 . 0 1 3 2 • 1 9 5 6 2 . 0 1 1 0 6 ( 5 . 0 2 9 ) * 3 . 7 2 5 6 . 0 5 0 8 1 . 6 3 1 1 1 ( 2 . 4 1 4 ) * 6 . 0 7 3 1 . 1 0 3 2 1 . 8 0 2 1 7 ( 4 . 9 7 5 ) * 5 . 0 5 9 3 . 1 6 3 4 1 . 8 3 1 1 1 ( 4 . 6 1 4 ) * 6 . 1 3 8 ^ . 1 4 2 8 1 . 6 3 1 1 1 ( 4 . 2 6 1 ) * 5 . 4 8 6 2 . 1 5 0 2 1 . 7 3 2 2 2 ( 6 . 2 3 6 ) * TABLE I I I : (cont i nued) Commodity : SOYBEANS A F u t u r e s Sample RP Y o C o n t r a c t P e r i o d (t v a l u e ) ( t v a l u e ) J a n u a r y 1962-66 .0339 .0376 (1 .777) (2 . 1 3 9 ) * 1967-71 .01 Ik .0191 ( • 940) (1 . 102) 1962 - 7 1 .0256 .0283 (1 .932) (2 . 3 0 0 ) * Ma r c h 1962-66 .0299 .0286 (1 .452) (1 .526) 1967-71 . 0 1 1 5 .0110 ( • 655) ( .664) 1962-71 . 0206 .0197 (1 .528) (1 .583) May 1962-66 .0257 . 0224 (1 . 2 2 8 ) (1 .214) 1967 - 7 1 .0077 . 0 0 9 3 ( .440) ( .570) 1 962-71 .0166 .01 62 (1 . 220) (1 • 312) No. of O b s e r v a t i o n s 5 -7899 . 1 5 8 7 1 .87 1 1 0 ( 4 . 5 1 3 ) * 6 . 0 1 1 6 . 1 337 1 .59 1 1 2 ( 4 . 1 2 1 ) * 5 . 8 7 5 3 .1456 1 . 7 3 222 ( 6 . 1 2 2 ) * 6 .4451 . 1 8 0 2 2 .21 1 10 ( 4 . 8 7 3 ) * 5-3019 . 1 1 2 3 1 .68 1 1 2 (3 .731 )* 5 . 9 8 0 4 . 1 496 1 .97 222 (6 .221 )* 7 .4448 . 2 2 7 7 2 .29 1 1 0 ( 5 . 6 4 3 ) * 5.6041 . 1274 1 .60 1 1 2 ( 4 . 0 0 8 ) * 6 . 6 9 3 2 . 1 829 2 .21 222 ( 7 . 0 1 7 ) * Y 2 R 2 D u r b i n -(t v a l u e ) Watson - 9 6 -Test #3 R e g r e s s i o n m o d e l : RP^ = yn + Y 0 NH + e t 0 3 t t The r e s u l t s o b t a i n e d are shown in T a b l e IV. At the 5% s i g n i f i c a n c e l e v e l , none o f the i n t e r c e p t terms f o r corn or s o y -beans i s s i g n i f i c a n t l y d i f f e r e n t f rom z e r o and o n l y one of the 5 yea r i n t e r c e p t terms f o r wheat i s s i g n i f i c a n t . Of the c o e f f i -c i e n t s of the net s h o r t hedg ing v a r i a b l e , none i s s t a t i s t i c a l l y s i g n i f i c a n t in the case of s o y b e a n s . Two of the 5 yea r r e -g r e s s i o n e q u a t i o n s f o r wheat d i s p l a y a s i g n i f i c a n t c o e f f i c i e n t on the net h e d g i n g v a r i a b l e w h i l e , f o r c o r n , one of the c o e f f i c i e n t s i s s i g n i f i c a n t but c a r r i e s a n e g a t i v e s i g n . For the 10 y e a r p e r i o d , the o n l y s i g n i f i c a n t c o e f f i c i e n t of the net hedg ing v a r i a b l e a p p e a r s in one of the corn e q u a t i o n s and i s of the wrong s i g n . I n c i d e n t a l l y , i t w i l l be noted w i t h r e g a r d to t h i s se t of r e s u l t s , as w i t h each of the o t h e r t e s t s , t h a t s i n c e the p r i c e changes of a l l f u t u r e s c o n t r a c t s in a g i v e n commodity in a g i v e n p e r i o d a re t y p i c a l l y p o s i t i v e l y c o r r e l a t e d , the t e s t s f o r a l l of the i n d i v i d u a l c o n t r a c t s a re not i ndependent of one a n o t h e r . The o b s e r v a t i o n t h a t the r i s k premium i s independent of the net hedg ing l e v e l i s r e v e a l i n g . The f i n d i n g t h a t the demand f u n c t i o n f o r hedg ing c o n t r a c t s i s p e r f e c t l y e l a s t i c a c c o r d s w i t h the o r i g i n a l T e l s e r p o s i t i o n but i s c o n t r a r y to C o o t n e r ' s p o s i t i o n and to the e x p e c t a t i o n of the s u p p l y - d e m a n d model in Chapte r I I I . W h i l e i n d i v i d u a l s p e c u l a t o r s may r e a l i z e -97-p o s i t i v e r e t u r n s , t h e c l a s s o f s p e c u l a t o r s do n o t r e c e i v e a p o s i t i v e r i s k p r e m i u m f o r t h e i n s u r a n c e t h e y p r o v i d e h e d g e r s , n o r do h e d g e r s as a c l a s s pay f o r t h e d e g r e e o f r e l i e f f r o m t h e r i s k o f p r i c e f l u c t u a t i o n a f f o r d e d by f u t u r e s c o n t r a c t s . C e r t a i n a n c i l l a r y t e s t s w e r e a l s o c o n d u c t e d . A t t h e 5% l e v e l o f s i g n i f i c a n c e , t h e l o w m a g n i t u d e o f t h e D u r b i n -W a t s o n s t a t i s t i c w h i c h was o b t a i n e d f o r a number o f t h e t e s t e q u a t i o n s i n d i c a t e s t h e p r e s e n c e o f p o s i t i v e s e r i a l c o r r e l a t i o n o f t h e d i s t u r b a n c e t e r m o f t h e r e g r e s s i o n m o d e l . The C o c h r a n e -O r c u t t i t e r a t i v e t e c h n i q u e was t h e r e f o r e e m p l o y e d and t h e m o d i f i e d t e s t r e s u l t s e x a m i n e d t o d e t e r m i n e any c h a n g e i n t h e s i g n i f i c a n c e o f t h e e s t i m a t e d c o e f f i c i e n t s . The p r o c e d u r e was a p p l i e d t o a m u l t i p l e r e g r e s s i o n e q u a t i o n e m b o d y i n g b o t h n e t h e d g i n g and c h a n g e i n n e t h e d g i n g as i n d e p e n d e n t v a r i a b l e s , and t h e r e s u l t s a r e r e p o r t e d i n T a b l e V. No a p p r e c i a b l e e f f e c t s on t h e s i g n i f i c a n c e . o f t h e e q u a t i o n p a r a m e t e r s w e r e r e a l i z e d and t h e c o n c l u s i o n s d r a w n r e m a i n u n a l t e r e d . B a s e d on b o t h T e s t s #2 and # 3 , and more p a r t i c u l a r l y f o r c o r n and s o y b e a n s t h a n f o r w h e a t , t h e c o m p a r a t i v e r e s u l t s f o r t h e f i r s t and s e c o n d 5 y e a r s o f t h e s a m p l e p e r i o d seem t o i m p l y c o n s i s t e n c y o f t h e m a r k e t c h a r a c t e r i s t i c s o v e r t h e 10 y e a r s t u d y p e r i o d . In an a t t e m p t t o v e r i f y t h i s i m p r e s s i o n , Chow t e s t s w e r e a p p l i e d t o t h e m u l t i p l e r e g r e s s i o n e q u a t i o n , w i t h b o t h n e t h e d g i n g and c h a n g e i n n e t h e d g i n g d e f i n e d as i n d e p e n d e n t v a r i a b l e s , t o t e s t t h e h y p o t h e s i s : -98-Hg: The sample data employed i n each of the 2 - 5 year s u b - p e r i o d s a r e drawn from the same p o p u l a t i o n . H j i The sample data employed in each of the 2 - 5 yea r s u b - p e r i o d s a r e drawn f rom a d i f f e r e n t p o p u l a t i o n . The Chow t e s t F - s t a t i s t i c s were computed f o r each of the f i v e wheat and corn f u t u r e s c o n t r a c t s and f o r the seven soybean f u t u r e s c o n t r a c t s , w i t h r e s u l t s as summarized b e l o w . On the b a s i s of t h i s t e s t , the soybean f u t u r e s market e x h i b i t s the most c o n s i s t e n t c h a r a c t e r i s t i c s over t ime w h i l e the wheat f u t u r e s market i s the l e a s t c o n s i s t e n t . CHOW TEST Commod i ty A c c e p t H ^ R e j e c t H 0 Wheat 2 3 Corn 3 2 Soybeans 7 0 TABLE IV: R e g r e s s i o n of the S e m i - M o n t h l y H o l d i n g P e r i o d R e a l i z e d R i s k Premium on the Leve l of Net Hedg i n g . R P t = Y 0 + ? 3 NH t + e t Commodity : WHEAT F u t u r e s Sample RP Y o Y 3 R 2 Du r b i n - No. of C o n t r a c t Pe r i od (t v a l u e ) (t v a l u e ) (t v a l u e ) Wa t son Obse r v a t i on s J u l y 1 9 6 1 - 6 5 _ . 0 1 6 9 - . 0 6 1 6 1 . 2 5 8 1 . 0400 1 . 7 0 1 0 8 ( - 1 . 1 2 8 ) ( - 2 . 3 8 1 ) * ( 2 . 1 0 1 ) * 1 9 6 6 - 7 0 - . 0 1 9 2 . 0 0 1 0 - . 5 1 1 9 . 0 0 2 3 1 . 6 2 1 1 1 (- • 7 4 9 ) ( . 0 2 1 ) ( - . 5 0 4 ) 1 9 6 1 - 7 0 - .0181 - . 0 3 0 5 . 3 3 0 7 .0014 1 .64 2 1 9 C - i . 2 1 2 ) ( - 1 . 1 3 4 ) ( . 5 5 5 ) S e p t . 1 9 6 1 - 6 5 - . 0 0 8 4 - . 0 5 3 2 1 . 2 1 3 4 . 0 3 5 0 1 . 6 6 1 1 1 (- • 5 2 5 ) ( - 1 . 9 3 3 ) (1 . 9 8 8 ) * 1 9 6 6 - 7 0 - . 0 0 1 0 . 0 0 6 9 - . 2 0 1 5 . 0 0 0 3 1 • 5 2 1 1 2 (- . 0 3 9 ) (.143) ( . 1 9 6 ) 1 9 6 1 - 7 0 - . 0047 - . 0246 • 5 2 4 7 . 0 0 3 5 1 . 5 7 2 2 3 (- • 3 0 8 ) ( - . 9 0 3 ) ( . 8 8 1 ) Dec. 1 9 6 1 - 6 5 . 0004 - . 0 3 8 2 • 9 3 7 6 . 0 2 0 8 1 - 7 5 1 1 0 ( . 024) ( - 1 . 2 3 8 ) (1 . 5 1 3 ) 1 9 6 6 - 7 0 - . 0 1 8 2 . 0 2 7 8 - 1 . 2 2 6 3 . 0 1 2 6 1 . 5 9 111 (- .746) ( . 5 8 7 ) ( -1 ,178) 1 9 6 1 - 7 0 - . 0 0 8 9 - . 0 0 7 8 - . 0 3 0 1 . 0 0 0 0 1 . 6 5 2 2 1 (- . 5 5 8 ) ( - . 2 7 4 ) ( - .051) TABLE IV: (continued) Commodity: WHEAT Futures Sample RP Y o Y 3 R 2 Dur b i n- No. of Contract Per i od (t va1ue) (t value) (t value) Wa t s on Observations March 1962 - 6 6 _ . 0004 -.0248 • 5 3 9 0 . 0 0 6 2 1 . 7 8 108 ( - • 0 2 3 ) (-.714) ( .814) 1967-71 - . 0 0 7 2 . 0 3 9 0 - 1 . 2 7 4 5 .0148 1 . 6 6 1 1 1 ( - . 2 7 3 ) ( . 8 7 3 ) ( - 1 . 2 8 0 ) 1962 -71 - . 0 0 3 8 .0104 - . 3 4 8 5 .0016 1 . 7 0 2 1 9 ( - . 2 3 8 ) ( . 3 5 8 ) ( - . 5 8 8 ) May 1 9 6 2 - 6 6 . 0 0 5 9 - . 0 2 8 8 . 7 5 5 7 . 0 1 0 5 1 . 9 6 1 1 0 ( . 2 7 7 ) ( - . 7 7 9 ) (1 . 0 6 8 ) 1 9 6 7 - 7 1 - . 0 2 3 0 . 0 3 6 2 - 1 . 6 0 8 6 . 0 2 3 5 1 . 8 9 1 1 2 ( - . 8 7 3 ) ( . 8 0 7 ) ( - 1 . 6 2 6 ) J 9 6 2 - 7 1 - . 0 0 8 7 . 0 0 7 5 - • 3 9 1 3 . 0 0 1 9 1 . 9 3 2 2 2 (- .546) ( . 2 5 1 ) ( - .642) TABLE IV: ( c o n t i n u e d ) Commodity : CORN F u t u r e s Sample RP Y o C o n t r a c t P e r i o d (t va1ue) ( t v a l u e ) J u l y 1 9 6 1 - 6 5 _ . 0 0 5 0 . 0028 (- . 339) ( .119) 1966-70 - . 0070 .0297 (- .381) (1 .246) 1 9 6 1 - 7 0 - . 0060 . 0209 (- .510) (1 • 302) S e p t . 1961-65 - . 0059 .0161 (- .381) ( • 678) 1 9 6 6 - 7 0 . 0061 .0173 ( • 255) ( .500) 1961-70 . 0002 .0130 ( .014) ( .627) Dec . 1961-65 - . 0010 . 01 54 (- • 063) ( • 744) 1 9 6 6 - 7 0 .0112 . 0256 ( .404) ( .623) 1961-70 . 0052 .0173 ( .326) ( .793) Y 3 R 2 Du rb i n - No. of (t v a l u e ) Wa t son O b s e r v a t i o n s - . 1 9 9 1 . 0 0 1 7 1 . 89 1 09 ( - . 4 3 3 ) - . 7 5 6 0 . 0482 1 - 5 2 111 ( - 2 . 3 4 9 ) * - . 6 1 5 2 . 0246 1 .66 220 ( - 2 . 4 3 0 ) * - . 5 6 2 7 .01 38 1 .47 1 0 8 ( - 1 . 2 1 9 ) - . 2 0 3 2 .0018 1 . 5 5 111 ( - . 4 4 8 ) - . 2 7 1 2 .0034 1 . 5 2 2 1 9 ( - . 8 5 5 ) - . 5 0 9 2 . 01 38 1 . 49 1 1 0 ( - 1 . 2 3 0 ) - . 2 3 5 3 . 002 1 1.47 1 1 1 ( - . 4 7 4 ) - . 2 6 0 4 . 0 0 3 0 1 .48 22 1 ( - . 8 1 6 ) TABLE IV: ( c o n t i n u e d ) Commod i t y : CORN A F u t u r e s Sample RP Y o C o n t r a c t P e r i o d (t va1ue) ( t v a l u e ) Ma r c h 1962-66 _ • 0075 01 02 (- • 491) 510) 1967-71 . 0020 0275 ( • 076) (• 696) 1962-71 - . 0027 01 52 (- .176) (• 724) May 1962-66 . 0006 0098 ( .044) (.' 523) 1967-71 . 0001 0406 ( . 004) (• 995) 1962-71 . 0004 # 0242 ( .026) (1 . 135) (t Y 3 v a l u e ) R 2 Du rb i n-Wa t son No. of O b s e r v a t i o n s • 5575 .01 70 1 .72 110 ( -1 . 3 6 8 ) - . 4006 .0067 1.52 1 1 3 (- . 8 6 7 ) - • 3737 . 0 0 7 0 1 . 56 223 ( -1 .245) — . 2640 . 0049 1 .83 110 (- • 727) - .632 1 .0161 1 . 49 1 1 2 ( -1 .340) - . 4822 .0116 1 .74 222 ( -1 • 609) TABLE IV: ( c o n t i n u e d ) Commodity : SOYBEANS F u t u r e s Sampl e RP Y o C o n t r a c t P e r i o d . (t va1ue) (t v a l u e ) J u l y 1961-65 . 0 2 5 8 _ . 0061 ' ( .847) (- • 1 32) 1966 - 7 0 . 0 2 5 3 . 0 2 5 9 (1 . 2 8 9 ) :.(i • 327) 1961-70 . 0256 . 0 1 2 9 (1 . 4 3 1 ) ( . 6 3 9 ) August 1962-65 - . 0 0 2 9 - . 0001 (- .1339) (- . 003) 1966-70 . 0 3 3 0 . 0 3 1 4 (1 • 563) ( i . 4 8 0 ) 1962-70 .01 70 . 0 1 6 7 (1 . 1 1 2 ) ( i . 000) S e p t . 1961-65 . 0 2 2 6 . 0054 (1 . 0 2 3 ) ( . 1 7 9 ) 1966-70 . 0255 . 0229 (1 . 3 6 3 ) ( i .214) 1961-70 . 0241 . 0 1 5 9 (1 . 6 7 9 ) ( • 979) Nov. 1961-65 . 0 3 4 9 . 0267 (2 . 0 6 5 ) * ( i . 280) 1966 - 7 0 . 0237 . 0224 (1 . 3 0 7 ) ( i . 2 2 8 ) 1 96 1 -70 . 0293 .0231 (2 . 3 6 6 ) * ( i . 7 1 8 ) Y 3 R 2  (t v a l u e )  Du rb i n -Watson No. of Observa t i ons . ' i7'6722 . 0 0 7 9 1 . 7 6 1 06 ( . 9 0 9 ) . 9 3 9 7 . 0 2 2 9 2 . 0 3 1 1 1 ( 1 . 5 6 0 ) • 5545 . 0088 1 . 8 3 217 ( 1 . 3 7 8 ) - . 0 7 3 1 . 0002 2 . 2 3 88 ( - . 1 3 5 ) . 6996 . 0 1 0 2 1 . 8 9 1 1 0 ( 1 . 0 5 4 ) . 01 62 . 0000 1 . 9 7 1 98 ( .042) .4148 . 0069 1 .89 1 06 ( .850) • 5931 . 0 0 7 8 1 . 6 7 1 1 1 ( . 9 2 7 ) . 3628 . 0 0 5 3 1 . 7 9 217 (1 . 0 6 7 ) . 2 3 7 9 . 0041 1 .64 1 1 1 ( . 6 7 3 ) . 5 7 6 5 . 0 0 8 6 1 . 6 5 1 1 1 ( . 9 7 4 ) . 3381 . 0063 1 .64 222 (1 .185) TABLE IV: ( c o n t i n u e d ) Commodity : SOYBEANS A F u t u r e s Sample RP Y o C o n t r a c t Per i od (t va1ue) (t v a l u e ) J a n u a r y 1962-66 .0339 .0337 (1 • 777) (1 .448) 1967-71 . 01 74 . 0 1 7 0 ( • 940) ( .915) 1962-71 . 0256 .0236 (1 .932) (1 .644) March 1962-66 . 0 2 9 9 .0381 (1 .452) (1 .513) 1967-71 . 0 1 1 5 .0111 ( . 6 5 5 ) ( .630) 1962-71 .0206 . 0208 (1 .528) (1 .426) May 1962-66 .0257 .0373 (1 . 2 2 8 ) (1 • 427) 1967-71 .0077 .0077 ( .440) ( • 439) 1962-71 . 01 66 . 0 1 8 5 (1 .220) (1 . 2 5 7 ) A Y 3 R 2 D u r b i n - No. of (t v a l u e ) Watson 0 b s e r v a t i o n s . 0 0 6 6 . 0000 1 . 7 3 1 1 0 ( .016) . 1 701 . 0 0 0 7 1 .64 1 1 2 ( . 2 7 2 ) . 1 2 0 5 . 0 0 0 6 1 . 69 222 ( .373) - . 2 6 4 5 . 0 0 3 0 2 . 07 1 1 0 ( - . 5 6 9 ) .2620 . 0 0 1 6 1 .72 1 1 2 ( .423) - . 0 1 0 2 . 0000 1 . 9 2 222 ( - . 0 3 0 ) - . 3 5 8 5 . 0 0 5 1 2 . 0 5 1 1 0 ( - . 7 4 3 ) • 0343 . 0000 1 . 5 8 1 1 2 ( .054) - . 1 1 5 0 . 0 0 0 5 2.01 222 ( - . 3 3 5 ) TABLE V: C o c h r a n e - O r c u t t I t e r a t i v e Techn ique A p p l i e d t o the R e g r e s s i o n of the S e m i - M o n t h l y H o l d i n g P e r i o d R e a l i z e d R i s k Premium on the Change in Net Hedging and the Leve l o f Net H e d g i n g . RPt = Y 0 + Y 2 ANH t + Y 3 N H t + e t Commodity : WHEAT F u t u r e s Sample P e r i o d Y 1 0 (t va1ue) /\ Y 2 (t va1ue) Y 3 (t va1ue) R2 Du rb i n -Watson No. of O b s e r -va t i on s No. o f I t e r a -t i o n s F i n a l p (t v a l u e 1 9 6 1 - 6 5 - .0651 - . 0 1 7 7 1 .4883 .0763 1 . 9 6 1 0 3 1 . 1 604 ( - 2 . 1 0 7 ) * ( - . 0 1 0 ) ( 1 . 9 5 1 ) ( 1 . 6 4 9 ) 1966 -70 - . 0 3 9 7 12 .0852 . 8 3 1 0 . 1 840 1 . 9 4 1 06 1 .1697 ( - . 7 3 5 ) ( 4 . 3 7 3 ) * (.683) ( 1 . 7 7 3 ) 1 9 6 1 - 7 0 - .0528 6.7208 1.1656 .0991 1 . 9 2 2 0 9 1 . 1 7 6 6 ( - 1 . 6 5 2 ) ( 3 . 8 2 7 ) * ( 1 . 5 4 9 ) ( 2 . 5 9 4 ) * 1 9 6 1 - 6 5 - . 0 5 8 4 . 2 8 8 1 1 . 4 4 7 0 . 0 6 5 5 1 . 9 5 1 0 6 1 . 1 5 3 9 ( - 1 . 8 0 8 ) ( . 1 5 8 ) ( 1 . 9 7 9 ) ( 1 . 6 0 4 ) 1 9 6 6 - 7 0 . 0 0 2 8 5 . 8 9 0 2 - . 1 2 0 9 . 0 8 8 2 1 . 8 9 1 0 7 2 . 2 6 5 0 (.045) ( 2 . 2 4 2 ) * ( - . 0 8 8 ) ( 2 . 8 4 3 ) * 1 9 6 1 - 7 0 - . 0 3 2 1 3 . 3 3 4 7 . 7 4 9 8 . 0 6 0 2 1 . 9 2 2 1 3 1 . 2 0 6 3 ( - . 9 5 4 ) ( 2 . 0 3 2 ) * (1 .004) ( 3 . 0 7 7 ) * 1 9 6 1 - 6 5 - . 0 3 6 3 - 1 . 0 2 8 0 . 8 7 0 1 . 0 3 8 0 2 . 0 0 1 0 5 1 . 1 1 9 4 ( - 1 . 0 0 1 ) ( - . 5 3 4 ) (1 . 2 2 1 ) (1 . 2 3 3 ) 1 9 6 6 - 7 0 . 0 2 9 8 7 . 3 0 9 0 - . 8 9 3 4 . 1 2 2 0 1 . 9 3 1 0 6 2 . 2 5 6 7 (.491) ( 2 . 8 7 7 ) * ( - . 6 6 7 ) ( 2 . 7 3 4 ) * 1 9 6 1 - 7 0 - . 0 0 9 1 3 . 6 3 9 8 . 1 2 0 5 . 0 5 3 8 1 . 9 7 21 1 1 . 1 9 5 4 ( - . 2 5 9 ) ( 2 . 2 0 4 ) * (.166) ( 2 . 8 9 4 ) * J u l y Sept Dec. TABLE V: ( c o n t i n u e d ) C o m m o d i t y : WHEAT F u t u r e s C o n t r a c t S amp 1e P e r i o d A Y 1 0 ( t v a l u e ) ( t A Y 2 v a 1 u e ) A Y 3 Ct v a l u e ) R 2 Durb i n -Wa t s o n N o . o f Obse r -v a t i on s No. o f 1 t e r a -t i on s F i n a l p ( t v a l u e M a r c h 1962-66 - . 0 3 9 5 .1994 • 7 7 3 1 . 0 1 5 1 1 .95 1 0 3 1 .0702 ( - .938) ( . 1 0 5 ) ' ( .983) ( .714) 1967-71 .0168 8 . 702 - . 6 4 7 5 . 1 236 1 .98 106 2 .2346 ( . 2 9 1 ) (3 .266)* ( - .508) (2 .485)* 1 9 6 2 - 7 1 - . 0 0 9 5 4 .5492 .0904 . 0504 1 . 9 8 209 2 .1657 ( - . 2 6 1 ) (2 . 6 8 8 ) * ( .122) ( 2 . 4 3 0 ) * May 1962-66 - . 0 2 9 2 1 . 1 1 0 8 .8111 . 0 1 3 0 1 .95 105 1 . 0 0 6 8 ( - .734) ( .542) ( 1 . 0 7 6 ) ( .070) 1 9 6 7 - 7 1 . 0 1 9 1 8 . 3 1 9 6 - 1 . 0 6 4 6 . 1 1 7 8 2 . 04 107 2 . 1 0 9 3 ( . 3 8 6 ) (3 . 4 3 6 ) * ( - .979) (1 . 1 3 8 ) 1 9 6 2 - 7 1 - . 0 0 2 2 5 . 6 3 0 0 - .0527 . 0 5 3 1 2 . 04 2 1 2 2 . 0 8 2 9 ( - .066) (3 .402)* ( - .078) (1 -211) N o t e : When a p p l i e d t o t h e d i s c o n t i n u o u s d a t a s e r i e s o f a f u t u r e s c o n t r a c t , t h e t r a n s f o r m a t i o n o f t h e v a r i a b l e s i n t h e C o c h r a n e - O r c u t t t e c h n i q u e r e s u l t s i n o f a number o f o b s e r v a t i o n s . The mean r i s k v a l u e s a r e t h e r e f o r e n o t i d e n t i c a l t o t h o s e p r e v i o u s t a b l e s and h a v e been o m i t t e d . t h e " l o s s " p rem i um o f t h e TABLE V: ( c o n t i n u e d ) Commod i t y : CORN F u t u r e s Samp 1e ( t Y 2 Y 3 R 2 Durb i n - No. of No. of C o n t r a c t P e r i o d va1ue) (t v a l u e ) ( t v a l u e ) Wa tson O b s e r - 1te r a -va t i on s t i 0 n s J u l y 1961-65 (-.01 54 6.3762. .1295 . 1 308 2.03 104 2 .562) (4.061)* (.244) 1 966-70 - .0234 8 .8177 .0278 .5852 1 .98 1 06 2 (-1 • 043) (11.109)* (.091) 1 961-70 - .0178 8.3508 .0317 .4078 2 . 02 2 1 0 2 (1 .014) (11.338)* ( .114) Sept . 1961-65 ( .0306 7.0230 - . 6 7 2 0 .2207 2 .02 1 03 2 • 997) (4.337)* ( -1 .161) 1 966-70 - .0460 10.3781 .4852 .6071 1 .98 106 1 (-1 • 725) (12.271 )* (1 .416) 1961-70 - . 0065 9.6069 .0220 .4767 2 .03 209 2 (- • 313) (12.830)* (.071) Dec . 196I-65 .001 7 7.1701 - .2338 .2898 1 .82 105 1 ( .090) (5.914)* (- .595) 1966-70 - . 0096 11.2137 .2821 .5771 2. 04 1 06 1 .318) (11 .486)* (.773) 1961-70 (-.0053 10.2269 .1559 .4996 1 .96 21 1 1 • 298) (13.754)* (.599) . 1521 (1 .569) .21 54 (2.271)* .2 1 43 (3.179)* .2912 (3.089)* . 092 1 (.952) .2181 (3 .23D* .1079 (1.113) .0753 (.778) .1110 (1.622) T A B L E V : ( c o n t i n u e d ) C o m m o d i t y : CORN F u t u r e s C o n t r a c t S a m p l e P e r i o d / \ Y o ( t v a l u e ) /\ Y 2 ( t v a l u e ) A . Y 3 ( t v a l u e ) R 2 D u r b i n -W a t s o n N o . o f O b s e r -v a t i o n s N o . o f 1 t e r a -t i o n s F i n a l p ( t v a l u e ) Ma r c h 1 9 6 2 - 6 6 - . 0 0 5 5 6 . 8 6 4 1 - . 3 1 7 6 . 2 5 0 4 2 . 0 1 1 0 5 2 . 1 2 0 5 ( - . 2 6 8 ) ( 5 . 3 9 8 ) * ( - . 7 4 4 ) ( 1 . 2 4 4 ) 1 9 6 7 - 7 1 - . 0 0 9 4 1 1 . 1 4 1 6 . 1 7 2 6 . 5 9 0 0 2 . 0 3 1 0 8 1 . 0 4 3 4 ( - . 3 4 1 ) ( 1 2 . 0 1 5 ) * ( . 5 3 3 ) ( . 4 5 1 ) 1 9 6 2 - 7 1 - . 0 1 1 5 1 0 . 0 8 2 2 . 0 8 6 3 . 4 9 3 1 2 . 0 3 2 1 3 1 . 1 1 7 9 ( - . 6 5 7 ) ( 1 3 . 6 6 2 ) * ( . 3 4 3 ) (1 , 7 3 2 ) May 1 9 6 2 - 6 6 - . 0 0 3 6 5 . 7 2 5 8 - . 1 2 7 5 . 1 8 0 0 1 . 9 0 1 0 5 2 . 1 0 2 0 ( - . 1 8 1 ) ( 4 . 6 5 8 ) * ( - . 3 3 5 ) (1 . 0 5 1 ) 1 9 6 7 - 7 1 - . 0 0 4 0 1 0 . 3 1 0 1 - . 0 2 0 2 . 61 22 2 . 0 2 1 0 7 1 . 0 8 3 0 ( - . 1 4 7 ) ( 1 2 . 2 7 D * ( - . 0 6 5 ) ( . 8 6 1 ) 1 9 6 2 - 7 1 - . 0 0 4 9 9 . 3 6 2 6 - . 0 7 7 3 . 4 9 8 9 1 - 9 7 2 1 2 1 . 1 4 1 8 ( - . 2 7 9 ) ( 1 3 . 7 4 3 ) * ( - . 3 1 7 ) ( 2 . 0 8 5 ) * T A B L E V : ( c o n t i n u e d ) C o m m o d i t y : S O Y B E A N S A F u t u r e s S a m p l e Y o C o n t r a c t P e r i o d ( t v a l u e ) A. A Y -2 ' 3 ( t v a l u e ) ( t v a l u e ) R D u r b i n - N o . o f Wa t s o n O b s e r -v a t i o n s . 2 2 9 3 2 . 0 4 101 . 1 0 5 4 1 . 9 4 1 0 6 . 1 6 2 0 2 . 0 0 2 0 7 J u l y A u g u s t S e p t , N o v . 1 9 6 1 - 6 5 1 9 6 6 - 7 0 1 9 6 1 - 7 0 1 9 6 2 - 6 5 1 9 6 6 - 7 0 1 9 6 2 - 7 0 1 9 6 1 - 6 5 1 9 6 6 - 7 0 1 9 6 1 - 7 0 1 9 6 1 - 6 5 1 9 6 6 - 7 0 1 9 6 1 - 7 0 - . 0 3 9 7 ( - . 8 3 6 ) . 0 2 0 5 ( 1 . 0 9 9 ) - . 0 0 4 9 ( - . 2 3 8 ) . 0 0 5 7 ( . 2 3 7 ) . 0 2 8 6 ( 1 . 3 1 6 ) . 0 1 3 1 ( . 8 0 7 ) • 0 5 7 7 ( 2 . 0 6 8 ) * . 0 2 6 2 ( 1 . 1 7 6 ) . 0 3 4 1 ( 1 . 9 8 7 ) * . 0 2 0 8 ( 1 . 0 1 7 ) . 0 2 5 0 ( 1 . 2 3 6 ) . 0 2 1 5 ( 1 . 5 2 3 ) 1 0 . 8 7 8 2 ( 5 . 1 1 7 ) ' 4 . 9 0 2 0 ( 3 . 0 9 5 ) ; 8 . 1 8 1 3 ( 6 . 0 1 7 ) = 1 . 3 2 4 5 ( 1 . 7 8 7 ) 1 . 3 6 3 9 ( 2 . 3 5 9 ) * 1 . 0 2 5 3 ( 2 . 4 8 6 ) * 7 . 0 7 3 9 . 0 0 1 1 . 2 4 7 9 2 . 1 4 8 4 ( 5 . 1 9 D * ( . 0 0 3 ) 3 . 7 6 3 4 1 . 1 0 0 5 . 0 4 4 7 1 . 8 3 1 0 5 ( 2 . 0 3 5 ) * ( 1 . 4 9 1 ) 5 . 2 1 6 4 . 2 5 9 9 . 0 9 5 9 1 . 9 0 1 89 ( 4 . 4 3 2 ) * ( . 6 9 2 ) 1 1 . 8 5 2 0 . 4 3 1 3 . 2 5 1 4 2 . 0 5 101 2 ( 5 . 6 7 2 ) * ( . 9 9 2 ) 6 . 3 2 0 4 . 8 6 8 7 . 1 0 3 6 1 . 8 8 1 0 6 2 ( 3 . 1 5 9 ) * ( 1 . 1 3 2 ) 8 . 7 2 7 4 . 6 1 5 2 . 1 5 9 9 1 . 9 8 2 0 7 2 ( 6 . 0 7 2 ) * ( 1 . 7 0 3 ) 5 . 3 9 0 5 . 5 3 4 7 . 1 8 5 7 1 . 9 6 106 1 ( 4 . 6 2 1 ) * ( 1 . 4 9 5 ) 6 . 7 5 2 4 1 . 0 3 6 6 . 1 9 2 5 1 . 9 9 1 0 6 1 ( 4 . 4 1 3 ) * ( 1 . 5 7 3 ) 5 . 8 8 4 4 . 6 4 6 0 . 1 8 3 5 1 .98 2 1 2 1 ( 6 . 2 4 1 ) * ( 2 . 1 0 7 ) * . 0 7 2 1 ( . 7 2 7 ) - . 0 5 2 8 ( - . 5 4 4 ) . 0 4 9 7 ( . 7 1 6 ) - . 0 9 8 6 ( - . 9 0 8 ) - . 0 1 7 7 ( - . 1 8 2 ) - .0177 ( - . 2 4 4 ) ( 0 2 6 4 2 6 6 ) . 1 3 9 4 (1 . 4 4 9 ) . 0 6 6 1 ( . 9 5 2 ) . 0 4 5 9 ( . 4 7 3 ) . 1 5 8 2 ( 1 . 6 5 0 ) . 1 0 8 0 ( 1 . 5 8 2 ) TABLE V: ( c o n t i n u e d ) Commodity : SOYBEANS Ai A A F u t u r e s Sample Y o Y 2 Y 3 C o n t r a c t P e r i o d (t v a l u e ) (t v a l u e ) (t v a l u e . 2 2 0 5 •(.566) VI'."0 729 Cl -429) .4643 (1.354) - . 0 0 9 1 ( - .025) .6962 (.981) .2085 (.663) May 1962-66 .0132 7 L ] Q 7 .1562 (.409) .4405 (.765) .2987 (1 .032) 1 9 6 2 - 6 6 . 0 2 7 3 (1 . 3 2 6 ) 1 9 6 7 - 71 . 0 1 9 4 ( • 9 2 3 ) 1 9 6 2 - 71 . 0 2 0 2 (1 . 3 9 8 ) 1 9 6 2 - 6 6 . 0 2 3 4 (1 . 2 0 7 ) 1 9 6 7 - 71 . 0 0 8 1 ( . 4 0 6 ) 1 9 6 2 - 71 . 0 1 2 8 ( • 9 5 1 ) 9 6 2 - 6 1  ( . 6 3 8 ) 1 9 6 7 - 71 - . 0 0 2 7 ( - . 1 6 7 ) 1 9 6 2 - 71 . 0 0 3 6 ( . 2 9 0 ) 5. 8298 (4. 557)* 6. 9862 (4. 31 8) * 6. 2385 (6. 064) * 6. 8037 (5. 636)* 5. 8949 (3 . 797)* 6. 3891 (6. 538)* 7. 4193 (6. 002) * 5. 2538 (3. 963)* 6. 7354 (7. 366)* 2 Durb i n - No. o f No. o f F i n a l p Watson O b s e r - 1 t e r a - ( t v a l u e v a t i o n s t i ons 1645 1 .73 105 - . 0 6 5 4 ( - .671) 1 733 1. 92 107 1 :-. 1 6 0 3 (1 . 6 8 0 ) 1 5 6 0 1 .81 2 1 2 1 . 0 5 9 8 ( .872) 2392 2.03 105 1 - . 1667 ( -1 .732) 1 400 2. 04 107 1 .1464 (1.531) 1 690 1 .99 2 12 1 - . 0 1 8 8 ( - .273) 2542 1 .97 1 0 5 1 - . 1 6 1 2 ( -1 .674) 1 5 1 7 2. 74 107 1 . 0906 (.941) 2005 2 . 3 2 212 1 - . 0 5 0 9 ( - .742) Test #k Tes t #2 o f f e r s s u b s t a n t i a t i o n of the t h e o r y t h a t RP i s c o r r e l a t e d w i t h A N H t . T a b l e V I , wh ich i s r e p r e s e n t a t i v e of the c o r r e l a t i o n m a t r i x app1 i c a b 1e to a soybean f u t u r e s c o n t r a c t f o r the 1 0 year sample p e r i o d , i n d i c a t e s p o s i t i v e s e r i a l c o r r e l a t i o n between ANH^. and A N H t _ j . If these two r e l a t i o n s h i p s h o l d , a q u e s t i o n a r i s e s c o n c e r n i n g whether i t i s p o s s i b l e f o r an i n v e s t o r to r e a l i z e p o s i t i v e r e t u r n s in p e r i o d t based on a knowledge of the change in net hedg ing in p e r i o d t - 1 . T h i s q u e s t i o n w a r r a n t s the e x t e n s i o n of the s t u d y to examine the e f f i c i e n t market p r o p e r t i e s of commodity f u t u r e s m a r k e t s . An e f f i c i e n t market c o r r e c t l y uses a l l r e l e v a n t i n -f o r m a t i o n in s e t t i n g c u r r e n t p r i c e s . As a p p l i e d to commodity m a r k e t s , market e f f i c i e n c y r e q u i r e s t h a t in s e t t i n g f u t u r e s p r i c e s at t - 1 and t , t h e r e b y e s t a b l i s h i n g the r e t u r n in p e r i o d t , the market c o r r e c t l y use a l l i n f o r m a t i o n c o n c e r n i n g hedg ing a c t i v i t y . If the market i s e f f i c i e n t , then a l l pas t i n f o r m a t i o n c o n c e r n i n g the change in net hedg ing t o g e t h e r w i t h any p r e d i c t a b l e e lement of the change in net hedg ing in p e r i o d t w i l l be i n c o r p o r a t e d i n the f u t u r e s p r i c e at the b e g i n n i n g of p e r i o d t . Hence, the e f f i c i e n t markets h y p o t h e s i s r e q u i r e s t h a t RP be c o r r e l a t e d o n l y w i t h the u n a n t i c i p a t e d e lement of A N H t . The h y p o t h e s i z e d r e l a t i o n s h i p between R P t and ANH^ i s of the f o r m : RP = bANH t + e (4.2) and the s t o c h a s t i c p r o c e s s f o r ANH may be r e p r e s e n t e d by the s i m p l e f i r s t o r d e r a u t o r e g r e s s i v e r e l a t i o n ANH t = c A N H t _ ] + n t (4.3) where the d i s t u r b a n c e term n i s the u n a n t i c i p a t e d e lement of ANH^. S u b s t i t u t i n g f o r ANH t in E q u a t i o n (4.2) f rom E q u a t i o n (4.3), R P t = b ( c A N H t _ ] + nt) + e t From Test #2 i t i s known t h a t Cov(RP ANH ) ={= 0 B u t , ' Cov(RP , ANH ) -•=•. Cov(RP , cANH ^ _ ^  + n ) •/-•=*' C o v ( R P , c A N H t _ 1 ) + Cov(RP ,nt) The e f f i c i e n t markets h y p o t h e s i s r e q u i r e s t h a t RP be independent o;f"ANH t _ 1 such t h a t C o v ( R P t > cANH ^_ ^ ) = 0 so, t h a t C o v ( R P t , A N H t ) = Cov (RP t,n t) Hence i t i s p o s s i b l e t h a t RP can be c o r r e l a t e d w i t h ANH , and ANH^ can be c o r r e l a t e d w i t h A N H ^ j , but R P t not be c o r r e l a t e d w i t h A N H t _ j , o n l y i f RP i s c o r r e l a t e d o n l y w i t h the u n a n t i c i p a t e d e lement of ANH^. In terms of f u t u r e s p r i c e s , - 1 13 -to the degree t h a t the change in net hedg ing in p e r i o d t i s p r e d i c t a b l e , i t s e f f e c t i s i n c o r p o r a t e d in the f u t u r e s p r i c e at the end of the p e r i o d t - l . To the degree i t i s not p r e -d i c t a b l e , changes in net h e d g i n g become r e f l e c t e d in R P t -That i s , the e f f i c i e n t m a r k e t s h y p o t h e s i s i m p l i e s t h a t a l t h o u g h R P t and ANH , and ANH^ and ANH^ , , a r e c o r r e l a t e d , 3 t t t t - l R P t and ANH t _ j a r e u n c o r r e l a t e d . If the commodity f u t u r e s market i s e f f i c i e n t t h e n : H^: The s e m i - m o n t h l y h o l d i n g p e r i o d r e a l i z e d r i s k premium i s independent of the change in net h e d g i n g in the p r e v i o u s s e m i - m o n t h l y p e r i o d . H|: The s e m i - m o n t h l y h o l d i n g p e r i o d r e a l i z e d r i s k premium i s p o s i t i v e l y c o r r e l a t e d w i t h the lagged change in net h e d g i n g . / R e g r e s s i o n m o d e l : R P , = Y . + Y „ ANH^ , + e^ 3 t 1 0 1 2 t - l t T e s t s were run f o r each of the seven soybean f u t u r e s c o n t r a c t s u s i n g the 10 year sample p e r i o d . T a b l e VI I summar-i z e s the t e s t r e s u l t s . Wi th the s i n g l e e x c e p t i o n of the November f u t u r e s c o n t r a c t , none of the 10 year r e g r e s s i o n e q u a t i o n s d i s p l a y s an e s t i m a t e d c o e f f i c i e n t on the lagged change in net hedg ing v a r i a b l e w h i c h i s s i g n i f i c a n t l y d i f f e r e n t f rom z e r o at the 5% s i g n i f i c a n c e l e v e l . The n u l l h y p o t h e s i s i s t h e r e f o r e a c c e p t e d and i t i s c o n c l u d e d t h a t the soybeans f u t u r e s market conforms w i t h the e f f i c i e n t markets h y p o t h e s i s - 1 \k-J in the sense t h a t no i n v e s t o r can r e a l i z e p o s i t i v e r e t u r n s in the c u r r e n t p e r i o d based on a knowledge of the change in net hedg ing in the p r i o r p e r i o d . W h i l e the e f f i c i e n t m a r k e t s h y p o t h e s i s r e q u i r e s t h a t RP and ANH^_j be u n c o r r e 1 a t e d , i t imposes no such r e s t r i c t i o n on RP and A N H t + j . I ndeed , as in T a b l e V I I I , the r e g r e s s i o n of RP on ANH . i n d i c a t e s t h a t they a re p o s i t i v e l y c o r r e l a t e d . - 1 1 5 -TABLE V I : C o r r e l a t i o n M a t r i x A p p l i c a b l e t o J u l y S o y b e a n s F u t u r e s C o n t r a c t ( 1 9 6 1 - 7 0 ) . R P t NH ANH ANH . ANH . t t t t - l t+1 RP . 0 9 3 5 . 3 6 6 6 . 0 8 3 5 . 1 6 6 7 NH - . 1 7 1 9 . 1 2 4 4 - . 3 1 9 3 ANH ^ . 5 0 9 9 . 4 9 2 8 A N H t _ 1 . 2 1 5 0 A N H t + ] TABLE V I I : R e g r e s s i o n o f t h e S e m i - M o n t h l y H o l d i n g P e r i o d R e a l i z e d R i s k P r e m i u m on t h e L a g g e d Change i n Net H e d g i n g . A A ( . A R P t = Y Q + Y 2 A N H t _ ! + e t C o m m o d i t y : SOYBEANS F u t u r e s S a m p l e C o n t r a c t Pe r i od RP ( t v a l u e ) A y. A / Y o ( t v a l u e ) ( t va 1 ue) J u l y 1 9 6 1 - 7 0 . 0 2 5 6 (1.431) . 0247 (1.380) 1 . 6 8 0 3 ( 1 . 2 2 3 ) A u g u s t 1 9 6 2 - 7 0 . 01 7 0 ( 1 . 1 1 2 ) . 0 1 72 ( 1 . 1 2 5 ) 2 3 1 5 1 9 8 ) S e p t . 1961-70 . 0241 (1.679) .0247 (1.715) . 841 0 (.698) Nov 1961-70 . 0 2 9 3 ( 2 . 3 6 6 ) * . 0 3 0 6 ( 2 . 4 9 8 ) * 2 . 2 3 2 0 ( 2 . 3 2 5 ) J a n u a r y 1 9 6 2 - 7 1 . 0 2 5 6 ( 1 . 9 3 2 ) . 0264 ( 1 . 9 8 8 ) * 1 . 2 2 7 8 ( 1 . 1 9 2 ) M a r c h 1 9 6 2 - 7 1 . 0 2 0 6 ( 1 . 5 2 8 ) . 0 2 0 5 ( 1 . 5 1 4 ) . 6 5 1 9 ( . 6 2 0 ) May 1 9 6 2 - 7 1 .0166 (1.220) . 0 1 6 6 ( 1 . 2 1 9 ) 1 . 1 5 2 2 ( 1 . 1 1 1 ) D u r b i n - No . o f Wa t s o n Obse r v a t i ons 0 0 7 0 1 . 8 6 2 1 7 0 0 0 2 1 . 9 6 1 9 8 0 0 2 3 1.81 2 1 7 0 2 4 0 1 . 7 6 2 2 2 0 0 6 4 1 . 7 4 2 2 2 0 0 1 7 1 . 9 6 2 2 2 0 0 5 6 2 . 1 0 2 2 2 TABLE V I I I : R e g r e s s i o n of the S e m i - M o n t h l y H o l d i n g P e r i o d R e a 1 i z e d R i s k Premium on the Subsequent P e r i o d Change i n Net H e d g i n g . R P t = Y o + Y 2 / A N H t + l + ^ t F u t u r e s C o n t r a c t Sample Pe r i od (t RP va1ue) Ct /\ Y o va1ue) A // Y 2 (t v a l u e ) R 2 Durb i n -Wa t s on No. of O b s e r v a t ions J u l y 1961-70 (1 .0256 . 4 3 1 ) (1 . 0249 .407) 3 . 3 8 0 2 (2 . 4 8 0 ) * . 0278 1 .89 217 August 1962-70 (1 . 01 70 .112) (1 .01 72 .140) 2 . 5 3 5 5 ( 2 . 1 0 1 ) * .0220 2 . 0 3 198 S e p t . 1961-70 (1 .0241 .679) (2 . 0321 . 2 2 8 ) * 3 .7831 ( 2 . 8 7 2 ) * .0369 1.93 217 Nov . 1961-70 (2 . 0 2 9 3 . 3 6 6 ) * (2 .0302 . 4 9 5 ) * 3 . 0 8 1 8 ( 3 . 3 6 4 ) * .0489 1 .76 222 J a n u a r y 1962 -71 (1 .0256 • 932) < 2 . 0269 . 0 9 1 ) * 3 . 8 5 8 4 ( 3 . 9 5 5 ) * .0664 1 .83 222 Ma rch 1962 -71 (1 . 0206 • 528) (1 .021 1 .609) 3 . 6 8 8 3 ( 3 . 6 8 0 ) * .0580 2 . 0 8 222 Ma y 1962 -71 (1 .0166 . 220) (1 .0165 .261) 4 . 2 5 7 4 ( 4 . 2 1 2 ) * . 0746 2 . 2 5 222 CHAPTER V SUMMARY AND CONCLUSIONS The p r i m a r y o b j e c t i v e o f t h i s s tudy has been to examine an a s p e c t of the t h e o r y of commodity m a r k e t s : the n a t u r e and magn i tude of the r i s k premiums, i f a n y , wh ich a re r e c e i v e d by s p e c u l a t o r s f rom h e d g e r s ; and the s i g n i f i c a n c e of hedg ing a c t i v i t y r e l a t i v e to the payment of any such r i s k premiums. T h i s o b j e c t i v e i n v o l v e s the t e s t of a t h e o r y of the demand f u n c t i o n . However , s i n c e the r i s k premium i s d e t e r m i n e d by both the s u p p l y and demand f o r f u t u r e s c o n t r a c t s , i t was n e c e s s a r y a l s o to s p e c i f y the s u p p l y f u n c t i o n . S p e c i f i c a l l y , the r i s k premium was assumed to be d e t e r m i n e d by the f o l l o w i n g se t of s i m u l t a n e o u s r e l a t i o n s h i p s . Q_s = f { I , P , E (RP) } Hedgers 1 - S u p p l y F u n c t i o n Qp = f { E ( R P ) } S p e c u l a t o r s ' Demand F u n c t i o n In the t h e o r y s u g g e s t e d , the i m p l i c a t i o n s of r i s k a v e r s i o n and o f w e a l t h e f f e c t s as d e t e r m i n a n t s of h e d g e r s 1 d e c i s i o n s r e g a r d i n g the s u p p l y of f u t u r e s c o n t r a c t s was s t r e s s e d . The commerc ia l s t o c k s o f a commodity ( l ) , h e l d by h a n d l e r s , i s a d e t e r m i n a n t of- the t o t a l r i s k r e q u i r e d to be borne by someone. For any g i v e n magn i tude of commodity spot p r i c e and e x p e c t e d r i s k premium, each h a n d l e r w i l l s a t i s f y h i s r i s k p r e f e r e n c e s by hedg ing some p o r t i o n of h i s t o t a l i n v e n t o r y . Summing a c r o s s a l l h a n d l e r s d e t e r m i n e s the t o t a l e x c e s s - 1 19 -s u p p l y of f u t u r e s c o n t r a c t s . Shou ld the spot p r i c e (Pg.) s u b -s e q u e n t l y r i s e , the long h a n d l e r w i l l e x p e r i e n c e a w e a l t h e f f e c t by reason of the unhedged p o r t i o n of h i s i n v e n t o r y . If the h a n d l e r d i s p l a y s c o n s t a n t or i n c r e a s i n g r e l a t i v e r i s k a v e r s i o n , i t i s o p t i m a l t o a l l o c a t e a p o r t i o n of h i s p o s i t i v e w e a l t h i n c r e m e n t to a l e s s r i s k y a s s e t f o r m . S i n c e spot p r i c e s and f u t u r e s p r i c e s a r e n o r m a l l y p o s i t i v e l y c o r r e l a t e d , the f u t u r e s market a f f o r d s the h a n d l e r the o p p o r t u n i t y to a l l o c a t e a p o r t i o n of h i s w e a l t h inc rement to f u t u r e s c o n -t r a c t s . A d e c r e a s e in the spot p r i c e w i l l , s i m i l a r l y , r e s u l t in a d e c r e a s e in the s u p p l y of f u t u r e s c o n t r a c t s . An e x p e c t a t i o n a r i s i n g from t h i s a n a l y s i s was t h a t changes in net s h o r t hedg ing w i l l be p o s i t i v e l y c o r r e l a t e d w i t h changes in the f u t u r e s p r i c e and hence w i t h r e a l i z e d r i s k premiums. F i n a l l y , i t was assumed t h a t the s u p p l y of f u t u r e s c o n t r a c t s i s a n e g a t i v e f u n c t i o n of the e x p e c t e d r i s k premium. It was a l s o assumed t h a t the s p e c u l a t o r s ' demand f u n c t i o n i s l e s s than p e r f e c t l y e l a s t i c and t h a t the l a r g e r the t o t a l volume of f u t u r e s c o n t r a c t s , and hence the l a r g e r the t o t a l a b s o l u t e p r i c e r i s k r e q u i r e d to be a b s o r b e d by the s p e c u l a t i v e p o p u l a t i o n , the g r e a t e r w i l l be the e x p e c t e d r i s k premium n e c e s s a r y to i n d u c e s p e c u l a t i v e p a r t i c i p a t i o n . The t h r e e c o m m o d i t i e s a n a l y z e d in the s t u d y a r e w h e a t , c o r n , and s o y b e a n s . Data on p r i c e s and t r a d i n g volume were - 1 2 0 -drawn f rom the C h i c a g o Board of Trade f o r the nominal p e r i o d 1961 to 1970. S e m i - m o n t h l y h o l d i n g p e r i o d s were employed and the c l a s s i c normal l i n e a r r e g r e s s i o n model was used as the b a s i c a n a l y t i c a l t e c h n i q u e f o r e x a m i n a t i o n of the demand f u n c t i o n . The s p e c i f i c c o n c l u s i o n s of t h i s s t u d y a r e as f o l l o w s : i ) The mean r i s k premium i s not s i g n i f i c a n t l y d i f f e r e n t from z e r o . T h i s f i n d i n g i s c o n s i s t e n t w i t h t h a t of Dusak and conforms w i t h the p o s i t i o n t a k e n by T e l s e r and Hardy . As s u c h , i t o f f e r s f u r t h e r e v i d e n c e a g a i n s t the K e y n e s - H i c k s t h e o r y to the e f f e c t t h a t f u t u r e s p r i c e s a r e downward b i a s e d e s t i m a t e s of the e x p e c t e d f u t u r e s p o t p r i c e such t h a t s p e c u l a t o r s need o n l y c o n t i n u o u s l y m a i n t a i n a l o n g f u t u r e s p o s i t i o n in o r d e r to r e a l i z e p o s i t i v e r e t u r n s , i i ) In the c o n t e x t of the c a p i t a l a s s e t p r i c i n g m o d e l , the s y s t e m a t i c r i s k measure f o r each of the t h r e e c o m m o d i t i e s s t u d i e d i s not s i g n i f i c a n t l y d i f f e r e n t f rom z e r o . T h i s c o n c l u s i o n i s a l s o c o m p a t i b l e w i t h Dusak who s i m i l a r l y r e g r e s s e d the s e m i - m o n t h l y r e a l i z e d r i s k premium on c o m p a r a b l e r e t u r n s on the S&P 500 i n d e x . Based on t h i s f i n d i n g , i t i s c o n -c l u d e d t h a t i n v e s t o r s w i l l not be compensated f o r the r i s k t h a t i s un ique to f u t u r e s c o n t r a c t s s i n c e t h a t r i s k i s independent of the r i s k of a l l a s s e t s c o n s i d e r e d c o l l e c t i v e l y and hence can be d i v e r s i f i e d - 1 2 1 -away. The l i m i t a t i o n s of the S&P 500 index as a proxy f o r a w e a l t h index a r e a c k n o w l e d g e d . i ) The s e m i - m o n t h l y h o l d i n g p e r i o d r e a l i z e d r i s k premium i s p o s i t i v e l y r e l a t e d to the change in net s h o r t h e d g i n g . T h i s i s c o n t r a r y to C o o t n e r ' s e a r l i e r h e d g i n g p r e s s u r e t h e o r y w h i c h c o n t e n d e d t h a t the r e a l i z e d r i s k premium i s n e g a t i v e l y r e l a t e d to the change in net s h o r t h e d g i n g . However , t h i s c o n -c l u s i o n i s c o n s i s t e n t w i t h the e x p e c t a t i o n s of the t h e o r y s u g g e s t e d h e r e i n wh ich i s p r e d i c a t e d upon an a n a l y s i s of the i m p l i c a t i o n s of w e a l t h e f f e c t s and the t h e o r y of r i s k a v e r s i o n . v) C o n t r a r y to e x p e c t a t i o n s , the r e a l i z e d r i s k premium i s u n r e l a t e d to the l e v e l o f net hedg ing and i t i s c o n c l u d e d t h a t the e l a s t i c i t y of the s p e c u l a t o r s ' demand f u n c t i o n f o r f u t u r e s c o n t r a c t s i s i n f i n i t e . C o n s i s t e n t w i t h modern f i n a n c e t h e o r y , i t had been e x p e c t e d t h a t the demand f u n c t i o n would be l e s s -t h a n - p e r f e c t 1 y e l a s t i c r e f l e c t i n g a p o s i t i v e r i s k -r e t u r n t r a d e o f f by the s p e c u l a t i v e p o p u l a t i o n . Such i s not the c a s e . S p e c u l a t o r s e i t h e r do not a s s o c i a t e i n c r e a s e d t o t a l r i s k w i t h i n c r e a s e d volumes of net hedg ing or the c h a r a c t e r i s t i c s of the s p e c u l a t i v e p o p u l a t i o n a r e such t h a t any r i s k premium i s b i d away. T h i s i s indeed r e v e a l i n g and i d e n t i f i e s the commodity m a r k e t s s t u d i e d as un ique f i n a n c i a l m a r k e t s . -1 22-v) A t e s t of the e f f i c i e n t market c h a r a c t e r i s t i c s of commodity m a r k e t s r e v e a l s t h a t , n o t w i t h s t a n d i n g t h e f a c t t h a t t h e r e a l i z e d r i s k premium i s c o n t e m -p o r a n e o u s l y c o r r e l a t e d w i t h the change in net s h o r t h e d g i n g and the change in net s h o r t h e d g i n g i s p o s i t i v e l y s e r i a l l y c o r r e l a t e d , the r e a l i z e d r i s k premium i s n e v e r t h e l e s s u n c o r r e l a t e d w i t h the lagged change in net s h o r t h e d g i n g . I t i s t h e r e f o r e c o n c l u d e d t h a t commodity m a r k e t s confo rm to the e f f i c i e n t m a r k e t s h y p o t h e s i s in the sense t h a t the c u r r e n t f u t u r e s p r i c e i n c o r p o r a t e s a l l a v a i l a b l e i n f o r m a t i o n and no i n v e s t o r can r e a l i z e p o s i t i v e r e t u r n s in the c u r r e n t p e r i o d based on a knowledge of the change in net hedg ing in the p r i o r p e r i o d . W h i l e i t may be r e a s o n a b l y assumed t h a t the c o n c l u s i o n s of t h i s s tudy a r e r e p r e s e n t a t i v e of h a r v e s t c o m m o d i t i e s wh ich a re h e a v i l y t r a d e d on m a t u r e , w e l l - r e g u l a t e d , f u t u r e s m a r k e t s , i t i s not w a r r a n t e d to g e n e r a l i z e the f i n d i n g s to encompass a l l f u t u r e s m a r k e t s and a l l c o m m o d i t i e s . N o n - h a r v e s t c o m m o d i t i e s whi/'ch a re t r a d e d in f u t u r e s markets w a r r a n t r e s e a r c h to d e t e r m i n e the c o m p a r a t i v e n a t u r e o f the r i s k premiums and the s i g n i f i c a n c e of h e d g i n g a c t i v i t y . Such r e s e a r c h c o u l d encompass not o n l y such as s u g a r , wh ich by reason of the g e o g r a p h i c d i s t r i b u t i o n of w o r l d s u p p l i e s would - 1 2 3 " be e x p e c t e d t o be l a r g e l y d e v o i d o f d i s t i n c t h a r v e s t c h a r a c -t e r i s t i c s , b u t a l s o s u c h as c o p p e r , w h e r e p r o d u c t i o n i s g e n e r a l n o t a f u n c t i o n o f s e a s o n a l o r c l i m a t i c e f f e c t s . S i m i l a r a n a -l y t i c a l t e c h n i q u e s c o u l d a l s o be e m p l o y e d i n t h e e x a m i n a t i o n o f t h i n l y t r a d e d c o m m o d i t i e s , w h i c h may o r may n o t d i s p l a y t h e p r o p e r t i e s o f an e f f i c i e n t m a r k e t , t o a s c e r t a i n i f t h e f i n d i n g s o f t h i s s t u d y and t h e t h e o r y o f t h e r i s k p r e m i u m s u g g e s t e d a r e u n i f o r m l y a p p l i c a b l e i n s u c h m a r k e t s . F o r s u c h s t u d i e s , and w h e r e d a t a p e r m i t s , c o m m o d i t i e s s h o u l d a l s o be s e l e c t e d w h e r e t r a d i n g i n f o r m a t ro n i s a v a i l a b l e f o r i n d i v i d u a l f u t u r e s c o n -t r a c t s a s w e l l as i n t o t a l . F i n a l l y , t h e c o n c l u s i o n t h a t t h e s p e c u l a t o r s ' demand f u n c t i o n f o r f u t u r e s c o n t r a c t s i s v e r y h i g h l y i f n o t i n f i n i t e l y e l a s t i c r a i s e s i m p l i c a t i o n s c o n -c e r n i n g t h e c h a r a c t e r i s t i c s o f o t h e r m a r k e t s f o r r i s k y a s s e t s w h i c h a r e w o r t h y o f e x a m i n a t i o n . - 1 2 4 -FOOTNOTES 1 . S e e , f o r e x a m p l e , Roger W. G r a y , "The C h a r a c t e r i s t i c B i a s on Some Th in F u t u r e s M a r k e t s , " Food R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) November, 1 9 6 0 . 2 . Ha r r y M a r k o w i t z , P o r t f o l i o S e l e c t i o n : E f f i c i e n t D i v e r s i -f i c a t i o n of Inves tments (New Y o r k : John W i l e y S S o n s , 1 9 5 9 ) . 3- W i l l i a m F. S h a r p e , " C a p i t a l A s s e t P r i c e s : A Theory of Market E q u i l i b r i u m under C o n d i t i o n s of R i s k , " J o u r n a l o f F i n a n c e , V o l . X I X , N o . 3 , September 1964. 4. K . J . A r r o w , Essays in the Theory of R i s k - B e a r i n g , ( C h i c a g o : Markham P u b l i s h i n g C o . , 1971). 5. Eugene F. Fama, " R i s k , Return and E q u i l i b r i u m , " Repor t N o . 6 8 3 1 , U n i v e r s i t y of C h i c a g o , C e n t r e f o r M a t h . S t u d i e s in B u s i n e s s and E c o n o m i c s , J u n e , I 9 6 8 . 6. John L i n t n e r , "The V a l u a t i o n of R i s k A s s e t s and the S e l e c t i o n of R i s k y A s s e t s in S t o c k P o r t f o l i o s and C a p i t a l B u d g e t s , " Review of Economics and S t a t i s t i c s , F e b r u a r y 1965-7 . M i c h a e l J e n s e n , " R i s k , the P r i c i n g of C a p i t a l A s s e t s , and the E v a l u a t i o n of Investment P o r t f o l i o s , " J o u r n a l of B u s i n e s s , Ap r i 1 1 9 6 9 . 8 . C h a r l e s 0. H a r d y , R i s k and R i s k B e a r i n g ( C h i c a g o : U n i v . Ch i cago P r e s s , 1940) . 9 . J . M . K e y n e s , A t r e a t i s e on M o n e y , V o l . I I (New York 1 9 3 0 ) . 1 0 . In p a r t i c u l a r , see P . H . C o o t n e r , " S p e c u l a t i o n and H e d g i n g , " Food R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) 1967. 1 1 . In p a r t i c u l a r , see L . G . T e l s e r , "The S u p p l y of S p e c u l a t i v e S e r v i c e s in Wheat , C o r n , and S o y b e a n s , " Food R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) 1967 ( S u p p l . ) . 1 2 . In d e v e l o p i n g a comprehens ion of commodity m a r k e t s , the w r i t e r has drawn upon the works of v a r i o u s of the a u t h o r s c i t e d in the b i b l i o g r a p h y , e s p e c i a l l y C o o t n e r ( 1 9 6 7 ) , Hieronymus ( 1 9 7 1 ) , and Work ing ( F e b . , I 9 6 0 ) . 1 3 . H . S . H o u t h a k k e r , "Normal B a c k w a r d a t i o n , " in V a l u e , C a p i t a l and Growth , J . N . W o l f e , Ed. ( E d i n b u r g h U n i v e r s i t y P r e s s , 1 9 6 8 ) . 14. I b i d , p. 1 9 8 . - 1 2 5 -1 5 . I b i d , p . 1 9 8 . 1 6 . T h e p o s s i b i l i t y t h a t t h e p r i c e r i s k p e r u n i t o f t h e c o m m o d i t y may b e g r e a t e r w h e n t o t a l s t o c k s a r e l o w t h a n w h e n t o t a l s t o c k s a r e h i g h i s i g n o r e d . 1 7 . I t w a s t h e r e c o g n i t i o n o f t h e r e l a t i o n s h i p b e t w e e n t h e c u r r e n t f u t u r e s p r i c e a n d t h e e x p e c t e d f u t u r e s p o t p r i c e n e c e s s a r y t o p r o v i d e t h e s p e c u l a t o r w i t h a p o s i t i v e e x p e c t e d r e t u r n w h i c h l e d e a r l i e r a u t h o r s t o a d o p t t h e " c l a s s i c " r i s k p r e m i u m d e f i n i t i o n . T h e d e f i n i t i o n o f t h e r i s k p r e m i u m i s d i s c u s s e d f u r t h e r i n t h e s u b s e q u e n t s e c t i o n o f t h i s c h a p t e r . 1 8 . In t h i s s e c t i o n , r e f e r e n c e s t o r i s k p r e m i u m a r e , e x c e p t w h e r e e x p l i c i t l y n o t e d t o t h e c o n t r a r y , e x p r e s s e d i n t h e c l a s s i c s e n s e ( i . e . e x p e c t e d f u t u r e s p o t p r i c e m i n u s c u r r e n t f u t u r e s p r i c e ) s o a s t o b e c o m p a t i b l e w i t h t h e w o r k s o f t h e a u t h o r s r e f e r r e d t o . 1 9 - C h a r l e s 0 . H a r d y , R i s k a n d R i s k b e a r i n g ( C h i c a g o : U n i v . C h i c a g o P r e s s , 1SkO) . 2 0 . C h a r l e s S . R o c k w e l l , " N o r m a l B a c k w a r d a t i o n , F o r e c a s t i n g , a n d t h e R e t u r n s t o C o m m o d i t y F u t u r e s T r a d e r s , " F o o d R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) , 1 9 6 7 ( S u p p l . ) 2 1 . J . M . K e y n e s , A T r e a t i s e o n M o n e y , V o l . I I ( N e w Y o r k 1 9 3 0 ) . 2 2 . J . R . H i c k s , V a l u e a n d C a p i t a l ( 2 n d E d . , O x f o r d , 1 9 4 6 ) . 2 3 . I b i d , p . 1 3 8 . 2 4 . P . H . C o o t n e r , " R e t u r n s t o S p e c u l a t o r s : T e l s e r v s . K e y n e s , " J o u r n a l o f P o l i t i c a l E c o n o m y , A u g u s t i960. 2 5 . I b i d , p . 4 0 0 . 2 6 . I b i d , p . 4 0 0 . 2 7 . I b i d , p p . 3 9 8 - 3 9 9 . 2 8 . A h e d g e r may b e l o n g i n t h e f u t u r e s m a r k e t w h e n p r i c e s a r e e x p e c t e d t o d r o p i f h e w i s h e s t o e s t a b l i s h t h e p r i c e r e l a t i o n s h i p b e t w e e n t h e c o m m o d i t y i n p u t s a n d h i s c o m m i t t e d p o s i t i o n i n t h e p r o c e s s e d p r o d u c t m a r k e t . A l s o , C o o t n e r i s i n c o r r e c t i n t h e u n l i k e l y c a s e t h a t m o v e m e n t s i n f u t u r e s p r i c e s e x h i b i t s t r o n g n e g a t i v e c o r r e l a t i o n w i t h t h e r e t u r n o n n a t i o n a l w e a l t h . T h e n a t u r e o f t h i s r e l a t i o n s h i p i s i n v e s t i g a t e d i n C h a p t e r I V . - 1 2 6 -2 9 - For e x a m p l e , b u y i n g b e f o r e the end of a p r i c e d e c l i n e due to e r r o n e o u s e x p e c t a t i o n s c o n c e r n i n g the magn i tude of the net s h o r t hedg ing to be accommodated. 30. i . e . , i n f l u e n c e of c a p i t a l g a i n s tax l e g i s l a t i o n . 3 1 . P . H . C o o t n e r , " S p e c u l a t i o n and H e d g i n g , " Food R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) , 1967= PP- 8 2 - 8 3 . 32. The e x c e p t i o n where f u t u r e s p r i c e s a r e n e g a t i v e l y c o r r e l a t e d w i t h the r e t u r n on n a t i o n a l w e a l t h i s noted p r e v i o u s l y . 33. L . G . T e l s e r , " F u t u r e s T r a d i n g and the S t o r a g e of C o t t o n and W h e a t , " J o u r n a l of P o l i t i c a l Economy, J u n e , 1958. 34. I b i d , p. 235-35. For a d i s c u s s i o n of the c o s t of s t o r a g e and the c o n -v e n i e n c e y i e l d see M . J . B r e n n a n , "The S u p p l y of S t o r a g e , " A m e r i c a n Economic Rev iew , March 1958 and H. W o r k i n g , "The Theory of P r i c e of S t o r a g e , " A m e r i c a n Economic R e v i e w , December, 1 9 4 9 -36. L . G . T e l s e r , " F u t u r e s T r a d i n g and the S t o r a g e of C o t t o n and W h e a t , " J o u r n a l o f P o l i t i c a l Economy, J u n e , 1958 p. 241 . 37- P . H . C o o t n e r , " R e t u r n s to S p e c u l a t o r s : T e l s e r vs K e y n e s , " J o u r n a l o f P o l i t i c a l Economy A u g u s t , 1 9 6 0 . 38. I b i d , p. 400. 39- I b i d , p. 400. 40. " R e p l y " by L . G . T e l s e r and " R e j o i n d e r " by P . H . C o o t n e r , J o u r n a l of P o l i t i c a l Economy, A u g u s t , i 9 6 0 . 41. R.W. Gray , "The S e a r c h f o r a R i s k P r e m i u m , " J o u r n a l o f P o l i t i c a l Economy, June I96I: p. 259. 42. L . G . T e l s e r , "The S u p p l y of S p e c u l a t i v e S e r v i c e s in Wheat , Corn and S o y b e a n s , " Food R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) 1 9 6 7 ( S u p p l . ) . 43. I b i d , p. 174. 44. I b i d , p. 1 7 4 . 45. I b i d , p. 174. 46. I b i d , p. 140. - 1 2 7 " K. D u s a k , " F u t u r e s T r a d i n g a n d I n v e s t o r R e t u r n s : An I n v e s t i g a t i o n o f C o m m o d i t y M a r k e t R i s k P r e m i u m s , " J o u r n a l o f P o l i t i c a l E c o n o m y , N o v . / D e c . 1 9 7 3 . I b i d , p . 1 4 0 3 . T h r o u g h o u t C h a p t e r I I I t h e t e r m " r i s k p r e m i u m " i s e m p l o y e d c o n s i s t e n t w i t h m o d e r n f i n a n c e t h e o r y . T h e r e l a t i o n s h i p s e n c o m p a s s t h e t o t a l r a n g e o f h e d g i n g a c t i v i t y . In t h e e m p i r i c a l a n a l y s i s , n e t s h o r t h e d g i n g e n t e r s t h e r e g r e s s i o n e q u a t i o n s w i t h a p o s i t i v e s i g n a n d n e t l o n g h e d g i n g w i t h a n e g a t i v e s i g n . A g g r e g a t i n g o v e r a l l h a n d l e r s , t h e t o t a l u n h e d g e d s t o c k s h e l d i s a f u n c t i o n o f t h e r i s k p r e m i u m , a n d o f t h e w e a l t h a n d r i s k c h a r a c t e r i s t i c s o f t h e i n d i v i d u a l h a n d l e r s . S i n c e t h e a m o u n t o f u n h e d g e d s t o c k s i s e q u a l t o t o t a l i n v e n t o r y m i n u s t h e a m o u n t h e d g e d , t h e a m o u n t h e d g e d ( a n d t h e r e f o r e n e t s h o r t h e d g i n g ) , i s a f u n c t i o n o f t o t a l i n v e n t o r y . K . J . A r r o w , A s p e c t s o f t h e T h e o r y o f R i s k - B e a r i n g , ( T h e A c a d e m i c B o o k S t o r e , H e l s i n k i , F i n l a n d , 1 9 6 5 ) . In c o m m o d i t y m a r k e t s , t h e e x p e c t e d r e t u r n o n r i s k y a s s e t s ( i . e . , u n h e d g e d i n v e n t o r y ) f o r a n y a n t i c i p a t e d h o l d i n g p e r i o d i s E "V - E (PS.t+n> - P S , t P s , t w h e r e E ( R D ) = e x p e c t e d r e t u r n o n r i s k y a s s e t s . R P S , t = c u r r e n t s p o t p r i c e ( t i m e t ) E(P<. t + p ) = e x p e c t e d s p o t p r i c e a t t h e e n d o f t h e ' a n t i c i p a t e d h o l d i n g p e r i o d ( t i m e t + n ) . T h e r e t u r n o n s e c u r e a s s e t s ( i . e . h e d g e d i n v e n t o r y ) o v e r t h e s a m e h o l d i n g p e r i o d ( a s s u m i n g f u t u r e s c o n t r a c t m a t u r i t y i s c o i n c i d e n t w i t h t h e a n t i c i p a t e d h o l d i n g p e r i o d ) , i s R s = F P t - p s . t p s , t w h e r e R<. = r e t u r n o n s e c u r e a s s e t s . FP = c u r r e n t f u t u r e s p r i c e ( t i m e t ) -1 2 8 -S u b t r a c t i n g , E ( V - R S = E ( P S , t + n } - P S . t " F P t - P S , t p S , t P S , t S , t + n t p s , t T h a t i s , t h e e x p e c t e d c o s t o f h e d g i n g i s b y d e f i n i t i o n e q u a l t o t h e e x p e c t e d r e t u r n o n u n h e d g e d i n v e n t o r y l e s s t h e r e t u r n o n h e d g e d s t o c k s . T h i s c o s t o f h e d g i n g i s e q u i -v a l e n t t o t h e r a t e o f r e t u r n o n r i s k y a s s e t s ( X ) a s d e f i n e d o n p . 53. 54. K . J . A r r o w , A s p e c t s o f t h e T h e o r y o f R i s k - B e a r i n g , ( T h e A c a d e m i c B o o k S t o r e , H e l s i n k i , F i n l a n d , 1965) p . 4 0 . 55. I b i d , p . 44 56. I f t h e w e a l t h e l a s t i c i t y o f d e m a n d f o r c a s h b a l a n c e s i s a t l e a s t 1, t h e n _ A . d £ 1 c d A -w h e r e c = c a s h b a l a n c e s ( i . e . s e c u r e a s s e t s ) A = i n i t i a l w e a l t h B u t d_c = 1 - d a dA dA w h e r e a = r i s k y a s s e t s S u b s t i t u t i n g f o r d_c i n t h e f i r s t e x p r e s s i o n , dA A c (1 • - d a ) > 1 dA 1 • - d a > c d A A d a < 1 dA A i e . , i n c r e a s i n g r e l a t i v e r i s k a v e r s i o n i m p l i e s t h a t 4T < 1 dA -57. T h e e c o n o m e t r i c s t e x t b o o k s m o s t f r e q u e n t l y c o n s u l t e d b y t h e w r i t e r a r e J . K m e n t a , E l e m e n t s o f E c o n o m e t r i c s ( T h e M a c m i l l a n C o m p a n y , 1971) a n d C . F . C h r i s t , E c o n o m e t r i c M o d e l s a n d M e t h o d s ( J o h n W i l e y & S o n s , I n c . 1968) . - 1 29-58. The sample p e r i o d employed in t h i s s tudy ( n o m i n a l l y J u l y 1 5 , I960 to J u l y 15, 1971) p a r t i a l l y o v e r l a p s t h a t employed by Dusak (May 15, 1952 to N o v . 1 5 , 1967). Dusak a p p r o x i m a t e d the r i s k premium as the p e r c e n t a g e change in f u t u r e s p r i c e s over the s e m i - m o n t h l y h o l d i n g p e r i o d whereas t h i s s t u d y uses the "modern" r i s k premium as def i ned in the t e x t . 59. H . S . H o u t h a k k e r , "Normal B a c k w a r d a t i o n , " in V a l u e , C a p i t a l and Growth , J . N . W o l f e , Ed . ( E d i n b u r g h U n i v e r s i t y P r e s s , 1968) . 60. P . H . C o o t n e r , " S p e c u l a t i o n and H e d g i n g " , Food R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) , 1967: p. 81. 6 1 . I b i d , p. 8 1 . 62. The c o e f f i c i e n t of the change in net h e d g i n g v a r i a b l e i s assumed to be b i a s e d upwards as d i s c u s s e d in C h a p t e r I I I . - 1 3 0 -B I BLIOGRAPHY 1 . K . J . A r r o w , A s p e c t s of the Theory of R i s k - B e a r i n g , (The Academic Book S t o r e , H e l s i n k i , F i n l a n d , 196 5) -2 . M . J . B r e n n a n , "The Supp ly of S t o r a g e , " The A m e r i c a n Economic R e v i e w , March 1 9 5 8 . 3. C . F . C h r i s t , E c o n o m e t r i c Models and Methods (John W i l e y and S o n s , Inc . 1968). 4. P . H . C o o t n e r , " R e t u r n s to S p e c u l a t o r s : T e l s e r v s . K e y n e s , J o u r n a l of P o l i t i c a l Economy, August I960. 5 . , " R e j o i n d e r , " J o u r n a l of P o l i t i c a l Economy, August I960. 6 . , " S p e c u l a t i o n and H e d g i n g , " Food R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) 1 9 6 7 -7 . K. Dusak, " F u t u r e s T r a d i n g and I n v e s t o r R e t u r n s : An I n v e s t i g a t i o n of Commodity Market R i s k P r e m i u m s , " J o u r n a l of P o l i t i c a l Economy, N o v . / D e c . 1 9 7 3 -8 . Eugene F. Fama, " S h o r t Term I n t e r e s t Rates as P r e d i c t o r s of I n f l a t i o n , " The Amer ican Economic R e v i e w , V o l . LXV, No. 3 , J u n e , 1 9 7 5 -9 . R.W. G r a y , "The C h a r a c t e r i s t i c B i a s on Some Th in F u t u r e s M a r k e t s , " Food Research I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) November 19 6 0 . 0. , "The Search f o r a R i s k P r e m i u m , " J o u r n a l of P o l i t i c a l Economy, June I 9 6 I . 1 1 . , " P r i c e E f f e c t s of a Lack of S p e c u l a t i o n , " Food R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) , 1 9 6 7 ( S u p p l . ) 1 2 . C h a r l e s 0 . H a r d y , R i s k and R i s k B e a r i n g ( C h i c a g o : U n i v . C h i c a g o P r e s s , 1 9 4 0 ) . 1 3 . J . R . H i c k s , V a l u e and C a p i t a l ( 2 n d . ed . , O x f o r d , 1 9 4 6 ) . 14. Thomas A. H i e r o n y m u s , Economics of F u t u r e s T r a d i n g f o r Commerc ia l and P e r s o n a l P r o f i t (Commodity R e s e a r c h B u r e a u , I n c . , 1 9 7 1 ) . 1 5 - H .S . H o u t h a k k e r , "Can S p e c u l a t o r s F o r e c a s t P r i c e s ? " Review of Economics and S t a t i s t i c s , May 1 9 5 7 . 16. , "Normal B a c k w a r d a t i o n , " in V a l u e , C a p i t a l and G r o w t h , J . N . W o l f e , Ed . ( E d i n b u r g h U n i v e r s i t y P ress , 1 9 6 8 ) . - 1 3 1 -1 7 . J . M . K e y n e s , A T r e a t i s e o n M o n e y , V o l . I I ( N e w Y o r k 1 9 3 0 ) . 1 8 . J . K m e n t a , E l e m e n t s o f E c o n o m e t r i c s ( T h e M a c M i l l a n C o m p a n y , 1 9 7 1 ) . 1 9 - C h a r l e s S . R o c k w e l l , " N o r m a l b a c k w a r d a t i o n , F o r e c a s t i n g , a n d t h e R e t u r n s t o C o m m o d i t y F u t u r e s T r a d e r s , " F o o d R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) , 1 9 6 7 ( S u p p l . ) 2 0 . P . A . S a m u e l s o n , " I n t e r t e m p o r a l P r i c e E q u i l i b r i u m : A P r o l o g u e t o t h e T h e o r y o f S p e c u l a t i o n , " We 1 t w i r t s c h a f 1 1 i c h e s , V o l . L X X I X , N o . 2 , 1 9 5 7 -2 1 . L . G . T e l s e r , " F u t u r e s T r a d i n g a n d t h e S t o r a g e o f C o t t o n a n d W h e a t , " J o u r n a l o f P o l i t i c a l E c o n o m y , J u n e 1 9 5 8 . 2 2 . , " R e t u r n s t o S p e c u l a t o r s : T e l s e r v s . K e y n e s : R e p l y , " J o u r n a l o f P o l i t i c a l E c o n o m y , A u g u s t I 9 6 0 . 2 3 - , " T h e S u p p l y o f S p e c u l a t i v e S e r v i c e s i n W h e a t , C o r n a n d S o y b e a n s , " F o o d R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) 1 9 6 7 ( S u p p l . ) . 2k. U . S . D e p a r t m e n t o f A g r i c u l t u r e , C o m m o d i t y E x c h a n g e A u t h o r i t y . C o m m o d i t y F u t u r e s S t a t i s t i c s . W a s h i n g t o n : G o v e r n m e n t P r i n t i n g O f f i c e . 2 5 . H . W o r k i n g , " T h e o r y o f t h e I n v e r s e C a r r y i n g C h a r g e i n F u t u r e s M a r k e t s , " J o u r n a l o f F a r m E c o n o m i c s , F e b r u a r y 1 9 ^ 8 . 2 6 . , " T h e T h e o r y o f P r i c e o f S t o r a g e , " T h e A m e r i c a n E c o n o m i c R e v i e w , D e c e m b e r 1 9 ^ 9 . 2 7 . , " F u t u r e s T r a d i n g a n d H e d g i n g , " T h e A m e r i c a n E c o n o m i c R e v i e w , J u n e 1953-2 8 . , " P r i c e E f f e c t s o f F u t u r e s T r a d i n g , " F o o d R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) , F e b r u a r y 19 6 0. 2 9 . , " S p e c u l a t i o n o n H e d g i n g M a r k e t s , " F o o d R e s e a r c h I n s t i t u t e S t u d i e s ( S t a n f o r d U n i v . ) , May I 9 6 0 .

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The risk premium in commodity markets Scott, Ernest Maurice 1976

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The risk premium in commodity markets Scott, Ernest Maurice 1976

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