UBC Theses and Dissertations

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UBC Theses and Dissertations

The risk premium in commodity markets Scott, Ernest Maurice 1976

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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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