elton, gruber, rentzler

7/22/2019 Elton, Gruber, Rentzler

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J o u r n a l o f B a n k i n g a n d F i n a n c e 7 ( 19 8 3) 1 3 5 - 1 4 6 . N o r t h - H o l l a n d P u b l i s h i n g C o m p a n y

A S I M P L E E X A M I N A T I O N O F T H E E M P I R IC A L R E L A T I O N S H I PB E T W E E N D I V I D E N D Y I EL D S A N D D E V IA T I O N S F R O M T H EC A P ME d w i n E L T O N a n d M a r t i n G R U B E R *Ne w Yo r k Un iv er sit y Ne w Yo r k N Y 1 0 0 0 6 U S A

J oe l R E N T Z L E RCi ty Univers it y o f New York New York N Y 10010 U SARece ived Oc t ob er 1981, f inal ve rs ion rece ived March 1982

Severa l papers have been publ i shed in recent yea rs dea l ing wi th both the theore t i ca l and theempi r i ca l impac t of d iv idend y ie lds on secur i ty re turns . Div iden ds hav e been pos tu la t ed asa f fec t ing s tock re turns b ecau se of t ax e f fect s , agency cos t s and the W ea l th Trans fe r H ypothe s i s .I n t h is p a p e r w e p e r f o r m a p u r e l y e m p i r ic a l e x a m i n a t i o n o f w h e t h e r a n d t o w h a t e x t e n td e v i a t io n s f r o m t h e z e r o b e t a f o r m o f t h e C A P M a r e e x p la i n e d b y d i v i d e n t y i el ds . T h e p a p e rdem ons t ra t es tha t d iv iden d y ie ld has a l a rge and s t a t i st i ca lly s igni f icant impac t o n re turn abov ea n d b e y o n d t h a t e x p l a i n ed b y t h e z e r o b e t a f o r m o f t h e C A P M . T h i s i s c o n s i s te n t w i t h t h ef in d i ng s o f L it z e n b e rg e r a n d R a m a s w a m y . I n a d d i t i o n o u r r e s u lt s a r e c o n s i s te n t w i t h t h efindings of small firm effects.

1 . I n t r o d u c t i o nSeveral papers have been publ i shed in recent years deal ing wi th both the

theoret ical and the emp ir ical imp act of d iv idend yields on secur i ty returns .Dividends have been postu lated as af fect ing s tock returns because of taxef fec ts [ see El ton and Gru ber 1970 , 1978), L i t zenberger and Ram asw am y1979 )] , . informat ion effects [see A ha ron y and Swary 1980) , Ta ub 1976),

Pet t i t 1972, 1976) and W at ts 1973, 1976)], agency costs [see Jensen andM eckl ing 1976)] , and the We al th T ransfer Hy pothesis [see K ala y 1980)] . 1In t hi s paper we per fo rm a pu re ly em pi r ica l examina t ion o f whether an d towhat ex t en t dev i a ti ons f rom the zero be t a fo rm o f t he CA P M are exp la inedby div idend yields . The paper demonst rates that d iv idend yield has a largeand s tat i s t ical ly s igni f icant impact on return above and beyond thatexplained by the zero beta form of the CAPM. This i s consis tent wi th thef indings of Li tzenbe rger and R am as w am y 1979). In addi t ion our resul ts are

* T h e a u t h o r s w o u l d l i ke t o th a n k D e x t e r C o r p o r a t i o n , W i n d s o r L o c k s , C o n n e c t i c u t f o rfunding this research.I T h e W e a l t h T r a n s f e r H y p o t h e s i s r ef e rs t o t h e a b i l i ty o f s to c k h o l d e r s t o t r a n s f e r w e a l t h f ro mc r e d it o r s t o s t o c k h o l d e r s b y p a y i n g o u t a s s e ts i n t h e f o r m o f d i v id e n d s .

0378-4266/83/ 03 .00


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136 E. El ton e t a l . Div idend y ie lds and CA P M deviations empirical re lationshipc o n s i s t e n t w i t h t h e f i n d i n g s o f s m a l l f i rm e ff ec ts w h i c h a r e d o c u m e n t e d b yR o l l (1 9 8 0 ), B a n z ( 1 9 8 1 ) a n d R e i n g a n u m ( 19 81 ). T h e n e x t s e c t i o n o f t h i sp a p e r d e s c r i b e s o u r p r o c e d u r e w h i le th e fo l l o w i n g s e c t i o n p r e s e n t s t h er e s u l t s .

2 MethodologyT h e s t u d y u t i l i z e s t h e m o n t h l y d a t a o n d i v i d e n d s , p r i c e s a n d r e t u r n s f o r

N e w Y o r k S t o c k E x c h a n g e s e c ur it ie s a v a i l a b le o n t h e U n i v e r s i t y o fC h i c a g o s C R S P t a p e. T h e p e r i o d c o v e re d b y th i s st u d y is f r o m J a n u a r y 1 9 27t h r o u g h D e c e m b e r 1 9 76 . S i n c e w e a r e i n t e r e st e d in e x a m i n i n g t h er e l a t io n s h i p b e t w e e n d e v i a t io n s f ro m t h e z e ro b e t a C A P M a n d d i v i d e n dy i el d , w e m u s t c a l c u l a t e e s t i m a t e s o f e a c h o f th e s e v a r i a b le s .

O u r f i rs t s t e p w a s t o e s t i m a t e t h e z e r o b e t a C A P M . I n o r d e r t o r e d u c e t h ee r r o r in m e a s u r i n g b e t a w h i c h i s u s ed a s i n p u t i n e s t im a t i n g t h e C A P M , t h ep o r t fo l i o g r o u p i n g p r o c e d u r e e m p l o y e d b y s e v e ra l p r e v i o u s r e s e a rc h e r s w a se m p l o y e d [ se e B la c k , J e n s e n a n d S c ho le s (1 97 2), a n d F a m a a n d M a c B e t h( 19 7 3 )] . T h e b e t a f o r e a c h s t o c k w a s c a lc u l a t ed b a s e d o n f iv e y e a r s o f d a t a( e.g ., 1 9 2 7 - 1 9 3 1 ) a n d u s i n g t h e C R S P v a l u e w e i g h t e d i n d e x . 2 A l l s t o c k s w e r er a n k e d a n d g r o u p e d i n t o t w e n t y p o r t fo l i o s o n t h e b a s i s o f t h e s e b et a s . T h eb e t a f o r e a c h p o r t f o l i o w a s t h e n c a l c u l a t e d u s i n g d a t a f o r t h e n e x t f iv e y e a r s(e .g ., 1 9 3 2 - 19 3 6 ) . T h i s b e t a w a s t h e n e m p l o y e d a s t h e b e s t e s t i m a t e o f t h eb e t a o f e a c h p o r t f o l i o f o r 1 9 37 . T h i s p r o c e d u r e w a s r e p e a t e d c h a n g i n g e a c ho f t h e 5 y e a r p e r i o d s b y 1 y e a r so t h a t w e h a d b e t a e s t i m a t e s f o r 2 0p o r t f o l io s f o r 4 0 y e a r l y p e r i o d s ( 1 93 7 -1 9 7 6 ). 3 F o r e a c h o f t h e s e y e a r s t h ea v e r a g e r e t u r n o n e a c h p o r t f o l i o j w a s c a l c u la t e d a n d t h e f o ll o w i n g c r o s s -s e c t i o n a l r e g r e s s i o n w a s r u n :

/~) = 75 + ?~fl~+ e ~ , j = 1 , . . . , 20 , wh ere/ ~ = a v e r a g e r e t u r n o n p o r t f o l i o j i n y e a r t ,

fl~ = e s t i m a t e d b e t a f o r p o r t f o l i o j i n y e a r t ,? 5, ?~ = c r o s s - s e c t i o n a l c o e f f i ci e n t s e s t i m a t e d f o r y e a r t ,~ = r a n d o m e r r o r t e r m i n y e a r t.

The a n a l y s is in t h i s p a p e r w a s a l s o c o n d u c t e d u si n g t h e C R S P e q u a l w e i g h t e d in d e x T h e s eresu l t s were ind i s t ingui shable f rom those repor t ed in th i s pape r3 T he c o m p o s i t i o n a n d s iz e o f e a c h o f th e s e p o r t fo l i o s c h a n g e d f r o m y e a r t o y e a r T h e n u m b e ro f s t o c k s w h i c h h a d t h e r e q u i r e d d a t a o v e r e a c h 1 1 y e a r p e r io d a n d s o w e r e p l a c e d i n t opor t fo l ios va r i ed f rom a low of 419 to a h igh of 880 wi th an ave rage n um ber of 740


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E . E l ton e t a l . D iv idend y i e lds and C A P M dev ia t ions empiri cal r e la t ions h ip 137

T h e e x c e ss r e t u r n a~ f o r e a c h s e c u r i t y i i n y e a r t w a s t h e n d e f i n e d a st ~ - - t t t t+ ~ l f li ) , i = 1 , . . . ,~ i R i Y o N ,

w h e r e fl~ i s t h e e s t i m a t e d b e t a o f th e p o r t f o l i o t o w h i c h s e c u r i t y i b e lo n g s , ~ ,~ ] a re t h e e s t i m a t e d c r o s s - s e c t i o n a l c o e f f ic i e n t s f o r y e a r t . T h i s v a l u e f o ra l p h a w a s u s e d a s t h e b e s t e s t i m a t e o f a l p h a f o r e a c h o f t h e s e c u r i t i e s i n ap a r t i c u l a r p o r t f o l i o .

O u r n e x t s t e p w a s t o o b t a i n a f o r e c a s t o f t h e d i v i d e n d y i e l d f o r y e a r t( y e a r 11 ) w h e r e t h e f i rs t f o r e c a s t o f d i v i d e n d y i e l d w a s m a d e w h e n y e a r 1 1w a s 1 9 3 7 . I n o r d e r t o o b t a i n t h i s e s t i m a t e w e d e c i d e d t o u s e t h e d i v i d e n dy i e l d o n a p o r t f o l i o o f s t o c k s r a t h e r t h a n o n e a c h i n d i v i d u a l s t o c k . T h e r e i ss u b s t a n t i a l f o r e c a s t e r r o r i n t h e e s t i m a t e o f a s e c u r i t y s y ie l d . B y u t i l i z in g t h ed i v i d e n d y ie l d fo r a p o r t f o l i o o f s t o c k s r a t h e r t h a n a n i n d i v i d u a l s e cu r i ty w eh o p e d t o r e d u c e t h i s f o r e c a s t e r r o r. S t o c k s w e r e g r o u p e d b y t h e i r d i v i d e n dy i e l d i n y e a r 9 - - t w o y e a r s b e f o r e t h e f o r e c a s t y e a r . 4 T w e n t y g r o u p s w e r ef o r m e d . T h e f i rs t 1 9 g r o u p s w e r e f o r m e d b y o r d e r i n g a l l s t o c k s w h i c h p a i dp o s it iv e d i v i d e n d s f r o m h i g h e s t t o l o w e s t a n d t h e n d i v i d i n g t h es e s t o c k s i n t o1 9 e q u a l g r o u p s . T h e 2 0 t h g r o u p c o n t a i n e d a l l s to c k s t h a t p a i d z e r od i v i d e n d s d u r i n g y e a r t - 2 ( y e a r 9 ).

P l a c i n g a l l st o c k s w i t h z e r o d i v i d e n d s i n t o o n e g r o u p i s i n c o n t r a s t w i t ht h e p r o c e d u r e u s e d i n s o m e p r i o r s t u d i e s [ e . g . , B l a c k a n d S c h o l e s ( 1 9 7 4 ) ] .O u r p u r p o s e i n g r o u p i n g w a s t o r e d u c e f o r e c a s t e r ro r w h i le a t t h e s a m e t i m eo b t a i n i n g p o r t fo l i o s w i t h a w i d e r a n g e o f d iv i d e n d y i e ld s . I n s o m e p e r i o d ss to c k s w i t h z e ro d i v i d e n d y i e ld s w e r e s o n u m e r o u s t h a t i f w e h a d a n e q u a ln u m b e r o f st o c k s i n e ac h p o r t f o l io g r o u p i n g , t h e n a l a rg e n u m b e r o f t h e s ep o r tf o li o s w o u l d h a v e h a d z e r o d i v i d e n d y i e ld s . T a b l e 1 s h o w s t h e p e r c e n t a g eo f s to c k s i n o u r s a m p l e t h a t d i d n o t p a y a d i v i d e n d i n y e a r t - 2 . F o re x a m p le p u t ti n g a n e q u a l n u m b e r o f s to c k s i n e a c h g r o u p w o u l d h a v er e su l te d i n a b o u t h a l f th e p o r t f o l i o s h a v i n g z e r o d i v i d e n d y i e l d in t h e e a r l yy e a r s a n d t w o o r t h r e e w i t h t h i s z e r o y i e l d i n l a te r y e a rs . H a v i n g f o r m e d t h e2 0 p o r tf o l i o s w e t h e n h a d t o f o r e c a s t t h e d i v i d e n d y i e l d f o r y e a r t ( y e a r 1 1).W e u s e d a s o u r f o r e c a s t t h e a c t u a l d i v i d e n d y i e l d i n y e a r t - 1 ( y e a r 1 0 ). 5

T h e n e x t s t e p w a s t o r e l a t e e x c e s s r e t u r n t o d i v i d e n d y i e l d . F i r s t t h ea v e r a g e e x c e s s re t u r n , 0 ?j, a n d a v e r a g e f o r e c a s t e d d i v i d e n d y i e l d , ~ , f o r e a c h

4 T h e a r g u m e n t s b e h i n d g r o u p i n g o n d i v i d e n d y i e l d s a r e d i r ec t ly a n a l o g o u s t o t h e a r g u m e n t su s e d i n g r o u p i n g o n b e t a s t o p r o v i d e b e t t e r e s t i m a t e s . I n f o r m i n g g r o u p s w e d e f i n e d d i v i d e n dyie ld as d iv idend s in yea r 9 d iv ided b y the ending pr i ce . Ou r pu rpose w as to ob ta in a s e t o fpor t fo l ios w i th a w ide range of y ie lds in y ea r 10 .5We have em ploy ed the s im ples t pos s ib le forecas t mode l in th i s pape r s e t t ing n ex t yea r sd iv idend y ie ld equa l to l a s t yea r s d iv iden d y ie ld . I f we had found no d iv idend y ie ld e f fec t i tm i g h t h a v e b e e n d u e t o t h e u s e o f t h is n a i v e f o r e c a s t in g m o d e l . H o w e v e r , t h e f a ct t h a t w e d o g e ts t rong re su l ts w i th th i s na ive mode l h igh l igh ts th e imp or tan ce of the d iv idend e ffec t. A moresophi s t i ca t ed forecas t ing mode l might l ead to even s t ronger re su l t s .


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138 E . E l to n e t a l . D iv idend y i e lds and C A P M dev ia t ions empir i ca l re la t ions h ipT a b l e 1

Percent of s tocks wi th ze ro d iv idend y ie ld ingrouping yea r .

G r o u p i n g F o r e c a s t A ll S t o c k s u n d e ryear yea r s tocks 5 e l imina ted1935 1937 5~ 4% 45.4%1939 1941 44.0 32.01943 1945 23.6 17.81947 1949 13.6 10.61951 1953 11.3 9.31955 1957 11.5 10.61959 1961 14.5 13.81963 1965 13.2 11.51967 1969 9.1 9.11971 1973 16.2 14.81974 1976 11.0 6.1

p o r t f o l i o j w a s c o m p u t e d . T h e a v e r a g e w a s t a k e n o v e r t h e 40 f o r e c a s t y e a r s1 9 3 7 - 1 9 7 6 ) . T h e n a c r o s s - s e c t i o n a l r e g r e s s i o n o f t h e f o r m

f f j = A o + A a ~ + g~, j = 1 , . .. , 2 0w a s r u n t o o b t a i n e s t i m a t e s o f A o a n d A t. T h i s a v e r a g i n g p r o c e s s w a sr e p e a t e d u s i n g a l l e i g h t n o n - o v e r l a p p i n g 5 - y ea r s u b p e r i o d s i n o u r 4 0 y e a rs a m p l e g i v i n g e i g h t o t h e r e s t i m a t e s o f A o a n d A 1.A s w i l l b e c o m e c l e a r l a t e r , th e r e w e r e r e a s o n s t o s u s p e c t t h a t t h e z e r od i v i d e n d g r o u p o f s t o c k s w o u l d b e h a v e p e rv e r se l y . T o t e s t th i s , a r e g r e s s i o no f t h e f o l l o w i n g fo r m w a s r u n :

~j=A o+A ~+A zD+~, j = 1 , . . . , 2 0 .I n t h is r e g r e s s i o n D i s a d u m m y v a r i a b l e h a v i n g a v a l u e o f 1 f o r t h e p o r t f o l ioo f s to c k s w h i c h p a i d z e r o d i v i d e n d s in t h e g r o u p i n g y e a r a n d a v a l u e o f 0 f o ra l l o t h e r g r o u p s .

N o t e t h a t t h i s m e t h o d o l o g y i s d e s i g n e d so t h a t fo r e ca s ts o f b o t h t h e b e t a sa n d t h e d i v i d e n d y i e ld s e m p l o y e d i n t h e a n a l y s is u s e o n l y d a t a w h i c h i sa v a i l a b l e p r i o r t o t h e d a t e s o v e r w h i c h t h e r e tu r n s a r e c a l c u l a t e d . T h u s , t h ee x i s t e n c e o f a n e x c e s s r e t u r n w i t h r e s p e c t t o d i v i d e n d y i e l d i n d i c a t e s t h a t a ni n v e s t o r i n t h e a b s e n c e o f t r a n s a c t i o n c o st s c o ul d h a v e a c t e d i n a w a y t oe a r n a n e x t r a r e t u r n u s i n g a v a i l a b l e i n f o r m a t i o n . T h i s w o u l d n o t n e c e s s a r il yi n d i c a t e t h a t h e c o u l d h a v e e a r n e d a n e x ce ss r e t u rn b e c a u s e o f th e p r e s e n c eo f t r a n s a c t i o n c o s ts a n d a d d i t i o n a l n o n - m a r k e t r i sk i n c u rr e d . H o w e v e r i td o e s i n d i c a t e a n a d d i t i o n a l i n f lu e n c e o n e q u i l i b r i u m r e t u rn s . N o t e a l s o t h a to u r p r o c e d u r e i s d e s i g n e d s o t h a t i f t h e r e i s a b i a s it i s against f i n d i n g a


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E . E l ton e t a l. D iv idend y i e lds and C A P M dev ia t ions empir i ca l r e la tions h ip 139div idend i n f luence. I f be t a s a r e co r r e l a t ed w i th d iv idend y i e lds t hen o ur twos t ep p rocedure would have a b i a s t owards f i nd ing no d iv idend e f f ec t evenwhen one was p resen t . T h i s was a de l i be ra t e cho i ce on our pa r t . As has beend i scussed i n t he l i t e r a tu re , t he re i s cons ide rab l e d i sagreement on t hereasonab l eness o f t he p rocedures used fo r the j o in t e s t ima t ion o f d iv idendand be t a e f f ec t s . Our p rocedure , whi l e b i a sed aga ins t obse rv ing d iv idendeffects , avoids the es t imat ion cont roversy. Thus , f inding a dividend ef fec t wi thth i s p rocedure wo uld p rov ide s t rong ev idence i n supp or t o f such an e f fect.

3 R e s u l t sT able 2a summar i zes t he s t a t i s t i ea l r e l a t i onsh ip be tween t he ave rage yea r ly

excess r e tu rn a lpha ) and t he ave rage d iv idend y i e ld i n each o f t he 20 g rou pswhere t he ave rages a r e t aken ove r t he en t i r e fo recas t pe r iod 1937-1976 . Byexam in ing t he f ir s t r ow of da t a i n t ab l e 2a we see t ha t a l t h oug h t he re is a

T a b l e 2 aC r o s s - s e c t o n a l r e g r e s si o n s o f a v e r a g e e x c e s s r e t u r n o n d i v i d e n d y i e ld o v e r 4 0 y e a r

f o r e c a s t p e r i o d ( t - v a l u e s i n p a r e n t h e s e s ) .D u m m y

D i v i d e n d v a r i a b l eF o r e c a s t p e r i o d I n t e r c e p t c o e f f ic i e n t c o e f f ic i e n t R 21 9 3 7 . 1 9 7 6 - 2 . 2 6 3 0 . 34 4 0 . 18 8

(2.59) (2.04)- 4 . 7 7 4 0 . 7 9 4 6 . 1 8 9 0 . 8 7 4( - 10.87) (9.60) (9.64)

T a b l e 2 bC r o s s - s e c t i o n a l r e g r e s s i o n s o f a v e r a g e e x c e s s r e t u r n o n d i v i d e n d y i e ld , o v e r f iv e

y e a r p e r i o d s ( t - v a l u e s i n p a r e n t h e s e s ) .D u m m y

D i v i d e n d v a r i a b l eF o r e c a s t p e r i o d I n t e r c e p t c o e f f ic i e n t c o e f f ic i e n t R 21 9 3 1 9 4 1 1 . 0 7 8 - 0 . 0 9 1 - 0 . 2 0 4 0 . 0 0 2194 2-19 46 - 13 .790 1 .076 25 .745 0 .853194 195 1 - 1 .298 0 .221 1 .211 0 .0371 9 5 2 - 1 9 5 6 - 1 .0 8 2 0 . 2 16 - 0 . 4 1 9 0 . 0 7 71 9 5 1 9 6 1 1 . 4 2 5 - 0 . 3 3 7 - 0 . 2 9 9 0 . 0 8 21 9 6 2 - 1 9 6 6 - 1 . 4 48 0 . 2 1 8 5 . 5 8 8 0 . 4 7 71 9 6 7 - 1 97 1 - 4 . 9 0 7 1 .4 5 7 2 . 05 9 0 . 5 7 01 9 7 2 - 1 9 7 6 - 1 1 . 86 8 2 . 6 2 9 1 0 . 7 2 7 0 . 8 8 3M e a n - 3 . 9 8 6 0 . 6 7 3 5 .5 5 1

(2.075) (2.062) (1.862)


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140 E . E l to n e t a l . D iv idend y i e lds and C A P M dev ia t ions empiri cal r e la t ions h ip

s ign i f i c an t pos i t ive re l a t ionsh ip be tween excess r e tu rn and d iv idend y ie ldove r the en t i r e pe r iod , t he re l a t ion sh ip i s sma ll . The R 2 fo r the re l a t ions h ip i sonly 0.188.

An examina t ion o f the da ta u sed in ob ta in ing the se reg re ss ion re su l t s( t ab le 3 ) shows tha t t he weak pos i t ive a ssoc ia t ion may be due to the p re senceof two d i s t inc t r e l a t ionsh ips . 6 N o te tha t po r t fo l io 20, wh ich was fo rm ed twoyea rs be fo re the fo reca s t yea r u s ing a l l s tocks wh ich d id no t pay a d iv idend ,has a h igh pos i t ive excess r e tu rn (a lpha ) . The re tu rn on th i s g roup i sc o n s i d e r a b l y h i g h e r t h a n t h e r e t u r n o n a n y o t h e r g r o u p t h o u g h i t h a s b y f a rthe lowes t y i e ld in the yea r p r io r to the fo reca s t (yea r 10 ) and so the lowes tfo recas t ed y ie ld . These ze ro d iv idend s tocks cons t i tu t e an ou t l i e r g roup . Th i sf ind ing i s no t su rp r i s ing and has been no ted ea r l i e r by B lume (1979) . La te r i nth i s sec t ion we wi l l examine some poss ib le exp lana t ions fo r the obse rved h ighexcess re turn in th is group. Before turn ing to th is d iscussion we wi l l f i rs te l imina te the e ffec t th is group has on the d iv idend y ie ld-excess re turnre l a t ionsh ip . Th i s cou ld be accompl i shed e i the r by de le t ing th i s g roup f romt h e d a t a o r b y a d d i n g a d u m m y v a r i a b l e w h ic h h a s a v a lu e o f o n e f o r th enon-d iv idend po r t fo l io g roup (number 20 ) and ze ro fo r a l l o the r g roups .These two p rocedure s a re iden t i ca l i n the i r e f fec t s on the in t e rcep t and s lopete rm. The a dva n tag es o f u s ing a dum m y va r i ab le i s t ha t i t a l lows a d i rec tm easu rem en t and a t e s t o f s ign i f ic ance fo r the d if fe rence o f behav io r o f theexcess r e tu rn in the ze ro d iv idend g roup . T he re su lt s o f i nc lud ing th i sdummy va r i ab le in the reg re ss ion fo r the en t i r e fo reca s t pe r iod a re shown inthe second l ine o f t ab le 2a . No t i ce th a t now the pos i tive re l a t ionsh ip be tweenexcess re tu rn and d iv idend y ie ld i s bo th l a rge (0 .794) and s t a t i s ti c a l lys ign if i c an t a t t he 1 l evel. Fu r the rm ore the po r t fo l io cons t ruc ted f rom s tocksw h i c h h a d p a i d z e r o d i v i d e n d s h a s a n e x c e s s r e t u r n b e y o n d w h a t o n e w o u l dexpec t g iven the behav io r o f the o the r po r t fo l io s . The va lue o f 6 .189 i ss t a t i s ti c a l ly s ign i f ic an t a t t he 1 l evel. The inc lus ion o f the du m m y va r i ab lea l so ra i se s the coe f f ic i en t o f de te rm ina t ion on the reg re ss ion f rom 0 .188 to0.874.

As a fu r the r check on the fo rm o f th i s r e l a tionsh ip , t he reg re ss ion inc lud ingt h e d u m m y v a r i a b l e w a s r u n f o r e a c h o f t h e e i g h t f i v e y e a r n o n - o v e r l a p p i n gsubpe r io ds b e tween 1937 and 1976 . These re su l ts , r epo r t ed in t ab le 2b , a resuppor t ive o f the ove ra l l r e l a t ionsh ip . The re l a t ionsh ip be tween excess r e tu rnand d iv idend y ie ld is pos i tive in s ix o f the e igh t pe riods and on ave rage theregressio n coeff ic ient i s s igni f icant ly d i f fe rent f rom zero a t the 5 level . Theimp ac t o f the du m m y va r i ab le i s pos i tive in five o f the e igh t pe r iods and i tsaverag e va lu e i s pos i t ive and s igni f icant a t the 5 leve l.

The h igh pos i t ive excess r e tu rn a ssoc ia t ed w i th ze ro d iv idend s tocks i sim po r tan t an d wo r thy o f add i t io na l a t t en t ion . I s t h is an ef fect c aused b y low6In examining table 3 recall that group 20 has many more members than other portfolios.Thus a lthough mos t groups have negative alphas the average overall alpha is close to zero.


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E. E l to n e t a l. D iv idend y i e ld s and C A P M de v ia t ions e m p i r i c a l r e la t ions h ip 4

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7 T h e u s e o f m o n t h l y d a t a r a t h e r t h a n d a i ly r e d u c e s t h e i m p o r t a n c e o f th i s ef fe ct8Many f inanc ia l i ns t i tu t ions wi l l no t ho ld low pr i ced s tocks due to e i the r t ransac t ion cos t s o rperceived r isk


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E . E l ton e t a l . D iv idend y i e lds and C A P M dev ia t ions empir i ca l r e la t ions h ip 143

L ow cap i t a l i za t i on s t ocks i n gene ra l se ll f o r le ss t han 5 . T h us l ow pr i cecan se rve a s a p roxy fo r l ow cap i t a l i za t i on and i t i s d i f f i cu l t t o be su re whichfac to r migh t be caus ing pos i t i ve excess r e tu rns . Ro l l ' s a rgument conce rn ingin f r equen t t r ad ing o f l ow cap i t a l i za t ion s t ocks ho lds equa l l y we ll f o r s t oc ksse ll ing und er 5 . How ever , t he m arg in r e s t r i c t ions ap p ly t o s t ocks se ll ing fo rl es s t han 5 and n o t to l ow cap i t a l i za t i on s t ocks . T h us we dec ided t ha t , i nord e r t o sep a ra t e t he ef fect o f l ow pr i ced sma l l cap i t a l i za t i on s t ocks f rom thee f fec t o f ze ro d iv idend pay me nt , i t was mo s t r e l evan t t o e l imina t e s t ocksse ll ing fo r und er 5 f rom our popu la t i on . 9

T ab les 4 and 5 a r e ana logous t o t ab l e s 2 and 3 excep t t ha t a l l s t ocksse ll ing fo r l es s than 5 pe r sha re were e l imina t ed . E x am in ing t he f i rs t r ow int ab l e 4 shows t ha t e l imina t i ng such s tocks had a ma jor e f f ec t . T he impac t o fd iv idend y i e ld on excess r e tu rns a s measured by t he r egres s ion coe f f i c i en t hasgrown f rom 0.344 to 0 .549 and i s s ta t i s t ica l ly s igni f icant a t the 1% level . Thecoef fi c ien t o f de t e rm ina t i on be tween d iv idend y i e ld and excess r e tu r n haschan ged f rom 0 .188 t o 0 .471. E l imina t i ng s tocks und er 5 pe r sha re r educe dthe unexp la ined excess r e tu rn a s soc i a t ed wi th t he ze ro d iv idend g roup . T h i sind i ca t e s t ha t pa r t o f t he pecu l i a r behav io r o f t h i s g rou p was due t o t heinclus ion of these low pr iced f i rms.

Ho we ver n o t a ll o f t he pecu l ia r beh av io r o f t h i s g rou p i s e l imina t ed byrem ovin g 5 s t ocks f rom the sample . T ab l e 5 show s t ha t t he r e tu rn onpor t fo l i o 20 which had p rev ious ly pa id a ze ro d iv idend i s 0 . 86% whereasthe be hav io r o f t he o the r 19 g rou ps w ould l ead us t o expec t a nega t i ve excessr e tu r n fo r por t fo l i o 20 . T o t e s t f o r pe rve r se behav io r o n t he p a r t o f t he ze rod iv idend por t fo l i o , t he r egres s ion was r e run wi th a dummy va r i ab l e . T heresu l t s aga in improved . As seen i n t he second l i ne o f t ab l e 4a , t he t -va lue o fthe in tercept and dividend yie ld coef f ic ient both increase , the coef f ic ient ofd e t e r m i n a t i o n i n c r e a s e s , a n d t h e d u m m y v a r i a b l e e n t e r s w i t h a p o s i t i v e a n dstat ist ical ly signif icant (at the 1% level) coeff icient .

T a b l e 4 aCross -sec t iona l regres s ions of averag e excess re turn o n d iv idend y ie ld over 40year forecas t pe r iod wi th und er 5 stocks e limina ted ( t -va lues in pa rentheses ) .

D i v id e n d D u m m y v a r ia b leFor ecas t pe r iod In te rcept coef f ic i en t coe f fi c ien t R 21 9 3 % 1 9 7 6 - 2.623 0.549 0.471(3.69) (4.00)

-4 .3 98 0.865 4.445 0.841(8.95) (9.36) (6.28)9 A t a n u m b e r o f p o i n t s i n t he s t u d y w e e l i m in a t e d l o w c a p i t a li z a ti o n s t o c k s r a t h e r t h a n t h o s ese l ling for le ss than 5 . Thi s d idn ' t s ignif i cant ly impac t on the resu l t s and so these resu l t s a re no trepor t ed .


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144 E. El ton e t a l . D iv idend y ie lds and C A P M deviat ions empirical re lationshipT a b l e 4 b

C r o s s - s e c t i o n a l r e g r e s s i o n s o f a v e r a g e e x c e s s r e tu r n o n d i v i d e n d y i e ld o v e r f iv ey e a r s u b p e r i o d s w i t h u n d e r 5 st o c k s e l im i n a t e d ( t -v a l u e s i n p a re n t h e s e s) .

D u m m yD i v i d e n d v a r i a b l eF o r e c a s t p e r i o d I n t e r c e p t c o e f f ic i e n t c o e f f ic i e n t R 21 9 3 % 1 9 4 1 - 0 . 7 8 9 0 . 3 6 9194 2- 19 46 - 5 .054 0 .6321 9 4 7 - 1 9 51 - 0 . 5 1 8 0 .1 0 11 9 5 2 - 1 9 5 6 - 0 . 6 1 2 0 .1 1 11 9 5 7 - 1 9 61 1 .1 1 9 - 0 . 2 6 91 9 6 2 - 1 9 6 6 0 . 41 6 - 0 . 1 9 21967 - 1971 - 4 .631 1 .4371972 - 1976 - 8 .869 2 .085M e a n - 2 . 3 6 7 0. 5 3 4

( - 2 . 0 7 2 ) ( 1 . 9 5 1 )1 9 3 7 - 1 9 4 1 - - 0 . 0 9 3 0 . 2 4 61 9 4 2 - 1 9 4 6 1 . 4 0 21947 - 1951 - 1 .316 0 .218195 2- 19 56 - 1 .185 0 .2011 9 5 7 - 1 9 61 1 .1 7 6 - 0 . 2 8 1196 2- 19 66 - - 1 .451 0 .2601967 - 1971 - 4 .838 1 .4881 9 7 2 - 1 9 7 6 2 . 4 5 0M e a n - 3 . 7 07 0 . 7 48

(2.337) (2 .443)

0 .0440 .1390.0120.0160.0510.0290.6020 .734

- 1.341 0.05 215.063 0 .765

1.665 0.0431.246 0 .036- 0 . 1 3 2 0 . 0 5 2

5.046 0 .4150.733 0 .6048.181 0.8453.808(2.102)

Table 4b presents the regression results for all five year non-overlappingperiods with and without the dummy variable. The results continue tosupport the earlier findings that there is a strong positive association betweenexcess returns and forecasts of dividend yield except for the group of stockswhich had previously not paid a dividend. These stocks seem to sell at a realpremium above that which one would expect based on their forecasted betaand dividend yield.

4 C o n c lu s io n sIn this article we have examined the relationship between residuals from

the zero beta form of the capital asset pricing model and dividend yields. Wehave found a persistent relationship between dividend yield and excessreturns. In particular except for those stocks which had previously paid zerodividends the higher the dividend yield the higher the excess return. Onegroup of stocks those which had previously paid no dividends had excessreturns which were above what we would expect from this relationship. Par tof this differential was shown to be due to the effect of low priced stocks but


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E . E l t o n e t a l . D i v i d e n d y i e l d s a n d C A P M d e v i a t i o n s e m p i r i c a l r e l a t i o n s h i p 45

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elton, gruber, rentzler

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