The Pricing of Capital Assets in a Multiperiod World

8/11/2019 The Pricing of Capital Assets in a Multiperiod World

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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 (1 9 83 ) 3 1- -4 4 . N o r t h - H o l l a n d P u b l i s h in g C o m p a n y

T H E P R I C I N G O F C A P I T A L A SS ET S IN A M U L T I P E R I O D W O R L D

M a r s h a l l E . B L U M E *

The U niversity of Pennsylvania Philadelphia PA 19104 USA

Rece ive d M arc h 1981, f ina l ve rs ion rece ived Septem ber 1982

T h i s p a p e r p r o p o s e s a g e n e r a l f r a m e w o r k f o r t h e p r ic i ng o f c a p it a l a s s e ts i n a m u l t i p e r i o d

w o r l d . U n d e r q u i t e g e n e r al c o n d i t i o n s , t h e a n a l y s is s h o w s t h a t t h e e q u il i b r iu m e x p e c t e d n o m i n a l

r e t u r n o n a n y a s s e t c a n a l w a y s b e e x p r e s se d a s t h e s u m o f th e r i sk - f re e r a t e a n d v a r i o u s r is k

p r e m i u m s . T h e f i r s t r i s k p r e m i u m i s i d e n t i c a l t o t h e u s u a l r i s k p r e m i u m i n t h e S h a r p e - L i n t n e r -

Mo ss in capi t a l a s se t pr i c ing mode l . Th e mathem at i ca l forms of a l l t he remain ing r i sk prem ium s

a r e i d e n t i c a l ev e n t h o u g h e a c h i n d i v i d u a l r i s k p r e m i u m m a y b e p r es e n t f o r a d i f f e r e n t r e a s o n .

I I n t r o d u c t i o n

R e c e n t e mpi r i c a l t e s t s o f t he t r a d i t iona l c a p i t a l a sse t p r i c ing mode l o f

S h a r p e , L i n t n e r a n d M o s s i n h a v e f o u n d t h a t t h i s m o d e l i s n o t f u l l y

c o n s i s t e n t w i t h o b s e r v e d r e t u r n s o n c o m m o n s t o c k ? P a r t l y i n r e s P o n s e ,

va r ious a u tho rs ha ve de ve lope d a l t e rna t ive p r i c ing mode l s . Fo r in s t a nc e , i n a

m u l t i p e r i o d w o r l d, M e r t o n 1 97 3) p o s t u la t e s a c h a n g i n g i n v e s t m e n t

oppor tun i ty se t a s a func t ion o f a s toc ha s t i c in t e re s t r a t e . In a no the r e a r ly

e x te ns ion , Ma ye rs 1972) a l lows fo r hu m a n c a p it a l. M a n y o the r e x te ns ions

h a v e b e e n p r o p o s e d , b u t a n y a t t e m p t t o r ev ie w e v e r y o n e w o u l d r e q u i r e a n

article in itself.

Th e pu rp ose o f th i s pa p e r i s t o p ropo se a ge ne ra l f r a me wo rk in wh ic h to

i n t e r p r e t t h e s e v a r i o u s e x t e n s io n s a n d b y im p l i c at i on t o d e m o n s t r a t e t h e ir

c onc e p tua l s imi l a r i t i e s . Spe c i f i c a l ly , t he e xpe c te d nomina l r e tu rn on a ny a sse t

in e qu i l ib r ium c a n be v i e we d a s the sum o f the nomin a l r i sk -f re e a sse t, a nd

f o u r b a s i c k i n d s o f p r e m i u m s . T h e f i r st p r e m i u m i s t h e o n e c o m m o n t o t h e



























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The Pricing of Capital Assets in a Multiperiod World