The Evolution of Capital
Asset Pricing Models
Sheng-Syan Chen, National Taiwan University
Cheng-Few Lee, Rutgers University
Yi-Cheng Shih, National Taipei University
Po-Jung Chen, National Taiwan University
Outline
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Introduction
Intertemporal Models
Supply-Side Effect Models
International CAPM
Equilibrium Models with Heterogeneity
Dividend and Taxation Effect Models
Skewness Effect Models
Behavioral Finance
Liquidity-based Models
Existence of Equilibrium
Empirical Tests
Conclusion
Abstract
Based upon Markowitz (1952, 1959) Mean-Variance Portfolio Theory and six critical
assumptions, Sharpe (1964), Lintner (1965), and Mossin (1966) have derived and
developed the static Capital Asset Pricing Model. During the four past decades, the CAPM
has been the benchmark of asset pricing models, and most empirical apply it to calculate
asset returns and the cost of capital. To relax the original six assumptions, many
researchers have tried to generalize the static CAPM by Sharpe, Lintner, and Mossin. In
addition, many researchers have also tried to develop the dynamic Capital Asset Pricing
Models.
In this paper, we survey the important alternative theoretical models of the Capital
Asset Pricing for last four and half decades. We organize these theoretical models, as
follows: (i) Merton’s Intertemporal CAPM, (ii) Consumption-based Intertemporal CAPM, (iii)
Production-based Intertemporal CAPM, (iv) CAPM with Supply-side Effect, (v) International
Equilibrium CAPM with Heterogeneity Beliefs and Investors, (vi) Equilibrium CAPM with
Heterogeneity Investment Horizon, (vii) CAPM with Dividend and Taxation Effect, (viii)
CAPM with Skewness Effect, and (ix) Behavioral Finance, and Liquidity-based CAPM. The
interrelationship among these models is also discussed in some detail.
The results of this paper might be used as a guideline for future theoretical and
empirical research in capital asset pricing. More specifically, we suggest three possible
directions for future research. To the best of our knowledge, this is one of the most
complete reviews of the evolution of theoretical capital asset models.
1.
Introduction
dPi
  i dt   i dzi
Pi
(1)
n
n

dW   wi  i  r f   r f Wdt   wiW i dzi   y  c dt
i 1
 i 1

(2)
2. Intertemporal Models
2.1 Merton Model
2.2 Consumption-based Models
2.3 Production-based Models
2. Intertemporal Models
2.1 Merton Model
 i  r  i  M  r 
(i=1, 2,…,n),
(3)
where i   iM /  M2 ,  iM is the covariance of the return on the ith asset with
the return on the market portfolio and  M is the expected return on the
market portfolio.
i  r 
 i iM  in nM 
 i in  iM nM 


 n  r 


r

M
2
2
 M 1  nM 
 n 1  Mn 
(4)
2. Intertemporal Models
2.2 Consumption-based Models
U (Ck ,t )   Et 1  Ri ,t 1 U (Ck ,t 1 )

U (Ck ,t 1 ) 
1  Et (1  Ri ,t 1 ) 
  Et 1  Ri ,t 1  M k ,t 1 
U (Ck ,t ) 

(5)
(6)
where M k ,t 1   U (Ck ,t1 ) / U (Ck ,t ) is the intertemporal
marginal rate of substitution of the investor,
also known as the stochastic discount factor.
2. Intertemporal Models
2.2 Consumption-based Models
1  Et 1  Ri ,t 1  M t 1 
(7)
Et 1  Ri ,t 1  M t 1 
 Et 1  Ri ,t 1  Et  M t 1   Covt  Ri ,t 1 , M t 1 
(8)
2. Intertemporal Models
2.2 Consumption-based Models
1  Covt Ri ,t 1 , M t 1 
1  Et Ri ,t 1  
Et M t 1 
1  R f ,t 1
1

Et M t 1 
(9)
(10)
2. Intertemporal Models
2.2 Consumption-based Models
1  Et Ri ,t 1   1  R f ,t 1  1  Covt Ri ,t 1 , M t 1 
1
(Ct  X t )
E
1 
t 1

t
Uc (Ct , X t )  (Ct  X t )
(11)
1
(12)


 Ct St

(13)
2. Intertemporal Models
2.2 Consumption-based Models
M t 1
 Ct 1 
U c (Ct 1 , X t 1 )


  
U c (Ct , X t )
 Ct 

 St 1 


 St 

(14)
M t 1  at  (b0  b1 zt )  ct 1
(15)
Wt 1  Rm,t 1 (Wt  Ct )
(16)
2. Intertemporal Models
2.2 Consumption-based Models
Wt 1
Ct
 Rm,t 1 (1  )
Wt
Wt
wt 1
 1
 rm,t 1  a  1  ct  wt 
 
k
ct  wt    (rm,t i  ct i ) 
1 
i 1
(17)
(18)

i
(19)
2. Intertemporal Models
2.2 Consumption-based Models

ct  wt  Et   (rm,t i
i
i 1
k
 ct i ) 
1 
1

1

U t  1   Ct   EtU t 1







1
(20)

1
1
1 /  







C
1





1  Et   t 1   
1  Ri ,t 1 

  Ct   

1  Rm,t 1 





(21)
(22)
2. Intertemporal Models
2.2 Consumption-based Models

1 / 



  Ct 1 
 

 Rm,t 1 
1  Et  
  Ct 


 


0   log  Et ct 1    1Et rm,t 1  Et ri ,t 1 
(23)

2

1   
2
2
2
(  1)(Vcm )  Vci  2(  1)Vim 
  Vcc  (  1) Vmm  Vii 
2   



(24)
Et ri ,t 1  rf ,t 1
Vii
Vic
  
 (1   )Vim
2

(25)
2. Intertemporal Models
2.2 Consumption-based Models
 k  m 
ct  wt  1    Et   (rm,t i ) 
(26)
1 
i 1

i

ct 1  Et ct 1  rm,t 1  Et rm,t 1  1   Et 1  Et   i rm,t 1i
i 1
(27)
Covri ,t 1 , ct 1   Vic  Vim  1   Vih
(28)
2. Intertemporal Models
2.2 Consumption-based Models



i
Vih  Cov ri ,t 1  Et ri ,t 1 , ( Et 1  Et )  rm,t 1i 
i 1


(29)
Et ri ,t 1  rf ,t 1
Vii
   Vim  (  1)Vih
2
(30)
2. Intertemporal Models
2.3 Production-based Models

E0
1 
t
Ri  dt



t 0 i 0
(31)
dt  yt  it  yt  kt 1

yt  AB t kt
t
(32)
(33)
2. Intertemporal Models
2.3 Production-based Models


Et Rt 1    yt 1 / kt 1   1
1

E0
  uc 
t
t 0
(34)
(35)
t
ct  pt  yt st 1   pt  yt   dt  yt st
(36)
2. Intertemporal Models
2.3 Production-based Models
pt  yt uct   Et  pt 1  yt 1   dt 1  yt 1 uct 1 
(37)
Rt 1  yt 1 , yt    pt 1  yt 1   dt 1  yt 1 / pt  yt 
(38)
2. Intertemporal Models
2.3 Production-based Model

pt  Et   i uct i  / uct d t i
(39)
uct   a ln ct 
(40)
i 1

pt  Et   d t   / 1   d t
i
i 1
(41)
2. Intertemporal Models
2.3 Production-based Model
Rt 1  1 /  dt 1 / dt 
Rt 1  1/   yt 1 / yt 

yt 1  t 1 yt
t
M t 1  b0  zt b1   f t 1
(42)
(43)
(44)
(45)
2. Intertemporal Models
2.3 Production-based Models
M t 1  b0 f t 1  b1  f t 1  zt 1 
(46)
V kt , t   Max u ct , n  nt    Et V kt 1 , t 1  (47)
nt ,kt 1
t 1  H t ,  t 1 
(48)
ct  f t , nt , kt   kt 1
(49)
2. Intertemporal Models
2.3 Production-based Models
M t 1 

t 1
f k  t 1 , nt 1 , kt 1 
(50)

Et r V kt 1 ,t 1 / Fk t 1 , nt 1 , kt 1   0
iE
t 1 k
for all i,
(51)
3. Supply-Side Effect Models
3.1 Demand function of capital assets
3.2 Supply function of securities
3.3 Multiperiod Equilibrium Models
3. Supply-Side Effect Models
3.1 Demand function of capital assets
{bWt 1}
U  a  he
(52)
X j ,t 1  Pj ,t 1  Pj ,t  D j ,t 1 j = 1,…,N, (53)
x j ,t 1  Et X j ,t 1  Et Pj ,t 1  Pj ,t  Et D j ,t 1
j = 1,…,N,
(54)
3. Supply-Side Effect Models
3.1 Demand function of capital assets
wt 1  EtWt 1  Wt  r  Wt  qt1 Pt   qt1 xt 1
(55)

V Wt 1   E Wt 1  wt 1 Wt 1  wt 1   qt1S q ,t 1
b
Max wt 1  V(Wt 1 )
2
(56)
(57)
3. Supply-Side Effect Models
3.1 Demand function of capital assets


b

Max 1  r Wt  qt1 xt 1  r  Pt    qt1S qt 1
2
*
1
qt 1  b S
1
xt1  r  Pt 
(58)
(59)
m
Qt 1   qtk1  cS 1Et Pt 1  (1  r*)Pt  Et Dt 1 
k 1
(60)
3. Supply-Side Effect Models
3.2 Supply function of securities
1
Min Et Di ,t 1Qi ,t 1    Qi,t 1 Ai Qi ,t 1  (61)
2
Qi,t 1  A i Pi,t  Et Di,t 1 
1
i
(62)
3. Supply-Side Effect Models
3.2 Supply function of securities
1
i
Qt 1  A
BPt  Et Dt 1 
(63)
where
 A11

1
A
2
A1  




1I


2 I
,B  



1 
AN 


 Q1 

Q 
 ,and Q   2 

 

 
N I 
QN 
3. Supply-Side Effect Models
3.3 Multiperiod Equilibrium Models
Qt 1  cS
1
E P
t t 1
1
i
Qt 1  A


 1  r Pt  Et Dt 1
*
BPt  Et Dt 1 
 (64)
(65)
3. Supply-Side Effect Models
3.3 Multiperiod Equilibrium Models
cS 1  Et Pt 1  Et 1Pt  1  r *   Pt  Pt 1   Et Dt 1  Et 1Dt 
A
 BPt  Et Dt 1   Vt


1
(66)

cS 1 Et 1 Pt 1  Et 1 Pt  1  r * Et 1 Pt  Pt 1   Et 1 Dt 1  Et 1 Dt
 A1 BEt 1 Pt  Et 1 Dt 1 .
1  r cS
*
1

(66´)
 A1 B Pt  Et 1 Pt  


(67)
cS 1 Et Pt 1  Et 1 Pt 1   cS 1  A1 Et Dt 1  Et 1 Dt 1   Vt

4. International CAPM
Without a model showing how assets are priced in a world in which asset
markets are fully integrated, it is impossible to determine whether asset
markets are segmented internationally or not. Stulz (1981a) provide an
intertemporal model of international asset pricing, which admits differences
in consumption opportunity sets across countries. The model shows that the
real expected excess return on a risky asset is proportional to the
covariance of the return of that asset with changes in the world real
consumption rate. It has no barriers to international investment, but it is
compatible with empirical facts, which contradict the predictions of earlier
models and which seem to imply that asset markets are internationally
segmented. Besides, Stulz (1981b) also presents a simple model in which it
is costly for domestic investors to hold foreign assets. The implications of
the model for the composition of optimal portfolios at home and abroad are
*
derived. It is shown that all foreign assets with a beta larger than some beta
plot on either one of two security market lines. Some foreign assets with a
beta smaller than  * are not held by domestic investors even if their
expected return is increased slightly.
4. International CAPM
After the above two papers, Stulz (1982) examines the conditions under
which a risk premium is incorporated in the forward exchange rate. A new
condition for the existence of a risk premium is proposed. He shows that
earlier models of the risk premium, which emphasize either the role of net
foreign investment or of the relative supplies of “outside” assets, are not
suited for assessing the effects of changes in macroeconomic policy. Finally,
Stulz (1984) summarizes that how differences across countries of 1) inflation
rate, 2) consumption baskets of investors, and 3) investment opportunity
sets of investors matter when one applies capital asset pricing models in an
international setting. In particular, the fact that countries differ is shown to
affect the portfolio held by investors, the equilibrium expected returns of
risky assets, and the financial policies of firms. In empirical studies, Chang
and Hung (2000) employ a two-factor international equilibrium asset pricing
model to examine pricing relationships among the world's five largest equity
markets. Their paper suggests that the intertemporal asset pricing model
proposed by Campbell (1993) can be used to explain the returns on the five
largest stock market indices.
5. Equilibrium Models with Heterogeneity
5.1 Heterogeneous Beliefs and Investors
5.2 Heterogeneous investment horizon
5. Equilibrium Models with Heterogeneity
5.1 Heterogeneous Beliefs and Investors



   1
  Ct 1 



*


Et  
exp
Vart 1   i ,t 1   1

Ct 
2







M
*
t 1
M
RA
t 1

 (  1)
2
Var ck ,t 1
*
t 1
(68)
(69)
6. Dividend and Taxation Effect Models
E(Ri )  rf  b i   (di  rf )
*
(70)
E(Ri )  rf  a  bi  c(d i  rf )
(71)
7. Skewness Effect Models
Sharpe (1964), Lintner (1965), and Mossin (1966), following the work of Markowitz (1959),
develope the first formulations of the mean-variance CAPM. However, many researchers
criticize the widely used mean-variance analysis of portfolio selection and argue that assets
pricing models should subsume the effects of the higher moments. Borch (1969) contends
that any system of upward sloping mean-standard deviation indifference curves can be
shown to be inconsistent with the basic axiom of choice under uncertainty. Feldstein (1969)
shows that Tobin (1958, 1965) is incorrect in asserting that the μ-σ indifference curves of a
risk-averter are convex-downwards whenever the possible investment outcomes are
assumed to follow a two-parameter probability distribution. Although Tobin‘s proof is correct
for normal distributions, for a number of economically interesting distributions, the
indifference curves are not convex, showing that when more than one asset has positive
variance, an analysis in terms of only μ and σ is not strictly possible unless utility functions
are quadratic or the possible subjective probability distributions are severely restricted.
Tsiang (1972) argues that although the mean-standard deviation analysis was at first
introduced by Tobin to explain liquidity preference in the sense of an investment demand
for cash, in his defense of it against its critics, he actually finds that it is quite incapable of
doing what Tobin has expected of it. Furthermore, he claims that the importance of
skewness preference for major risk-takers should obviously be taken into consideration in
problems of investment incentives.
7. Skewness Effect Models
Therefore, Jean (1971) begins a general extension of the two-parameter analysis to three
or more parameters; however, Ingersoll (1975) corrects several errors in Jean’s model
(1971) and derives a normative, individual pricing model for risky securities analogous to
the capital market line within the framework of a perfect market. Finally, Schweser (1978)
clarifies and corrects certain parts of Ingersoll’s correction of Jean’s work.
Although many researchers pay more attention to the skewness effect on capital asset
pricing models, Lee (1977) first employs the transformation technique developed by Box
and Cox (1964) to determine the true functional form for testing the risk-return relation and
to examine the possible impact of the skewness effect on capital asset pricing. According to
Sears and Wei (1988) although the estimated coefficient of co-sknewness gives important
information on the marginal rate of substitution between skewness preferences, that is
independent of the effects of the market risk premium. Moreover, Harvey and Siddique
(2000) suggest that if asset returns have systematic skewness, expected returns should
include rewards for accepting this risk. They formalized this intuition with an asset pricing
model that incorporates conditional skewness. Their results show that conditional skewness
helps to explain the cross-sectional variation of expected returns across assets and is
significant even when factors based on size and book-to-market are included.
8. Behavioral Finance
if x  0
 w
V ( x)  

  ( w )

x ( P) 
x  ( P) 
P
P
P

(72)

(73)

 (1  P)
P

if x  0
 (1  P )
 1/ 

 1/ 
9. Liquidity-based Models
D  Pt
R 
i
Pt 1
i
t
i
t
i
(74)
i
Tt
t  i
Pt 1
(75)
i
t
i S ( D  P )
R 
i S P
i
M
t
i
i
t
t
i i
t 1
(76)
9. Liquidity-based Models
t
M
t
i
t 1
Et ( R
 i S i Tt i

i i
 i S Pt 1
(77)
covt ( R  t , R  t )
 t )  r f  t
vart ( R  t ) (78)
i
t 1
i
t 1
i
t 1
M
t 1
M
t 1
M
t 1
M
t 1
i
M
i
M
cov
(
R
,
R
)
cov
(
t
,
t
i
i
t
t 1
t 1
t t 1 t 1 )
Et ( Rt 1 )  r f  Et (t t 1 )  t
 t
M
M
vart ( Rt 1  t t 1 )
vart ( RtM1  t tM1 )
covt ( Rti1 , t tM1 )
covt (t ti1 , RtM1 )
 t
 t
M
M
vart ( Rt 1  t t 1 )
vart ( RtM1  t tM1 )
(79)
10. Existence of Equilibrium
Hart (1974) argues that in deriving the properties of equilibrium prices, it has
been assumed that equilibrium does in fact exist. Surprisingly, no attempt
appears to have been made to establish the existence of equilibrium in the
basic Lintner-Sharpe model or in more general versions of the model. Yet,
the existence of equilibrium is not implied by any of the standard existence
theorems because these theorems assume that consumption sets are
bounded below. By contrast the assumption that investors can hold
securities in unlimited negative amounts implies that consumption sets are
unbounded below. In his paper, he finds the conditions for the existence of
equilibrium in a very general version of the Lintner-Sharpe model; moreover,
Nielsen (1989) presents simple conditions and a simple proof of the
existence of equilibrium in asset markets where short-selling is allowed and
satiation is possible. Unlike standard non-satiation assumptions, the one
used here is weak enough to be reasonable in the mean-variance CAPM
and in asset market models where investors maximize expected utility and
where total returns to individual assets may be negative.
11. Empirical Tests
Black et al. (1972) and Fama and MacBeth (1973) test the implication of
CAPM and find empirical evidence to support the linear relationship between
risk and return and efficient market; therefore, their empirical studies support
the CAPM. Roll (1977), however, criticizes their empirical results by
declaring that (a) no correct and unambiguous test of the theory has
appeared in the literature, and (b) there is practically no possibility that such
a test can be accomplished in the future. Besides, Cheng and Grauer (1980)
also criticize the tests of Black et al. (1972) and Fama and MacBeth (1973)
based only on the assumption of constant β and stationarity of the
distribution of return; therefore, their paper argues that it makes no sense to
attempt a test of the CAPM based on stationarity because the validity of the
CAPM over time implies stationarity cannot hold in any but a very
degenerate sense. Thus, they find the CAPM generally does poorly in their
tests. Finally, Fama and French (1992) conclude that market capitalization
(a measure of size) and the ratio of the book to the market value equity
should replace beta altogether.
12. Conclusion
We have surveyed the evolution of CAPM from 1964 to 2009. We use both
figures and a table to summarize this paper. Figure 1 shows the research
flow chart, and Table 1 provides the literature summary. Sharpe (1964),
Lintner (1965), and Mossin (1966) derive their original static CAPM according
to the six critical assumptions. Many scholars have tried to get more
generalized asset pricing models by relaxing the assumption to meet the real
world situation. Because of the limitation of six critical assumptions and
possible model misspecification, we should carefully use the original static
CAPM to acquire the required return of an asset and calculate its abnormal
return. Fama and French (2004) argue that the CAPM’s empirical problems
may reflect theoretical failings, the result of many simplified assumptions;
however, they may also be caused by difficulties in implementing valid tests
of the model. Fama and French’s empirical research is based only upon the
original static CAPM, but we believe that empirical research should not only
be based upon the original static CAPM
.
12. Conclusion
In this paper, we have carefully reviewed papers which have extended the
original static CAPM. These papers have been classified into (i) Merton’s
Intertemporal CAPM, (ii) Consumption-based Intertemporal CAPM, (iii)
Production-based Intertemporal CAPM, (iv) CAPM with Supply-side Effect,
(v) International Equilibrium CAPM with Heterogeneity Beliefs and Investors,
(vi) Equilibrium CAPM with Heterogeneity Investment Horizon, (vii) CAPM
with Dividend and Taxation Effect, (viii) CAPM with Skewness Effect, and
(ix) Behavioral Finance, and Liquidity-based CAPM. As a result of our
review, we believe that some important issues remain for future researchers.
Now we discuss these potential important research issues as follows:
First, we can try to subsume behavioral finance into asset pricing models,
for example, investor sentiment. Obviously, many noise traders affect stock
returns, but we still have no theoretical asset pricing model that includes
their behaviors into a pricing factor.
12. Conclusion
Second, we can further explore the supply side of asset pricing models. In the past, there was
relatively few literature on the supply side; however, it is important. Holmstrom and Tirole (2001)
suggest, for example, new determinants of asset prices, such as the distribution of wealth within
the corporate sector and between the corporate sector and the consumers. Also, leverage ratios,
capital adequacy requirements, and the composition of saving affect the corporate demand for
liquid assets and, thereby, interest rates.
Third, although Fama and French’s (1996) three-factor model has good empirical performance,
they acknowledge that there are important limitations in their model. Their empirical results still do
not cleanly identify the two consumption-investment state variables of special hedging concern to
investors that would provide a neat interpretation of their results in terms of Merton’s (1973) ICAPM
or Ross’ (1976) APT. Merton’s (1973) ICAPM not only has a complete and solid theoretical
framework but also provides better empirical performance than the static CAPM, such as Fama
and French’s (1996) three-factor model if we can find those solid and robust state variables. We
suggest that future researchers should pay more attention to how to identify those solid and robust
state variables. Moreover, it will make bring Merton’s (1973) ICAPM closer to real world, and its
implication will be useful for empirical studies.
Fourth, the relationship between perspective theory and CAPM needs further research in both
theoretically and empirically, and especially the relationship between skewness type of CAPM and
perspective theory needs to be carefully investigated.
Figure1. Flow Chart
The Static CAPM
(single-period)
Dividend and Taxation Effect
Models
Miller and Modigliani(1961,Journal
of Business)
Brennan (1970, National Tax
Journal)
Black and Scholes (1974,Journal of
Financial Economics)
Sasson and Kolodny(1976, The
Review of Economics and Statistics)
Miller and Scholes (1978,Journal of
Financial Economics)
Litzenberger and Ramaswamy
(1979, Journal of Financial
Economics)
Morgan (1982,The Journal of
Finance)
Litzenberger and Ramaswamy
(1982,The Journal of Finance)
Hagiwara and Herce (1997, The
American Economic Review)
Skewness Effect Models
Borch (1969, Review of
Economics Studies)
Feldstein (1969, Review of
Economics Studies)
Jean (1971, Journal of Financial
and Quantitative Analysis)
Tsiang (1972, American Economic
Review)
Ingersoll (1975, Journal of
Financial and Quantitative
Analysis)
Schweser (1978, Journal of
Financial and Quantitative
Analysis)
The Original CAPM
Sharpe (1964), Lintner (1965),and Mossin (1966)
Existence of Equilibrium
Hart (1974, Journal of Economic
Theory)
Nielsen (1989, Review of Economic
Studies)
Equilibrium Models with
Heterogeneity Investment Horizon
Lee (1976, The Review of Economics
and Statistics)
Levhari and Levy (1977, The Review
of Economics and Statistics)
Lee, Wu, and Wei (1990, Journal of
Financial and Quantitative Analysis)
Supply-Side Effect Models
Black (1976, American
Economic Review)
Grinols (1984, Journal of
Finance)
Lee, Tsai, and Lee (2009,
Quarterly Review of Economics
and Finance)
The Dynamic CAPM
(multi-period)
Intertemporal CAPM－Merton
Model
Merton (1973, Econometrica)
Behavioral Finance
Kahneman and Tversky
(1979, Econometrica)
Tversky and Kahneman
(1992, Journal of Risk and
Uncertainty)
Levy (2010, European
Financial Management)
International CAPM
Stulz (1981a, Journal of Finance)
Stulz (1981b, Journal of Financial
Economics)
Stulz (1982, Journal of
International Economics)
Stulz (1984, Journal of
International Business Studies)
Equilibrium Models with
Heterogeneity Beliefs and Investors
Constantinides (1982, Journal of
Business)
Constantinides and Duffie (1996,
Journal of Political Economy)
Brav, Constantinides, and Geczy
(2002, Journal of Political Economy)
Basak (2005, Journal of Banking and
Finance)
Levy, Levy, and Benita (2006, Journal
of Business)
Intertemporal CAPM－Consumption-based Models
Breeden (1979, Journal of Financial Economics)
Campbell (1993, American Economic Review)
Campbell and Cochrane (1999, Journal of Political Economy)
Jagannathan and Wang (1996, Journal of Finance)
Lettau and Ludvigson (2001a, Journal of Finance)
Lettau and Ludvigson (2001b, Journal of Political Economy)
Lewellen and Nagel (2006, Journal of Financial Economics)
Balvers and Huang (2009, Journal of Financial and Quantitative
Analysis)
Liquidity-based Models
Pastor and Stambaugh (2003,
Journal of Political Economy)
Acharya and Pedersen (2005,
Journal of Financial Economics)
Yoel(2009,working paper)
Intertemporal CAPM－Production-based Models
Balvers, Cosimano, and McDonald (1990, Journal of Finance)
Cochrane (1991, Journal of Finance) (1996, Journal of Political
Economy)
Balvers and Huang (2007, Journal of Financial Economics)
Figure2. The Dynamic CAPM
The Dynamic CAPM
(multi-period)
Supply-Side Effect Models
Black (1976, American Economic Review)
Grinols (1984, Journal of Finance)
Lee, Tsai, and Lee (2009, Quarterly Review of
Economics and Finance)
Intertemporal CAPM－
Merton Model
International CAPM
Merton (1973, Econometrica)
Stulz (1981b, Journal of Financial Economics)
Stulz (1981a, Journal of Finance)
Stulz (1982, Journal of International Economics)
Stulz (1984, Journal of International Business Studies)
Chang and Hung (2000, Review of Quantitative
Finance and Accounting)
Intertemporal CAPM－Consumption-based Models
Breeden (1979, Journal of Financial Economics)
Campbell (1993, American Economic Review)
Campbell and Cochrane (1999, Journal of Political Economy)
Jagannathan and Wang (1996, Journal of Finance)
Lettau and Ludvigson (2001a, Journal of Finance)
Lettau and Ludvigson (2001b, Journal of Political Economy)
Lewellen and Nagel (2006, Journal of Financial Economics)
Balvers and Huang (2009, Journal of Financial and Quantitative Analysis)
Intertemporal CAPM－Production-based Models
Balvers, Cosimano, and McDonald (1990, Journal of Finance)
Cochrane (1991, Journal of Finance) (1996, Journal of Political Economy)
Balvers and Huang (2007, Journal of Financial Economics)
Figure 3. The Static CAPM
The Static CAPM
(single-period)
Dividend and Taxation Effect
Models
Miller and Modigliani(1961,Journal of
Business)
Brennan (1970, National Tax Journal)
Black and Scholes (1974,Journal of Financial
Economics)
Sasson and Kolodny(1976, The Review of
Economics and Statistics)
Miller and Scholes (1978,Journal of Financial
Economics)
Litzenberger and Ramaswamy (1979, Journal
of Financial Economics)
Morgan (1982,The Journal of Finance)
Litzenberger and Ramaswamy (1982,The
Journal of Finance)
Hagiwara and Herce (1997, The American
Economic Review)
Skewness Effect Models
Borch (1969, Review of Economics Studies)
Feldstein (1969, Review of Economics Studies)
Equilibrium Models with
Heterogeneity Investment
Horizon
Lee (1976, The Review of Economics and
Statistics)
Levhari and Levy (1977, The Review of
Economics and Statistics)
Lee, Wu, and Wei (1990, Journal of Financial and
Quantitative Analysis)
Equilibrium Models with
Heterogeneity Beliefs and
Investors
Constantinides (1982, Journal of Business)
Constantinides and Duffie (1996, Journal of
Political Economy)
Brav, Constantinides, and Geczy (2002, Journal
of Political Economy)
Basak (2005, Journal of Banking and Finance)
Levy, Levy, and Benita (2006, Journal of Business)
Jean (1971, Journal of Financial and
Quantitative Analysis)
Tsiang (1972, American Economic Review)
Ingersoll (1975, Journal of Financial and
Quantitative Analysis)
Schweser (1978, Journal of Financial and
Quantitative Analysis)
Liquidity-based Models
Pastor and Stambaugh (2003, Journal of Political
Economy)
Acharya and Pedersen (2005, Journal of Financial
Economics)
Yoel(2009,working paper)
Table 1. Literature Summary
Models
Literature
Merton (1973, Econometrica)
Intertemporal CAPM
－Merton Model
Breeden (1979, Journal of Financial Economics)
(1993, American Economic Review)
Campbell and Cochrane (1999, Journal of Political Economy)
Jagannathan and Wang (1996, Journal of Finance)
Intertemporal CAPM
－Consumption-based Models
Lettau and Ludvigson (, Journal of Finance)
Results and Contributions
Merton (1973) relaxes the single-period assumption to develop
the intertemporal CAPM model with stochastic investment
opportunities, stating that the expected return on any asset is
deduced from a multi-beta version of CAPM in a continuoustime model.
Breeden (1979) utilizes the same continuous-time economic
framework as used by Merton (1973), shows Merton’s multibeta pricing equation can be collapsed into a single-beta
equation. The expected return on any asset is proportional to its
beta with respect to aggregate consumption alone.
(1993) substitutes consumption out of the model to get a
discrete-time version of the intertrmporal CAPM of Merton
(1973).
Campbell and Cochrane (1999) present a habit persistence
model to explain the dynamic pricing phenomena, that is, using
lagged consumption as the state variable to explain the
procyclical variation of stock prices, the long-horizon
predictable of excess stock returns, and the countercyclical
variation of stock market volatility.
Jagannathan and Wang (1996) argue that the CAPM holds in a
conditional sense that betas and the market premium vary over
time. They add the labor income to explain the cross-section
asset returns.
Lettau and Ludvigson () investigate the power of fluctuations in
the log consumption-wealth ratio for forecasting asset returns.
Lettau and Ludvigson (2001b, Journal of Political Economy)
Lettau and Ludvigson (2001b) is the first reexamination of a
consumption-based factor model, the first recent paper that finds
some success in pricing the value premium from a macro-based
model. They examine a conditional version of the linear
consumption-based CAPM model with time-varying coefficients.
Lewellen and Nagel (2006, Journal of Financial Economics)
Lewellen and Nagel (2006) criticize consumption model on the
argument that the low covariance between the risk premium and
the betas. The covariance between consumption betas and the
consumption risk premium obtained from a series of estimates
over small time windows is too small to support the importance
of any conditional variable.
Balvers and Huang (2009, Journal of Financial and Quantitative Analysis)
Balvers and Huang (2009) exclude Merton (1973) factors by
assuming that there are no changes over time in the exogenous
dividend processes, ruling out shifts in the investment
opportunities set and conclude that real money growth as an
additional factor determine asset returns.
Table 1. (Continued)0
Models
Intertemporal CAPM
－Production-based Models
Literature
Balvers, Cosimano, and McDonald (1990, Journal of Finance)
Cochrane (1991, Journal of Finance) (1996, Journal of Political Economy) Cochrane (1991, 1996) extend the production-based CAPM by deriving
from producer’s first order condition for optimal intertemporal
investment demand to describe the asset returns.
Balvers and Huang (2007, Journal of Financial Economics)
Balvers and Huang (2007) derive the productivity shocks in the marginal
value of capital to obtain an explicit production-based CAPM expression
for the asset pricing model.
Black (1976, American Economic Review)
Black (1976) examined the effects of disequilibrating shocks on
individual behavior in financial markets and the effects of such modified
behavior on market outcomes. A short-run dynamic, multi-period capital
asset pricing model is constructed by assuming rational expectations and
adding the supply side to the static model of capital asset pricing.
Grinols (1984, Journal of Finance)
Grinols (1984) extended Merton's intertemporal capital asset pricing
model with multiple consumers to include a description of the supply of
traded securities.
Lee, Tsai, and Lee (2009, Quarterly Review of Economics and Finance)
Lee, Tsai, and Lee (2009) first theoretically extend the dynamic,
simultaneous CAPM model of Black (1976) to the existence of the
supply effect in the asset pricing process. They use price, dividend per
share and earnings per share to test the existence of supply effect with
domestic stock markets.
Stulz (, Journal of Finance)
Stulz (1981b, Journal of Financial Economics)
Stulz (1982, Journal of International Economics)
Stulz (1984, Journal of International Business Studies)
Chang and Hung (2000, Review of Quantitative Finance and Accounting)
Stulz () provided an intertemporal model of international asset pricing
which admits differences in consumption opportunity sets across
countries.
Stulz (1981b) also presented a simple model in which it is costly for
domestic investors to hold foreign assets. The implications of the model
for the composition of optimal portfolios at home and abroad are derived.
Stulz (1982) examined the conditions under which a risk premium is
incorporated in the forward exchange rate.
Stulz (1984) summarized that how differences across countries of 1)
inflation rate, 2) consumption baskets of investors, and 3) investment
opportunity sets of investors matter when one applies capital asset pricing
models in an international setting.
Supply-Side Effect Models
International CAPM
Results and Contributions
Balvers, Cosimano and McDonald (1990) present a general equilibrium
theory relating returns on financial assets to macroeconomic fluctuations
in a context that is consistent with efficient markets in that no excessprofit opportunities are available. Aggregate output is equal or
proportionate to aggregate consumption and that one can evaluate the
marginal utility of consumption at the observed level of output so that
aggregate output growth becomes the key asset pricing factor.
Chang and Hung (2000) suggest that the intertemporal asset pricing
model proposed by Campbell (1993) can be used to explain the
returns on the five largest stock market indices.
Table 1. (Continued)
Models
Literature
Constantinides (1982, Journal of Business)
Results and Contributions
Constantinides (1982) argue the equilibrium model of a
heterogeneous-household, full-information economy
under the assumption that the households insure against
idiosyncratic income shocks.
Constantinides and Duffie (1996, Journal of Political Constantinides and Duffie (1996) construct a discount
factor to represent any asset pricing anomalies under the
Economy)
assumption that investors have the same power utility
function.
Brav, Constantinides, and Geczy (2002, Journal of
Political Economy)
Equilibrium Models with
Beliefs and Investors
Heterogeneity Basak (2005, Journal of Banking and Finance)
Levy, Levy, and Benita (2006, Journal of Business)
Yoel (2009,working paper)
Brav, Constantinides, and Geczy (2002) test the
stochastic discount factor given by the equally weighted
sum of the household’s marginal rates of substitution to
be a valid stochastic discount factor based on the set of
Euler equation of household consumption.
Basak (2005) provides a continuous-time pure-exchange
framework to study asset pricing implication of the
present of heterogeneous beliefs, within a rational
Bayesian setting.
Levy, Levy, and Benita (2006) relax the homogeneous
beliefs assumption of CAPM. They employ the
mathematical analysis and numerical simulations to study
the effect of the introduction of heterogeneity of beliefs
on asset prices.
Yoel (2009) derives a general equilibrium asset pricing
model, low-status investors hold a single high volatility
asset in order to move up the status ladder. Since highstatus investors are concerned about the risk of losing
their status, they demand assets that co-vary with high
volatility assets, as a hedge against low-status investors.
Table 1. (Continued)
Models
Equilibrium Models with Heterogeneity
Investment Horizon
Dividend and Taxation Effect Models
Literature
Lee (1976, The Review of Economics and Statistics)
Levhari and Levy (1977, The Review of Economics and Statistics)
Results and Contributions
Lee (1976) first prove the observed function form of CAPM can become
nonlinear and show that either the likelihood ratio method or constant elasticity
of substitution function methods can employed to improve the explanatory
power of CAPM.
Levhari and Levy (1977) investigate the empirical implications of
heterogeneous investment horizons.
Lee, Wu, and Wei (1990, Journal of Financial and Quantitative Analysis)
Lee, Wu, and Wei (1990) examine the effect of heterogeneous investment
horizons on the functional form of capital asset pricing and suggest a translog
model for estimating the relation between risk and return.
Miller and Modigliani (1961,Journal of Business)
Brennan (1970, National Tax Journal)
Black and Scholes (1974,Journal of Financial Economics)
Sasson and Kolodny (1976, The Review of Economics and Statistics)
Miller and Scholes (1978,Journal of Financial Economics)
Miller and Modigliani (1961) present a cogent argument for the fact that the
value of the firm is unaffected by dividend policy in a world without tax or
transaction costs.
Brennan (1970) first propose an extended form of the single period CAPM
model that accounted for the differential taxation of dividends over capital
gains.
Black and Sholes (1974) suggest that it is not possible to demonstrate, using the
best available empirical methods, that the expected returns on high yield
common stock differ from the expected returns on low yield common stocks
either before or after taxes.
Sasson and Kolodny (1976) argue that once a security's beta coefficient is given,
the CAPM implies that knowledge of a firm's dividend policy is of no use in
assessing the security's return, or correspondingly, its market value. However,
they provide the evidence in their paper against this premise.
Litzenberger and Ramaswamy (1979) extend the model of Brennan (1970) to
account for restrictions on investors’ borrowing. The model is the standard twoparameter pricing models adjusted for differential taxation of dividends and
interest income relative to capital gains.
Morgan (1982) summarize three distinct views of the importance of dividends
to investors have received support at one time or another. According to the two
most important views, dividends have a neutral and a negative effect on security
prices respectively. Miller and Modigliani(1961) and Miller and Scholes (1978)
favor complete substitutability of dividends and capital gain. Brennan (1970)
and Litzenberger and Ramaswamy (1979) have developed models which
incorporate differential taxation of income and capital gain.
Litzenberger and Ramaswamy (1982) present some new empirical results to
show that there is a positive and non-linear relationship between common stock
returns and expected dividend yield. The prediction rule for expected dividends
is based solely on information that would have been available to the investor exante.
Hagiwara and Herce (1997) consider dividend-based and consumption-based
capital asset pricing models. Their estimation results suggest that the dividend
asset pricing model provides a better explanation of the data than the
consumption asset pricing model.
Litzenberger and Ramaswamy (1979, Journal of Financial Economics)
Morgan (1982,The Journal of Finance)
Litzenberger and Ramaswamy (1982,The Journal of Finance)
Hagiwara and Herce (1997, The American Economic Review)
Table 1. (Continued)
Models
Literature
Borch (1969, Review of Economics Studies)
Results and Contributions
Borch (1969) contended that any system of upward sloping
mean-standard deviation indifference curves can be shown to be
inconsistent with the basic axiom of choice under uncertainty.
Feldstein (1969, Review of Economics Studies)
Feldstein (1969) showed that Tobin (1958, 1965) was incorrect in
asserting that the μ-σ indifference curves of a risk-averter are
convex-downwards whenever the possible investment outcomes
are assumed to follow a two-parameter probability distribution.
Although Tobin's proof is correct for normal distributions, for a
number of economically interesting distributions the indifference
curves are not convex shows that when more than one asset has
positive variance, an analysis in terms of only μ and σ is not
strictly possible unless utility functions are quadratic or the
possible subjective probability distributions are severely
restricted.
Jean (1971, Journal of Financial and Quantitative Analysis)
Jean (1971) began a general extension of the two-parameter
analysis to three or more parameters.
Schweser (1978, Journal of Financial and Quantitative Analysis)
Ingersoll (1975) developed a normative multidimensional
security pricing model for individual investor in which he
corrected errors in an earlier attempt by Jean (1971) at
developing such a model. Schweser (1978) clarified and
corrected certain parts of Ingersoll’s correction of Jean’s work.
Sears and Wei (1988, The Financial Review)
Sears and Wei (1988) indicated that although the estimated
coefficient of co-sknewness gives important information on the
marginal rate of substitution between skewness preferences that is
independent of the effects of the market risk premium.
Harvey and Siddique (2000, Journal of Finance)
Harvey and Siddique (2000) suggested that if asset returns have
systematic skewness, expected returns should include rewards for
accepting this risk. They formalized an asset pricing model that
incorporates conditional skewness. Their results showed that
conditional skewness helps to explain the cross-sectional
variation of expected returns across assets and is significant even
when factors based on size and book-to-market are included.
Skewness Effect Models
Table 1. (Continued)
Models
Literature
Kahneman and Tversky (1979, Econometrica)
Results and Contributions
Kahneman and Tversky (1979) developed the prospect theory to describe that people behave more in
accordance with a psychologically based theory rather than seek to maximize the expected utility.
Tversky and Kahneman (1992, Journal of Risk and Uncertainty)
Barberis, Huang and Santos (2001, Quarterly Journal of
Economics)
Levy, De Giorigi and Hens (2003, Working paper)
Levy (2006, Encyclopedia of Finance)
Barberis, and Huang (2008, The American Economic Review)
Tversky and Kahneman (1992) modified the prospect theory by using a cumulative distribution function
for the domain of gains and losses rather than separate decisions called Cumulative Prospect Theory.
Barberis, Huang and Santos (2001) argue that investors are loss averse over these fluctuations, and the
degree of loss aversion depends on their prior investment performance.
Levy, Giorgi and Hens (2003) show that under the assumption of normally distributed returns, the
cumulative prospect theory is consistent with the CAPM in every financial market equilibrium.
Levy (2006) argue that experimental findings in particular prospect theory and cumulative prospect
theory contradict expected utility theory .
Behavioral Finance
Barberis and Huang (2008)’s main result, derived from a novel equilibrium with nonunique global
optima, is that, in contrast to the prediction of a standard expected utility model, a security's own
skewness can be priced: a positively skewed security can be "overpriced" and can earn a negative
average excess return..
Levy (2010, European Financial Management)
Levy suggested that a modified version of mean-variance analysis and the traditional CAPM can be
justified in the Cumulative Prospect Theory framework, despite the fact that under the Cumulative
Prospect Theory, the expected utility theory is invalid
Pastor and Stambaugh (2003, Journal of Political Economy)
Pastor and Stambaugh (2003) find that stocks whose prices decline when the market gets more illiquid
receive compensation in expected returns. Dividing stocks into 10 portfolios based on liquidity betas,
the portfolio of high-beta stocks earned more than the portfolio of low beta stocks, after accounting for
market, size, and value-growth effects.
Acharya and Pedersen (2005, Journal of Financial Economics)
Acharya and Pedersen (2005) performed a similar but more general investigation on four channels for a
liquidity premium. Their largest premium is the covariance of liquidity with market return — the chance
the stock may get more illiquid if the market goes down.
Liquidity-based Models
Black, Jensen and Scholes (1972,Studies in the Theory of Black, Jensen and Scholes (1972) find the empirical evidence to support the linear relationship between
Capital Markets)
risk and return and efficient market.
Empirical Tests
Fama and MacBeth (1973, Journal of Political Economy)
Cheng and Grauer (1980,The American Economic Review)
Fama and French (1992,Journal of Finance)
Fama and MacBeth (1973) improve the methodology of Black, Jensen and Scholes (1972) to provide
empirical evidence to support the CAPM.
Cheng and Grauer (1980) argue that it makes no sense to attempt a test of the CAPM based on
stationarity , since validity of the CAPM over time implies stationarity cannot hold in any but a very
degenerate sense. Thus, they find the CAPM generally does poorly in their tests.
Fama and French (1992) conclude that market capitalization (a measure of size) and the ratio of the book
to the market value equity should replace beta altogether.