This document provides a critical review of the 1996 paper "The Conditional CAPM and the Cross-Section of Expected Returns" by Jagannathan and Wang. The review summarizes the key findings of the original paper, which showed that conditional CAPM can explain the cross-sectional variation in stock returns better than static CAPM. However, the review also notes some limitations in the assumptions around time-varying betas and use of R-squared. Overall, it evaluates the original paper as influential but also discusses subsequent research that built on its findings or identified weaknesses.

1. Examination No. B025068
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Examination Number: B025068
Title of Course: Investment and Securities Markets
Course Organiser’s Name: Mr Ismail Gucbilmez
Date of Submission: 14 November 2013
Word Count: 1498
Title of Essay
A Critical Review of Jagannathan, R.J. & Wang, Z.Y. (1996) The Conditional CAPM and the
Cross-Section of Expected Returns. The Journal of Finance, Vol 51, No 1, pp. 3-53.

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A Critical Review of Jagannathan, R.J. & Wang, Z.Y. (1996) The Conditional CAPM
and the Cross-Section of Expected Returns. The Journal of Finance, Vol 51, No 1, pp.
3-53.
Over the past three decades, it has been generally agreed that investors can obtain high returns
by investing in riskier projects. However, how investors evaluate the risk portfolio and how
they determine what risk premium to charge is still a big problem. Fama and French (1992)
present evidence suggesting the inability of static CAPM to explain cross-sectional average
returns. Later, Jagannathan and Wang (1996) conducted a study on whether conditional
CAPM, which is the successful extensions of CAPM, could explain the cross-sectional
expected returns. The results is convincing although there are some problems. In the rest of
this review, ‘The conditional CAPM and the Cross-Section of Expected Returns’ will be
summarized first; then, it is followed by two contributions to the literatures and
critically-thinking of two criticisms in terms of time variations of beta (assumptions) and
R-square. Moreover, there are some developments after this paper published. Finally, the last
part concludes with my own opinion.
The purpose of the paper is to examine the relation between unconditional betas and the
cross-section of unconditional expectation. One finding authors developed is that when the
conditional CAPM is assumed to hold period-by-period, cross-sectionally, the unconditional
expected returns on any asset is a linear function of its unconditional market beta (value
weighted beta) and unconditional premium beta (beta-premium sensitivity) (Jagannathan and
Wang (1996). In other words, the one-factor conditional CAPM leads to a two-factor
unconditional CAPM. This substantially improves the model as two factors explain nearly 30%
of the cross-sectional average returns. (Jagannathan and Wang,1996).Yet another finding is

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that the unconditional model implied by conditional CAPM explains more than 55% of the
cross-sectional variation in average returns after adding human capital to it, which performs
much better than the two-factor model (Jagannathan and Wang,1996). In particular, for the
three betas model, size and book-to-market have little or no power to explain the left variables
which are unexplained. (Jagannathan and Wang,1996) During the analysis, the
premium-labour model (PL model) is established and used to set up four various CAPM
specifications. Among them, the performance of conditional CAPM with human capital is the
most appropriate as it achieves the highest r-square 0.55. Additionally, there is further test to
determine whether residual size effects have the ability to explain the cross-sectional returns.
The answer is ‘No’. As Jagannathan and Wang (1996) makes clear:
“The distribution of the points around the 45-degree line does not significantly change when
we add log (ME) as an additional explanatory variable” (Jagannathan and Wang, 1996,
p.25).
There are two main assumptions used to form the PL model, the first one is the choice of the
yield spread between BAA- and AAA rated bonds as a proxy for market risk premium. Its
attribution to the conditional market premium depends on the nature of the information
available to the investors and how they make use of it. (Jagannathan and Wang, 1996) The
second one is to the use of the return on the value-weighted portfolio of all stocks traded in
the United States as a good proxy for the return on the portfolio of the aggregate wealth since
the return on the aggregate wealth portfolio of all assets in the economy is not observable.
(Jagannathan and Wang, 1996).

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Jagannathan and Wang (1996) propose an appealing model that has become one of the most
influential models in empirical asset pricing. For one, it makes the transition from static
CAPM to conditional CAPM by making an assumption that CAPM hold in conditional sense
(variables are time-varying) and applying the implication of unconditional CAPM to set up
new PL model, which links three kinds of beta, in particular, labor-beta with unconditional
expected returns. Furthermore, the authors’ proxy for the market portfolio by including labour
income as the measure of human capital substantially improves the conditional model.
Specifically, Wang (2003) motivated by Jagannathan and Wang (1996) that including labour
income risk in their model as a proxy for return on human capital. As a result, the average
absolute bias reaches a minimum value of 0.13%, obtained at y50.94, which is more than a 30%
reduction in average pricing errors. Similar evidence was also obtained by Palacios-Huerta
(2003), the pricing error is almost zero when human capital was included in the conditional
CAPM model.
However, there are some problems. For one, modelling assumption of the time variations in
betas is somewhat simplistic in the authors’ paper. Indeed, Ferson and Korajczyk (1995) find
that estimate betas exhibits statistically significant time variations. At the same time, Ghysels
(1998) make serious criticisms of condition CAPMs and revealed that the performance of the
conditional CAPM is sensitive to the specification of time-varying betas. More specifically,
he shows that dynamic beta were seriously miss-specified in some distinguished time-varying
models. Also, Compared with constant beta models, it had larger pricing errors in some cases.
Another shortcoming in this paper is the invalid use of r-square in measuring model
performance. In this paper, it is estimated that the conditional CAPM using default spread as
the instrumental variable and they get a cross-sectional r-square of 55.21 (Jagannathan and

5. Examination No. B025068
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Wang, 1996). At the same time, Lettau and Ludvigson (2001) find that scaled multifactor
version of (C) CAPM model can explain 0.75 of the cross-sectional variation in average
returns. Tuzel (2005) using the changes in the aggregate share of real estate in total capital as
the scaling variable and report an R2
of 0.74, and Acharya and Pedersen (2005) get an R2
of up
to 0.79. It looks like the latter three findings have higher R2
than the first one. Are they
outperforming? However, the validity of relying on the cross-sectional R2
as a measure of the
model performance is currently a matter of controversy.(Golubeva and Lemmon, 2007) Most
important idea comes from Lewellen, Nagel and Shanken(2006), who argued that using
cross-sectional R2
on a set of know strong covariance structure such as size portfolios to
measure the performance of CAPM will not be successful. This is because obtaining a high
cross-sectional R2
s is easy and almost any proposed factor is likely to produce betas that line
up with expected returns, and all that required is a factor that is only weakly corrected with
SLM and HML. This result deepens the concerns that it is not only easy to produce a good fit
(as measure by r-square) but also not difficult to deliver performance that appears plausible.
With reference to the first problem, however, there is a suggestion that using a pricing kernel
approach incorporate conditioning information to estimate conditional CAPM can succeed in
capturing the dynamic of the beta risk, and the model significantly outperforms the nonlinear
model (such as nonlinear APT) of Ghysels in explaining the cross-section of time-varying
expected returns. (Kan and Wang, 2000). Meanwhile, in relation to the second problem, the
suggested solution is to expand the set of test assets, that is, adding industry portfolios. At the
same time, another suggestion is to replace OLS R2
cross-sectional regression by GLS R2
,
which has a useful economic interpretation in terms of relative the mean-variance efficiency
of a model’s factor-mimicking portfolios. (Lewellen, Nagel and Shanken, 2006).

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After this paper was published, it motivated researchers to compare the capacity of
conditional CAPM with other methods in explaining cross-sectional returns. For example,
Wang (2003), who made a comparison between the conditional CAPM and conditional Fama
and the French three factors model, finds that when the former is cast in a nonparametric form,
it out-performs the latter. There are plenty of comparisons with conditional CAPM, although
it is not performing well all the time, those comparisons drives up the developments of
conditional CAPM. For instance, Bali, Cakici and Tang (2009) re-examine conditional beta
by using portfolio-level and firm-level analysis indicate that the positive relation between
conditional beta and cross-section of average expected returns is statistically significant.
In conclusion, there is a consensus that static CAPM is unable to explain the cross-sectional
expected returns; authors make an assumption that CAPM holds in a conditional sense and
they reveal that conditional expected returns on an asset is a linear function of conditional
CAPM. Additionally, a labour income risk factor as a proxy for return on human capital is a
significant development in this paper. Nevertheless, the time variation of beta is greater than
assumed, so misspecification might be quite possible for conditional CAPM as opposed to
other constant beta models. Also, the validity of r-square as a measure of cross-sectional
performance is not reliable in some sense. In my opinion, although there are some problems
with the conditional model, this is a valuable paper as two authors find the way that CAPM
could influence the cross-sectional expected return and also, this paper fills a gap in the
literature and has become the cornerstone of conditional CAPM in cross-sectional area. It is a
quite meaningful paper with regard to further CAPM development.

7. Examination No. B025068
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Reference:
Acharya, V.V. & Pedersen, L.H. (2005) Asset Pricing with Liquidity Risk. Journal of Financial
Economics, Vol 77, Issue 2, pp. 375-410.
Bali, T.G., Cakici, N. & Tang, Y. (2009) Source The Conditional Beta and the Cross-Section of
Expected Returns. Financial Management, Vol 38, No 1, pp. 103-137.
Ferson, W.E. & Korajczyk, R.A. (1995) Do arbitrage pricing models explain the predictability of stock
returns? Journal of Business, Vol 68, pp. 309–349.
Fama, E.F. & French, K.R. (1992) The cross-section of expected stock returns, Journal of Finance,
Vol 47, Issue 2, pp. 427-465.
Ghysels, E. (1998) On stable factor structures in the pricing of risk: Do time varying betas help or hurt?
Journal of Finance, Vol 53, NO 2, pp. 549-573.
Golubeva, E. & Lemmon, M. (2007) Estimations of Scaled Multifactor CAPM: Simulation Evidence.
Working Paper, University of Oklahoma & University of Utah.
Jagannathan, R.J. & Wang, Z.Y. (1996) The conditional CAPM and the cross-section of expected
returns. Journal of Finance, Vol 51, Issue 1, pp. 3-53.
Kan, R. & Wang, K.Q. (2000) Does the Nonlinear APT Outperform the Conditional
CAPM. Working paper.

8. Examination No. B025068
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Lettau, M. & Ludvigson, S. (2001) Resurrecting the (C)CAPM: A Cross-­‐Sectional Test When Risk
Premia Are Time-­‐Varying. The Journal of Political Economy, Vol 109, No 6, pp. 1238-1287.
Lewellen, J., Nagel, S. & Shanken, J. (2006) A skeptical Appraisal of Asset Pricing Tests. Working
paper.
Palacios-Huerta, I. (2003) The Robustness of the Conditional CAPM with Human Capital. Journal of
Financial Econometrics, Vol 1, No 2, pp. 272-289.
Tuzel, S. (2005) Corporate Real Estate Holdings and the Cross Section of Stock Returns. Working
paper, University of Southern California.
Wang, K.Q. (2003) Asset Pricing with Conditioning Information: A New Test. The Journal of Finance,
Vol 58, NO 1, pp. 161–196.