Is CAPM still alive

ADENIRAN OLOLADE JANET (000527487)

The Capital Asset Pricing Model: Is it still alive?

Introduction

The CAPM is a model that describes the relationship between

risk and expected return for an asset when the market is in

equilibrium. This suggests there are a number of underlying

assumptions for the CAPM to hold considering the fact that

models are abstractions from reality and certain condition has

to exist for the market to be in equilibrium. The Capital

Asset Pricing Model (CAPM) can be traced back to Sharpe

(1964), Lintner (1965) and Black (1972). The model has been

widely used in estimating the cost of capital for firms and

evaluating the performance of managed portfolios since its

introduction among others. The development of the CAPM gave

theoretically sound tool for long term resource allocation

under conditions of risk (Geppert et al, 2007).

In order to evaluate the model, it is important to note some

of the main predictions. The model predicts that the expected

returns are linear in beta and that beta dominates all other

explanatory factors as a measure of risk hence there should be

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no added return for bearing non-market risk. The beta as

measured by the covariance of the assets returns and the

return on market portfolio, provides information for a

rational investor not only on how to measure the risks of

stock market investment but also on how to determine the risk

premium for rational investors to hold an individual stock at

its market weight (Huang & Wu, 2005). No doubt the CAPM broke

new grounds and gave rise to criticisms from the field of

finance and economics.

Early empirical works of Sharpe & Cooper (1972) presents clear

and easily interpreted evidence that, as general equilibrium

theory suggests, there is a positive relationship between

return and Beta. Further examination by them provides

confidence that the relationship is both strong and linear.

Black, Jensen & Scholes (1972) conducted an in-depth time

series analysis test of the CAPM and the result was consistent

with the two-factor model rather than the standard CAPM. They

also carried out a cross-sectional test (second-pass

regressions) but encountered a problem of inability of

identifying the true beta. To control for error in estimating

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beta, they measured betas for portfolios rather than

securities and the high percentage of the variation in returns

explained (98%) shows that a straight line describes returns

very well as predicted by the theory.

The aim of this article is to try to assert from recent

empirical evidence whether the CAPM is still alive. To do

this, there will be a detailed examination of recent studies

based on the CAPM. The studies to be examined will include

both arguments for and against the CAPM. From the available

evidence, the conclusion will then emerge.

Recent empirical arguments for CAPM

Isakov (1999) claims that usual tests do not leave much

opportunity for beta to appear as a useful variable capable of

explaining returns, because tests are often performed in

periods where the average realised market excess return is not

significantly different from zero. This is contrary to the

evidence by Fama & French (1992, 1996) and others which shows

that beta and returns are not related empirically. They

interpret this evidence against the validity of the capital

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asset pricing model and they conclude that beta is not a good

measure of risk. In order to access the usefulness of beta,

an alternative approach that dissociates results obtained in

periods where the realised market excess is positive from

those where it is negative is proposed. These new tests are

then applied to a representative sample of the Swiss stock

market over the period 1983-1991 by Isakov (1999). The

different results unambiguously support the fact that beta is

a measure of risk, because beta is strongly related to the

cross section of realised returns. These results also confirm

that there are no arbitrage opportunities on this market. The

results obtained here are interesting for another reason. They

confirm those obtained in the few similar studies performed on

the US stock market. The data set used by Isakov (1999) also

covered much longer periods and involved more stocks.

Moreover, the US markets are more liquid than the Swiss stock

market. The important point here is that the same results are

obtained, even in different structural conditions. An

interesting avenue of research would be to check if similar

evidence is obtained for other European markets. Another

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remark is that these results also have implications for tests

of other asset pricing models, showing that researchers should

first examine the behaviour of the realised returns on the

factors they consider, before concluding that the associated

risk measures are inappropriate.

The study by Jagannathan & McGrattan (1995) concludes in their

article by suggesting that, while the academic debate

continues, the CAPM may still be useful for those interested

in the long run. Even though, capital budgeting decisions were

made before there was a CAPM, and they can be made again

without it. But the data seem to suggest that those who choose

to use the CAPM now despite the academic debate will actually

not be getting a worthless advice. They plotted the

returns/beta relationship for four types of assets over a

period of 66years. The result was more or less a positively

sloped, straight line just as the CAPM predicts. From the

study, the straight line relationship breaks down over shorter

time periods. But for those interested in the longer view, the

CAPM still seems to have something to offer.

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A study by Bhaduri & Dhurai (2006) opined that significant

role played by beta in various aspects of financial decision

making has forced people from small investors to investment

bankers to rethink on beta in the era of globalization with

ever changing market conditions.

Standing on the edge of a free capital mobile world with

technological innovations happening in no time, it is

imperative to understand the stability of beta in accordance

to these changes and also it would augments an efficient

investment decisions with additional information on the beta.

This study examined the stability of beta for India from a

developing country perspective with a series of possible

competing definitions of market conditions and alternative

model specification. The results strongly validate Fabozzi and

Francis (1977) claim of stable beta for individual stocks in

all market conditions.

This study was a re-examination of Fabozzi and Francis (1977)

claim of stable beta for individual stocks in all market

conditions from a developing country perspective. For India,

using monthly returns of 78 highly liquid stocks of BSE 100

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for the time period January 1999 to December 2004 substantiate

Fabozzi and Francis’s arguments. The results from alternative

model specifications are also bearing same inferences in

support of stable beta.

Emergence of a positive threshold parameter in the endogenous

model specification indicates that the stocks examined are

strong even before the market reacts. Altogether this study

provides clear evidence that for fundamentally strong

individual stocks the stability of beta is not significantly

affected by different market conditions.

John Leusner, 1999 extended the CAPM to account for the

effects of differences between unobservable and observable

stock and market portfolio returns of excluded variables and

of departures from a linear relationship between the

observable returns on individual stock and market portfolios.

The extended CAPM is tested using a stochastic-coefficients

methodology. For purposes of comparison, both consistent and

inconsistent sets of assumptions are made in these tests.

Tests based on a consistent set of assumptions show that the

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relation between the observable returns on stock and market

portfolios is nonlinear. A long standing puzzle in the Capital

Asset Pricing Model (CAPM) has been the inability of empirical

work to validate it. Roll (1977) was the first to point out

this problem, and recently, Fama and French (1992, 1993)

bolstered Roll’s original critique with additional empirical

results. Does this mean the CAPM is dead? This paper presents

a new empirical approach to estimating the CAPM. This approach

takes into account the differences between observable and

expected returns for risky assets and for the market portfolio

of all traded assets, as well as inherent nonlinearities and

the effects of excluded variables. From this approach,

evidence has it that the CAPM is alive and well.

Jonathan Fletcher (1997) examines the conditional relationship

between beta and return in UK stock returns. There is no

evidence of a significant risk premium on beta when the

unconditional relationship between beta and return is

considered. When the sample is split into periods according to

whether the excess market return is positive or negative,

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there is a significant relationship between beta and return..

Subsidiary results of the paper also indicate the absence of

the size effect in UK stock returns. The evidence within the

paper does suggest that there is a conditional relationship

between beta and return in UK stock returns. It also indicates

that beta may still have a useful role to play for portfolio

managers. Investors who are concerned about the risk of

periods where the market return falls below the risk-free

return, could protect themselves by investing in low beta

stocks. Beta seems to be a good indicator of how stocks react

in periods of down market months.

This paper examined the conditional relationship between beta

and return in the UK between January 1975 and December 1994.

Consistent with the findings of Fama and French (1992) and

Strong and Xu (1994), there was no evidence of a significant

risk premium on beta when the unconditional relationship

between beta and return was examined. Also, there was no

significant relationship between size and returns. This

appears to be due to a possible non-linear relationship

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between portfolio average returns and the proxy for portfolio

size.

When the sample period was split into periods of whether the

excess market return was positive or not, there was a

significant positive relationship between beta and return in

periods of positive excess market returns, and a significant

negative relationship between beta and return in periods of

negative excess market return. This is consistent with

Pettengill et al. (1995), and suggests the need to focus on

the conditional relationship between beta and return. However,

the conditional relationship between beta and return in up

market and down market months was not symmetrical, as

predicted by Pettengill et al. (1995). The relationship

was stronger in down markets. The results of the paper do

suggest that the market beta still has a role to play for

portfolio managers.

According to Liang Zou (2006) the issue of ‘best-beta’ arises as

soon as potential errors in the Sharpe-Lintner-Black Capital

Asset Pricing Model (CAPM) are acknowledged. By incorporating

a target variable into the investor preferences, this study

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derives a best-beta CAPM (BCAPM) that maintains the CAPM’s

theoretical appeal and analytical simplicity yet unambiguously

improves its pricing accuracy. Empirical observations suggest

that the BCAPM predicts expected returns better than the CAPM

by 20% to 30% annually

The work of Liang Zou (2006) records that despite the lengthy

debate over its theoretical and empirical validity, the CAPM

continues to be taught at universities and endorsed by

practitioners (e.g., recent reviews by Jagannathan and

McGrattan, 1995; Dimson and Mussavian, 1999; Campbell, 2000;

Cochrane, 2001; Rubinstein, 2002).

Even though the model may be imperfect in pricing assets or

predicting expected returns, it offers an effective standard

for discussing market efficiency, identifying attractive

stocks, evaluating performance, estimating opportunity costs

of risky capital by firms, regulators, and so on. Lou derived

a simple variation (rather than extension) of the CAPM, to be

called the BCAPM, that unambiguously improves the CAPM’s

pricing accuracy while retaining its theoretical appeal,

simplicity, and applicability. This improvement is derived as

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a theoretical property of the model, which is shown to be

directly related to the Sharpe ratio of the market portfolio.

By calibrating the US historical data to the model it is found

that the BCAPM typically improves the pricing accuracy of the

CAPM by 20 to 30% on an annual basis. Considering the extent

of applications of the CAPM in the real world, the results

reported in this paper could be of both theoretical and

practical interest.

Recent empirical arguments against the CAPM

A study by Huang & Wu (2005) takes into account two important

features found in most time series, namely, nonlinearity and

structural instability, in the test of the Sharpe-Lintner

CAPM. They implemented the multiple structural change approach

of Bai & Peron (2003) and have the following interesting

findings. First, there is overwhelming evidences in support of

at least one break in betas for all the portfolios under

investigation. In most, but not all cases, there exist

asymmetries in betas, indicating that the risk measures can be

different depending on the market conditions. It is found out

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that the CAPM can be consistent with the data in some regimes

but may appear to be inconsistent with the data in some other

regimes once the possibility of simultaneous nonlinearity and

parameter instability are taken into account. As implied by

the CAPM, the difference in risk premium across assets is

mainly due to difference in the riskiness of the returns on

the assets. Empirical results show that the beta risk changes

through time with the changes in the environment. In contrast,

the variation in beta might accrue due to the fact that in

practice, many portfolio managers constantly update and re-

adjust factor returns so that the beta changes over time.

Evidence found in support of structural changes in all test

portfolios. Ample evidence discovered to favour existence of

asymmetric betas. These points suggest that tests of the

Sharpe-Lintner CAPM with constant betas can lead to

inappropriate conclusions

Fama & French (1996) in line with Kothari, Shanken, and Sloan

(1995) claim that betas from annual returns produce a stronger

positive relation between, betas and average return than,

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betas from monthly returns. They also contend that the

relation between average return and book-to-market equity

(BE/ME) is seriously exaggerated by survivor bias. They

further argued that survivor bias does not explain the

relation between BE/ME and average return. They also show that

annual and monthly betas produce the same inferences about the

beta premium. Our main point on the beta premium is, however,

more basic. It cannot save the Capital asset pricing model

(CAPM); given the evidence that beta alone cannot explain

expected return.

It is, of course, according to Fama & French possible that

the apparent empirical failures of the CAPM are due to bad

proxies for the market portfolio. In other words, the true

market is mean-variance-efficient, but the proxies used in

empirical tests are not. The true market portfolio will cast

aside the average return anomalies of existing tests and

reveal that beta suffices to explain expected return. This

bad-market-proxy argument, however, does not justify the way

the CAPM is currently applied, for example, to estimate the

cost of capital or to evaluate portfolio managers. The bad

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market proxies used in tests of the CAPM are similar to those

used in applications of the model. If the common market

proxies are inefficient, then applications that use them rely

on the same flawed estimates of expected return that undermine

empirical tests of the CAPM. Fama & French (1996) conclude

that the payoffs in empirical asset pricing shows that the

failures of the CAPM can be explained by multifactor ICAPM or

APT alternatives or that they are consistent with specific

irrational-asset-pricing stories.

Javier Estrada (2007) faulted a major characteristic of the

CAPM that risk is measured by beta, which follows from an

equilibrium in which investors display mean-variance

behaviour. In that framework, risk is assessed by the variance

of returns, a questionable and restrictive measure of risk. He

however, opines that the semi-variance of returns is a more

plausible measure of risk and can be used to generate an

alternative behavioural hypothesis, mean-semi-variance

behaviour; an alternative measure of risk for diversified

investors, the downside beta; and an alternative pricing model

based on this downside beta. The empirical evidence discussed

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in this article for the entire MSCI database of developed and

emerging markets clearly supports the downside beta and the

pricing model based on it over beta and the CAPM. Furthermore,

the semi-variance of returns can be used to generate an

alternative behavioural hypothesis, mean-semi variance

behaviour (MSB). As shown in Estrada (2004a), MSB is almost

perfectly correlated with expected utility (and with the

utility of expected compound return) and can therefore be

defended along the same lines used by Levy and Markowitz

(1979) and Markowitz (1991) to defend MVB. In this article, an

alternative measure of risk for diversified investors, the

downside beta, and an alternative pricing model based on this

measure of risk were proposed. I also report evidence from

joint and separate samples of developed markets (DMs) and

emerging markets (EMs) supporting the downside beta over beta,

and, therefore, the pricing model based on downside risk over

the CAPM.

Most of the arguments against beta have been by and large

empirical, focusing on whether beta explains the cross section

of stock returns. Estrada (2004a) shows that MSB is almost

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perfectly correlated with expected utility and with the

utility of expected compound return, thus providing a

theoretical defence of MSB similar to that provided by Levy

and Markowitz (1979) and Markowitz (1991) with respect to MVB.

This article reports and discusses evidence that shows that

the data supports the downside beta and the model based on it

over beta and the CAPM. In the article, Javier Estrada made a

parallel between the standard framework based on MVB, beta,

and the CAPM, and an alternative framework based on downside

risk; that is, on MSB, downside beta, and the model based on

it. He also showed the appropriate way to estimate the

downside beta which is the measure of risk proposed in the

study, and how to integrate it into an alternative pricing

model, proposed in this article to replace the CAPM. The

evidence discussed supports the downside risk measures over

the standard risk measures, and particularly the downside

beta, which explains over 45% of the variability in the cross

section of returns of a joint sample of DMs and EMs, and

almost 55% of the variability in the cross section of EMs

returns.

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The evidence also shows that mean returns in both DMs and EMs

are much more sensitive to differences in downside beta than

to equal differences in beta. Furthermore, unlike the CAPM,

the model based on downside risk plausibly generates a higher

(average) required return for EMs than for DMs. Finally, in

EMs, this alternative model generates average required returns

on equity over 250 basis points a year higher than those

generated by the CAPM, a substantial difference that can make

or break many investment projects and affect significantly the

valuation of companies. Differences of this magnitude are

simply too large for practitioners to ignore.

In sum, then, the work of Javier Estrada questions the

standard framework based on MVB, beta, and the CAPM, and

proposes to replace it with an alternative framework based on

MSB, the downside beta, and the model based on it.

Conclusion

The principle of CAPM is easily stated and intuitively

appealing but opens up a new series of problems (Elton et al,

2007).

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Merton H. Miller said, ‘the aim of science is to explain a lot

with a little’, and few models in finance or economics do so

more dramatically that the CAPM. According to him, the current

consensus within the profession is that a single risk factor

is not quite enough for describing the cross-section of

expected returns. Apart from the market factor, two other risk

factors have been identified for common stocks. They are the

size effect and the ratio of a firm’s accounting book value to

its market value. Merton Miller (1999) however, said that,

this should detract in no way, from appreciating the enormous

influence of the original CAPM on the theory of asset pricing.

It can then be conveniently concluded from the various

evidences from recent studies that the CAPM is still alive.

Even though a lot of arguments went against the CAPM, the mere

fact that it is still been criticized sends a sharp signal

that the CAPM is important and worth criticizing. If not for

anything as a basis for further studies considering the fact

that change is inevitable.

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Is CAPM still alive

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