The Capital Asset Pricing Model and the Arbitrage Pricing Model: A critical Review

Dr. Monirul Alam Hossain

Associate Professor, E-mail: monirulhossain@yahoo.com

The Capital Asset Pricing Model and the Arbitrage

Pricing Model: A critical Review

Introduction

When security prices fully reflect all available information, the capital markets are said to be

efficient. In the efficient capital market, security prices adjust very rapidly to new information.

The risk of a portfolio of a security depends not only on the standards deviations but also on the

correlation of possible returns (Van Horne, 1989). The capital market line (CMI) expression

deals with the expected return on efficient portfolio investment.

The capital Assets Pricing Model (CAPM) is developed by W.F. Sharpe in 1964. The CAPM is

the basis of modern portfolio theory. The CAPM is a model for determining the required rate of

return on an asset, taking into the risk of the asset. The CAPM is an equilibrium theory of how to

price and measure risk, where beta (), the measure of risk is at the heart of the CAPM. The significant contribution of the CAPM is provides a measure of risk of an individual security

which is consistent with the portfolio theory (Weston and Copeland, 1986). It enables us to

estimate the undiversifiable risk of a well-diversified portfolio (Weston and Copeland, 1986).

Most probably, the most important challenge to the CAPM is the Arbitrage Pricing Theory

9APT). This theory is developed by Stephen R. Ross in 1976. The APT is a theory of asset

pricing in which the risk premium is based on specified set of risk factors in addition to or other

than correlation with the expected excess return on market portfolio. The APT is based on the

idea that in competitive financial markets, arbitrage will ensure that riskless assets provide the

same expected return (Van Horne, 1989).

The CAPM and the APT are the theories of how risky assets are priced in market equilibrium.

Both the models provide decision makers with estimates of the required rate of return on risky

securities. However, both the theories differ from each other in many respects. This article is an

attempt to draw contrast and compare between the CAPM and the APT with special reference to

their assumptions, implications and practical usefulness.

Assumptions of the CAPM and the APT

The assumption of the CAPM relating to market, investors and assets are as follows:

1. Assumption about the market-

a. There are no taxes and no transaction costs-cost of buying and selling. b. Information is costless and simultaneously freely available to all investors. c. There are many buyers and sellers in the market; so that none can influence security

prices.

2. Assumptions about investors-

a. Investors are risk adverse individuals. It is a one period model. Asset returns are defined to be over the next period, and the investors are assumed to be maximizing their returns

over a single period (Emmery and Finnerty, 1991).

b. Investors have homogeneous expectation about asset returns in the future.

3. Assumptions about assets-

a. There exists a risk-free asset such that investors may borrow or lend unlimited amounts at the risk-free rate.

b. The quantities of assets are fixed and all assets are marketable and perfectly divisible.

The assumptions of the APT are as follows (John Wei, 1988):

1. All investors exhibit homogeneous expectations that the stochastic properties of capital assets return are consistent with a linear structure of K factors.

2. Either there are no arbitrage opportunities in the capital markets or the capital markets are in competitive equilibrium.

3. The number of securities in the economy is either infinite or so large that the theory of large numbers are applied.

4. The APT hold in both the multi-period and single period cases.

Both the CAPM and the APT are built on the principle of capital market efficiency. Therefore

both the theories posses the assumptions of capital market efficiency. In the case of the CAPM, it

considers only single period. On the other hand, the APT considers both multi-period and single

period cases. Though consistent with every conceivable prescriptions for the portfolio

diversification, no particular portfolio plays a role in the APT (Roll and Ross, 1980). Unlike the

CAPM, there is no requirement that market portfolio on mean variance efficient. Both the

theories hold that all investors have homogeneous expectations to maximize their returns. In

case of the APT, the law of large numbers are used for infinite or large number of securities. But

in case of the CAPM, it is used for an accurate approximation of the market portfolio.

Implications of the CAPM and the APT

The CAPM does try to explain the underlying causes of securities, whereas the APT does not.

The CAPM is a single factor model: expected return is determined by a single factor systematic

risk or beta; whereas the APT is a muli-factor model: expected return is determined by more than

one single factor (Lumby, 1980). For the empirical test of the APT, a variety of factors have

emerged as possible determinants of actual common security returns and as statistical tool or

method called factor analysis has been used to attempt to identify the relevant factors (Emmery

and Finnerty, 1991). But the APT does not say what the factors are or why they are economically

or behaviorally relevant. The APT simply implies that there is a relationship between security

returns and a limited number of factors (Van Horne, 1989). However, these factors cannot be

identified easily.

The APT is derived in a completely different way. However, it looks like to the CAPM, except

that it has got multiple beta factors. In the CAPM, each assets estimated by regressing its return on the market portfolio return. On the other hand, the APT does not allow us to simply an assets return against arbitrarily determined factors (Weston and Copeland, 1986). Instead, factor

analysis must be employed to extract the fundamental factors underlying all security returns.

The APT states that, if there are sufficient securities, it must be possible to construct a diversified

portfolio that has zero senility to each factor. Such a portfolio would be effectively risk-free and

therefore it should offer a zero risk premium. According to the APT, securities risk premium depends upon two things- the risk premiums associated with each other and the securities sensitivity to each of the factors (Brealy and Myers, 1981). But in case of the CAPM, the risk

premium is determined by the product of the market price of risk and the securities systematic (undiversitiable) risk level. This later value is given by the product of the securities total risk and the degree to which the returns on securities are correlated to the returns on the market

portfolio. But, if the expected risk premium of each of the portfolios is proportional to the

portfolios market risk, then the CAPM and the APT are equivalent (Brealy and Myers, 1981). The APT is very similar to the CAPM in the sense that the expected return of any security is

equilibrium will be equal to the risk free rate plus a risk premium. Not only that, the APT is

similar to the CAPM in the application of the, model that it can be used in exactly the same way

as the CAPM for determining the cost of capital, for valuation and for capital budgeting (Weston

and Copeland, 1986).

The Practical Usefulness of the CAPM and the APT

The significant contribution of CAPM is that it provides a measure of the risk of an individual

security which is consistent with portfolio theory. It enables us to estimate the undiversifiable

risk of a single asset and compare it with the undiversifiable risk of a well diversified portfolio

(Weston and Compland, 1986). Practical use of the CAPM requires that estimate of beta for

securities should be reliable. It estimates the beta based on historical data are unrelated to actual

risk, now or in future, then the CAPM is not a good tool for decision making (Weston and

Copeland, 1986). In case of the CAPM, it is very difficult to estimate an accurate beta, because

betas tend to change overtime. In addition, the CAPM stresses one-dimensional measure of risk

(beta).

Despite the theoretical debate and the difficulty in obtaining accurate betas, some investors use

the CAPM, because it systematically relates return with risk and shows how key variables

interact (Cooley and Roden, 1986). In any event, the CAPM provides us with an understanding

of the investiors behaviour and market dynamics (Cooley and Roden, 1986). The CAPM is

useful in that it provides several significant views into the major factors of security price

determination, and so it is of direct interest of the decision makers within corporations. Although

it involves some unrealistic assumptions and it is not perfect and complete representation of the

real would, it is reasonably adequate (Lumby, 1980). The CAPM may not be perfect, but it does

appear to give a reasonable approximation of the world and it does have predictive ability. For

example, high beta securities tend to be more volatile and produce a higher expected return than

low beta securities.

One of the great advantage of the CAPM is its simplicity. But to test the CAPM two problems

arise. Firstly, the CAPM is concerned with expected returns and secondly, the market portfolio

should include all risky investment, whereas most of the market indexes contain only a sample of

common stocks (Brealy and Myers, 1981).

There is a debate about how much improvement can be obtained using the APT rather than the

CAPM. The study of Roll and Ross (1980) claimed that the APT is amenable to empirical

testing, in a way that the CAPM is no because (i) it is not necessary to test the returns on all

assets, nor (ii) there is any special role for the market portfolio. The studies of Chen (1983) and

Roll and Ross (1983) seem to suggest that the APT is an improvement over the CAPM, specially

when security returns contain some CAPM anomaly. Other studies (e.g., Brown and Weinstein,

1983) of portfolio performance find no significant differences between the APT and the CAPM.

Whether the APT should replace the CAPM is subject to much debate. Enough research is

required for the determination of whether the APT would replace the CAPM nor not. However, it

could be well that the APT will become the principal theory of asset pricing, with the CAPM as a

subject of it (Van Horne, 1989).

Conclusion

The CAPM and the APT are built on the principle of capital market efficiency. Both the models

state how risky assets are priced in the market equilibrium and they provide decision makers

with estimates of required rate of return on risky securities. In spite of their similarities, they

differ from various corners in relation to their assumptions, implications, practical use and the

like. The CAPM considers one factor the return is determined by a single factor, the securities beta value. Therefore, the CAPM is often referred to as a single-factor model. The APT is called

as multi-factor variable and it is derived in a completely different way from the CAPM.

The APT emphasizes the role of the co-variance between asset returns and the exogenous

factors, while the CAPM stresses on the co-variance between asset returns and the endogenous

market portfolio (John Wei, 1988). The CAPM is a one period model, whereas the APT holds in

both the multi-period cases. The CAPM tries to explain the underlying causes of security returns,

whereas the APT does not. Certain studies find that the APT has better explanatory power of

security returns than does the CAPM. On the other hand, some other studies of portfolio

performance find no significant differences between the APT and the CAPM. Whether the APT

should displace the CAPM is a subject of much debate. More empirical research is needed in this

respect.

Bibliography

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