The building of the Capital Asset Pricing Model (CAPM) based on the Markowitz portfolio theory give the linear relationship between expected return and risk by using beta ratio, and shows the power of its prediction. However, resent the empirical studies find the unrealistic assumptions and the anomalies that make the CAPM not hold in the empirical work, thus cannot be adopted in application. They suggest that the CAPM might be missing something or missing everything. Then, other asset pricing models are developed to try to modify or substitute the CAPM. This project will choose the most of main stream literatures from 1959-1996. By presenting these academic papers through a critical and logic flow, this review article of the asset pricing models will tell the story the derivation of the CAPM, its problems in application, and solve these problems.
Generally, this project is a review article of the asset pricing models based on most of existing main stream literatures from 1959-1996. To be more specific, this article presents what is the CAPM, why it is failed when adopting in application, and how other asset pricing models modify and develop the CAPM.
In the first section, it will tell the story of the assumptions and the derivation of the CAPM. The CAPM is built on the Markowitz Portfolio Theories, and it also requires other assumptions, such as homogeneous beliefs, risk-free borrowing and lending rate, and no taxes and transaction costs. Then, the CAPM equation can be derived and presents a linear relation between asset return and risk (captured by the beta). Due to powerful and intuitively pleasing predictions, the CAPM has been applied estimating the cost of capital for firms and evaluating the performance of managed portfolios.
However, empirical tests give more challenges than supports to the CAPM when it is used in application. In section two, the most important literatures of the empirical tests will be presented. The early two classical tests do support the CAPM. However, after 1981, accumulative empirical studies find many other variables, which are considered to be the CAPM anomalies, can explain the returns. Fama and French's (1992) famous work then pulls most of these variables together to test the CAPM, and find that the relationship between return and the beta has disappeared.
Due to the failure of return explanation in empirical work, there might be something wrong with the CAPM and its assumptions. Then, in the third part, the Intertemporal Capital Asset Pricing Model (ICAPM), the Arbitrage Pricing Theory (APT), the Consumption-Oriented Capital Asset Pricing Model (CCAPM), and the three-factor model, which are considered to be the modifications or substitutions of the CAPM, are presented as other asset pricing models for explaining the expect returns.
However, the story of the CAPM might not have the end. The CAPM might only take the role of a theoretical tour de force and provide a basic idea to build more complicated models as its development.
Table of Contents
Abstract
Executive Summary
Introduction 1
The CAPM and its Application 2
Empirical Tests and Critiques of the CAPM with its Application 3
3.1 Classical Supports 4
3.2 The Roll Critique 5
3.3 Empirical Tests Against 5
The Development of the CAPM 6
4.1 The ICAPM 7
4.2 The APT 7
4.3 The CCAPM 8
The Three-Factor Model 9
Conclusion 9
Bibliography 11
Introduction
Due to extraordinary returns can be offered by the financial market, considerable attentions have been paid by the investors and financial researchers to this area. They try to understand and capture the nature and rule of the financial market in order to help them make reasonable investment decisions. Then, asset pricing models are developed as the tools to support investors to estimate the expected returns.
The capital asset pricing model (CAPM) is considered to be the first model of asset pricing and one of the most important developments in modern capital theory. Due to its predicted power, it has been dominant in empirical work in financial market over past 40 years. The CAPM give a positive linear relation between expected return and risk. It suggests that high expected return as the compensations for bearing high level of risk. However, many researches then appear to doubt the abilities of the CAPM for its empirical application, and new asset pricing models are developed to give a more precise explanation of the expected returns.
This project, which mainly reviews the asset pricing models, will initially present the concept of CAPM, exploit the reason why it fails in application, and finally state other asset pricing models as the development to solve the problems of CAPM. This review article is based on selected existing main stream literatures ranging from 1959 to 1996.
Section 2 generalise the derivation of the CAPM and its applications. In Section 3, the empirical studies which test the CAPM will be presented to support and contradict the CAPM for its empirical application. Section 4 will introduces and critically comments the most important asset pricing models as the development of the CAPM. Finally, section 5 will give the conclusion.
The CAPM and its Application
Sharp (1964), Lintner (1965) and Mossin (1966) develop the Capital Asset pricing Model (CAPM) based on the assumption of the model of Markowitz Portfolio Theory (1959). The portfolio theory assumes that investors are risk averse who maximize their own utility, and they only care about the mean and variance of their single-period investment return. This assumption allows the risk to be measured by variance of the portfolio's return. Then, "mean-variance-efficient" portfolio, which is efficient frontier showed in Figure 1, is the best choice for investors. Therefore, portfolio theory suggests that: (i) with a certain acceptable level of expected return, investors' objective is to minimize the variance (risk) of the portfolio; (ii) with certain acceptable variance (risk), they will maximize the return. Besides, the CAPM further assumes that there is an asset that investors can borrow or lend at risk-free interest rate. With risk-free asset, efficient frontier is no longer the best choice for investors. The Capital Market Line (CML) is then introduced so that investors can invest along this line to maximize their utilities. As shown in Figure 1, the CML is the straight line that crosses the point of risk-free rate (Rf) and tangencies with efficient frontier at the point M. The point M then is defined as the market portfolio that every rational investor will choose, which thus contains all the risky assets in order for market equilibrium. Therefore, CML shows the combination of the risk free asset and the market portfolio M. Moreover, the CAPM needs the support from the assumption of perfect capital market. Under this assumption, investors are price takers; there are no taxes or transaction costs; perfect information is freely available to all investors, who thus have the same expectation - homogeneous belief; risk-free borrowing and lending rate are not restricted. According to above assumptions and rational logics, it leads to the CAPM equation:
Rf
M
E(R)
Capital Market Line (CML)
Efficient Frontier
Figure 1
The CAPM equation presents a positive linear relation between expected return on an asset and its systematic risk as measured by portfolio beta for any mean-variance-efficient portfolio, and beta is the only variable that explains asset returns. Then, the CAPM is widely used in applications. First, financial managers employ the CAPM to estimate the cost of capital in order to help them know the market risk premium. Then, the cost of the capital in the CAPM is equals the risk-free rate plus a risk premium. Second, by adopting the CAPM beta in the Traynor ratio (), investors can evaluate the performance of managed portfolios.
Empirical Tests and Critiques of the CAPM with its Application
The birth of the new theory and model will be accompanied by a serial of arguments, and the CAPM is no exception. During last 40 years, a great number of academic debates on the usefulness and validity of the CAPM. Baily et al (1998) divide these empirical tests into two broad purposes: (i) to test whether or not the theories should be rejected (ii) to provide information that can aid financial decisions in application.
3.1 Classical Supports
One of earliest empirical studies from Black, Jensen and Scholes (1972) gives the evidence to support the CAPM. The aim of the study is to test whether the cross-section of expected returns has a linear relation with beta. They use monthly return data and portfolios rather than individual stocks. Therefore, all of the stocks on the NYSE during 1931-1965 have been used to form 10 portfolios with different historical beta estimates. It is considered that each portfolio they have produced is able to diversify away most of the firm-specific component of the returns. Therefore, the precision of the beta estimates and the expected rate of return of the portfolio securities has been enhanced, which can mitigate the statistical problems when measuring the estimates of the beta. The authors then find that the relation between the average return and beta is very close to linear, and support the CAPM story that high (low) betas have high (low) average returns.
Fama and McBeth's (1973) empirical study also supports the CAPM. The aim of the study is to examine whether there is a positive linear relation between average returns and the beta. They collect data from the monthly return of stocks traded on the NYSE during January 1926 to June 1968. To obtain more precise beta estimates, they employ portfolio betas rather than individual stock betas. Moreover, they create the term of the squared value of beta and the volatility of the return on an asset. The aim is to examine whether the residual variation in average returns across assets can be explained by this term rather than by the beta alone. Then the authors give the conclusion: on average, there is linear relationship with a positive trade-off between a security's portfolio and its expected return; there is no other measure of risk that systematically affect expected returns.
3.2 The Roll Critique
Roll (1977) argues that it is impossible to get true market portfolio for the CAPM. In theory, the market portfolio should include all risky assets in the economy. However, in practice, it is not theoretical clear what kind of the assts should be included or excluded in the market portfolio. To solve the problem, empirical proxy has been introduced, due to its ability of bearing a high correlation with the true market portfolio. Then, the problem of benchmark error is arising, and leads to the following problems: (i) the slope of security market line (SML) is underestimated because the empirical proxy used for market portfolio is not as efficient as the true market portfolio; (ii) Beta is underestimated because true market portfolio will be more diversified than its empirical proxy and therefore has lower variance; (iii) according to the Traynor ratio, the CAPM overestimate the performance of the evaluated asset. Roll then argues that the CAPM has never been tested and probably never will be tested.
3.3 Empirical Tests Against
The CAPM passed early major empirical tests. However, later studies are presented to contradict it. They suggest that the CAPM might be missing some important elements that highly relates with the asset returns.
Banz (1981) uses a procedure similar to the portfolio grouping procedure of Black, Jensen, and Scholes (1972), and produces 25 portfolios based on the firms of the NYSE with the time period from 1936-1975. However, he introduces a new variable -- size of the firm. Then, he estimates the cross-sectional relation among return, beta, and relative size. Finally, his finding is known as "size effect", which shows that firm size do have the relation with return, and the stocks of firms with low market capitalizations have higher average returns than large-cap stocks.
Follow Banz's work, empirical studies find many other different variables that might explain the expected return. DeBondt and Thaler (1985) find Long-Term Return Reversals, which shows that losers have much higher average returns than winners over the next three to five years. Their work is then proved by Chopra, Lakonishok and Ritter (1992). Statman (1980) and Rosenberg, Reid and Lanstein (1985) show that stocks with high (book-to-market equity or BtM) have significantly higher returns than stocks with low BtM. Chan, Hamao and Lakonishok (1991) then show the evidence in the Japanese market. Bhandari (1988) finds that firms with high leverage (high debt/equity ratios) have higher average returns than firms with low leverage. Jegadeesh (1990) finds that the stock returns tend to exhibit short-term momentum that the CAPM cannot explains, and Jegadeesh and Titman (1993) later confirm these results.
All those variables presented in the empirical studies have been concluded as the CAPM anomalies. Fama and French (1992) bring most of the early empirical work together to test the CAPM. By adopting the same procedure as Fama and MacBeth (1973), they run a single cross-sectional study to pull size, leverage, E/P, and BtM together with the data period from 1926-1990. However, the authors find significant different result, which shows that if the beta is not related to these variables, there will be no relation between the return and the CAPM beta. They also find that size which is proxied by market capitalization has significant negative association with stock returns, and BtM has significantly positive associated with stock returns.
Fama (2004) finally points out because of its empirical problems the CAPM probably does not work when it is adopted in application. The CAPM might only take the role of a theoretical tour de force.
The Development of the CAPM
The CAPM might be failed for its unrealistic assumptions as well as the some variables it is missing. Therefore, it is only the introduction to the fundamental concepts of portfolio theory and asset pricing, which provide a basic idea to build more complicated models as its development to explain the expected returns.
4.1 The ICAPM
The CAPM is a static and single-period model that ignores the multi-period natures of participation in the capital market. By using a number of examples, Merton's (1973) shows that investment opportunity set is not a constant concept and it will shift over time. Therefore, investors will change their own portfolio behaviour as a response in order to hedge against unfavourable shift in the set of available investments. Then Merton introduces the Intertemporal Capital Asset Pricing Model (ICAPM) as a natural extension of the CAPM. In the ICAPM, he combines the mean-variance-efficient portfolio with hedge portfolios to create the multifactor-efficient portfolio, and adds consumption-investment state variable as the factor for it. Like the CAPM investors, the ICAPM investors dislike wealth uncertainty and they use Markowitz's mean-variance-efficient portfolios to optimize the trade-off of expected return for general sources of return variance. However, the ICAPM investors also concerned with the opportunities they will have to consume or invest the payoff. In other words, they are concerned with the covariances of portfolio returns with state variables. As a result, optimal portfolios are "multifactor efficient", which means they have the largest possible expected returns, subject to their return variances and the covariances of their returns with the relevant state variables (Fama and French, 2004). Then, the factor that appears in the ICAPM satisfied for the following two conditions: (i) They describe the evolution of the investment opportunity set over time; (ii) Investors care enough to hedge their future effects.
4.2 The APT
Ross (1976a, 1976b) tends to overcome the weakness of the CAPM for its assumptions. Thus, he does not simply extend the existing theories in the CAPM, but develop a completely different model: the Arbitrage Pricing Theory (APT). Compared to the CAPM, the assumption of the APT is much less restrictive, which only assumes that arbitrage opportunities should not be existed in efficient financial markets. Unlike the CAPM which only has one resource (beta) of systematic risk, there are n sources in the APT. The APT introduces n factors to explain the cause of systematic deviation between asset returns and their expected values. The APT adopts the risky asset's expected return and the risk premium of a number of macro-economic factors. This theory predicts a relationship between the returns of a portfolio and the returns of a single asset through a linear combination of many independent macro-economic variables. In this case, the CAPM can be viewed as a special case of the APT with single factor. However, the theory does not give the specific large of the number of the factors, nor does it identifies the factors. In theory, the model suggests that arbitrageurs use the APT model to make profit by taking advantage of mispriced securities. By going short an overpriced security, while simultaneously going long the portfolio based on the APT calculations, the arbitrageur can take a position to make a risk-free profit.
4.3 The CCAPM
Breeden (1979) introduces Consumption-Oriented Capital Asset Pricing Model (CCAPM) to extension of the previous work in asset pricing. He finds that when the level of aggregate consumption is relatively low, an extra dollar of consumption is worthier to a consumer. Based on this "diminishing marginal utility of consumption", if aggregate consumption is low, those securities with high returns will become more attractive and investors will increase their demand for holding them. Then, the price is rising and investors require lower expected returns. On the contrary, stocks that co-vary negatively with aggregate consumption will require higher expected returns. Therefore, in the CCAPM, expected returns should be a linear function of consumption betas, and the consumption beta measures the sensitivity of the return of asset to changes in aggregate consumption. Unfortunately, empirical test from Breeden et al (1989) does not support its prediction. However, Lettau and Ludvigson (2001) show that the CCAPM do provide a cross-sectional explanation of equity returns, and show the evidence that an increase in the consumption/wealth ratio would be the signal for high expected returns.
4.4 The Three-Factor Model
To solve the CAPM anomalies argued by most early empirical studies, Fama and French introduce the three-factor model (1993, 1996). Evidence shows that the cross-sectional pattern of stock returns can be explained by characteristics, such as size, leverage, past returns, dividend-yield, earnings-to-price ratios, and book-to-market ratios. They examine all of these variables simultaneously and argue that all these CAPM average-return anomalies are related. Therefore, they conclude that the cross-sectional variation in expected returns can be explained by only two of these characteristics, size and book-to-market. Fama and French (1996) present the evidence that the three-factor model captures most of the average-return anomalies of the CAPM. The model says that the expected return on a portfolio in the excess of the risk-free rate is explained by the sensitivity of its return to three factors: 1. The excess return on a broad market portfolio; 2. The difference between the return on a portfolio of small stocks and large stocks; 3. The difference between the return on a portfolio of high BtM stocks and low BtM stocks. Moreover, their work is consistent with rational ICAPM or APT asset pricing, and also considers irrational pricing and data problems as possible explanations. Due to the successful explanation of stock returns, the three-factor model has been used to test mutual fund performance, post-corporate event, long-run performance, and corporate cost equity. However, the model still cannot explain the momentum effect.
However, the story does not end. The above models only solve part of the problems for the CAPM. As Fama (2004) suggests, more complicated models need to be built basic on the CAPM to explain the expected return.
Conclusion
The capital asset pricing model (CAPM) is developed by Sharp (1964), Lintner (1965) and Mossin (1966). The model bases on the assumption of the Markowitz market portfolio theory with other assumptions such as risk-free borrowing and lending rate and homogeneous belief, and no taxes and transaction costs. The CAPM equation explains the existing linear relations between expected return and risk through beta ratio.
Although early empirical studies from Black, Jensen and Scholes (1972), and Fama and Mcbeth (1973) do support the CAPM. However, Roll (1977) critique argues that it is impossible to get the true market portfolio to test the CAPM, and the empirical proxies being used might lead to incorrect results. After 1981, studies find many factors that the CAPM cannot explains, which is known as the CAPM anomalies, which are size effect (Banz, 1981), long-term return reversals (DeBondt and Thaler, 1985), book-to market value (Reid and Lanstein, 1985), leverage (Bhandari, 1988), and momentum effect (Jegadeesh, 1990). Then, a famous work from Fama and French (1992) pulls most of above the CAPM anomalies together, and find that the relation between the CAPM beta and return disappeared.
To solve the problem the CAPM faces, financial researchers have build other asset pricing models. Merton (1973) questions the static and single-period CAPM, and introduce ICAPM to the multi-period natures of the customs. The CCAPM shows linear function between expected returns and consumption betas. To solve the weakness of the assumptions in the CAPM, Ross (1976a, 1976b) develops the APT, which only assumes no arbitrage opportunities in efficient financial market. Fama and French (1993, 1996) create three-factor model that captures most of the CAPM anomalies but does not explain momentum effect.
