Is the Capm a Good Model

The Capital Asset Pricing Model (CAPM) was developed in the mid-1960s by William Sharpe, John Lintner, and Jan Mossin who built upon the portfolio management theory developed by Harry Markowitz a dozen years before (Bodie, Kane, and Marcus 1999: 251). CAPM is defined as “a set of predictions concerning the equilibrium expected returns on risky assets” (Bodie, Kane, and Marcus 1999: 251). By using CAPM, it is hoped that we can determine certain information about the relationship between an asset’s risk and its expected return. This information would be useful for evaluating risky investments and even for determining if an investment is undervalued or overvalued.

In addition to the assumptions which CAPM inherits from Markowitz’ model, there are an additional eight which are unique to the model. First is that all investors will use the same information to generate an efficient frontier using Markowitz’ theory (Jones 1998: 226) Secondly, all investors have the same “one-period time horizon” (Jones 1998: 227). The third assumption is that all investors are able to borrow or lend money at a certain risk-free rate of return (Jones 1998: 227). Fourthly, as with Markowitz’ theory, there are no transaction costs involved (Jones 1998: 227). The fifth assumption is that there are no taxes on income, this is needed because tax advantages may drive some investors to put more value on capital gains or dividends due to tax liability (Jones 1998: 227). The next assumption is that there is no inflation (Jones 1998: 227). Seventh, CAPM assumes that there are “many investors” and that no one can impact the price by their own trades (Jones 1998: 227). The final and most important assumption is that “capital markets are in equilibrium” (Jones 1998: 227).

These assumptions are hardly realistic. For example, not all investors are investing for the same time-frame. One investor may want to turn a quick profit while another is investing for retirement twenty years away. There are of course also inflation and income tax considerations for most investors. Jones, et al in Investments: Analysis and Management point out that a test of a model should not rest entirely on unrealistic assumptions. If tests of the model prove accurate, then a model is useful even if it seems to be unrealistic based on what is assumed by the model alone (Jones 1998: 227).
CAPM is built upon Markowitz’ portfolio theory, so the same assumptions that underlie this theory are assumed for CAPM. These stipulate that the time period looked at is a single investment period, that the positions are liquid (and have no transaction costs), and that investor preferences are only based on a “portfolio’s expected return and risk” (Jones 1998: 205). Markowitz’ theory allows the investor to determine the “optimal risky portfolio” or “market portfolio.”

The Market Portfolio by definition includes all risky assets: stocks, bonds, options, real estate, metals, etc. and is thus said to be “completely diversified (Jones 1998: 229). This is important, because the portfolio is only impacted by systematic risk, that risk which is impossible to diversify away because it is intrinsic in the market itself (Jones 1998: 229). In reality, most investors will approximate the Market Portfolio using common stock. The most common means of simplifying and approximating this portfolio is by using a sufficiently broad stock index. Such simplifications open the use of CAPM to distortions because a subset of the total market is representing the total market, thus it is logical assume that predictions will neglect non-systematic risk inherent in whatever subset that is chose which would be diversified out in a complete Market Portfolio.

CAPM looks at expected risk and expected portfolio return. Because it is assumed that all investors are logical and thus all of them will hold the Market Portfolio, all investors will hold a portfolio which lies somewhere on the line drawn from the return guaranteed by risk free investments through the Market portfolio as found from Markowitz analysis (Jones 1998: 231). This line is known as the Capital Market Line. The Capital Market Line is interesting, because it’s slope is, according to CAPM, equal to the “additional return that the market demands for each percentage increase in a portfolio’s risk” (Jones 1998: 231).

Much more interesting, however are the implications which CAPM predicts about individual securities. This can be graphically related by the Security Market Line (SML) which is found when the expected return equation of the Capital Market Line is re-written to examine the expected return from an individual security. When the CML equation is written in such a from, a useful term appears (Jones 1998: 233). This term is known as Beta, which is a commonly used measure of the risk of a security (Jones 1998: 233). Beta is defined as “a measure of systematic risk of a security…. [Beta shows] the risk of an individual stock relative to the market portfolio of all stocks” (Jones 1998: 234). The Beta value for various stocks can be determined or simply found in various investor resources (Jones 1998: 234).

One of the most useful predictions of CAPM is this “Expected Return Beta” relationship (Jones 1998: 235). If a stock has a known Beta value and the “risk-free rate of return” is known, then calculating the required rate of return predicted by CAPM can be easily calculated. This can be useful, because the real-world rate of return can be compared to an expected rate of return generated from fundamental analysis (Jones 1998: 237). Such a test will tell an investor if a stock is overvalued or undervalued.

With such useful predictions claimed by CAPM, it would make a useful model if indeed the predictions that it finds match up with reality. Studies performed by John Lintner as well as Merton Miller and Myron Scholes are mentioned by Bodie, Kane, and Marcus in Investments as an example of a real-world test of CAPM theory (1999: 373). They followed New York Stock Exchange data over ten years and produced a Security Market Line that had too “flat” of a slope to fit the projections of the CAPM model (Bodie, Kane, and Marcus 1999: 373). Richard Roll takes a more in depth shot at the very nature of CAPM itself. Roll claims that the flaws of CAPM include the lack of testable relationships (Bodie 373). Roll states in “A Critique of the Asset Pricing Theory’s Tests” that the sole testable relationship is that “the market portfolio is mean-variance efficient” (Bodie, Kane, and Marcus 1999: 373). All other relationships rely on this “efficiency of the market portfolio” (Bodie, Kane, and Marcus 1999: 373). Since we can never hope to know the full contents of the market portfolio, nothing is really testable (Bodie, Kane, and Marcus 1999: 374). Using a estimate such as a Stock index will never be able to replace a portfolio of each and every individual security in the world. A “proxy… might be mean-varience efficient even when the true market portfolio is not” (Bodie, Kane, and Marcus 1999: 374). In further work Richard Roll, Stephen Ross, and others have declared that “tests that reject a positive relationship between average return and beta” as predicted by CAPM “point to inefficiency of the market proxy used… rather than refuting” CAPM’s predicted relationship (Bodie, Kane, and Marcus 1999: 374).

The data from empirical tests is conflicting. On one hand, it seems as if CAPM does not live up to its promise. On the other, hand, it seems as if it may be the tests at fault, not CAPM itself. Bodie et al propose in Investments that this is because CAPM “implies relationships among expected returns” (Bodie, Kane, and Marcus 1999: 289). When the model is evaluated, it is only possible to examined is historical data. Testing the model requires looking for relationships between realized returns. Since expected data is never going to be testable, it is impossible to ever create a fully useful test of CAPM’s predictions. Thus, the model is essentially un-testable. A model which cannot be accurately tested is of little value to an investor and is more of a superstition than a scientific theory.

Works Cited

Bodie, Z., Kane, A., and Marcus, A. (1999) Investments. New York: McGraw-Hill

Jones, C. (1998) Investments: Analysis and Management. New York: John Wiley and Sons

Gruber, M. and Elton, E. (1995). Modern Portfolio Theory and Investment Analysis. New York: John Wiley and Sons

Poitras, G. (2005). Security Analysis and Investment Strategy. Oxford: Blackwell

Roll, R. (1977). “A Critique of the Asset Pricing Theory’s Tests; Part I: On Past and Potential Testability of the Theory.” Journal of Financial Economics 4, 129-176.