The Mathematics of Financial Modelingand Investment Management

17-Capital Asset Pricing Model Page 520 Wednesday, February 4, 2004 1:10 PM

520 The Mathematics of Financial Modeling and Investment Management

General Findings of Empirical Tests of the CAPM

The general results of the empirical tests of the CAPM are as follows:

1. The relationship between beta and return appears to be linear, hence
   the functional form of the CAPM seems to be correct.


2. The estimated intercept term, bo, is significantly different from zero
   and consequently different from what is hypothesized for this value.


3. The estimated coefficient for beta, b 1 , is less than RM – RF. The combi-
   nation of results 2 and 3 suggests that low beta stocks have higher
   returns than the CAPM predicts and high beta stocks have lower
   returns than CAPM predicts.


4. Beta is not the only factor priced by the market. Several studies have
   discovered other factors that explain stock returns. These include a
   price/earnings factor,^5 a dividend factor,^6 a firm size factor,^7 and both a
   firm size factor and a book/market factor.^8


5. Over long periods of time (usually 20–30 years), the return on the mar-
   ket portfolio is greater than the risk-free rate.

A Critique of Tests of the CAPM

One of the most controversial papers written on the CAPM is Richard

Roll’s “A Critique of the Asset Pricing Theory’s Tests.”^9 We will discuss

the major points of Roll’s argument here. Following Roll’s argument,

the CAPM is a general equilibrium model based upon the existence of a

market portfolio that is defined as the value-weighted portfolio of all

investment assets. Furthermore, the market portfolio is defined to be ex

ante mean-variance efficient. This means that the market portfolio lies

on the ex ante Markowitz efficient frontier for all investors.

Roll demonstrates that the only true test of the CAPM is whether the

market portfolio is in fact ex ante mean-variance efficient. However, the

(^5) See Sanjoy Basu, “Investment Performance of Common Stocks in Relation to Their
Price-Earnings Ratios,” Journal of Finance (June 1977), pp. 663–682 and “The Re-
lationship Between Earnings’ Yield, Market Value and Return for NYSE Common
Stocks,” Journal of Financial Economics (June 1983), pp. 129–156.
(^6) Robert Litzenberger and Krishna Ramaswamy, “The Effect of Personal Taxes and
Dividends on Capital Asset Prices,” Journal of Financial Economics (June 1979), pp.
163–195.
(^7) Rolf Banz, “The Relationship Between Return and Market Value of Common
Stocks,” Journal of Financial Economics (March 1981). pp. 3–18.
(^8) Eugene Fama and Kenneth French, “The Cross-Section of Expected Returns,” Jour-
nal of Finance (June 1992), pp. 427–465.
(^9) Richard Roll, “A Critique of the Asset Pricing Theory’s Tests.”