The Mathematics of Financial Modelingand Investment Management

17-Capital Asset Pricing Model Page 519 Wednesday, February 4, 2004 1:10 PM

Capital Asset Pricing Model 519

[ER( M )– Rf ]

ER[]i – Rf = ----------------------------------cov(RiR )

var(RM )

m

The above is the CML in “risk-premium form” because the value on

the left-hand side of the equation is the portfolio’s expected return over

the risk-free rate. By adding an error term and a constant term, bo, the

above equation becomes

E(Rp) – RF = bo + βp [E(RM) – RF] + ep

The actual process of testing the CAPM using the two-pass regression

methodology involves the consideration of some econometric problems

(e.g., measurement error, correlated error terms, and beta instability).^4

Empricial Implications

Assuming that the capital market can be described as one in which there

is no opportunity for investors to use information from previous periods

to earn abnormal returns, several testable hypotheses for the empirical

analogue of the CML implied by the CAPM can be listed:

1. The relationship between beta and return should be linear.


2. The intercept term, bo, should not differ significantly from zero.


3. The coefficient for beta, b 1 , should equal the risk premium (RM – RF).


4. Beta should be the only factor that is priced by the market. That is,
   other factors such as the variance or standard deviation of the returns,
   and variables that we will discuss in later chapters such as the price/
   earnings ratio, ratio, dividend yield, and firm size should not add any
   significant explanatory power to the equation.


5. Over long periods of time, the rate of return on the market portfolio
   should be greater than the return on the risk-free asset. This is because
   the market portfolio has more risk than the risk-free asset. Hence, risk-
   averse investors would price it so as to generate a greater return.

(^4) The interested reader should consult Merton H. Miller and Myron S. Scholes,
“Rates of Return in Relation to Risk,” Chapter 2 in Michael C. Jensen (ed.), Studies
in the Theory of Capital Markets (New York: Praeger, 1972), pp. 79–121; Eugene
F. Fama, Foundations of Finance (New York: Basic Books, 1976); Richard Roll,
“Performance Evaluation and Benchmark Errors II,” Journal of Portfolio Manage-
ment (Winter 1981), pp. 17–22; and Richard Roll, “A Critique of the Asset Pricing
Theory’s Tests,” Journal of Financial Economics (March 1977), pp. 129–176 for a
discussion of these issues.