The Mathematics of Financial Modelingand Investment Management

17-Capital Asset Pricing Model Page 521 Wednesday, February 4, 2004 1:10 PM

Capital Asset Pricing Model 521

true market portfolio is, in fact, ex ante since it includes all investment

assets (e.g., stocks, bonds, real estate, art objects, and human capital).

The consequences of this “nonobservability” of the true market

portfolio are:

1. Tests of the CAPM are extremely sensitive to which market proxy is
   used, even though returns on most market proxies (e.g., the S&P 500
   and the NYSE index) are highly correlated.


2. A researcher cannot unambiguously discern whether the CAPM failed
   a test because the true market portfolio was ex ante mean-variance
   inefficient, or because the market proxy was inefficient. Alternatively,
   the researcher cannot unambiguously discern whether a test supported
   the CAPM because the true market portfolio was ex ante mean-vari-
   ance efficient or because the market proxy was efficient.


3. The effectiveness of variables such as dividend yield in explaining risk-
   adjusted asset returns is evidence that the market proxies used to test
   the CAPM are not ex ante mean-variance efficient.

Hence, Roll submits that the CAPM is not testable until the exact

composition of the true market portfolio is known, and the only valid

test of the CAPM is to observe whether the ex ante true market portfo-

lio is mean-variance efficient. As a result of his findings, Roll states that

he does not believe there ever will be an unambiguous test of the

CAPM. He does not say that the CAPM is invalid. Rather, Roll says that

there is likely to be no unambiguous way to test the CAPM and its

implications due to the nonobservability of the true market portfolio

and its characteristics.

Does this mean that the CAPM is useless to the financial practitio-

ner? The answer is no, it does not. What it means is that the implica-

tions of the CAPM should be viewed with caution.

Merton and Black Modifications of the CAPM

Several researchers have modified the CAPM. Here we will briefly

describe two modifications.

Suppose that there is no risk-free rate and that investors cannot bor-

row and lend at the risk-free rate (Assumption 6). How does that affect

the CAPM? Fischer Black examined how the original CAPM would

change if there is no risk-free asset in which the investor can borrow

and lend.^10 He demonstrated that neither the existence of a risk-free

asset nor the requirement that investors can borrow and lend at the risk-

(^10) Fischer Black, “Capital Market Equilibrium with Restricted Borrowing,” Journal
of Business (July 1972), pp. 444–455.