76 Corporate Finance
R – Rf = γ 0 + γ 1 β + ∈In this regression, R represents the returns of many securities at a particular cross section of time and beta
represents the betas of many firms. According to the CAPM, γ 0 should be equal to zero and γ 1 should equal
the expected excess return on the market portfolio. The earliest tests of the CAPM were carried out by
Black et al. (1972) and Fama and MacBeth (1973). Both of these tests were cross sectional tests. To test the
theory, B-J-S created portfolios on the basis of beta (high to low). A cross sectional regression was run to see
if the betas were able to explain the differences in the returns across securities.
R – Rf = γ 0 + γ 1 β + ∈The results were:
R – Rf = 0.0036 + 0.0108β
[6.53] [20.77]The t-statistics are in parenthesis. The CAPM suggests that γ 0 = 0 and γ 1 > 0 (and is equal to the expected
market return less the risk-free rate). The regression evidence does not support this.
Gupta and Sehgal (1993)^5 conducted one such study in India for the period April 1979–March 1989,
using monthly returns of 30 stocks included in the Bombay Stock Exchange Index (Sensex). They found that
the model seems to perform well in explaining returns on the BSE for the period 1979–86. Interestingly, the
relationship between risk and return is not linear as suggested by CAPM. They conclude that the model
may not be rejected on the basis of their findings as the time period studied was limited and the number of
stocks sampled was small. Another recent study suggests that there is a significant relationship between
quarterly portfolio returns and beta.
Criticisms of CAPM
The CAPM is based on certain restrictive assumptions such as investors can borrow and lend at risk-free rate,
etc. Clearly, some of these assumptions are unrealistic. It is not the assumptions that one should question but
the predictive ability of the model. In a CAPM universe, high beta portfolios are supposed to yield high
returns and low beta portfolios should yield low returns. But empirical evidence does not support this
hypothesis, at least for the time period chosen by some researchers. A number of studies have found that
betas of stocks do not adequately explain cross sectional differences in stock returns. Instead, other vari-
ables with no presence in current asset pricing models seem to have a more significant predictive ability than
beta. The most prominent is the size effect noticed by Banz (1981). He finds that market equity adds to the
explanation of the cross section of average returns provided by βs. Average returns on small cap stocks are
too high given their beta estimates and average returns on large stocks are too low. Another contradiction
is the positive relation between leverage and average return. Fama and French (1992) argue that a multi-
dimensional model of risk and return is necessary to explain differences in stock returns. Their model
incorporates company size (as measured by market capitalization), the ratio of book to market value (B.V. of
equity divided by market capitalization).
(^5) Gupta, O P and Sanjay Sehgal (1983). ‘An Empirical Investigation of Capital Asset Pricing Model in India’, Finance
India, Vol. 7, No. 4.