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In an economy in which returns are Gaussian and independent; and in which standard
deviation risk is priced; and in which investors hold portfolios similar to the sum
portfolio, it can be shown that investors will only price the additive component of
standard deviation risk (called the systematic risk) of a risky asset. The remainder of the
risk, called 'diversifiable risk', simply cancels out on addition to the sum portfolio.
The only economic theory we have used so far are: (1) standard deviation risk is priced in
the economy, (2) the sum portfolio is observable, and (3) investors hold well diversified
portfolios similar to the sum portfolio. It is therefore only these aspects of the theory that
may be put to empirical tests.
Let us now examine the Fama and French (1992) paper in some detail. The authors
collect beta and returns data over a moving window of time from 1962 to 1989 and find
no relationship between beta and returns. We would expect to see such a relationship
only if the market volatility Sm were constant. This is not the case. Therefore no
conclusion may be drawn from their test.
The real question is whether standard deviation risk is priced. And corollary questions;
are how should the standard deviation be measured? and is the S&P500 index an
adequate proxy for the sum portfolio?
When Fama and French (1992) removed the size effect from the data they may have also
removed that which they intended to measure - the beta effect. A failure to find a beta
effect in the residuals of the size effect does not imply an absence of a beta effect. There
are better ways to find the unique contributions of the two correlated variables. For
example, one might first regress beta against size and use these residuals as the unique
contribution of beta and then regress size against beta and use those residuals as the
unique contribution of size. Alternately, one might look for orthogonal principal
components of size and beta.
An added complication in asset pricing research is that some of the empirical models
include the PE ratio (PE = stock price over accounting earnings) as an explanatory
variable in addition to the risk measure beta. But PE too contains a risk measure. Current
financial theory interprets PE as a combination of two effects. Ceteris paribus higher
perceived risk would lower the PE ratio and higher perceived growth would raise the PE
ratio. Empirical studies are complicated by a high collinearity between PE and beta.
There are other problems with asset pricing studies that have to do with the time series
nature of the data and the methods by which the concept of risk is rendered and we
review these concerns in a later section of this paper.
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just as good as multifactor apt)
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