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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