The capital asset pricing model (CAPM) asserts that, in equilibrium, the expected return on any asset equals the risk-free rate plus a risk premium proportional to the asset’s “beta”—a measure of the asset’s covariance with the market as a whole; any two assets with the same beta will have the same expected return. In particular, the model implies that small firms will command higher risk premiums only if they have higher betas.

In order to test whether premiums that are not explained by beta exist, the author collected aggregate stock market values and returns for firms represented both on the University of Chicago’s CRSP tapes and the Compustat Merged Annual Industrial tape. He ranked all firms in the resulting sample on the basis of their aggregate stock market values. Then he combined the ranked securities into 10 equal-weighted portfolios, all of which turned out to have betas near one. If the simple one-period CAPM is correct, rates of return for these portfolios should approximate the rate of return for the market as a whole.

The author analyzed performance of the resulting portfolios two ways. First, he computed for each of 10 portfolios ranked by size the average over the years from 1962 through 1975 of the rate of return in the year subsequent to formation to determine whether ranking had any effect. The portfolio containing the smallest firms realized average rates of return more than 20 per cent per year higher than those of the portfolio containing the largest firms. Then the author averaged rates of return over the second year following formation of each portfolio. The abnormal returns of the smallest firms persisted at about the same level in the second year after formation as in the first.

The simple one-period CAPM is an inadequate description of the behavior of real world capital markets.