An Empirical Bayes Estimate of Market Risk

Starting with a market model of security returns, we describe how the parameters of a distribution for security characteristics can be estimated in a manner correcting for a subtle but significant source of error. When this error is removed, strong negative correlations between “alpha” and “beta” and between “alpha” and “sigma squared,” and a strong positive correlation between “beta” and “sigma squared” are observed. With this feature in the prior distribution, and with the results of a regression for a particular security, we develop an empirical Bayes estimate of the security's three parameters (alpha, beta and sigma squared) which makes use of more information than other estimates described in the literature.