i (2)The framework introduced here allows a decision maker to adjust a stock’s estimated expected excess return away from the value implied by a pricing model and toward the historical average excess return on the firm’s stock (since the posterior mean of a is adjusted away from zero and toward the OLS intercept a). That is, instead of either taking the strict implication of a pricing model or completely abandoning the model in favor of the simpler historical average return, the decision maker can combine those estimates

The weight on the historical average essentially depends, for a given sample length, on the decision maker’s prior uncertainty about the model’s mispricing (aa) and his prior expectation of the stock’s residual variance (Е(<т2)). If the stock is a priori judged likely to possess average residual variance, and if the prior mispricing uncertainty is, say, less than 5% per annum, then the weight on the stock’s historical average return is low. In such a case, even if the mispricing uncertainty seems substantial in economic terms, the traditional use of the pricing model— taking its exact implication as the cost-of-equity estimate—generally yields a reasonably close approximation to the posterior mean. Of course, that simpler estimate does differ somewhat from the posterior mean, and the latter can be computed using our methodology.

There are scenarios in which even those who favor simpler methods might be advised to estimate the cost of equity using our Bayesian approach. Adjusting the cost-of-equity estimate toward the stock’s historical average return becomes more important when one believes a priori that the stock’s residual variance is lower than that of the typical stock. The weight on the historical average return is generally decreasing in E(cr2).

Therefore, when the stock’s characteristics lead one to assign a lower prior mean for cr2, the cost-of-equity estimate should place less weight on the traditional pricing-model estimate and more weight on the average return. Such a scenario is illustrated in this study for the case of utility stocks.

In such a scenario, if it happens that the historical average return for the stock of interest is far from the pricing model’s prediction, and if the sample generating that estimate is fairly long, then the information contained in the stock’s historical average excess return should probably be incorporated, even for modest values of aa. Our framework provides a method for doing so.