# COSTS OF EQUITY CAPITAL: Introduction 2

In the presence of mispricing uncertainty, a decision maker might wish to combine a cost-of-equity estimate produced by a pricing model with an alternative estimate, such as the stock’s historical average return. Suppose for example that, apart from any empirical evidence, a manager believes that there is a one-third probability that the difference between his stock’s expected return and the value implied by the CAPM is at least 5% per annum in absolute value. In other words, the manager’s “prior” standard deviation for his stock’s a is about 5%. Given this degree of skepticism in the accuracy of the pricing model, how much attention should the manager pay to the historical average return on the firm’s stock when estimating the firm’s equity cost of capital? Specifically, suppose that, based on the last twTo decades, the firm’s stock has a sample estimate of its CAPM a equal to 8% per annum with a /-statistic greater than two. To what extent should this skeptical manager make use of that historical information? With complete faith in the CAPM, such information would be ignored—only the market risk premium and the stock’s beta would be used in estimating the cost of equity. With an extreme degree of uncertainty about the model’s accuracy, one might simply ignore the CAPM and estimate the firm’s cost of equity as the stock’s historical average rate of return, wThich wrould be 8% higher than the CAPM value. We explore solutions to this problem with intermediate degrees of mispricing uncertainty, as in the example given here.

We develop and apply a method for estimating the cost of equity using a Bayesian approach. In this setting, the decision maker does not know the true expected excess return but instead uses the conditional expectation Е(гг|Ф), where Ф denotes the information available at the time of the decision. We assume that excess returns have constant mean /i, so the decision maker’s estimate for the expected excess return is then simply the posterior mean of fj, given Ф, and the decision maker’s uncertainty about the cost of equity is reflected in the posterior variance of ц. As Cornell, Hirshleifer, and James (1997) conclude, “judgment enters the process at numerous points,” regardless of the method used to estimate the cost of capital.