A basic feature of the Bayesian approach is that a decision maker’s judgment, represented by prior beliefs, enters the estimation in a manner guided by a scientific principle (Bayes’s theorem) as opposed to more ad hoc methods. As discussed above, one aspect of the decision maker’s judgment that we can explore is uncertainty about whether a pricing model can deliver the precise expected excess return for a given stock. We find that, in many cases, mispricing uncertainty that seems important in economic terms does not impact greatly the estimated cost of equity. That is, the posterior mean of ц is close to the posterior mean obtained when mispricing is ruled out, even when the sample least-squares estimate of a departs significantly from zero. Suppose one’s prior beliefs are that the stock of interest is typical in terms of its betas and its variance of et. Then, wrhen the prior standard deviation of a is 5% per annum, as in the above example, the estimated cost of equity is less than 1% (per annum) above the CAPM value, even though the sample estimate of a is nearly 8% and its i-statistic exceeds two. In this sense, a pricing model that might be viewed by the decision maker as being only mediocre in its ability to price stocks accurately is still relied upon fairly heavily in estimating the cost of equity.
This study investigates factor-based models with a focus on the estimates they produce rather than on their asset-pricing abilities versus each other or versus non-factor-based approaches. Even though the latter issues continue to invite debate in the academic literature, we suggest that these factor-based models have received sufficient interest to merit investigating their potential use by decision makers. Three pricing models are used to illustrate our approach. The first is the CAPM, where the single factor is specified to be the excess return on a market index portfolio. The second model, proposed by Fama and French (1993), contains that market factor plus two additional factors: the difference in returns between small and large firms and the difference in returns between firms with high and low ratios of book value to market value. The third model also has three factors, but, instead of prespecifying them, we extract them from returns on a large cross-section of stocks using the asymptotic principal components method of Connor and Korajczyk (1986).