We have redone the calculations for that case and find similar results, except that, not surprisingly, the estimate of the expected excess return is affected even less by a. In other words, for any economically reasonable prior uncertainty about mispricing, the estimate of the expected excess return is very close to the estimate produced by zero prior uncertainty. Also, the uncertainty associated with b rises somewhat for most stocks. Although we could have just as easily reported those results, we find the longer-period results, especially those involving a, to be more interesting. Another approach that might be a fruitful direction for research would be to reformulate the Bayesian model to allow changes in b. In a frequentist setting, for example, Shanken (1990) specifies b to be a linear function of observable state variables. Fama and French (1997) implement such a procedure by letting an industry’s betas depend on its size and book-to-market ratio.
An Industry-Specific Approach: Utilities
For the 135 utilities having at least 60 months of data continuing through December 1995, we compute the posterior moments in the same manner as above, except that the prior is constructed using the cross-section of utilities instead of the all-stock cross-section (as explained in Section I.C.2). These two priors result in different estimated expected excess returns for the 135 utilities. Figure 4 plots, for each model and for aa = 3% and aa = 5%, the estimates of expected excess returns obtained with one prior versus those obtained with the other. Although the plots exhibit strong positive associations, and the ranges of estimates are similar for both priors, it is also clear that the differences between the two priors can produce non-trivial differences in estimated costs of equity.
Compared to the averages for the broad cross-section, the average posterior means of ji for the utilities are smaller, ranging roughly from 5% to 8%. (In the interest of space, we present only a brief summary of the results corresponding to those reported in Tables V through VII.) As before, the CAPM estimates are on average the smallest, and the FF estimates are the largest. The posterior standard deviations of ц are also smaller than their counterparts in the broad cross-section, by a factor of roughly two.
This lower uncertainty about the expected excess return for utilities is due both to lower average betas and to lower posterior standard deviations of the betas. For example, the average posterior mean of the CAPM betas for utilities is only about 0.57, which is less than the average of 1.01 for the broad cross-section, and the average posterior standard deviation of the CAPM betas is only 0.07, which is less than half the corresponding value of 0.16 for the broad cross-section.