The plots in Figure 7, for the CAPM versus the CK model, exhibit the highest correlation, but even those plots exhibit more dispersion than any of the top two plots in Figures 1 through 3. That is, the disagreement across models in estimates of expected excess returns appears to be greater than the disagreement within a given model produced by changing the degree of prior mispricing uncertainty (cra) from 0 to 5%.
Also recall that, as aa increases, the estimated expected excess returns from all three models generally move closer to the stock’s historical average excess return. As a result, the closest agreement across models is observed for the plots in which crQ = oo. The agreement in those plots is not perfect, however, due largely to the fact that the sample period used to estimate the factor premiums is longer than the period used to estimate the betas. Thus, the estimated expected excess return still differs from the historical average, and that difference varies across the pricing models.
The disagreements among models can be quantified further by associating a probability with each model and then computing the variance of a given stock’s fi associated with model uncertainty. (Part В of the Appendix provides a more formal treatment.) For each model, the prior and posterior distributions of the parameters in the model are conditioned on that model’s being the appropriate one. If there are Q models under consideration, q = 1,… , Q, let denote the posterior mean of ц obtained under model q, and let irq denote the decision maker’s posterior probability associated with model q. Then, taking the unconditional posterior mean across models, the decision maker ultimately estimates the expected excess return to be
Combining estimates across models occurs in practice. For example, the New York State Public Service Commission has endorsed the use of equal weights across three different models to estimate the cost of equity for public utilities under its supervision. The three models used by the Commission are the CAPM (more precisely, an average of four CAPM-based estimates) and two non-factor-based models—the “Discounted Cash Flows” model and the “Comparable Earnings” model. The commission has also considered the inclusion of multifactor models in estimating costs of equity for public utilities (DiValentino (1994)). one hour payday loans