We analyze the effects of model uncertainty using a range of values for aa, the prior within-model mispricing uncertainty, but each value of oa is held constant across models in order to limit the analysis to a manageable number of cases. Many more cases are possible, of course, since a decision maker’s prior uncertainty about a can differ across models. When crQ is (nearly) zero, so that the decision maker essentially believes a priori that a given model prices stocks without error, it seems unreasonable that the same decision maker would still assign non-zero probabilities to other models.
Although a decision maker might know that one of the models is exactly correct—just not which one—such a scenario seems unlikely. In general, uncertainty about which model to use would be accompanied by uncertainty about whether any one model prices all stocks accurately. Since estimates of expected excess return tend to differ less across models as ua increases, as can be seen in Figures 6-8, the values of model uncertainty obtained with equal model probabilities but aa = 0 in each model will, for most stocks, tend to overstate the model uncertainty that would be encountered in practice.
Table VIII reports the model uncertainty about //. as well as the amount of overall uncertainty, which includes the within-model parameter uncertainty. Calculations are reported for the various two-model subsets as well as for the set of all three models. The results are based on the longer 1926-95 period and are computed for the same alternative values of aa used in Section II. All values are reported as annualized percentage standard deviations.
Also shown, for comparison, are (square roots of) the expected values across the three models of the posterior variances of ji, ct, and fi’X. Panel A of Table VIII displays results for Bay State Gas, the individual stock examined previously. Recall from Tables II through IV that, when aa = 0, the estimate for the expected excess return on Bay State’s equity is lowest for the CAPM (3.77%) and highest for the FF model (6.94%). The model uncertainty for that pairing of models is 1.58% (annualized standard deviation), which is the highest value among those for the two-model sets in Panel A of Table VIII. payday loan lenders only