Tables III and IV report posterior moments for the components of Bay State Gas’s expected excess return under the Fama-French (FF) model and the Connor-Korajczyk (CK) model. In general, the observations made above for the CAPM apply to these three-factor models as well. In particular, Bay State Gas’s a is 5.04% in the FF model and 7.08% in the CK model, but, even with aa as large as 5%, the posterior means for a are only 0.85% and 1.90% in the two models.
Also, the information about A contained in the longer histories of the additional assets has a substantial effect on the estimated cost of equity. For both of the three-factor models, the expected excess return for Bay State Gas based on the longer 1926-95 period is higher than that based on the shorter 1963-95 period by about 1.5% for the FF model and 1.2% for the CK model. When mispricing uncertainty associated with each model is modest, the estimates of expected excess return for Bay State Gas differ substantially across the three models.
The CAPM implies the lowest estimates, which often lie below the estimates from the three-factor models by 2% or more. The FF estimates exceed the CK estimates by more than 1% at the lowest values of aa, but, at aa = 5% the differences between those models are less than 50 basis points. In Section III, we analyze the potential uncertainty about the cost of equity induced by such differenes across models, and we compare that component of uncertainty to the component that arises from uncertainty about the parameters within a given model.
Results for a Broad Cross-Section
For each stock on the NYSE and AMEX having at least 60 months of data continuing through December 1995, we compute the same posterior moments reported for Bay State Gas in Tables II-IV using the stock’s available monthly history back through July 1963. Each value in Tables V-VII is the arithmetic average across those 1,994 stocks of the corresponding value reported in Tables II-IV. As explained earlier, computing the posterior moments for each of these stocks using the Metropolis-Hastings algorithm would be computationally prohibitive. how do payday loans work
Instead, in constructing Tables V-VII we use the approximations to the first and second posterior moments of b discussed in the previous section. The approximations appear to work well. For example, when the values in Tables II-IV are recomputed using the approximations, none of the posterior means and standard deviations change by more than 2 basis points.