COSTS OF EQUITY CAPITAL: Introduction 4

Uncertainty about which of the three factor-based models to use can contribute non-trivially to a decision maker’s overall uncertainty about the cost of equity, but this source of uncertainty is typically less important than the parameter uncertainty within any given model. For example, when each model is assigned an equal probability of being the “correct” one, we obtain an overall posterior standard deviation for the cost of equity of 5% or more per year, depending on the prior uncertainty about a, but that value is typically no more than 0.75% above the posterior standard deviation of ^ obtained within any single model.

Uncertainty about /3 contributes substantially to the overall uncertainty about the cost of equity for an individual firm, but somewhat more important is the uncertainty about A, the vector of factor premiums. Fama and French (1997) estimate expected returns for industry portfolios using both the CAPM as well as the Fama-French (1993) three-factor model. Based on frequentist standard errors, they conclude that by far the largest source of imprecision in industry costs of equity arises from estimation of A. Ferson and Locke (1997), also in a frequentist setting, examine sources of error in CAPM-based estimates of expected returns on portfolios of stocks grouped by industry or market capitalization. They similarly conclude that errors in /5 are likely to be less important than errors in estimating the market premium. Although uncertainty about /3, not surprisingly, is more important for individual firms than for portfolios, our conclusion regarding the importance of uncertainty about A is otherwise similar to the conclusions of these studies. In all three of the models, the histories of the factors are available beginning in July 1963, but the factors are correlated with other series whose histories begin earlier. As a result, the longer-history series contain additional information about A, as discussed by Stambaugh (1997). We find that, in the absence of uncertainty about mispricing, uncertainty about A remains the most important source of uncertainty about a firm’s cost of equity, even after incorporating information about A that is contained in series whose histories begin in 1926.