The prior mean of a is set equal to zero: in the absence of any observations of the firm’s historical stock performance, the decision maker is viewred as unable to sign the potential mispricing. This assumption about the prior mean of a, although perhaps the most natural, is made for simplicity and is not required by the methodology’. In particular, one could instead set the prior mean of a equal to the average OLS estimate of a for a cross-section of firms writh characteristics similar to the given firm in question, as done with (3. The latter approach would be one way to incorporate the type of characteristics-based pricing effects investigated by Daniel and Titman (1997).
The decision maker is assumed to have “diffuse” prior beliefs about A, the vector of factor premiums. In other words, without observing any past realizations of the factors, the decision maker would have essentially no idea about their expected values. The histories of the factor realizations are often longer than the firm’s return history used in the cost-of-capital estimation. Moreover, additional information about the factor premiums is obtained from variables whose histories are longer than those of the factors. In the one-factor CAPM and the two three-factor models used here, the histories of the factors begin in July 1963, but the returns on the factors are correlated with longer series that provide additional information about the factor premiums.
For example, the Fama-French NYSE-AMEX-Nasdaq market index, which we use as the market factor in the CAPM and in the Fama-French three-factor model, has returns available starting in July 1963, but those returns are highly correlated with the returns on the value-weighted NYSE portfolio, which CRSP supplies beginning in 1926. As shown by Stambaugh (1997), that longer-history series contains additional information about the mean of the shorter-history market factor. For each of the pricing models used here, the cost-of-equity estimates incorporate the additional information about factor means that is contained in three series whose histories begin in January 1926: the value-weighted NYSE portfolio, the equally weighted NYSE portfolio, and the Ibbotson small-stock portfolio (all obtained from CRSP). The remainder of this section provides the details of the methodology. The reader who wishes to proceed directly to the empirical results may skip to Section II.