We construct prior distributions using two specifications for the cross-section of stocks. The first cross-section consists simply of all stocks on the NYSE and AMEX (subject to a data-availability requirement detailed below). In this first specification, which is used throughout much of our analysis, the stock to be analyzed is essentially viewed as a random draw from the universe of all stocks. Although this approach strikes us as a reasonable starting point, at least for our exploratory study, it is only one of many methods that might be used to specify the prior. In a statistical sense, the normal-inverted-gamma prior in (9) and (10) is generally characterized as “informative” as opposed to diffuse (non-informative), but this first specification of the prior does not rely on specific knowledge about the firm. In an economic sense, therefore, this prior is rather uninformative. In contrast, our second cross-section of stocks consists solely of utilities, so the prior thereby constructed can be viewed as economically informative. In other words, the prior incorporates knowledge of a characteristic—industry classification—of the firm whose cost of equity is to be estimated.
The cross-sectional moments of b and a2 are not directly observable. We take an empirical-Bayes approach and estimate those moments using values of b and a2 computed for a large cross-section. Fama and French (1997) apply a similar methodology, following Blattberg and George (1991), in computing shrinkage estimates of (3 for industry portfolios. The first prior, based on the broad cross-section, is constructed as follows. For each stock in the CRSP monthly NYSE-AMEX file with at least 24 months of data in the period from July 1963 through December 1995, we compute b and a2 using all of that stock’s available data during that period. The stock returns are in excess of the return on a one-month Treasury bill (from CRSP’s SBBI file).
For the CAPM and the Fama-French (1993) three-factor model (hereafter the FF model), the factor data begin in July 1963 and consist of monthly realizations of three factors: (i) the excess return on a market-index portfolio of NYSE, AMEX, and Nasdaq stocks, (ii) the difference in returns between a small-stock portfolio and a large-stock portfolio, and (iii) the difference in returns between a portfolio of high book-to-market (B/M) stocks and a portfolio of low B/M stocks. Only the first of these factors is used in the CAPM.
To construct the three factors for the Connor-Korajczyk (1986) model (hereafter the CK model), we take all stocks with at least one year of data on the NYSE-AMEX monthly CRSP file for the 7/63-12/95 period and then extract one set of factors for that entire period using the method in Connor and Korajczyk (1987) that allows for missing observations.