# COSTS OF EQUITY CAPITAL: Factor Means

The sample statistics in (27) through (30) prove useful in computing the posterior first and second moments of A, which are derived in Part A of the Appendix. The posterior mean

# COSTS OF EQUITY CAPITAL: Posteriors 2

Hence, the conditional posterior distribution for b given a is normal with mean ba and covariance matrix Af-1, so it is easily sampled directly, as noted in the above description of the MH algorithm. Observe that ba is a (matrix) weighted average of the prior mean b and the sample estimate 6, where the weights […]

# COSTS OF EQUITY CAPITAL: Posteriors

The posterior density for the parameters is proportional to the product of the prior density and the likelihood function. Given the factorizations of the likelihood function in (6) and the prior density in (16), the posterior density can also be factored as the posterior for b and cr multiplied by the posterior for в and […]

# COSTS OF EQUITY CAPITAL: Prior Parameters 3

Panel A of Table I reports the parameter values used in the prior constructed from the entire cross-section of stocks. Note that in the CAPM the prior correlation between a and (3 is positive. This occurs in spite of a negative cross-sectional correlation between the sample estimates a and /?, as has been observed in […]

# COSTS OF EQUITY CAPITAL: Prior Parameters 2

The statistics b and a2, computed for each stock, are used to construct the prior parameters 6, V&, Sq, and v. The prior mean of b, 6, is set equal to the cross-sectional average of the b’s, except that the first element, a, is set to zero. The prior covariance matrix of 6, Vb, where […]

# COSTS OF EQUITY CAPITAL: Prior Parameters

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 […]

# COSTS OF EQUITY CAPITAL: Priors 2

The structure of the covariance matrix for b, Ф(сг) in (11), produces a prior that is essentially a hybrid of two more standard alternative priors for the regression model. In one alternative, the normal density for b and the inverted-gamma density for cr2 are independent, so that no part of the covariance matrix for b […]

# COSTS OF EQUITY CAPITAL: Priors

General Specification In the above,