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
where “tr” denotes the trace operator. When S = L, A in (31) simplifies to the vector of sample means of the factors over the S periods. That is, the more common estimate of the factor premia arises as a special case of our estimate when no longer-history asset returns are included in the estimation.
Cost of Equity
Recall that the stock’s expected excess return is given by
Once we have obtained the posterior first and second moments of A and b, it is straightforward to compute the first and second moments of ц, since the posterior distributions of those parameters are independent. As noted at the outset, the decision maker’s estimate of the expected excess return is the posterior mean of ц, which, given the independence of A and