Substituting this relation in the basic equation, we find that:
(8.17)(8.18)Using the matrix algebra formula for variance, the risk equation becomes:
Risk = XFXT+ ∆ (8.19)where X= exposure matrix of companies upon factors
F= covariance matrix of factors
XT= transpose of Xmatrix
∆= diagonal matrix of specific risk variances
This is the basic equation that defines the matrix calculations used in risk
analysis in the BARRA equity models.
Let us address some of the estimated earnings forecasting components of
the CTEF model discussed earlier in the chapter for the Russell 3000 uni-
=+Var(Xf u ̃ ̃)Risk Var= (r ̃j)222 THE USE OF FINANCIAL INFORMATION IN THE RISK AND RETURN OF EQUITY
FIGURE 8.2 The BARRA Multiple-Factor Structure