three steps: Step 1 Generate an estimate of each specific return variance using the exponential model described above. This results in N variance estimates where s2(t I t -1) represents the Kth estimate. Step 2 Compute the average specific return variance estimate (taken over all N assets). Denote this value by s£{t). Step 3 The estimate of specific risk is given by a weighted combination of s2n(t I t - 1) and s2(t). In other words, we shrink each specific return variance computed in the first step to the average specific return. b1n(t\t-l)={l-1)sl(t\t-l) + rs1Jt)Q<1<l (20.42) where y is the shrinkage parameter. On average, large-cap stocks tend to have smaller specific volatilities than smaller-cap stocks. Consequently, we observe the specific volatilities of large-cap stocks falling below the sample average-that includes both large and smaller-cap stocks-and the specific volatility estimator presented in (20.42) would tend to increase the specific volatilities of large-cap stocks and reduce the specific volatilites of smaller-cap stocks. In order to minimize the effect that (20.42) has on the specific volatility of large-cap stocks, we can modify it so that it applies only to assets whose specific volatilities are greater than the average, s2(t). In this case, (20.42) becomes b2{t\t_1) = \^-^n{t\t-l) + fsi{t) lisl(t\t-l)>Sl(t) \sl(t\t-l) )i£{t\t-\)<%{t) and 0 < y < 1 When estimating a specific returns covariance matrix, there are numerous practical issues that arise. Among them are: 11 New assets may not have enough historical return data to estimate specific returns. Reasons for this may include initial public offerings (IPOs) and mergers/spin-offs. In this case, using some average of specific variances as a proxy may be reasonable. II Specific variances may exhibit extreme outliers, to the extent that they dominate risk analysis. In this case, a large value of the shrinkage parameter may be required to mitigate the effect of such outliers on the resulting risk estimates. II Specific return variances may be excessively volatile over time. This concludes our discussion on estimating the covariance matrices of returns based on factor models. Next, we turn our attention to global equity factor models.