Now that we have the matrix of factor variances and covariances, we also want to get values to fill in the matrix of specific variances which contain the variances of the specific returns for each stock. If there are two stocks in the stock universe, then there are two specific risk variances to calculate. Let’s look at the specific risk variants of the first stock. The data to input into the variance is a time series of the specific returns for the stock. The specific return is the residual or the difference from taking the stocks actual return minus the stocks estimated return using the chosen risk factors. So for each time period, we have the actual stock return and can calculate the estimated return based on the chosen risk factors. We can get the estimated return of the stock at each time period by inputting values that we’ve already calculated. The estimated return of the stock for a single time period is a stock’s factor exposure to country USA, multiplied by the factor return of USA for time t, plus the intercept term for time t. This is great. Now we have one data point for the specific return of stock one. We can do the same thing for multiple time periods and get a time series for the specific return of the stock. The variance of this time series is the estimate that we can use in the matrix of specific variances. So now we have all the pieces that go into the BFB transpose and S matrices.