This is why, in this paper, we study another way of imposing factor structure. It is to take a weighted average of the sample covariance matrix with Sharpe’s (1963) single-index model estimator. The weight ® (between zero and one) assigned to the single-index model controls how much structure we impose: the heavier the weight, the stronger the structure. This is a well-known technique in Statistics called shrinkage dating back to Stein (1956): ® is called the shrinkage intensity, and the single-index model is our choice of shrinkage target. The advantages are that there is strong consensus on the nature of the single factor (a market index), and.
