Muirhead (1987) reviews the large literature on shrinkage estimators of the covariance matrix in finite-sample statistical decision theory. All these estimators suffer from at least two severe drawbacks, either of which is enough to make them ill-suited to stock returns: (i) they break down when N T; (ii) they do not exploit the a priori knowledge that stock returns tend to be positively correlated to one another. Frost and Savarino (1986) show that the solution to the second problem is to use a shrinkage target that incorporates a market factor, but they ignore without justification the correlation between estimation error on the shrinkage target and on.
