The objective of this paper is to estimate the covariance matrix of stock returns. This is a fundamental question in empirical Finance with implications for portfolio selection and for tests of asset pricing models such as the CAPM. The traditional estimator — the sample covariance matrix — is seldom used because it imposes too little structure. When the number of stocks N is of the same order of magnitude as the number of historical returns per stock T, the total number of parameters to estimate is of the same order as the total size of the data set, which is clearly problematic. When N is larger than.
