This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing estimators: the sample covariance matrix and single-index covariance matrix. This method is generally known as shrinkage, and it is standard in decision theory and in empirical...

The central message of this paper is that nobody should be using the sample covariance matrix for the purpose of portfolio optimization. It contains estimation error of the kind most likely to perturb a mean-variance optimizer. In its place, we suggest using the matrix obtained from the sample...

The goal of this paper is to estimate time-varying covariance matrices. Since the covariance matrix of financial returns is known to change through time and is an essential ingredient in risk measurement, portfolio selection, and tests of asset pricing models, this is a very important problem in...

The central message of this paper is that nobody should be using the sample covariance matrix for the purpose of portfolio optimization. It contains estimation error of the kind most likely to perturb a mean-variance optimizer. In its place, we suggest using the matrix obtained from the sample...

The central message of this paper is that nobody should be using the sample covariance matrix for the purpose of portfolio optimization. It contains estimation error of the kind most likely to perturb a mean-variance optimizer. In its place, we suggest using the matrix obtained from the sample...

The goal of this paper is to estimate time-varying covariance matrices. Since the covariance matrix of financial returns is known to change through time and is an essential ingredient in risk measurement, portfolio selection, and tests of asset pricing models, this is a very important problem in...

The goal of this paper is to estimate time-varying covariance matrices. Since the covariance matrix of financial returns is known to change through time and is an essential ingredient in risk measurement, portfolio selection, and tests of asset pricing models, this is a very important problem in...

Many statistical applications require an estimate of a covariance matrix and/or its inverse. When the matrix dimension is large compared to the sample size, which happens frequently, the sample covariance matrix is known to perform poorly and may suffer from ill-conditioning. There already...

Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or even larger. In such settings, there is a common remedy for...

Markowitz (1952) portfolio selection requires estimates of (i) the vector of expected returns and (ii) the covariance matrix of returns. Many successful proposals to address the first estimation problem exist by now. This paper addresses the second estimation problem. We promote a nonlinear...