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Estimating the Covariance Matrix for Portfolio Optimization

We discuss the estimation of the covariance matrix of stock returns for portfolio optimization and show that for constructing the global minimum variance portfolio (GMVP), there is no statistically-significant gain from using more sophisticated shrinkage estimators instead of simpler portfolios of estimators. We introduce a new "two block estimator," which produces - in an unconstrained optimization - a positive GMVP, that can be found analytically and that is sensitive to even small changes in the covariance matrix. For constructing the GMVP, an example of our new estimator performs at least as well as a combination of imposing the short sale constraints and using the sample matrix.