Disentangling the Role of Variance and Covariance Information in Portfolio Selection Problems

Abstract

The covariation among financial asset returns is often a key ingredient used in the construction of optimal portfolios. Estimating covariances from data, however, is challenging due to the potential influence of estimation error involved specially in high dimensional problems, which can impact negatively the performance of the resulting portfolios. We address this question by putting forward a simple approach to disentangle the role of variance and covariance information in the case of mean-variance efficient portfolios. Specifically, mean-variance portfolios can be represented as a two-fund rule: one fund is a fully invested portfolio that depends on diagonal covariance elements whereas the other is a long-short, self financed portfolio depending on off-diagonal elements. We characterize the contribution of each of these two components to the overall performance in terms of out-of-sample returns, risk, risk-adjusted returns, and turnover. Finally, we provide an empirical illustration of the proposed portfolio decomposition using both simulated and real market data.