Do Conditional Covariance Estimates Generate Value?

Abstract

The success of modern portfolio theory critically depends on the use of reliable estimates of the covariance matrix of asset returns. Current statistical theory provides a variety of different models ranging from simple sample estimates to complex multivariate GARCH models to be used in portfolio optimization applications. While it is obvious that different covariance estimates exhibit different statistical properties (depending on the structure of the respective model), it is not so clear what the economic value of these estimates is. The present paper explores this problem by evaluating alternative covariance estimates on the basis of out of sample performance of corresponding minimum variance portfolios (MVP). Using data from four major stock markets we show that conditional covariance estimates based on alternative multivariate GARCH specifications may exhibit significant estimation errors and therefore produce unsatisfactory results evaluated on the basis of sample returns of the MVP. In contrast we find that unconditional covariance estimates generate relatively good results when applied to derive weights for the MVP. We give a theoretical justification for this finding and also compare the value of unconditional covariance estimates to the value of naive diversification.