Estimating correlation and covariance matrices by weighting of market similarity

Abstract: We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for similarity of previous market conditions to the present one. The resulting estimators are less biased and show lower variance than either unweighted or exponentially weighted estimators. The weighting scheme is based on a similarity measure which compares the current correlation structure of the market to the structures at past times. Similarity is then measured by the matrix 2-norm of the difference of probe correlation matrices estimated for two different times. The method is validated in a simulation study and tested empirically in the context of mean-variance portfolio optimization. In the latter case we find an enhanced realized portfolio return as well as a reduced portfolio volatility compared to alternative approaches based on different strategies and estimators.