  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.
