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 the similarity of previous market conditions to the present situation. 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 that 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 points in time. 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 risk compared with alternative approaches based on different strategies and estimators.

• Portfolio optimization
• Correlation structures
• Time series analysis
• Market dynamics

JEL Classification::

• C1
• C6
• C13
• C61
• D4
• G1
• G11

Acknowledgement

We acknowledge financial support from Studienstiftung des deutschen Volkes (M.C.M.) and Deutsche Forschungsgemeinschaft under grant No. SCHA 1462/1-1 (R.S.).

Notes

†See, for example, the cover story of Bloomberg Businessweek, March 12, 2007: What the market is telling us.