Exponential Weighting and Random-Matrix-Theory-Based Filtering of Financial Covariance Matrices for Portfolio Optimization

摘要

We introduce a covariance matrix estimator that both takes into account theheteroskedasticity of financial returns (by using an exponentially weightedmoving average) and reduces the effective dimensionality of the estimation (andhence measurement noise) via techniques borrowed from random matrix theory. Wecalculate the spectrum of large exponentially weighted random matrices (whoseupper band edge needs to be known for the implementation of the estimation)analytically, by a procedure analogous to that used for standard randommatrices. Finally, we illustrate, on empirical data, the superiority of thenewly introduced estimator in a portfolio optimization context over both themethod of exponentially weighted moving averages and the uniformly-weightedrandom-matrix-theory-based filtering.