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Robust and reliable covariance estimates play a decisive role in financialand many other applications. An important class of estimators is based onFactor models. Here, we show by extensive Monte Carlo simulations thatcovariance matrices derived from the statistical Factor Analysis model exhibita systematic error, which is similar to the well-known systematic error of thespectrum of the sample covariance matrix. Moreover, we introduce theDirectional Variance Adjustment (DVA) algorithm, which diminishes thesystematic error. In a thorough empirical study for the US, European, and HongKong market we show that our proposed method leads to improved portfolioallocation.

Directional Variance Adjustment: improving covariance estimates for high-dimensional portfolio optimization