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