title: Directional variance adjustment: bias reduction in covariance matrices based on factor analysis with an application to portfolio optimization.
abstract: 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 stock market we show that our proposed method leads to improved portfolio allocation.
authors.affiliation: Machine Learning Group, Computer Science Department, Technical University of Berlin, Berlin, Germany. daniel.bartz@tu-berlin.de
authors.forename: Daniel
authors.initials: D
authors.lastname: Bartz
authors.forename: Kerr
authors.initials: K
authors.lastname: Hatrick
authors.forename: Christian W
authors.initials: CW
authors.lastname: Hesse
authors.forename: Klaus-Robert
authors.initials: KR
authors.lastname: Müller
authors.forename: Steven
authors.initials: S
authors.lastname: Lemm
mesh_terms: D000465:Algorithms; D015982:Bias; D003198:Computer Simulation; D005163:Factor Analysis, Statistical; D016013:Likelihood Functions; D015233:Models, Statistical; D009010:Monte Carlo Method