Factor models for portfolio selection in large dimensions: The good, the better and the ugly - Gianluca De Nard; Olivier Ledoit; Michael Wolf (University of Zurich, Department of Economics, 2018)
This paper injects factor structure into the estimation of time-varying, large-dimensional covariance matrices of stock returns. Existing factor models struggle to model the covariance matrix of residuals in the presence of conditional heteroskedasticity in large universes. Conversely, rotation-equivariant estimators of large-dimensional time-varying covariance matrices forsake directional information embedded in market-wide risk factors. We introduce a new covariance matrix estimator that blends factor structure with conditional heteroskedasticity of residuals in large dimensions up to 1000 stocks. It displays superior all-around performance on historical data against a variety of state-of-the-art competitors, including static factor models, exogenous factor models, sparsity-based models, and structure-free dynamic models. This new estimator can be used to deliver more efficient portfolio selection and detection of anomalies in the cross-section of stock returns.
Keywords: C13; C58; G11; 330; Dynamic conditional correlations; factor models; multivariate GARCH; Markowitz portfolio selection; nonlinear shrinkage