Vast-Dimensional Asset Return Covariances

High-frequency data open up new and more efficient ways to estimate daily asset return volatilities and covariances. Hautsch and Podolskij (2010) provide new theoretical results and empirical evidence on the performance of various state-of-the-art estimators.

A still challenging task is the estimation and prediction of covariance matrices covering potentially several hundreds of assets, as required, e.g., in portfolio management, risk management and asset pricing. Moreover, today’s practitioners often need to manage the risk of portfolio positions over comparably short horizons, such as, a day, a week or a month while requiring well conditioned and numerically stable covariance estimates. Hautsch, Kyj and Oomen (2010) introduced an estimator for vast-dimensional covariances which is consistent, positive definite and well-conditioned while it exploits high-frequency data in a more efficient way than prevailing approaches. The fundamental idea is to overcome the efficiency loss stemming from required data synchronization by estimating the covariance matrix block-wise and imposing a regularization scheme in a second step. It is shown that the blocking approach induces significant efficiency gains which translate into better portfolio allocations.

Hautsch, Kyj and Malec (2011) build on this technique and address the open question to which extent high-frequency data are ultimately useful when it comes to the prediction of large-scale covariances. They propose a forecasting model based on a multi-scale spectral decomposition of covariance matrices where volatilities, correlation eigenvalues and eigenvectors evolve on different frequencies. In an extensive out-of-sample forecasting study, they show that the proposed approach yields less risky and more diversified portfolio allocations as prevailing methods employing daily data.

Selected Publications