Performance analysis of minimum variance asset allocation with high frequency data

We investigate the asset allocation optimization under the time-varying high frequency global minimum variance portfolio framework. The overall performance strongly relies on the estimate of the portfolio covariance matrix. However, for such applications, the sample size is often of similar order to the number of assets and in this case, the performance of the conventional covariance estimators are not very satisfactory. Additionally, the time variation effects will further amplify the estimation error and thus lead to inaccurate and high-risk investment decisions. In this paper, we propose to use the recently developed time variation adjusted realized covariance (TVARCV) estimator in a shrinkage structure, in order to address the above-mentioned problems. For this shrinkage TVARCV estimator, we provide a deterministic characterization of the portfolio realized risk in terms of the shrinkage parameter and the covariance matrix. At last, aiming to minimize the portfolio risk with respect to the shrinkage parameter, we also provide a consistent estimator for the realized variance, which depends only on the observable returns. Numerical results show that the proposed estimator is robust to time variation and has smaller portfolio risk.