Random matrix approach to minimum variance portfolio optimization with high frequency data

Abstract

In modern portfolio theory, the accuracy and robustness of the covariance estimator plays a critical role in defining the performance of the optimized portfolios. Traditional estimators such as the sample covariance matrix usually perform poorly when the number of observed daily returns is comparable to the number of assets. Moreover, the strong non-stationary effects will further amplify estimation errors and lead to inaccurate investment decisions. High frequency data allows one to consider a short enough history such that the covariance matrix remains relatively unchanged, whilst still potentially offering sufficient historical samples for accurate estimation. However, the use of sparse sampling to account for the microstructure noise places a restriction on the maximum number of intraday observations. The well-known realized covariance estimator for high frequency data will still perform poorly due to estimation errors, and it does not provide sufficient robustness with respect to unknown time-variation. The limited sample and complexity in handling time-variation further make previous works only focused on small number of assets. To address the issues caused by limited sample and time variation effects, in this thesis, we aim to design novel high frequency estimation techniques for optimizing large portfolios in the presence of unknown time variation, and for practical conditions in which the number of observed samples is of similar order to the number of assets. We focus on asset allocation optimization under high frequency global minimum variance portfolio framework. A key challenge is to develop suitably optimized covariance estimators for the portfolio optimization problem. For this purpose, we propose a new method based on using the recently developed time variation adjusted realized covariance (TVARCV) estimator in a shrinkage structure. The shrinkage parameter is difficult to optimize when considering both the limited sample and time variation effects. For this shrinkage TVARCV estimator, we provide a deterministic characterization of the realized portfolio risk in terms of the shrinkage parameter and the covariance matrix. Our main result is the proposal of a novel optimized covariance matrix estimator, designed to yield minimal realized portfolio risk, and which depends only on the observable returns. Numerical results show that the proposed estimator is robust to time variation and has a smaller realized portfolio risk compared with other benchmark estimators. Superior performance based on real financial data is also demonstrated.

Date of Award	2013
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology