High-Frequency Covariance Matrix Estimation Using Price Durations

Abstract

We propose a price duration based covariance matrix estimator using high frequency transactions data. The effect of the last-tick time-synchronisation methodology, together with effects of important market microstructure components is analysed through a comprehensive Monte Carlo study. To decrease the number of negative eigenvalues produced by the non positive-semi-definite (psd) covariance matrix, we devise an average covariance estimator by taking an average of a wide range of duration based covariance matrix estimators. Empirically, candidate covariance estimators are implemented on 19 stocks from the DJIA. The duration based covariance estimator is shown to provide comparably accurate estimates with smaller variation compared with competing estimators. An out-of-sample GMV portfolio allocation problem is studied. A simple shrinkage technique is introduced to make the sample matrices psd and well-conditioned. Compared to competing high-frequency covariance matrix estimators, the duration based estimator is shown to give more stable portfolio weights and higher Sharpe ratios while maintaining comparably low portfolio variances.

Keywords: Price Durations, Covariance Estimation, High-Frequency Data, Market Microstructure Noise, Minimum Variance Portfolio

JEL Classification: C41, C14, C13, C58