Vast Volatility Matrix Estimation using High Frequency Data for Portfolio Selection
Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of selected portfolios among a vast pool of assets, as demonstrated in Fan, Zhang and Zhang (2008). The required high-dimensional volatility matrix can be estimated by using high frequency financial data. This enables us to better adapt the local volatilities and local correlations among vast assets and to increase significantly the sample size for estimating the volatility matrix. This paper studies the volatility matrix estimation using high-dimensional high-frequency data from the perspective of portfolio selection. Specifically, we propose the use of ``pairwise-refresh time" and ``all-refresh-time" methods for estimation vast covariance matrix and compare their merits in the portfolio selection. We also establish the large deviation results of the estimates, which guarantee good properties of the estimated volatility matrix in vast asset allocation with gross exposure constraints. Extensive numerical studies are made via carefully designed simulation studies. Comparing with the methods based on low frequency daily data, our methods can capture the most recent trend of the time varying volatility and correlation, hence provide more accurate guidance of the portfolio allocation of the next time period. The advantage of use high-frequency data is significant in our simulation and empirical studies, which consist of 30 Dow-Jones industrial stocks.