Vast Volatility Matrix Estimation Using High-Frequency Data for Portfolio Selection

Abstract

Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of portfolios selection among a vast pool of assets, as demonstrated in Fan et al. (2011). The required high-dimensional volatility matrix can be estimated by using high frequency financial data. This enables us to better adapt to the local volatilities and local correlations among vast number of 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 based on the concept of “refresh time” proposed by Barndorff-Nielsen et al. (2008) for estimation of vast covariance matrix and compare their merits in the portfolio selection. We establish the concentration inequalities of the estimates, which guarantee desirable properties of the estimated volatility matrix in vast asset allocation with gross exposure constraints. Extensive numerical studies are made via carefully designed simulations. 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 for the portfolio allocation in the next time period. The advantage of using high-frequency data is significant in our simulation and empirical studies, which consist of 50 simulated assets and 30 constituent stocks of Dow Jones Industrial Average index.

High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data

“…This property is nevertheless essential to many applications in practice. To enforce it, one possibility consists in projecting the resulting symmetric matrix onto the space of positive semi-definite matrices: see for example an application to portfolio allocation in Fan, Li, and Yu (2010).…”

Modeling and forecasting (un)reliable realized covariances for more reliable financial decisions

“…Daily re-balancing schemes have also previously been employed in a number of studies concerned with volatility-timing strategies (see, e.g., Fleming, Kirby, and Ostdiek, 2003;Fan, Li, and Yu, 2012, among others). In Section 8, we also consider weekly and monthly investment horizons.…”

Generalized optimal wavelet decomposing algorithm for big financial data

“…Pourahmadi (2013) provides a comprehensive introduction of classical and modern approaches for estimating covariance matrices with respect to large correlated datasets. Fan et al (2012) estimate the volatility matrix using big financial data from the perspective of portfolio selection. He et al (2014) suggest an adaptive algorithm to detect changes in monitoring variable data.…”