Econometric Analysis of Vast Covariance Matrices Using Composite Realized Kernels and Their Application to Portfolio Choice

We propose a composite realized kernel to estimate the ex-post covariation of asset prices. These measures can in turn be used to forecast the covariation of future asset returns. Composite realized kernels are a data-efficient method, where the covariance estimate is composed of univariate realized kernels to estimate variances and bivariate realized kernels to estimate correlations. We analyze the merits of our composite realized kernels in an ultra high-dimensional environment, making asset allocation decisions every day solely based on the previous day's data or a short moving average over very recent days. The application is a minimum variance portfolio exercise. The dataset is tick-by-tick data comprising 437 U.S. equities over the sample period 2006-2011. We show that our estimator is able to outperform its competitors, while the associated trading costs are competitive.