Forecasting Large Stochastic Covariance Matrices
31 Pages Posted: 14 Aug 2018
Date Written: July 30, 2018
Modeling and forecasting high dimensional covariance matrices is a key challenge in data-rich environments. Most of the available multivariate stochastic volatility (MSV) models suffer from the curse of dimensionality since the number of parameters often increases exponentially as the cross-section dimension grows, which brings difficulties for practical applications involving hundreds or thousands of time series. We tackle this problem by considering a MSV specification that is particularly suitable for very high dimensional applications. Dynamic covariance matrices are treated as Wishart processes, respecting positive definiteness, and their parameterization does not increase with the number of time series analyzed. In particular, the MSV model considered in the paper is able to model and forecast time-varying conditional covariance matrices by estimating only one single parameter. A large scale portfolio selection exercise with up to 1000 assets over a 30-year time span reveals that the MSV model delivers more stable optimal compositions and outperform on an out-of-sample basis a number of alternative benchmarks in terms of risk-adjusted returns even when using moderate levels of transaction costs.
Keywords: covariance forecasting, mean-variance optimization, portfolio turnover, risk-adjusted returns
JEL Classification: C53, G17
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