Comparing Forecasts of Extremely Large Conditional Covariance Matrices
33 Pages Posted: 14 Aug 2018 Last revised: 30 Nov 2019
Date Written: November 27, 2019
Modelling and forecasting high dimensional covariance matrices is a key challenge in data-rich environments involving even thousands of time series since most of the available models suffer from the curse of dimensionality. In this paper, we challenge some popular multivariate GARCH (MGARCH) and Stochastic Volatility (MSV) models by fitting them to forecast the conditional covariance matrices of financial portfolios with dimension up to 1000 assets observed daily over a 30-year time span. The time evolution of the conditional variances and covariances estimated by the different models is compared and evaluated in the context of a portfolio selection exercise. We conclude that, in a realistic context in which transaction costs are taken into account, modelling the covariance matrices as latent Wishart processes delivers more stable optimal portfolio compositions and, consequently, higher Sharpe ratios.
Keywords: Covariance forecasting, GARCH, Minimum-variance portfolio, Portfolio turnover, Risk-adjusted return, Stochastic volatility
JEL Classification: C53, G17
Suggested Citation: Suggested Citation