Comparing Forecasts of Extremely Large Conditional Covariance Matrices

33 Pages Posted: 14 Aug 2018 Last revised: 30 Nov 2019

See all articles by Guilherme V. Moura

Guilherme V. Moura

Universidade Federal de Santa Catarina (UFSC) - Department of Economics

Andre A. P. Santos

Universidade Federal de Santa Catarina (UFSC) - Department of Economics; Universidad Carlos III de Madrid - Department of Statistics and Econometrics

Esther Ruiz

Universidad Carlos III de Madrid - Department of Statistics and Econometrics

Date Written: November 27, 2019

Abstract

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

Moura, Guilherme Valle and A. P. Santos, Andre and Ruiz, Esther, Comparing Forecasts of Extremely Large Conditional Covariance Matrices (November 27, 2019). Available at SSRN: https://ssrn.com/abstract=3222808 or http://dx.doi.org/10.2139/ssrn.3222808

Guilherme Valle Moura

Universidade Federal de Santa Catarina (UFSC) - Department of Economics ( email )

PO Box 476
Florianopolis, SC 88010-970
Brazil

Andre A. P. Santos (Contact Author)

Universidade Federal de Santa Catarina (UFSC) - Department of Economics ( email )

PO Box 476
Florianopolis, SC 88010-970
Brazil

HOME PAGE: http://sites.google.com/site/andreportela

Universidad Carlos III de Madrid - Department of Statistics and Econometrics ( email )

c/ Madrid 126
Getafe (Madrid), 28903
Spain

HOME PAGE: http://sites.google.com/site/andreportela

Esther Ruiz

Universidad Carlos III de Madrid - Department of Statistics and Econometrics ( email )

c/ Madrid 126
Getafe (Madrid), 28903
Spain

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