Comparing High Dimensional Conditional Covariance Matrices: Implications for Portfolio Selection

45 Pages Posted: 14 Aug 2018 Last revised: 20 Apr 2020

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: April 17, 2020

Abstract

Portfolio selection based on high dimensional covariance matrices is a key challenge in data-rich environments with the curse of dimensionality severely affecting most of the available covariance models. We challenge several multivariate Dynamic Conditional Correlation (DCC)-type and Stochastic Volatility (SV)-type models to obtain minimum variance and mean-variance portfolios with up to 1000 assets. We conclude that, in a realistic context in which transaction costs are taken into account, although DCC-type models lead to portfolios with lower variance, modeling the covariance matrices as latent Wishart processes with a shrinkage towards the diagonal covariance matrix delivers more stable optimal portfolios with lower turnover and higher information ratios. Our results reconcile previous findings in the portfolio selection literature as those claiming for equicorrelations, a smooth dynamic evolution of correlations or correlations close to zero.

Keywords: GARCH, Minimum variance portfolio, Mean-variance portfolio, Risk-adjusted returns, Stochastic volatility, Turnover-constrained portfolios

JEL Classification: C53, G17

Suggested Citation

Moura, Guilherme Valle and A. P. Santos, Andre and Ruiz, Esther, Comparing High Dimensional Conditional Covariance Matrices: Implications for Portfolio Selection (April 17, 2020). 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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