Modelling and forecasting high dimensional covariance matrices is a key challenge in data-richenvironments involving even thousands of time series since most of the available models sufferfrom 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 conditionalcovariance matrices of financial portfolios with dimension up to 1000 assets observed daily over a30-year time span. The time evolution of the conditional variances and covariances estimated bythe different models is compared and evaluated in the context of a portfolio selection exercise. Weconclude that, in a realistic context in which transaction costs are taken into account, modelling thecovariance matrices as latent Wishart processes delivers more stable optimal portfolio compositionsand, consequently, higher Sharpe ratios.Guilherme V. Moura is supported by the Brazilian Government through grants number 424942-
2016-0 (CNPQ) and 302865-2016-0 (CNPQ). André A.P. Santos is supported by the Brazilian
Government through grants number 303688-2016-5 (CNPQ) and 420038-2018-3 (CNPQ). Esther
Ruiz is supported by the Spanish Government through grant number ECO2015-70331-C2-2-R
(MINECO/FEDER)
