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.

We propose a novel approach to active risk management based on the recent Basel II regulations to obtain optimal portfolios with minimum capital requirements. In order to avoid regulatory penalties due to an excessive number of Value-at-Risk (VaR) violations, capital requirements are minimized subject to a given number of violations over the previous trading year. Capital requirements are based on the recent Basel II amendments to account for the ‘stressed’ VaR, that is, the downside risk of the portfolio under extreme adverse market conditions. An empirical application for two portfolios involving different types of assets and alternative stress scenarios demonstrates that the proposed approach delivers an improved balance between capital requirement levels and the number of VaR exceedances. Furthermore, the risk-adjusted performance of the proposed approach is superior to that of minimum-VaR and minimum-stressed VaR portfolios.