We propose a novel framework for modeling large dynamic covariance matrices via heterogeneous autoregressive volatility and correlation components. Our model provides direct forecasts of monthly covariance matrices and is flexible, parsimonious and simple to estimate using standard least squares methods. We address the problem of parameter estimation risks by employing nonlinear shrinkage methods, making our framework applicable in high dimensions. We perform a comprehensive empirical out-of-sample analysis and find significant statistical and economic improvements over common benchmark models. For minimum variance portfolios with over a thousand stocks, the annualized portfolio standard deviation improves to 8.92% compared to 9.75–10.43% for DCC-type models.

We consider the problem of maximizing the out-of-sample Sharpe ratio when portfolio weights have to be estimated. We apply an improved bootstrap-based estimator, and an approximative estimator derived from a Taylor series. In a simulation study and empirical analysis with 15 datasets the proposed estimators outperform the minimum variance and equally weighted portfolio strategies. Out-of-sample Sharpe ratios improve by 15 and 32 percent on average, respectively, in the empirical analysis. While effectively dealing with estimation risks, the estimators produce considerable amounts of turnover. Realized net Sharpe ratios improve by 40 percent on average when the effects of accruing transaction costs are incorporated ex-ante into estimation of portfolio weights. When adding a risk-free asset, net Sharpe ratios remain of the same magnitude and portfolio volatility does not exceed a predefined target level.