Combining the MGHyp distribution with nonlinear shrinkage in modeling financial asset returns

The present paper combines nonlinear shrinkage with the multivariate generalized hyperbolic (MGHyp) distribution, thereby extending a flexible parametric model to high dimensions. An expectation–maximization (EM) algorithm is developed that is fast, stable, and applicable in high dimensions. Theoretical arguments for the monotonicity of the proposed algorithm are provided and it is shown in simulations that it is able to accurately retrieve parameter estimates. Finally, in an extensive Markowitz portfolio optimization analysis, the approach is compared to state-of-the-art benchmark models. The proposed model excels with a strong out-of-sample portfolio performance combined with a comparably low turnover. •Combining the flexible MGhyp distribution with nonlinear shrinkage, enabling estimation in high dimensions.•Providing a monotone Expectation Maximization algorithm that allows for quick estimation even for thousands of assets.•Extensive Markowitz portfolio selection study.•Our proposed methodology provides a high average out-of-sample portfolio return, with low out-of-sample standard deviation and turnover.