Worst-Case Higher Moment Coherent Risk Based on Optimal Transport with Application to Distributionally Robust Portfolio Optimization

The tail risk management is of great significance in the investment process. As an extension of the asymmetric tail risk measure—Conditional Value at Risk (CVaR), higher moment coherent risk (HMCR) is compatible with the higher moment information (skewness and kurtosis) of probability distribution of the asset returns as well as capturing distributional asymmetry. In order to overcome the difficulties arising from the asymmetry and ambiguity of the underlying distribution, we propose the Wasserstein distributionally robust mean-HMCR portfolio optimization model based on the kernel smoothing method and optimal transport, where the ambiguity set is defined as a Wasserstein “ball” around the empirical distribution in the weighted kernel density estimation (KDE) distribution function family. Leveraging Fenchel’s duality theory, we obtain the computationally tractable DCP (difference-of-convex programming) reformulations and show that the ambiguity version preserves the asymmetry of the HMCR measure. Primary empirical test results for portfolio selection demonstrate the efficiency of the proposed model.

The risk interdependence of cryptocurrencies: Before and during the COVID-19 pandemic

In this paper, we measure the risk interdependence of 12 major cryptocurrencies before and during the COVID-19 pandemic, based on a GARCH-Copula-VaR approach and a dynamic network analysis. We find that cryptocurrencies generally show high levels of volatility, speculation, homogeneity and tail risk contagion. Furthermore, the COVID-19 pandemic has a continuous impact on the cryptocurrency market. When financial institutions are increasingly investing in crypto assets, the hidden risks in the cryptocurrency market remain high. Therefore, this paper calls for attention on the cryptocurrency market from both investors and regulators.