Uniform Pessimistic Risk and its Optimal Portfolio

The optimal allocation of assets has been widely discussed with the theoretical analysis of risk measures, and pessimism is one of the most attractive approaches beyond the conventional optimal portfolio model. The $\alpha$-risk plays a crucial role in deriving a broad class of pessimistic optimal portfolios. However, estimating an optimal portfolio assessed by a pessimistic risk is still challenging due to the absence of a computationally tractable model. In this study, we propose an integral of $\alpha$-risk called the \textit{uniform pessimistic risk} and the computational algorithm to obtain an optimal portfolio based on the risk. Further, we investigate the theoretical properties of the proposed risk in view of three different approaches: multiple quantile regression, the proper scoring rule, and distributionally robust optimization. Real data analysis of three stock datasets (S\&P500, CSI500, KOSPI200) demonstrates the usefulness of the proposed risk and portfolio model.