Paper: arXiv 2303.07158

Authors: Sungchul Hong, Jong-June Jeon

Abstract

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 $α$-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 $α$-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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.0/10 (capped from 7.5: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a mathematically robust uniform pessimistic risk measure using quantile regression, scoring rules, and distributionally robust optimization. It validates the theoretical results with empirical testing across three major equity indices (S&P500, CSI500, KOSPI200), offering both theoretical novelty and practical application.

Research Flowchart

  flowchart TD
    A[Research Goal: Develop tractable pessimistic risk measure & optimal portfolio] --> B[Proposed Methodology: Uniform Pessimistic Risk via integral of α-risk]
    
    B --> C[Theoretical Analysis: Quantile Regression, Scoring Rules & DRO]
    
    D[(Stock Datasets: S&P500, CSI500, KOSPI200)] --> E[Computational Process: Efficient Optimization Algorithm]
    B --> E
    
    C --> F[Key Outcomes: Computationally tractable model & superior empirical portfolio performance]
    E --> F