Paper: arXiv 2611.11803

Authors: Yang Liu, Yuhao Liu, Jiani Shen

Abstract

Traditional risk measures generally rely on a single probability model, potentially overlooking information from alternative models and leading to biased risk assessments. This limitation cannot be addressed by asset diversification alone in risk management. In this paper, we propose a Diversified-Risk-Perception (DRP) risk measure framework that integrates asset diversification and risk model diversification to provide a more comprehensive assessment of market risk while reducing reliance on any single model. First, we introduce a flexible exponential aggregation function to evaluate the risk of a portfolio, which accounts for the contributions of all loss components while placing greater emphasis on large losses. Second, we incorporate multiple risk models in the risk measure and optimize their weights based on their perceptions on the risk assessments. As a specific example, we introduce DRP expected shortfall (DRP-ES), establish its theoretical properties, and derive bounds quantifying its sensitivity to model parameters. Empirical experiments in the U.S., Chinese A-share, and South Korean stock markets show that trading strategies based on the DRP-ES achieve higher Sharpe ratios and lower maximum drawdowns than market benchmarks across different periods. Compared with asset diversification strategies based on individual probability models, the DRP strategy exhibits more stable and robust performance across different markets and periods. These findings suggest that the DRP framework can adapt to changing market conditions and improve the stability and effectiveness of portfolio risk management.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel DRP framework with strong theoretical foundations, including derivations of properties and bounds. It supports its claims with empirical backtesting across multiple markets, demonstrating robust performance. The methodology is clearly outlined, though full reproducibility would benefit from explicit code/data availability.

Research Flowchart

  flowchart TD
    A[Research Goal: Address limitations of single-model risk assessment & improve portfolio risk management] --> B{Proposed DRP Risk Measure Framework};
    B -- Key Components --> C1[Flexible Exponential Aggregation Function: Emphasizes large losses] & C2[Multiple Risk Models Integration: Optimized weights based on perceptions];
    C1 & C2 -- Specific Example & Properties --> D[DRP-Expected Shortfall (DRP-ES): Theoretical properties & sensitivity bounds];
    D -- Empirical Validation --> E[Data/Inputs: U.S., Chinese A-share, South Korean Stock Markets];
    E -- Trading Strategy & Performance Evaluation --> F[Computational Process: Compare DRP-ES strategies with benchmarks & asset diversification strategies];
    F --> G[Key Findings/Outcomes: Higher Sharpe Ratios, Lower Max Drawdowns, More Stable & Robust Performance];
    G -- Implication --> H[DRP framework adapts to market conditions, improves portfolio risk management effectiveness];