Paper: arXiv 2609.11905

Authors: Jaehyung Choi

Abstract

We develop Entropic Value-at-Risk (EVaR) parity for tempered stable returns. EVaR-based inverse risk parity (IRP) and equal risk contribution (ERC) portfolios are constructed using multivariate normal tempered stable models and independent component analysis with tempered stable components. We derive the corresponding asset-level EVaR and EVaR-deviation contributions and use the latter to separate the fitted location term from EVaR risk contributions. Under Gaussian returns, EVaR-deviation IRP and ERC recover conventional volatility IRP and ERC weights. We evaluate the resulting portfolios in three investment universes. Empirically, EVaR-based ERC portfolios achieve positive Sharpe differences relative to equal weight across the universes.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sophisticated framework for EVaR parity using tempered stable distributions, including detailed derivations of risk contributions. It then applies this framework to empirical data across three investment universes, demonstrating practical relevance and positive Sharpe differences. The combination of advanced mathematical modeling with empirical validation places it in the ‘Holy Grail’ quadrant.

Research Flowchart

  flowchart TD
    A[Research Goal: EVaR Parity for Tempered Stable Returns] --> B{Key Methodology: EVaR-based IRP & ERC Portfolios};
    B --> C[Models & Tools: Multivariate Normal Tempered Stable, ICA with Tempered Stable];
    C --> D{Derivations: Asset-level EVaR & EVaR-deviation Contributions};
    D --> E[Computational Process: Portfolio Construction & Optimization];
    E --> F[Data/Inputs: Three Investment Universes];
    F --> G{Key Finding: EVaR-based ERC achieve positive Sharpe differences vs. Equal Weight};
    D -- (Special Case) --> H[Validation: Gaussian returns -> Volatility IRP/ERC];