Paper: arXiv 2604.02126

Authors: Adele Ravagnani, Mattia Chiappari, Andrea Flori, Piero Mazzarisi, Marco Patacca

Abstract

Shorting for hedging exposes to risk when the market dynamics is uncertain. Managing uncertainty and risk exposure is key in portfolio management practice. This paper develops a robust framework for dynamic minimum-variance hedging that explicitly accounts for forecast uncertainty in volatility estimation to achieve empirical stability and reduced turnover, further improving other standard performance metrics. The approach combines high-frequency realized variance and covariance measures, autoregressive models for multi-step volatility forecasting, and a box-uncertainty robust optimization scheme. We derive a closed-form solution for the robust hedge ratio, which adjusts the standard minimum-variance hedge by incorporating variance forecast uncertainty. Using a diversified sample of equity, bond, and commodity ETFs over 2016-2024, we show that robust hedge ratios are more stable and entail lower turnover than standard dynamic hedges. While overall variance reduction is comparable, the robust approach improves downside protection and risk-adjusted performance, particularly when transaction costs are considered. Bootstrap evidence supports the statistical significance of these gains.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper successfully combines robust optimization theory with high-frequency realized volatility measures to solve practical hedging challenges under parameter uncertainty. It features rigorous empirical validation using a long multi-asset ETF dataset, demonstrating clear benefits in turnover reduction and net risk-adjusted performance.

Research Flowchart

  flowchart TD
    A[Goal: Dynamic Minimum-Variance Hedging under Volatility Uncertainty] --> B[Data Inputs: ETF High-Frequency Data 2016-2024<br/>Equities, Bonds, Commodities]
    B --> C[Volatility Forecasting: Realized Covariance & Autoregressive Models]
    C --> D[Optimization: Box-Uncertainty Robust Framework]
    D --> E[Closed-Form Solution: Uncertainty-Adjusted Robust Hedge Ratio]
    E --> F[Performance Outcomes: Reduced Turnover & Empirical Stability]
    E --> G[Risk Outcomes: Improved Downside Protection & Net Risk-Adjusted Returns]

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1 of 36 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.