Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Hedging market risk and uncertainty via a robust portfolio approach

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.

Hedging market risk and uncertainty via a robust portfolio approach

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.

Paper Structure

This paper contains 20 sections, 1 theorem, 41 equations, 16 figures, 14 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Robust hedge ratio
  4. Modeling volatility and uncertainty
  5. Data
  6. Results
  7. Robust vs. standard approach
  8. Predictions using longer horizons
  9. The role of memory
  10. Performance and risk-adjusted metrics
  11. Conclusions
  12. Proof of Proposition \ref{['prop:1']}
  13. Uncertainty box for AR(p) models
  14. $Var(y_{t+j}- \hat{y}_{t+j})$ for AR(1)
  15. $Var(y_{t+j}- \hat{y}_{t+j})$ for AR(p)
  16. ...and 5 more sections

Key Result

Proposition 2.1

Let $\sigma_{SF}\in\mathbb{R}$ be fixed and let $\Theta_S,\Theta_F\ge 0$. Let us assume $\sigma_F^2+\Theta_F>0$. Consider the robust optimization (min-max) problem Then the problem admits a unique global minimizer given by $\blacktriangleleft$$\blacktriangleleft$

Figures (16)

  • Figure 1: Comparison between the outputs of the standard and robust methodologies when realized variances and covariances are fitted by AR(1) processes. Each point is associated with a pair of instruments and its color is the return correlation $\rho$ of the pair. The threshold $\delta_1$ is the first quartile of the asset returns. The dark line corresponds to the bisector.
  • Figure 2: Standard deviation of the hedge ratios as a function of the prediction horizon $\tau$ employed for predictions. Two different instrument pairs are considered: in the title, the left label refers to the hedged asset and the right to the hedging instrument.
  • Figure 3: Comparison between the hedge effectiveness metrics of the robust methodology when realized variances and covariances are fitted by AR(1) processes, and two different prediction horizons are considered, i.e., $\tau = 1$ and $\tau = 10$. Each point is associated with a pair of instruments and its color is the return correlation $\rho$ of the pair. The threshold $\delta_1$ is the first quartile of the asset returns. The dark line corresponds to the bisector.
  • Figure 4: Comparison between the standard deviations of the hedge ratios that are obtained when realized variances and covariances are fitted by AR(1) and AR(5) processes. Two different prediction horizons are considered, i.e., $\tau = 1$ and $\tau = 10$. Each point is associated with a pair of instruments and its color is the return correlation $\rho$ of the pair. The dark line corresponds to the bisector.
  • Figure 5: Comparison between the hedge effectiveness metrics of the robust methodology when realized variances and covariances are fitted by AR(1) and AR(5) processes, and two different prediction horizons are considered, i.e., $\tau = 1$ and $\tau = 10$. Each point is associated with a pair of instruments and its color is the return correlation $\rho$ of the pair. The threshold $\delta_1$ is the first quartile of the asset returns. The dark line corresponds to the bisector.
  • ...and 11 more figures

Theorems & Definitions (3)

  • Proposition 2.1: Robust hedge ratio with box uncertainty
  • proof
  • proof