Dynamic currency hedging with non-Gaussianity and ambiguity

Abstract

This paper introduces a non-Gaussian dynamic currency hedging strategy for globally diversified investors with ambiguity. It provides theoretical and empirical evidence that, under the stylized fact of non-Gaussianity of financial returns and for a given optimal portfolio, the investor-specific ambiguity can be estimated from historical asset returns without the need for additional exogenous information. Acknowledging non-Gaussianity, we compute an optimal ambiguity-adjusted mean-variance (dynamic) currency allocation. Next, we propose an extended filtered historical simulation that combines Monte Carlo simulation based on volatility clustering patterns with the semi-parametric non-normal return distribution from historical data. This simulation allows us to incorporate investor's ambiguity into a dynamic currency hedging strategy algorithm that can numerically optimize an arbitrary risk measure, such as the expected shortfall. The out-of-sample backtest demonstrates that, for globally diversified investors, the derived non-Gaussian dynamic currency hedging strategy is stable, robust, and highly risk reductive. It outperforms the benchmarks of constant hedging as well as static/dynamic hedging approaches with Gaussianity in terms of lower maximum drawdown and higher Sharpe and Sortino ratios, net of transaction costs.

Keywords:

• Currency hedging
• Non-Gaussianity
• Ambiguity
• Filtered historical simulation
• Expected shortfall
• Currency risk management

JEL Classifications:

• C53
• C58
• F31
• G11
• G15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Note that such approaches still consider a single period optimization framework and should be differentiated from dynamic programming approaches solving recursive multi-period optimization problems.

2 Sortino ratio penalizes negatively skewed portfolio return distributions by computing the volatility of returns only below the risk-free rate, hence accounting for the downside risk.