Dynamic hedging requires prediction of correlations and “betas” across asset classes and contracts. A new paper on dynamic currency hedging proposes two enhancements of traditional regression for this purpose. The first is the use of option-implied volatilities, which are plausibly related to future actual volatility and correlation across assets. The second enhancement is the use of parameter shrinkage in regression estimation (LASSO method), which mitigates the risk of overfitting.

Bucher, Melk, “Dynamic Conditional Currency Hedging”, July 2017

*The post ties in with SRSV’s lecture on managing systemic risk, particularly the part on crisis strategies with early portfolio adjustment.*

*The below are excerpts from the paper. Emphasis and cursive text have been added. *

### The idea

“We propose __a simple and robust approach to hedge FX risk for investors globally__…We view currency risk in the context of total portfolio returns of given international equity, bond and commodity positions and take risk-minimizing FX positions.”

“[*The*] hedging framework…__can be traded in real-time by investors__. Such an ex-ante approach necessarily can only make use of past or current data.”

“We document that correlations between currencies, equities, and commodities vary over time and can be predicted by implied FX volatility.”

“Our proposed hedging model employs __regression shrinkage in order to avoid overfitting past correlation patterns__ determining FX positions. This approach proves more robust in out-of-sample testing and informs optimal FX hedging for investors in equities, bonds and commodities.”

“For equities and commodity investors, our hedging approach leads to __strongly reduced symmetric and downside risk at constant or improved returns__ per unit of risk. For bond investors, our approach converges to full hedging, corroborating the literature in that full hedging is optimal.”

### The benefits of using implied volatilities

“We introduce a variable from the global risk factor literature examining the links across asset classes: implied volatility [*derived from related options prices*].”

“__As FX market stress increases, the future expected correlation of most USD currency pairs with the equity markets increases__, which allows the investor to move out of or even short those currencies and go into the USD or negatively correlated safe haven currencies, such as the Swiss frank or Japanese yen. This conditional adjustment of FX hedges leads to…risk reduction relative to unconditional hedging, in particular during crisis periods.”

“As __options-implied FX volatility strongly predicts future correlation of international equities and commodities with different currenc__y pairs, it serves as useful conditioning information for an investor in these asset classes…[*We*] find strong evidence that implied volatility in the FX market can predict the future correlation patterns of global equities and commodities with individual currencies as well as entire FX styles (such as carry trade)…FX correlation properties are not stable, but vary conditionally depending on the perceived stress in FX markets as measured by the implied volatility of options in the FX market.”

“[*The figure below*] shows the correlation of an equally-weighted global equity portfolio against various USD-currency pairs across different lagged bins of implied volatility in the sample period of 1995 to 2014. We thereby find remarkable patterns. The typical carry trade currencies Canadian and Australian dollar are positively correlated to equities throughout. However, there is __a near monotonic increase in correlation as lagged FX volatility increases__, suggesting highly useful conditioning information for a risk-averse investor.”

“Conditioning on implied volatility, __equities and commodities investors shift into safe-haven currencies during crisis periods__, providing them with smoother return series (lower standard deviation) and significant downside protection particularly in bad times. In terms of standard deviation as well as downside risk our proposed implied volatility-based hedge dominates the relevant benchmarks of no hedging, full hedging as well as unconditional hedging.”

### The benefits of using parameter shrinkage

“The covariance matrix of equity- and commodity- FX returns is not just time-varying, but also stochastic and so our mean-variance __investor should be cautious not to overfit his regression based hedging model to past data__ when choosing optimal FX positions.”

“To this end, we introduce a simple yet effective regression shrinkage approach: the **least absolute shrinkage and selection operator LASSO**…The LASSO…has been shown to enhance prediction accuracy and interpretability of the statistical models it produces…The LASSO introduces __a penalty term that shrinks the absolute size that all coefficients in the regression can cumulatively take__… the LASSO weighs minimizing the squared residual against minimizing the sum of the absolute parameter values. The penalty term thereby determines the relative importance of shrinkage in the coefficients: the higher it is, the lower the resulting absolute parameters will be… the __LASSO performs a type of continuous subset selection by shrinking the less important coefficients__ (in terms of fit of the regression model) to zero while the more important ones are shrunk less.”

*For more on the LASSO and related methodologies view post here.*

“This LASSO-based __hedging strongly simplifies the hedging requirements of our real-world investor who now places more weight on the currencies with more stable correlation properties__ and takes zero positions (fully hedges) currencies with a lot of noise. This leads to more stable FX positions, lower FX turnover and lower absolute FX positions (long or short) which all make the hedging easier to implement in practice. Most importantly, it also has a strong impact on the risk-return performance in out-of-sample testing, leading to lower risk as well higher returns per unit of risk than the hedging model from the in-sample paradigm.”

“An intermediate estimation window is optimal. It trades off the higher relevance of more recent data with the necessity to have sufficient data points to accurately measure the equity market beta of the currencies.”