Cross-Hedge
A cross-hedge is a hedging strategy in which an investor uses a derivative or financial instrument based on one asset to hedge the price risk of a different but economically correlated asset when a direct hedge instrument is unavailable or impractical. The effectiveness of a cross-hedge depends on the correlation and relative volatility between the hedged asset and the hedging instrument.
Key takeaways
- Cross-hedges are necessary when no futures or derivatives contract exists for the exact asset being hedged, such as jet fuel hedged with crude oil futures.
- The optimal hedge ratio (OHR) for a cross-hedge is computed as the correlation between the two assets multiplied by the ratio of their volatilities.
- Cross-hedge basis risk—the risk that the price relationship between the hedged asset and hedge instrument changes—is the primary source of residual risk.
- Airlines, airlines, and processors routinely use cross-hedges; jet fuel is commonly hedged using crude oil or heating oil futures.
- The hedge effectiveness is measured by the R-squared of the regression of hedged asset returns on hedge instrument returns.
Explanation
A perfect hedge requires a derivative whose underlying perfectly mirrors the price dynamics of the exposure being hedged. In practice, this is rarely achievable: jet fuel lacks a liquid futures market, many exotic commodities have only thin forward curves, and individual equity positions can be only partially hedged using broad index futures. The cross-hedge is the practitioner's pragmatic solution, accepting imperfect but meaningful risk reduction through a correlated instrument.
The theoretical foundation of cross-hedging lies in the minimum-variance hedge ratio framework. If a portfolio manager holds quantity Q of an asset S and wishes to hedge using futures on a correlated asset F, the optimal number of futures contracts H is determined by minimizing the variance of the hedged portfolio: H = ρ(S,F) × (σ_S / σ_F) × (Q / Contract_Size). Here ρ is the correlation coefficient, and the ratio σ_S/σ_F adjusts for the different volatilities of the two instruments. If jet fuel price changes are 85% correlated with heating oil futures and jet fuel volatility is 1.1 times heating oil volatility, the optimal hedge ratio would be 0.85 × 1.1 = 0.935 heating oil futures contracts per unit of jet fuel exposure.
Basis risk—the unpredictable component of the price relationship between the hedged commodity and the hedging instrument—is the central risk of any cross-hedge. Basis can vary due to supply-demand imbalances specific to the hedged commodity, transportation or storage cost differentials, seasonal patterns, quality differentials, or regulatory changes affecting one product but not the other. During the COVID-19 crisis, the correlation between jet fuel and crude oil temporarily broke down as demand for aviation fuel collapsed while industrial crude demand remained more stable, causing significant losses for airlines that had hedged jet fuel exposure using crude oil futures.
In fixed income, cross-hedging appears when a portfolio manager hedges a corporate bond portfolio using Treasury futures. The hedge captures interest rate duration risk but leaves credit spread duration exposed. Similarly, hedging an emerging market bond portfolio with U.S. Treasury futures provides a partial hedge against global risk-off moves but fails when EM-specific factors drive spread widening independently of Treasury yields. Managers often supplement a Treasury cross-hedge with a CDS index overlay to address the residual credit spread component.
Formula
Optimal Hedge Ratio (OHR) = ρ(S,F) × (σ_S / σ_F); Number of Contracts = OHR × (Exposure_Size / Contract_Size)
Example
An airline has contracted to purchase 10 million gallons of jet fuel at spot price over the next six months. Lacking a direct jet fuel futures market, the airline's treasury team runs a regression of historical daily jet fuel price changes on NYMEX heating oil futures price changes and finds a correlation of 0.88 and a relative volatility ratio of 1.05. The optimal hedge ratio is 0.88 × 1.05 = 0.924. NYMEX heating oil contracts cover 42,000 gallons each, so the airline needs to short 10,000,000 × 0.924 / 42,000 ≈ 220 contracts. When jet fuel prices subsequently rise 15%, the heating oil futures position gains approximately 13.5% (0.924 × 15%), offsetting most but not all of the fuel cost increase, with the residual difference representing realized basis risk.
Related terms
Basis Basis Risk Bona Fide Hedging Bond Corporate Bond Correlation Cover Credit Spread Delta Margining Duration Equity Futures Price