Choosing a Cross-Hedge by Comparing Correlation

Summary

The document considers how to choose between two commodity futures for hedging jet fuel when their minimum-variance hedge ratios and recommended contract counts differ. It says the objective is to reduce the variance of the combined exposure and hedge, so the alternatives should be compared by the residual variance they leave, rather than by the size of their hedge ratios or positions.

Under the standard minimum-variance hedge setup, the fraction of the unhedged price variance remaining is one minus the squared correlation between the exposure and hedge instrument. The preferred commodity is therefore the one with the stronger absolute correlation to jet fuel, assuming comparable measurement periods and a correctly specified hedge. The note gives no correlation estimates or variance comparison for the two candidates, so it does not identify which commodity should be selected in the example. In practice, contract specifications, basis risk, liquidity, and implementation costs can also affect the choice.

Key ideas

• A cross-hedge should be judged by how much variance it removes from the combined position.
• The residual variance fraction under a minimum-variance hedge depends on the squared correlation with the hedged exposure.
• A stronger absolute correlation with jet fuel generally indicates the more effective hedge.
• Hedge ratios and contract counts alone do not measure hedge effectiveness.
• The document provides no correlations or residual variances for the two candidate commodities.

Tags

# Answer by nbbo2 (score 3)


# Cross hedge: Which commodity to hedge when you have to hedge the jet fuel price but you have option between two commodities












If we have an option between two commodities to hedge jet fuel and the commodities have results as follows: minimum variance hedge ratio: 1.07 for commodity 1 and 2.53 for commodity 2 Optimal number of contracts: 27 for commodity 1 and 63 for commodity 2

Out of these two options which commodity should we prefer for a hedging strategy?

## Answer by nbbo2 (score 3)

https://quant.stackexchange.com/a/54721

The objective of hedging is to reduce the variance of the (position+hedge) portfolio. So which of these two solutions gives a smaller variance?

You could calculate it numerically and compare the variances. However, in general ... the answer is going to be: whichever of commodity 1 or commodity 2 has higher correlation ($\rho$) with jet fuel. The percent of variance of jet fuel cost not hedged is $(1−\rho^2)$ and you want this to be as small as possible. The hedge ratio and number of contracts has nothing to do with the effectiveness of the hedge. It is the (absolute value of) the correlation that matters.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.