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?

• The objective of hedging is to reduce the variance of the position+hedge portfolio. So which of these two solutions gives a smaller variance? Jun 3 '20 at 0:05
• ...the answer is going to be: whichever of commodity 1 or commodity 2 has higher correlation ($\rho$) with jet fuel. The percent of variance 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 it. It is the (absolute value of) the correlation that matters. Jun 3 '20 at 9:42
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.