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The minimum variance hedge ratio is given by $h=p*\frac{\sigma_S}{\sigma_F}$.

I was wondering if you wanted to calculate the S.D yourself and the spot prices were in Dollars per barrel while futures prices were in Dollars per million BTU, would you have to change barrels into million BTU (ie. multiply 5.4)?

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Since SD in this case is usually the 1-day difference of log prices (i.e. 1-day returns) and corr is a dimensionless number, you shouldn't have to keep the units the same. After all that's how you're able to hedge a position using a different commodity that you have access to, for example jet fuel.

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