I have seen 2 ways to calculate the hedge ratio. First, assume we already know beta to be 0.975 from a regression of spot and futures price changes. Next assume we are hedging corn production. Assume a contract size of 10,000 bushels, a futures price of $10.00 per bushel, a spot exposure of 75,000 bushels, and a spot price of $9.50 per bushel. I have seen hedge ratio presented two ways:h* = 0.975(75,000/10,000) = 7.3125 so our hedge position would be to sell 7.3 contracts to hedge our spot positionI have also seen:h* = 0.975((75,000*$9.50)/(10,000*$10.00)) = 6.9469 so our hedge position would be to sell 6.9 contracts to hedge our position. Obviously, these round close to 7, but assume our hedge increases in size to 7,500,000 bushels? Now the difference adds up. Obviously, these both cannot be correct, but I have seen both methods in different books explaining the concept. HELP????

These methods can both be correct, it depends on whether you estimate your Beta based on dollar price movements (use the first formula) or percentage price movements (use the second).However, neither one is the unambiguous correct hedge. For example, suppose you are defining things in dollar terms, so your Beta means that if the spot price drops $1, you expect the futures price to drop $0.975. That could mean you are certain it will drop exactly $0.975 (correlation coefficient equals 1, standard deviation of futures price is 0.975 times standard deviation of spot price) or that the two are almost uncorrelated, but the standard deviation of the futures price is much greater than the standard deviation of the spot price. It's clear that you would want different hedges in these two situations, but using Beta gives the same hedge for both.In the first case, the correct hedge would be 1/0.975; in the second, any significant hedge will increase your risk.It makes more sense to use the Beta of spot price on futures price, but even then there is no automatic formula for detemining the optimal hedge.

Thank you!