A portfolio manager desires a position of $10m in physical gold, but chooses to get...

The optimal hedge ratio answers the question of how much of the hedge to buy to hedge a given position. If 103.11.e1 is the standard deviation of the asset to be hedged, and 103.11.e2 is the standard deviation the asset being used to hedge against price movements in x, then the minimum variance hedge ratio is given by the expression 103.11.e3. In this question, correlation = 0.00378/(6%*7%) = 0.9. The minimum variance hedge ratio is given by (6%/7%)*0.9 = 0.77

He should therefore hold 0.77 x $10m /$100k = 77 contracts.

[We can also do a direct covar based calculation for the min variance hedge ratio as follows:

103.11.a3

= 0.00378 / (0.07 * 0.07) = 0.7714]