Suppose that the variance of quarterly changes in the spot prices of a commodity is 0.49,the variance of quarterly changes in a futures price on the commodity is 0.81,and the coefficient of correlation between the two changes is 0.6.The optimal hedge ratio for the contract is:

Question

Quizplus · Accepted Answer

The formula to calculate the optimal hedge ratio (h*) is:

h* = (covariance between spot and futures changes) / (variance of futures changes)

We know the variance of the futures changes is 0.81. 
To calculate the covariance between spot and futures changes, we can use the formula:

covariance = correlation coefficient * (standard deviation of spot changes) * (standard deviation of futures changes)

The standard deviation of spot changes is the square root of the variance, so it's 0.7 (sqrt(0.49)). 
Plugging in the values we get:

covariance = 0.6 * 0.7 * 0.9 = 0.378

Finally, we can calculate the optimal hedge ratio:

h* = 0.378 / 0.81 = 0.4667

So the answer is B, 0.4667.

Suppose That the Variance of Quarterly Changes in the Spot