practice question

[MyLearn]

Dear All,

Could you please solve this question. Its a very simple question with straight forward application of optimal hedge ratio.

1. the standard deviation of quartely changes in the price of a commodity is 0.57, the standard deviation of quartely changes in the price of a futures contract on the commodity is 0.85, and the covariance between the two changes is 0.3876. what is the optimal hedge ratio for a 3-month contract?

My calculation: Correlation = 0.3876 / (0.57 * 0.85) = 0.8
Optimal Hedge Ratio = 0.8 * (0.57/0.85) = 0.5364


However the calculation in the material is as = 0.3876 * (0.57/0.85) = 0.2599 which i think is wrong. please clarify.

 

[ABFRM]

hedge ratio = correlation*(std of Spot/std of Futures)
however correlation =covariance/(std of spot*std of futures)
so formula becomes hedge ratio = covariance/(std of futures)^2
so answer is optimal hedge ratio = 0.3876/(0.85)^2 = 0.5364.

So your answer is correct might be he wants to talk about correlation but he has given covariance....

 

[David Harper CFA FRM]

I agree with abchaudh: optimal (MV) hedge ratio = correlation(f,s)*volatility(spot)/volatility(futures) = covariance(f,s)/variance(f) = 0.5364

 

[MyLearn]

thank you abchaudh and david