Problem #4: (Hypothetical Scenario) A portfolio manager wishes to hedge US dollar using Chinese Yuan and British pound

Optimal hedge ratio when we want to acheive minimum variance is calculated as follows:

hedge ratio = correlation x ( std dev of spot price of currency held / std dev of futures price of currency being hedged)

Since the question has asked us to take a hypothetical example, we can assume

If the correlation between dollar and yuan =  0.9

standard deviation of the percentage changes in dollar spot returns = 3

standard deviation of the percentage changes in yuan futures returns = 4

hedge ratio = 0.9 x ( 3/4)

hedge ratio = 0.675

similarly for british pound

If the correlation between dollar and pound =  0.8

standard deviation of the percentage changes in dollar spot returns = 3

standard deviation of the percentage changes in pound futures returns = 5

hedge ratio = 0.9 x ( 3/5)

hedge ratio = 0.54

thanks if you have any doubts please leave a comment and let me know