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Homework answers / question archive / Problem #4: (Hypothetical Scenario) A portfolio manager wishes to hedge US dollar using Chinese Yuan and British pound
Problem #4: (Hypothetical Scenario) A portfolio manager wishes to hedge US dollar using Chinese Yuan and British pound. Calculate optimal hedge ratios subject to minimum variance criterion.
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