Question

You work for Hong Kong Telecom and are considering ways to hedge a 10 million GBP cash inflow to be received in three months. The current spot rate is equal to the three-month forward exchange rate at S0GBP/HKD = F3GBP/HKD = 0.1000 GBP/HKD. The current spot rate for the U.S. dollar is S0USD/HKD = 0.1250 USD/HKD. a. The Hong Kong Exchange (HKEx) trades HKD/GBP contracts that expire in five months with a contract size of 50,000 GBP. You estimate ß = 1.02 based on the regression stHKD/GBP = α + ßfuttHKD/GBP + e. The r2 of this regression is 0.97. How many pound contracts should you sell to minimize the risk of your hedged position? b. An investment bank offers a HKD-per-USD futures contract with a 3-month maturity. You estimate ß = 1.10 based on the regression stHKD/GBP = α + ßstHKD/USD + e. The r2 of this regression is 0.42. What should be the dollar size of your futures position to minimize the risk of your hedged position? c. The Chicago Mercantile Exchange (CME) trades HKD futures contracts that expire in five months and have a contract size of HKD500,000.

Answer 1

SOLUTION

Delta hedges, cross hedges, and delta-cross-hedges:

a. The optimal hedge ratio for this delta-hedge is given by:

NFut* = (amount in futures) / (amount exposed) = 

( (amount in futures) = ()(amount exposed)

= (1.02)(£10 million) = £10.2 million.

This is equivalent to (£10,200,000) / (£50,000/contract) = 204 contracts.

b. The optimal amount in the futures position of this currency cross-hedge is:

( (amount in futures) = (1.10)(£10 million) = £11 million.

The $ equivalent is (£11,000,000)/(($0.1250/HK$)/(£0.1000/HK$)) = $13,750,000.

c. The optimal amount in the futures position of this delta-cross-hedge is:

( (amount in futures) = (1.06)(£10 million) = £10.6 million.

At current spot rates of exchange, this is equivalent to (£10,600,000)/(£0.1000/HK$) = HK$106,000,000, or (HK$106,000,000)($0.1250/HK$) = $13,515,000. In terms of CME HK$ contracts, this is equivalent to (HK$106,000,000)/(HK$500,000/contract) = 212 contracts.