Question

On April 1, an Australian investor decides to hedge a U.S. portfolio worth $10 million against exchange risk using AUD call options. The spot exchange rate is AUD/$ ? 2.5 or $/AUD ? 0.40. The Australian investor can buy November calls AUD with a strike price of 0.40 U.S. cents per AUD at a premium of 0.8 U.S. cent per AUD. The size of one contract is AUD 125,000. The delta of the option is estimated at 0.5.

a. How many AUD calls should our investor buy to hedge the U.S. portfolio against the AUD/$ currency risk?

b. A few days later the U.S. dollar has dropped to AUD/$ ? 2.463 ($/AUD ? 0.406) and the dollar value of the portfolio has remained unchanged at $10 million. The November 40 AUD call is now worth 1.2 cents per AUD and has a delta estimated at 0.7. What is the result of the hedge?

c. How should the hedge be adjusted?

Answer 1

Portfolio Value = $ 10 million

Spot Rate : $/AUD = 0.40

$0.40 per AUD strike option price = $ 0.8

Contract Size = AUD 125,000 & Detla = 0.5

Hence each contract will cover for (125000*0.5) = AUD 62500 which in USD will be $ 25000.

Now we answer - number of contracts required to hedge the US 10million portfolio = (10,000,000 / 25000) = 400 contracts.

When the exchange rate moves to $/AUD 0.406:

Portfolio value remains unchanged at $ 10 million. But the value of call has increased by [(1.2 - 0.8)/0.8] = 50%. Hence vaue of each contract in USD terms = 25000*1.5 = 37500 and the gain on 400 contracts = (400*12500) = $ 5 million.

Given that the delta has increased to 0.7, which means each contract is covering USD (37500*0.7) = USD 26250 value per contract. Hence for hedging $ 10 million portfolio we only need = (10000000/26250) = 380.95 or 381 contracts. Hence the balance 19 call contracts can be sold and the profit can be booked. The profit on these 19 contracts will be (19*12500) = USD 237,500 or AUD 584,962.5