- 15 Marks
FM – L2 – Q97 – Hedging with options
Question
A UK company, PrimeCare Plc, will receive US$2 million in six months’ time. It is now 20th March. The company is not sure whether the US dollar will rise or fall in value against sterling over the next few months, and it has decided to hedge its exposure to currency risk using traded currency options.
On the London Stock Exchange, traded currency options are available in a contract size of £31,250. Options are priced in cents per £1. Assume that option contracts expire on 20th of each month.
The following option prices are currently available:
| Exercise price | Calls | Puts | ||
|---|---|---|---|---|
| June | September | June | September | |
| 1.8500 | 1.4 | 1.9 | 4.0 | 5.1 |
The current spot exchange rate (US$/£1) is 1.8325–1.8375.
Required
(a) Explain how the company’s currency exposure could be hedged using traded currency options.
(b) Show what would happen if the options are still held by the company at expiry and the spot exchange rate is $1.9150–1.9200.
Answer
(a) The company, PrimeCare Plc, expects to receive US$2 million in six months, which it will convert to sterling. To hedge the risk of a fall in the US dollar’s value against sterling, the company should buy put options on sterling, as this gives the right to sell sterling at a fixed exchange rate (converting dollars to sterling).
- Contract size and number of contracts: Each option contract is for £31,250. To hedge $2,000,000, the company needs to determine the sterling equivalent at the exercise price of 1.8500: $2,000,000 ÷ 1.8500 = £1,081,081. Number of contracts = £1,081,081 ÷ £31,250 ≈ 34.6. Since fractional contracts are not possible, the company should buy 35 contracts to cover the exposure, leaving a small unhedged amount.
- Choice of options: The payment is due in September (six months from 20th March). Thus, September put options with an exercise price of 1.8500 should be used, with a premium of 5.1 cents per £1.
- Premium cost: Premium per contract = £31,250 × 5.1 cents ÷ 100 = $1,593.75. For 35 contracts, total premium = 35 × $1,593.75 = $55,781.25, payable in sterling at the spot rate (say, 1.8375): $55,781.25 ÷ 1.8375 = £30,350.
- Hedging mechanism: The put options allow PrimeCare Plc to sell £1,093,750 (35 × £31,250) at 1.8500, ensuring a minimum dollar receipt of £1,093,750 × 1.8500 = $2,023,437.50, protecting against a dollar depreciation. If the dollar appreciates, the company can let the options lapse and convert at the spot rate.
(b) At the expiry date, the options are in-the-money if the spot exchange rate is 1.9200. They will therefore be exercised, at a profit of $0.07 per £1 (1.9200 – 1.8500).
Gain on exercise of 35 option contracts = 35 × 31,250 × $0.07 = $76,562.50.
The total dollar income of the company will therefore be $2,076,562.50.
This can be exchanged into sterling at the spot rate, to obtain £1,081,543 ($2,076,562.50 ÷ 1.9200).
The option premium cost was £11,340, therefore ignoring the time value of money, the net revenue for the company is £1,081,543 – £11,340 = £1,070,203.
This gives an effective exchange rate for the $2 million dollar receipts of 1.8688 (2,000,000 ÷ 1,070,203).
- Topic: Hedging with options
- Uploader: Samuel Duah