Question

Question 5

A U.S. company is to sign a contract for 16 million HK dollars (HKD) that will be paid shortly in the future. Given the current exchange rate of HKD4.0 per U.S. dollar, this amount is consistent with the company’s target of 4 million U.S. dollars for its services. Assume it is July and that the contract amount will be paid on 30 September. The following September option quotes are available in the market today to help hedge against exchange rate risk: A call option with a strike of HKD4.03 at a premium of HKD0.02 A put option with a strike of HKD4.03 at a premium of HKD0.01 Note that the option premiums are quoted in exchange rate terms. The size of each option contract is for 1,000,000 HKD. The board of directors of the company has requested that you answer the following questions:

a) Which option and position should be used in this hedging strategy? Using min or max notation, what is the payoff and profit function of the preferred option?

)b) How many option contracts should the company buy or sell?

c) What is the cost of this hedging strategy in U.S. dollar terms?

d) Assume it is now September and the contract is paid as expected. What is the net cash flow implication of this contract to the company, assuming the HK dollar either appreciates to HKD3.5 or depreciates to HKD4.5 per U.S. dollar? Show all cash flows (in U.S. dollar terms) as well as the impact of the hedge in calculating the net cash flow for both scenarios.

e) Using an example, name a reason why an arbitrage opportunity could persist in the market?

Answer 1

a) current exchange rate of HKD4.0 per U.S. dollar,

Total Payment in US dollar =16 million/4=4 million USD

The risk is the exchange rate going up. Because if the rate goes up lower amount of US dollars will be received in exchange of 16 million Hongkong Dollar

To hedge the risk, CALL OPTION will be required to be bought.

CALL option with a strike of HKD4.03 at a premium of HKD0.02

PAYOFF=Max.((S-4.03),0) where S is the exchange rate at expiration

PROFIT =PAYOFF-0.02

b)Number of CALL options Contracts required to be bought=4000000/1000000=4

Buy 4 Contracts (HKD4000000 ) CALL Options at strike price=HKD 4.03

c) COST OF HEDGING STRATEGY:

Premium to be paid=HKD 0.02*4*1000000=HKD80,000

cost of this hedging strategy in U.S. dollar terms=80000/4=USD 20,000

d)If, HK dollar appreciates to HKD3.5

USD to be received in exchange of HKD16 million as per contract=16000000/3.5= $4,571,429

PAYOFF from CALL option =0

PROFIT=0-20000= -$20,000

NET CASH FLOW=$4,571,429-$20,000=$4,551,429

There will be net increase in receipt by $551,4290

If, HK dollar depreciates to HKD4.5

USD to be receivedin exchange of HKD16 million as per contract=16000000/4.5= $3,555,556

PAYOFF from CALL option =HKD (4.5-4.03)*4000000=HKD 1880000

PAYOFF in US dollars=1880000/4.5=$417,778

PROFIT=$417,778-20000= $397,778

NET CASH FLOW=$3555556+397778=$3,953,333

Net decrease in receipt =4000000-3953333=$46667