Question

Suppose the 6-month risk free spot rate in HKD is 1% continuously compounded, and the 6-month risk free rate in NZD is 3% continuously compounded. The current exchange rate is 5 HKD/NZD.

a. Suppose again that our usual assumptions hold, i.e., no constraints or other frictions. Suppose you can enter a forward contract to buy or sell NZD 1 for HKD 5. Is there an arbitrage? If yes, describe an arbitrage strategy. If no, briefly explain why not.

b. Suppose now that there are transaction costs is spot and forward exchange rates. That is, to buy NZD 1 you have to pay HKD 5.01 in the spot market today or HKD 5.03 in the 6-month forward contract, and to sell NZD 1 you receive HKD 4.99 in the spot market today or HKD 4.97 in the 6-month forward contract. Is there an arbitrage? If yes, describe an arbitrage strategy. If no, briefly explain why not.

c. Consider again the prices in (b) and further assume that your borrowing costs are 0.5% higher than the risk free rate, while the income from lending is equal to the risk free rate. That is, if you borrow HKD for 6 months then you have to pay a 1.5% continuous compounded interest rate, and similarly, if you borrow NZD for 6 months then you have to pay a 3.5% continuous compounded interest rate. Is there an arbitrage? If yes, describe an arbitrage strategy. If no, briefly explain why not.

Answer 1

Calculating Forward Rate

=

FR= 4.903

(a) Yes there exists is an arbitrage opportunity we can sell today at 5 HKD/NZD and buy after 6 months at SR of 4.9 HKD/NZD giving a profit of 0.1HKD/NZD

(b) No Since buying price is higher at SR and FR

(c) Yes borrow in HKD @ 1.5% and lend in NZD @ 3%

Borrow 100,000 HKD @1.5% convert to NZD at SR 5.01HKD/NZD we get 19960 NZD lending it @ 3.5% we get after 6 months 20309 NZD convert it to HKD @ 4.97HKD/NZD we get 100936 HZD.

we have to pay 100750 HKD after 6 months

we have received 100936 HKD after 6 months

Hence a Total gain of 186 HKD