(a) and (b) are solved, but I am not sure how to handle (c)...

Can anyone please help me with (c)?

Q. 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 our usual assumptions hold, i.e., no constraints or other frictions. What is the forward exchange rate with 6 months to maturity such that there is no arbitrage?

Forward rate HDK/NZD = 4.90

Explanation:

Current spot rate HKD/NZD = 5

HKD rate = 1%

NZD rate = 3%

Forward rate HDK/NZD = Current exchange rate * (1+HKD rate)/(1+NZD rate)

= 5 * (1+1%)/(1+3%)

= 4.90291262136

(b) Suppose 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.

Arbitrage opportunity exists

The strategy is to buy HKD in the market for 4.90 in six months and a concurrent forward contract to sell it for 5

Explanation:

The forward rate in six month's time can be computed using the below formula for forward exchange rate:

forward exchange rate=spot rate*(1+home country risk free rate)/(1+foreign country risk free rate)

spot rate=5 HKD/NZD, i.e 5HKD for 1 NZD

The rate is stated in terms of HKD, HKD is the home currency

home country risk free rate=1%

foreign country risk free rate=3%

forward exchange rate=5*(1+1%)/(1+3%)=4.90

Alternatively, we can buy HKD in the market for 4.90 in six months' time and enter a forward contract today to sell it in six months for 5.

profit=5-4.90=0.10

(c) Suppose 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.