Question

3. Citibank quotes NZ$1 = US$ 0.6624. Deutsche Bank quotes € 1 = US$1.1758. BNZ Bank quotes € 1 = NZ$1.7762.

a. If these quotes are simultaneously observed spot rates, can you make an arbitrage profit? If so, calculate what profit would you make if you started with N$ 1 million. Assume that there are no transaction costs.

b. What would be your arbitrage profit if you were to incur total transaction costs of 0.1% of the amount used for conversions?

Please, answer parts (a and b ) and step by step and in a very clear way

Answer 1

US$/ NZ$ = 0.6624 US$/ Euro = 1.1758 NZ$/ Euro= 1.7762

a.) NZ$ 1 million= 1000000*0.6624/1.1758*1.7762 = NZ$ 1000642

Arbitrage Profit = NZ$ 642

Steps: Firstly change NZ$ in US$ after that convert it in Euro and then NZ$ again as per triangular arbitrage.

Then we will get NZ$ 1000642 in change of NZ$ 1 million.

b.) If transaction cost is 0.1% then

NZ$ 1 million to US$ 1000000*(0.6624-0.1%) = US$ 655776

Now US$ to Euro = 655776/(1.1758+0.1%) = Euro 557170

Euro to NZ$= 557170*(1.7762-0.1%) = NZ$ 988655

No arbitrage profit will be there if we incur transaction cost of 0.1%