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?

Answer 1

Part A:

Cross rate NZ $ / EUro = [ NZ $ / USD ] * [ USD / Euro ]

Given USD / NZ$ = 0.6624

Indirect Quote = 1 / Direct Quote

= [ 1 / 0.6624 ] * [ 1.1758 ]

= 1.77506

Actual Rate NZ$ / Euro = 1.7762.

As these Rates are not equal, There is Arbitrage gain.

Step 1:

Convert NZ$ into USD = 1000000 * 0.6624

= USD 662400

Step2:

COnvert USD into Euro :

= 662400 / 1.1758

= 563361.12

Step 3:

Convert Euro Into NZ$

= 563361.12 * 1.7762

= 1000642.01

Book Profit = 1000642.01 - 1000000

= NZ$ 642.01

Part B:

Step 1:

Convert NZ$ into USD = 1000000 * 0.6624

= USD 662400

After adjusting  Transaction cost = 662400 * (100% - 0.1% )

= 662400* 99.9%

= 661737.60

Step2:

COnvert USD into Euro :

= 661737.60 / 1.1758

= 562797.76

After adjusting  Transaction cost = 562797.76 * (100% - 0.1% )

= 562797.76 * 99.9%

= 562234.96

Step 3:

Convert Euro Into NZ$

= 562234.96 * 1.7762

= 998641.73

After adjusting  Transaction cost = 998641.73 * (100% - 0.1% )

= 998641.73 * 99.9%

= 997643.09

Book Profit = 997643.09 - 1000000

= - NZ$ 2356.91

If there is transaction cost of 0.1% for each conversion, Arbitrage profit is not possible.