Question

1. The finance manager of USQ Limited has a surplus of AUD 1 million and is interested in using this money for triangular arbitrage. The Finance manager can either buy or sell at the quotes given below.

           

Citibank                             1 AUD = 0.76 USD

Westpac                           1 AUD = 1.05 NZD

NAB                                   1 USD = 1.39 NZD

Suppose we ignore all transaction costs. Show step by step how triangular arbitrage is possible using these quotes and show the resulting arbitrage profit. In your answer you must show the relevant cross rates which lead to the decision to undertake triangular arbitrage. Show all calculations to support your answer.                                                                                                                       

2. The finance manager has now been tasked with investing AUD 5 million (or US dollar equivalent) for a period of ninety (90) days i.e. three (3) months. Facing the rates shown in the table below, the finance manager wishes to enter into a covered interest arbitrage (CIA) investment.

Spot exchange rate	S (USD/AUD)	=	0.7102/AUD
90-day forward rate	F90 (USD/AUD)	=	0.6713/AUD
AUD discount rate	iAUD	=	6.00% p.a.
US dollar Discount rate	iUSD	=	4.00% p.a.

In your answer, you should demonstrate that a CIA profit is possible due to the relationship between

the spot rate and the forward rate; and calculate the resulting CIA profit using any relevant calculations.

If you wish, you can use a diagram to show your answer.

Answer 1

(a)

We have AUD 1 million.

We will first sell AUD and purchase USD at Citibank, then sell USD and purchase NZD at NAB and finally sell NZD to buy AUD at Westpac.

This will give us an arbitrage profit as follows:

=

(1*0.76*1.39/1.05)

=

1.006095238

(Assumed selling one AUD as per above mentioned transaction and getting 1.006095 AUD)

Thus the Arbitrage Profit reulting from above transaction is as follows

1 million AUD*.005095 AUD

$6,095.00

(b)

We have 5 million AUD/ UDS equilvalent.

Now we can either directly invest AUD or we can first convert AUD into USD using spot ate and then invest USD and then again convert USD into AUD at 90th day using forward rate

Closing Balance at day 90 if AUD is invested without conversion

Principal Amount invested.

AUD

5000000

Interest Income for 3 months @6% p.a

75000

Net Closing Balance including Interest

(5000000*6%*3/12)

5075000

Closing Balance at day 90 if AUD is invested after conversion conversion

Principal Amount Converted.

AUD

5000000

USD Received

USD

3551000

Interest Income for 3 months @4% p.a

(3551000*4%*3/12)

USD

35510

Net Closing Balance including Interest

USD

3586510

Net Closing Balance including Interest After Coversion into AUD at forward Rate of 0.6713

(3586510/0.6713)

AUD

5342634