Question

# You are given the following information: Spot exchange rate (AUD/USD) 0.9313 – 0.9321 Three-month forward rate...

You are given the following information:

 Spot exchange rate (AUD/USD) 0.9313 – 0.9321 Three-month forward rate (AUD/USD) 0.9412 – 0.9420 Australian three-month interest rate 5 - 5.5% pa U.S. three-month interest rate 1.5 - 2% pa

Is there an arbitrage opportunity from borrowing 10,000 USD and investing it in Australia over 3 months? Calculate the profit/loss made. (to the nearest dollar)

 Loss of 40 USD Loss of 31 USD Gain of 190 USD Gain of 181 USD

1. Borrow 10,000 USD at 2% p.a

10,000 * ( 1 + 2/100*12) ^ 1*3

10000 * 1.00167^3

= 10000 * 1.00501

= 10050.1 USD

2. Convert to AUD at 0.9313 AUD/ USD:

10,000 * 0.9313 = 9313 AUD

3. Invest at 5% p.a in Australia for 3 months

9313 * ( 1 + 5/100*12) ^ 1*3 [We do this to convert the annual rate to a monthly rate ]

9313 * 1.004167^3

= 9313 * 1.012553

= 9429.90762 AUD

4. After 3 months, we convert it to USD at 0.9420 AUD / USD

9429.90762 / 0.9420

= 10,010.5176 USD

5. After paying back the loan,

= 10010 - 10050

= Loss of 40USD

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