Question

4. a) You observe the following quotes for the USD/AUD in the spot market from two banks:

Bank of Sydney

Bank of New York

Bid	Ask	Bid	Ask
0.71711	0.71715	0.71708	0.71715

Do these quotes imply the possibility of earning a profit by using locational arbitrage? If so, calculate the potential profit if you are able to use AUD 25,000. If not, explain why arbitrage is not possible?

(b) You observe the following quotes for the GBP /AUD in the spot market from two banks:

Bank of Melbourne

Bank of London

Bid	Ask	Bid	Ask
0.5458	0.5459	0.5514	0.5515

Do these quotes imply the possibility of earning a profit by using locational arbitrage? If so, calculate the potential profit if you are able to use GBP 50,000. If not, explain why arbitrage is not possible?

c) You observe the following quotes for the EUR / USD in the spot market from two banks:

Deutsche Bank

Bank of America

Bid	Ask	Bid	Ask
1.18102	1.18102	1.18094	1.18100

Do these quotes imply the possibility of earning a profit by using locational arbitrage? If so, calculate the potential profit if you are able to use EUR 500,000. If not, explain why arbitrage is not possible?

Answer 1

a) Selling 1 AUD to bank of Sydney, one gets USD 0.71711  and buying AUD from this USD from Bank of New York gives 0.71711/0.71715 = AUD 0.999944 which is less than the starting amount, so arbitrage is not possible

Selling 1 AUD to bank of New York, one gets USD 0.71708 and buying AUD from this USD from Bank of Syndey gives 0.71708/0.71715 = AUD 0.999902 which is less than the starting amount, so arbitrage is not possible

So, in this case locational Arbitrage is not possible

b)

Selling 1 AUD to bank of Melbourne, one gets GBP 0.5458 and buying AUD from this GBP from Bank of London gives 0.5458/0.5515 = AUD 0.989665 which is less than the starting amount, so arbitrage is not possible

Selling 1 AUD to bank of London, one gets GBP 0.5514 and buying AUD from this GBP from Bank of Melbourne gives 0.5514/0.5459 = AUD 1.010075 which is more than the starting amount, so arbitrage is possible

So, if one starts with GBP 50000 and sells it to bank of Melbourne to get 50000/0.5459 = AUD 91591.87 and converting this amount to GBP again from Bank of London, one gets GBP 91591.87*0.5514 = GBP 50503.76

Potential Profit = GBP 50503.76- GBP 50000 = GBP 503.76

c)

Selling 1 EUR to Deutsche bank , one gets USD 1.18102 and buying EUR from this USD from Bank of America gives 1.18102/1.18100 = USD1.000017 which is more than the starting amount, so arbitrage is possible

So, if one starts with EUR 500000 and sells it to Deutsche bank to get 500000 * 1.18102 = USD 590510 and converting this amount to EUR again from Bank of Amercica, one gets EUR 590510/1.18100 = EUR 500008.50

Potential Profit = EUR 500008.50- EUR 500000 = EUR 8.50