Question

A young forex trader specializes in cross-rate arbitrage. She notices the following quotes:

Swiss franc/dollar = SFr1.0876/$


Australian dollar/U.S. dollar = A$0.8922/$


Australian dollar/Swiss franc = A$0.8223/SFr


Ignoring transaction costs, does she have an arbitrage opportunity based on these quotes? If there is an arbitrage opportunity, what steps would she take to make an arbitrage profit, and how would she profit if she has $1,000,000 available for this purpose.

Answer 1

HI,

An arbitrage opportunity occurs if we can able to make profit based on these exchange rate.

So here 1 USD = SFR 1.0876

1 USD = A$ 0.8922

1 SFR = A$0.8223

So forex trader is having $1,000,000

so at first she buys Swiss franc from these dollars

so 1,000,000 USD = 1.0876*1000000 SFR = 1,087,600 SFR

now from these SFR she can buy Australlian dollars

so 1,087,600 SFR = 1087600*0.8223 = A$ 894,333.48

again from these australian dollar she can convert back to USD

A$ 894,333.48 = 894333.48/0.8223 = $1,002,391.26

That means she was $1,000,0000 initially and she made $1,002,391.26

so here arbitrage profit = 1,002,391.26-1000000 = $2,391.26

Thanks