Question

You specializes in cross-rate arbitrage. You notices the following quotes:

Swiss franc/dollar = SFr1.5971/$

Australian dollar/US dollar = A$1.8215/$

Australian dollar/Swiss franc = A$1.1450/SFr

Ignoring transaction costs, does you have an arbitrage opportunity based on these quotes?

If there is an arbitrage opportunity, what steps would you take to make an arbitrage profit, and

how much would you profit if you has $1,000,000 available for this purpose?

Thank you!

Answer 1

We are given that the Cross-Exchange Rate = A$1.1450/SFr

Implied Cross-Exchange Rate (A$/SFr) = Direct Quote of SFr/Direct Quote of A$ = $0.62614/$0.54899 = A$1.14053/SFr. This means that the SFr should be worth only A$1.14053, but it is quoted at A$1.1450, i.e., the SFr is overvalued here. Therefore, we could go for a triangular arbitrage (because of the difference in the quoted cross-rates), and we would then buy the overvalued currency, i.e., the SFr. We would exchange the $1,000,000 to buy SFr at the spot (a total of $1,000,000 /0.62614 = SFr1,597,087). Then we would sell the SFr1,597,087 for A$ at the rate of A$1.1450/SFr. Then we would receive a total of A$1,828,665. We could then exchange the A$1,828,665 for $ at the rate of $0.54899/A$, and at the end we would have $1,003,919 (here there is an arbitrage profit of $3,919).