Question

Cross-Rate Arbitrage

0. Doug Bernard specializes in cross-rate arbitrage. He notices the following quotes. Swiss franc/dollar = SFr1.5971/$ Australian dollar/U.S. dollar = A$1.8215/$ Australian dollar/Swiss franc = A$1.1440/SFr Ignoring transaction costs, does Doug Bernard have an arbitrage opportunity based on these quotes? If there is an arbitrage opportunity, what steps would he take to make an arbitrage profit, and how much would he profit if he has $1,000,000 available for this purpose?

Answer 1

The cross-rate between Australian dollars and Swiss franc is A$/SFr = A$/$ x $/SFr = (A$/$)/(SFr/$) = 1.8215/1.5971 = 1.1405.

But, given cross-rate is higher A$1.1.1440/SFr than what we calculate implicitly.

So, arbitrage opportunity exists.

From given cross-rate of A$1.1440/SFr, 1 Swiss franc is worth A$1.1440, whereas the cross-rate based on the calculated rate implies that 1 Swiss franc is worth A$1.1405.

Thus, the Swiss franc is overvalued relative to the A$ in the given cross-rate, and Doug Bernard’s strategy for arbitrage should be to sell Swiss francs and buy A$ as per the given cross-rate.

Sell dollars to get Swiss francs Sell $1,000,000 to get $1,000,000 x SFr1.5971/$ = SFr1,597,100.

Then sell the Swiss francs to buy Australian dollars SFr1,597,100 to buy SFr1,597,100 x A$1.1440/SFr = A$1,827,082.40.

Sell Australian dollars for dollars  A$1,827,082.40 for A$1,827,082.40/A$1.8215/$ = $1,003,064.73.

Hence arbitrage profit is $1,003,064.73 - $1,000,000 = $3,064.73.