Question

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$1.1390/SFr

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

Answer 1

Given that

$1 = SFr 1.5971 => SFr 1 = $1/1.5971

1$ = A$1.8215 => SFr 1.5971 = A$1.8215 => 1 SFr = A$1.8215/1.5971 = A$1.1405

However, the exchange rate between A$ and SFR is given as 1 SFr = A$1.1390 => 1 A$ = SFr 1/1.1390

a. Actual exchange rate of A$/SFr is less than the exchange rate obtained by conversion from $ terms. Therefore, Doug Bernard has an arbitrage opportunity.

b.

Step 1: Doug Bernard should first convert $ to A$

$1,000,000 = 1,000,000 x A$1.8215 = A$1,821,500

Step 2: Doug Bernard should next convert A$ to SFr

A$1,821,500 = 1,821,500 x SFr 1/1.1390 = SFr 1,599,209.83

Step 3: Convert SFr to $

SFr 1,599,209.83 = 1,599,209.83 x $1/1.5971 = $1,001,321.04

Profit for Doug Bernard through arbitrage = $1,001,321.04 - $1,000,000 = $1,321.04