Doug Bernard specializes in cross-rate arbitrage. He notices the following quote

Question

Doug Bernard specializes in cross-rate arbitrage. He notices the following quotes: Swiss franc/dollar = SFr 1.5971/$ Australian dollar/U.S. dollar = A$ 1.8215/$ Australian dollar/Swiss franc = A$1.1444/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 would he profit if he has $1.000.000 available for this purpose. Suppose you start with the cross-rate between A$ and SFr. Hint: First, calculate the implied or "no arbitrage" cross rate between AUD anil SFr. Then compare the "no arbitrage" cross rate with the quoted cross rate and determine which currency to buy (borrow) and which one to sell.

Explanation / Answer

Cross Rate :

A $/SFr = 1.8215/1.5971

A $/SFr = A$ 1.1405/SFr

As the cross rate there is difference in rate than there is arbitrage oppurtunity by buying Swis franc through dollar

Step 1 : Convert $ 1000000 into Swis franc

Getting = 1.5971*1000000 = A$ 1,597,100

Step2: Convert SFr 1597100 into A$

Getting = 1597100*1.1444 = A$ 1,827,721.24

Step 3 : Now Selling  A$ 1,827,721.24

Getting = 1,827,721.24 /1.8215

Getting = $ 1,003,415.45

Arbitrage Gain = 1003415.45 - 1000000

Arbitrage Gain = $ 3415.45

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