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Doug Bernard specializes in cross-rate arbitrage. He notices the following quotes: Swiss franc/U.S. dollar = 1.5971...

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

Swiss franc/U.S. dollar = 1.5971 CHF/USD

Australian dollar/U.S. dollar = 1.8215 AUD/USD

Australian dollar/Swiss franc = 1.1300 AUD/CHF

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 USD?

Solutions

Expert Solution

Solution :

Yes. Doug Bernard does have an arbitrage opportunity based on the given quotes :

As per the information given in the question we have:

Availability of USD 1,000,000

Exchange rates

Swiss Franc / U.S. Dollar = 1.5971 CHF / USD

Australian Dollar / U.S. Dollar = 1.8215 AUD / USD

Australian Dollar / Swiss Franc = 1.1300 AUD / CHF

Steps to make arbitrage profit :

Step 1: Sell USD to buy AUD

We have USD 1,000,000 to look for an arbitrage opportunity

We know that 1 USD = 1.8215 AUD

Thus on sale /exchange of USD for AUD we will have

= USD 1,000,000 * 1.8215 = 1,821,500 AUD

Step 2: Sell AUD to buy CHF

We now have 1,821,500 AUD

We know that 1 CHF = 1.1300 AUD

Thus on sale or exchange of AUD for CHF we will have

= 1,821,500 AUD / 1.1300 AUD = CHF 1,611,947

Step 3 : Sell CHF to buy USD

We now have CHF 1,611,947

We know that 1 USD = CHF 1.5971

Thus on sale or exchange of CHF for USD we will have

= CHF 1,611,947 / CHF 1.5971 = USD 1,009,296

Thus the profit on the arbitrage opportunity = USD 1009296 – USD 1000000

= USD 9,296

jeff jeffy answered 1 year ago

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