Question

Assume you are a trader with Deutsche Bank. From the quote screen on your computer terminal, you notice that Dresdner Bank is quoting €0.855/$1.00 Credit Suisse is offering SF1.1825/$1.00. UBS’s current direct quoting €/SF currently @ € 0.754/SF

i. Prove and explain whether at these quoted rates there a chance for triangular arbitrage (Hint: Use the no arbitrage cross exchange rate here).

ii. Show and explain how you can make a triangular arbitrage profit by trading at these prices. (Ignore bid-ask spreads for this problem.) Assume you have $5,000,000 with which to conduct the arbitrage. If your answer in a is that there is no chance of arbitrage profits please say so.

Answer 1

i) There would be an arbitrage if cross rate calculated does not match the quoted rate :

Euro/SF=Euro/Dollar*Dollar/SF Euro/Dollar 0.855 SF/Dollar 1.1825 Dollar/SF 0.845666 Euro/SF 0.723044

Since Euro/SF cross rate is different from 0.754, there would be a chance for triangular arbitrage

II)
We start from dollar and covert to Swiss franc at 1.1825=5,000,000*1.1825=5,912,500 SF
Then we convert SF to Euro at 0.754 Euro/SF= 4,458,025 Euro
Now we convert Euros again to USD= 0.855Euro per USD = $5,214,064 USD