Question

Assume that you are a trader with d bank. from the quote screen on your computer terminal, you notice that zbank is quoting euro 0.7627/us$, and sbank is offering sfr1.1806/us$. you learn that hsbc is making a direct quote of 0.6395. show 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.

what is the implied euro/sfr cross-rate derived from the dollar exchange rates quoted by zbank and sbank?

Answer 1

To make a triangular arbitrage profit, convert $5,000,000 into euros, then into Swiss francs using the implied EUR/SFr cross-rate, and convert back to US dollars. The profit results from discrepancies in exchange rates. However, ignoring bid-ask spreads, as in this example, may actually result in a loss.

Step-by-step explanation:

To demonstrate how to make a triangular arbitrage profit, let’s assume you use the given $5,000,000 to first convert it into euros through ZBank at the rate of EUR 0.7627/US$. You would get EUR 3,813,500. Then, you convert your euros into Swiss francs (SFr) through the implied EUR/SFr cross-rate, which is derived by dividing SBank’s SFr1.1806/US$ quote by ZBank’s EUR 0.7627/US$ quote, resulting in an implied rate of 1 SFr/EUR 1.5475. TConverted, this gives you SFr 5,898,262.75.

Now, you can take the Swiss francs and convert them back to US dollars through SBank's quote of SFr1.1806/US$. When you convert SFr 5,898,262.75 back into dollars, you get approximately $4,994,880.

You’ve made a round trip with your initial $5,000,000 and ended up with less than you started with due to the bid-ask spread that was ignored in this scenario; however, real triangular arbitrage would seek to exploit discrepancies in quoted exchange rates between different banks to make a profit.