Question

Assume you are a trader with Royal Bank of Canada. From the quote screen on your computer

terminal, you notice that T-D Bank is quoting €1.1074/$1.00 and Bank of Montreal is offering
AUD1.4505/$1.00.
You learn that Scotiabank is making a direct market between the Australian dollar and the
euro, with a current €/AUD quote of 0.7228.
Assume you have $15,000,000 with which to conduct the arbitrage.
1. Find the cross rate that will eliminate triangular arbitrage.
2. Show how you can make a triangular arbitrage profit by trading at these prices

Answer 1

The cross rate that will eliminate triangular arbitrage is approximately €0.5484/$1.00. To make a triangular arbitrage profit, you can take advantage of a higher cross rate than €0.5484/$1.00.

Step-by-step explanation:

To find the cross rate that will eliminate triangular arbitrage, we can use the formula:

Cross rate = (Bid currency 1/Bid currency 2) / (Ask currency 1/Ask currency 2)

Using the given quotes, the cross rate between the euro, Australian dollar, and US dollar would be:

Cross rate = (€/AUD) / ($/AUD) * (€/$)

Substituting the given quotes, the cross rate is calculated as:

Cross rate = (0.7228) / (1.4505) * (1.1074) ≈ 0.5484

Therefore, the cross rate that will eliminate triangular arbitrage is approximately €0.5484/$1.00.

To show how you can make a triangular arbitrage profit, we need to identify an opportunity where the cross rate differs from the calculated cross rate. In this case, if the cross rate is higher than €0.5484/$1.00, you could buy Australian dollars with euros, convert the Australian dollars to US dollars, and finally convert the US dollars back to euros, resulting in more euros than the original amount.