Topic Test: Economics - Tremblay Q3

CFA Level II Economics
#1

Hi guys, can someone please clarify the thought process on the arbitrage calculation below. How is the profit in US currency? I calculated the implied rate by the interbank as CAD/BRL 0.50403/0.51375. So your arbitrage opportunity is to buy BRL in the interbank market at 0.51375 and sell to the dealer selling 0.5250. Wouldn’t the riskless profit be quoted in CAD?

Thanks!

3 of 6

If a dealer’s bid-side quote for the CAD/BRL is C$0.5250, Tremblay’s profit on a US$1,000,000 initial investment in the triangular arbitrage opportunity is closest to:

US$21,135. US$31,328. US$31,315.

It is cheaper to buy Canadian dollars indirectly through Brazilian reals than directly with U.S. dollars. This creates a triangular arbitrage opportunity:

US$1,000,000 × 2.3844 = BRL2,384,400

2,384,400 × 0.5250 = C$1,251,810

C$1,251,810/1.2259 = US$1,021,135

US$1,021,135 – US$1,000,000 = US$21,135 profit

2014 CFA Level II “Currency Exchange Rates: Determination and Forecasting,” by Michael R. Rosenberg and William A. Barker Section 2.1

#2

When you go to approach triangular arbitrage problems, it’s helpful to write out the steps you need to take in order to complete the overall transaction. In every triangular arbitrage problem you come across, there will be three currency transactions, the final involving a conversion to the original currency. In this problem, we are a U.S. investor and therefore our gains are notated in USD.

Write your needed transactions out in your margins. Here, the transactions (in sequential order) involve:

  1. Selling USD and purchasing BRL (buying the base currency at the low rate) 2) Selling BRL and purchasing CAD (selling the base currency at the high rate) 3) Selling CAD and purchasing USD (converting back to the original currency)

Remember, you are a U.S. based investor and you see an arbitrage transaction between the CAD and the BRL. We’re given that a dealer has quoted us a bid rate (the rate which we sell at) so therefore we have to use cross rates to find the offer rate (the rate at which we buy). Because we can buy low and sell high, we have an arbitrage opportunity by buying in the interbank implied market and selling to the dealer.

When doing this problem, have a keen understanding of bid and offer rates and understand that by buying one currency you are selling another. That’ll help you when doing this. Remember:

USD --> 1 BRL --> 2 CAD --> 3 USD

Transaction 1 involves buying BRL (buying low) and selling USD, your existing currency.

Transaction 2 involves selling BRL (selling high) and buying CAD, the currency in which an arbitrage opportunity exists

Transaction 3 involves converting CAD back to USD. Therefore we are selling CAD and buying USD.

Hope this helps.

#3

This was really helpful, thank you so much!

#4

There is a superb explanation of Triangular Arbitrage at 20:00 in the Youtube link below. Check it out. This should be able to help clear things up.

https://www.youtube.com/watch?v=RqUDegAvjD8&t=1511s