Eco- Triangular Arbitrage: Sample questions from CFA website

CFA Level II Economics
#1

Hello eveyrone, On the CFA website they provide sample questions. Under the Economics chapter you have the case of Louise Tremblay. I do not understand the answer and explanation for question 3:

Country Currency Spot Exchange Rate

United States US$ NA Canada C$ 1.2138–1.2259 Brazil Real (BRL) 2.3844–2.4082

3) 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: Anser is US$21,135 profit Explanation:

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

Can someone explain to me how the explanation knows right away that it is cheaper to buy Canadian Dollars indirectly through Brazilian reals? I mean how do they know that they have to proceed this way? Thanks a lot for your help

#2

I normally calculate the cross rate first.

0.5040 - 0.5141

It is more obvious that you can buy BRL in the market through CAD for 0.5141 and sell to the dealer at 0.5250.

#3

They don’t know right away. They had to try it one way, then, possibly, try it the other way. It looks as though they know right away because they don’t show you a calculation where they tried it the wrong way first.

I wrote an article on this that may be of some help: http://financialexamhelp123.com/triangular-arbitrage/.

#4

That’s great! thx a lot I will reqd it carefully. Thx for the explanation too!

#5

Hi S2000magician, Just wanted to say that you wrote a great article!!! I understood right away. And your mnemonic device is awesome: the dealer is stingy and divide by the bigger, multiply by the small. Great tools thx a lot!

#6

Thanks. I appreciate your kind words.

#7

I feel lucky to have bumped into this post… I guess they say you create your own luck. Magician, thank you.