# Simple three-pair triangulation question

I have a question I came across whilst self-studying and I need to use cross-currency triangulation. I am not too sure how to apply the cross-rate formula, and was hoping someone could show me how to apply it here.

As a market trader you are looking for an arbitrage opportunity. Using the following cross rates given by the banks you are working with, determine whether there is a triangular arbitrage opportunity for the US\$ 1 million that you would like to invest.

• Bank A quotes: RUB 64.42 /USD
• Bank B quotes: TRY 4.48 /USD
• Bank C quotes: RUB 14.39 /TRY

Thank you in advance for any help provided.

RUBUSD - how many RUB per USD
TRYUSD - how many TRY per USD
RUBTRY - how many RUB per TRY

RUBUSD/TRYUSD = RUBTRY 64.42/4.48 = 14.3795 which is less RUB per TRY compared to the direct RUBTRY quote.

Use your USD to get TRY - gives 4.48M
Use TRY to get RUB - gives 64.4672M
Use RUB to buy USD - gives ~ 1.000.732,692 USD

If you are unsure about the direction, you can simply try going around the circle in either direction. One way you will end up with a profit, the other with a loss.

There will be numerous online resources for questions like this if you spend some time with google. Searching cross triangle arbitrage should show Investopedia's Triangular Arbitrage Definition - Investopedia as the first result. This page also has a working example with EUR / GBP and USD:

EUR/USD = 0.8631, EUR/GBP = 1.4600 and USD/GBP = 1.6939. With these exchange rates there is an arbitrage opportunity:

Sell dollars for euros: $$1 million x 0.8631 = €863,100 Sell euros for pounds: €863,100 ÷ 1.4600 = £591,164.40 Sell pounds for dollars: £591,164.40 x 1.6939 =$$1,001,373
Subtract the initial investment from the final amount: $$1,001,373 –$$1,000,000 = $$1,373 From these transactions, you would receive an arbitrage profit of$$1,373 (assuming no transaction costs or taxes).