# Schweser FX Triangle Question

Hi guys,

I’m struggling on a concept checker in the Schweser book 1, p. 315, q. 13. I obviously get the same result when starting by selling vs. GBP. But fail to do so, when initially selling vs. EUR. I just don’t get it…

I start by selling the USD 1mn versus EUR at 0.7, which leaves me with EUR 700k. Then proceed by selling the EUR vs. GBP at 1.201 which gives GBP 582,8k. Finally exchanging back to USD at 1.7, equalling 990.8k. So according to my way, I’d be left with a negative arbitrage.

Can anyone spot my mistake? I assume one should get the same result no matter how you work up the triangle…

Since you end up neg this way you want to go the other route:

1000k usd -> buy gbp 588.24 (1/1.7) -> buy eur 706.457 (.7)-> 100.924k usd ==> .924k arb profit right?

If going around one direction results in profit, then going in opposite direction will produce a loss. The size of loss and gain may not be equal due to the bid-ask spread.

The reverse triangle would be (I think) 1. USD:EUR (bid), 2. EUR:GBP (bid)=1/(GBP:EUR(ask)), 3. GBP:USD (bid)

but if obviously various paths result in either arbitrage opportunities or not, how can i save time to pick the right ‘path’ from the very beginning? i guess there has to be another way than just calculating all the possibilities until you end up with an arbitrage profit…?

Calculate the implied cross rate to see if there is an arbitrage opportunity:

USD/GBP x EUR/USD = EUR/GBP

You are given all the above market exchange rates in the example. If the cross exchange rate implied by the the equation above is not equal to the market FX rate, you have an arbitrage opportunity. Implied is less than market in this case, we have a chance here !

A triangle arbitrator buy GBP spending USD + buy EUR with GBP + sell EUR to buy USD.

If you are asked only about the profits, you dont need to spend time with converting currencies…just calculate 1/1.7010 x 1.2000 / 0.7010= 1.0064. Your profit is (1.0064-1) x US\$1m.