# Triangular arbitrage formula error

I am struggling with a formula for calculating the above. I have been using the following example: https://www.youtube.com/watch?v=lKu2LAgEcpU

A = YEN82 / USD
B = USD1.6 / GBP
C = GBP128 / YEN


The implied JPY/GBP XRate is 131.2 (82 X 1.6).

As the difference between the implied JPY/USD XRate and the quoted XRate is a constant should my result not always be either positive or negative the same value? In my calculations I am getting a 2.5% margin when I calculate one way and a -2.44% margin when I calculate the other way. I would have expected the result to be either 2.5% or -2.5%

i.e. Starting with JPY100,000,000

Option A = 2.5% gain
====================
JPY to GBP = 781,250
USD to GBP = 1,250,000
JPY to USD = 102,500,000

Option B = 2.44% loss
=====================
JPY to USD = 1,219,512.20
USD to GBP = 762,195.12
JPY to GBP = 97,560,975.61


## 2 Answers

It is correct because a 2.50pct gain followed by a 2.44pct loss gets you back to where you started. I.e. (1+0.025)(1-0.0244)=1.

You can dowload the following Excel file that implements the triangular arbitrage. Just replace the numbers and currencies with yours and the solution to check your outcome.

Hope this helps :)