Question

Problem: triangular arbitrage

A. Bid 1 euro = 1.11$ Ask 1 euro = 1.12$

B. Bid $1 = 0.75 GBP   Ask $1 = 0.76 GBP

C. Bid 1 GBP = 1.2 euros Ask 1 GBP = 1.21 euros

Using 1000 GBP, show whether arbitrage is possible (show both scenarios and compute profits/losses).

Answer 1

Scenario 1:

Convert 1000 GBP into Euro and get 1000*1.2 = 1,200 Euro

Convert Euro into Dollar and get 1,200*1.11 = $1,332

Convert Dollar back into GBP = 1,332*0.75 = GBP 999

Profit/Loss = 999 GBP - 1,000 GBP = (1)GBP

i.e. Loss

Scenario 2:

Convert 1000 GBP into Dollar and get 1,000/0.76 = $1,315.78947

Convert into Euro 1,315.78947/1.12 = Euro 1,174.8120

Convert into GBP = 1,174.8120/1.21 = GBP 970.92

Profit/Loss = 970.92 - 1,000 = GBP (29.08)

Hence, arbitrage is NOT possible, since no profit