Question

You notice the following quotes in the foreign exchange market:

$.004/¥

€1.25/$

ACR: €.006/¥

Correct answer is 3,800,000

Please show formula and steps that was used

Find the maximum triangular arbitrage profit available to you (in dollars) if you have access to $20 million at a 1% interest rate.

Answer 1

Step1: what the triangular Arbitrage will be-

a) $ to Yen = 0.004:1

b) Euro to Yen = 0.006

c) Euro to $ - 1.25:1

Based on a) and b)

$ to Euro = a)/ b) = 0.004/0.006 = 1/1.5

=> Euro to $ = 1.5:1

While prevailing rate of Euro to $ is 1.25:1

Step 2: Execute the arbitrage

Buy Yen with $

=> $20,000,000 / 0.004 = Yen 5,000,000,000 (using a)

Buy Euro with Yen

=> 5,000,000,000 * 0.006 = Euro 30,000,000 (using b)

Buy $ with Euro

=>30,000,000 /1.25 = $24,000,000 (using c)

Gross Profit is

24000000 - 2000000 = $4000000

Interest cost @ 1% is

20,000,000 * 1% = $200,000

Thus,

Net Profit is 4000000 - 200000 = $3,800,000 = $3.8M