Question

Take the following two exchange rates and compute the EUR/INR cross exchange rate. INR12.1225/USD and EUR.8145/USD.

In the question above, if there is a direct cross exchange rate of EUR.066215/INR, is there a triangular arbitrage opportunity? If yes, start with $50,000 and indicate how much triangular arbitrage profit exists for 1 trip around the triangle. Show your work

Answer 1

Exchange rate 1: INR 12.1225/USD

Exchange rate 2: EUR 0.8145/USD

Exchange rate 3: EUR 0.066215/INR

First, let's find the cross rate between INR and EUR from exchange rates 1 and 2

Cross rate = 0.8145/12.1225

Cross rate = EUR 0.06718911116/INR

Yes, there is a triangular arbitrage opportunity as the cross rate is different from the direct cross exchange rate (exchange rate 3)

We follow the three steps below to exploit the opprotunity.

Step 1: Sell $50,000 to buy EUR at exchange rate 2

$50,000 = 50,000 * 0.8145 = EUR 40,725

Step 2: Sell EUR 40,725 to buy INR at exchange rate 3

EUR 40,725 = 40,725/0.066215 = INR 615,041.9089330212

Step 3: Sell INR 615,041.9089330212 to buy USD at exchange rate 1

INR 615,041.9089330212 = 615,041.9089330212/12.1225 = USD 50,735.5668329982

Triangular arbitrage = 50,735.5668329982 - 50,000

Triangular arbitrage = USD 735.5668329982