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## Q. 8.MSE.10

You go to a bank and are given these quotes:
You can buy a euro for 14 Mexican pesos.
The bank will pay you 13 pesos for a euro.
You can buy a U.S. dollar for .9 euros.
The bank will pay you .8 euros for a U.S. dollar.
You can buy a U.S. dollar for 10 pesos.
The bank will pay you 9 pesos for a U.S. dollar.
You have \$1,000. Can you use triangular arbitrage to generate a profit? If so, explain the order of the transactions that you would execute and the profit that you would earn. If you cannot earn a profit from triangular arbitrage, explain why.

## Verified Solution

Yes, you can generate a profit by converting dollars to euros, and then euros to pesos, and then pesos to dollars. First convert the information to direct quotes:

 Bid Ask Euro in \$ 1.11 1.25 Pesos in \$ \$.10 \$.11 Euro in pesos 13 14

Use \$1,000 to purchase euros: \$1,000/1.25 = 800 euros.
Convert 800 euros to buy pesos: 800 euros × 13 10,400 pesos.
Convert the 10,400 pesos to U.S. dollars: 10,400 × \$.10 = \$1,040.
There is profit of \$40 on a \$1,000 investment.

The alternative strategy that you could attempt is to first buy pesos:
Use \$1,000 to purchase pesos: \$1,000/\$.11 = 9,090.9 pesos.
Convert 9,090 pesos to euros: 9,090.9/14 = 649.35 euros.
Convert 649.35 euros to dollars: 649.35 euros × 1.11 = \$720.78.
This strategy results in a loss.