Given $1,000.00, the following spot exchange rates, and assuming zero transaction costs, illustrate and explain how you could use triangular arbitrage to profit on the disequilibrium in the foreign exchange market. The price of the euro (€) in terms of U.S. dollars is $1.20. The price of the British pound (£) in U.S. dollars is $1.30, and the cross rate between the € and the £ is 0.89 pounds per euro.
What will be an ideal response?
POSSIBLE RESPONSE: Triangular arbitrage, which is also referred to as cross-currency arbitrage, is the process of exploiting an arbitrage opportunity that results from a pricing discrepancy among three different currencies in the foreign exchange market. A triangular arbitrage strategy involves three trades, exchanging the initial currency for a second, the second currency for a third, and the third currency for the initial currency. The discrepancy exists when the market cross exchange rate is not equal to the implicit cross exchange rate. Given the above spot exchange rates and assuming no transactions costs, one could use triangular arbitrage to make an instantaneous, risk-free profit. With the $1,000.00 first purchase £769.23 (1,000/1.30). Next, use the £769.23 to purchase €864.30 at the cross-rate 0.89 pounds per euro (769.23/0.89). Finally, convert the €864.30 back into $1037.16 (864.30 × 1.20) to make a profit of $37.16. In this case the quoted market cross-rate is 0.89 pounds per euro and the implicit market cross-rate is 0.92 pounds per euro.
Implicit market cross-rate (the number of British pounds per euro)
$/€ = 1.20
$/£ = 1.30
$/€ × £/$ = £/€
1.2 × 0.7692 = 0.92 ? 0.89
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