# Bilateral arbitrage

FIGURE 7

(b) London

Dollars per Pound

Dollars per Pound

Dollars per Pound
Millions of British Pounds per Month

Initially, the price of the pound is \$1.20 in New York—panel (a)—and \$1.80 in London—panel (b). Traders take advantage of this exchange rate differential by buying pounds in New York and simultaneously selling them in London. As they do so, the demand curve shifts rightward in New York, and the supply curve shifts rightward in London. Arbitrage continues until the exchange rate attains the same value—\$1.50 per pound—in both locations.

Bilateral arbitrage ensures that the exchange rate between any two currencies is the same everywhere in the world.2

Triangular Arbitrage. Another form of arbitrage—called triangular arbitrage—

involves trades among three (or more) countries' currencies. Triangular arbitrage ensures that the number of dollars that exchange for one pound is the same whether you make the trade directly—in the dollar-pound market—or indirectly, by buying and selling a third currency.

To see how triangular arbitrage works, suppose that the exchange rates among the U.S. dollar, the British pound, and the Mexican peso are as shown in the left-hand column of Table 2: The price of a pound in dollars is \$1.80, the price of a peso in dollars is \$0.10, and the price of a pound in pesos is 10 pesos.

With these exchange rates, the direct price of the pound to Americans is \$1.80. But the indirect price is \$1.00. Why? Because an American, starting with \$1.00, could purchase 10 pesos in the dollar-peso market and then use those 10 pesos to purchase 1 pound in the peso-pound market. This difference between the direct and indirect prices for the pound would allow traders to make huge profits. They could

Triangular arbitrage Arbitrage involving trades among three (or more) currencies.

2 Exchange rates will sometimes appear to be different in different locations because a commission for the broker is often built into the rate. These commissions can differ by location, depending on the cost structure and degree of competition among brokers. For example, if you buy pounds in a small-town bank, which faces little competition and may have higher costs, you may pay more for them than if you bought them in a big-city bank. But this is only because the small-town bank is charging a higher commission.

 TABLE 2 before and after triangular arbitrage Exchange Rate Before Arbitrage Exchange Rate After Arbitrage Price of pound in dollar-pound market \$1.80 \$1.50 Price of peso in dollar-peso market \$0.10 \$0.125 Price of pound in pound-peso market 10 pesos 12 pesos

acquire pounds indirectly for \$1.00 each and then sell them directly for \$1.80 each, for a huge profit of 80 cents per pound sold.

However, such large potential profits from triangular arbitrage would never arise in practice. Even the tiniest potential profits would be eliminated, almost immediately, by the arbitrage process itself. In our example, when traders buy pesos with dollars, they drive up the price of the peso in the dollar-peso market. When they buy pounds with pesos, they drive up the price of the pound in the pound-peso market. Finally, when they buy dollars with pounds to make their profit, they drive down the price of the pound in the dollar-pound market.

Each of these movements decreases the potential profits from arbitrage, and the process ends when no opportunity for such profits remains. The third column in Table 2 shows where the exchange rates might end up after the arbitrage process is completed. With these exchange rates, the direct price of the pound is \$1.50. And this is also what it would cost to buy a pound indirectly: \$1.50 gets you 12 pesos, and 12 pesos gets you one pound. There are no more opportunities for arbitrage, because arbitrage has eliminated them.

Triangular arbitrage ensures that the price of a foreign currency is the same whether it is purchased directly—in a single foreign exchange market—or indirectly, by buying and selling a third currency.3