Triangular Arbitrage
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Arbitrage
Note that if the above relationship did not hold there would be opportunities for cross currency arbitrage. For example suppose that S(F Fr/ÐЈ) falls to 8. Then this implies that the exchange rate of the Lira against the French franc, S(Lira/F Fr) =298.875. Thus a French dealer with one million francs but wanting Lira could exchange these for 125,000 pounds in London and then simultaneously exchange them for 298,875,000 Lira. Which is more than he would have obtained at the 277.3 Lira per French franc rate. However the increased demand for pounds would quickly cause the value of the pound vis-Д -vis the French franc to appreciate to its equilibrium value.
By comparing the cross rate with the exchange rate between two currencies in other markets, a FX dealer can ascertain whether there is any profit from triangular arbitrage. By triangular arbitrage we mean exchanging currency A for currency B for currency C and currency C for the original currency A, to take advantage of any inconsistencies among exchange rates.
Example,
Currency
US Dollars
Pounds
Market
New York
0.4264
1.4205
Frankfurt
2.3452
3.3450
London
0.7040