# Geographical arbitrage

In principle, the exchange rate for a given currency should be the same in every geographical market. However, geographical arbitrage could arise when local demand-and-supply conditions might create temporary discrepancies among various markets. Arbitrage specialists would buy the currency in a market where its price is lower and then sell the currency where its price is higher. If the exchange rate differential is larger than the transaction cost, an arbitrage profit would be made.

Two-point arbitrage The arbitrage transaction between two currencies is called a two-point arbitrage. Suppose, for example, that the quotes of the South African rand against the US dollar are \$0.20 in New York and \$0.25 in Johannesburg. The price of rands in terms of dollars is higher in Johannesburg than in New York. An arbitrageur could benefit by buying rands with dollars in New York and then selling the rands in exchange for dollars in Johannesburg. Arbitrage tends to wipe out the exchange rate differential that originally triggered it. The purchase of rands in New York would drive the price of rands against the dollar up toward the Johannesburg rate. The sale of rands in Johannesburg would drive the price of rands against the dollar down toward the New York rate. This arbitrage process would continue until the price of rands in terms of the dollar was the same in both markets.

The basic economic principle of "buy low and sell high" dominates the arbitrage transaction of buying and selling currencies in two national money markets. Exchange rates in two different locations must be stated in a given currency if this principle is to be applied in foreign exchange. Thus, the arbitrage process becomes slightly more difficult to understand if exchange rates are quoted in different currencies. Let us restate our previous example in a slightly different way. The price of rands against the dollar is \$0.20 in New York. The price of dollars against the rand is R4 in Johannesburg. The quotes in both locations in terms of \$/R are as follows:

 New York Johannesburg \$0.20/R (as initially given) \$0.25/R (1 n 4)

The rand enjoys a higher price against the dollar in Johannesburg than in New York. This price differential would lead to the following transactions in each market:

1 In New York, investors would buy rands and sell dollars.

2 In Johannesburg, investors would sell rands and buy dollars.

Three-point arbitrage An arbitrage transaction among three currencies is called a three-point arbitrage and is also commonly known as a triangle arbitrage. This type of arbitrage can occur if any of the three cross rates is out of line. Consider the possibility that the cross rates of exchange are Rs60/\$, Rs10/HK\$, and HK\$3/\$. An arbitrageur could make a profit of \$1. She would buy 60 Indian rupees for \$1, then purchase six Hong Kong dollars for 60 Indian rupees, and finally buy \$2 for the six Hong Kong dollars. A large volume of such transactions would strengthen the rupee against the dollar, strengthen the Hong Kong dollar against the rupee, and strengthen the dollar against the Hong Kong dollar. This arbitrage process causes some consistent patterns of rates to emerge at which no further arbitrage would be profitable. In other words, the arbitrage will continue until dollars can no longer be bought more cheaply in one market than the price at which they are sold in another market. Currency cross rates such as those given in table 5.1 can be prepared to ensure that the exchange rates are consistent with each other in all markets.

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### Responses

• heike
What is geographical arbitrage?
8 years ago