Arbitrage traditionally has been defined as the purchase of assets or commodities on one market for immediate resale on another in order to profit from a price discrepancy. In recent years however arbitrage has been used to describe a broader range of activities. The concept of arbitrage is of particular importance in International finance because so many of the relationships between domestic and international financial markets, exchange rates, interest rates and inflation rates depend on arbitrage for their existence. In fact it is the process of arbitrage that ensures market efficiency.
The purchase of currencies on one market for immediate resale on another in order to profit from the exchange rate differential is known as currency arbitrage. If perfect conditions prevail in the market, the exchange rate for a currency should be the same in all centers. Until recently, the pervasive practice among bank dealers was to quote all currencies against the US dollar when trading among them. Now, however, a growing percentage of currency trades don‘t involve the dollar. For example Swiss banks may quote the Euro against Swiss franc, and German banks may quote pound sterling in terms of Euros. Exchange traders are continually alert to the possibility of taking advantage, through currency arbitrage transactions, of exchange rate inconsistencies in different money centers. These transactions involve buying a currency in one market and selling it in another. Such activities tend to keep exchange rates uniform in the various markets.
For example, if US dollar is quoted at Rs. 42.4000 in Mumbai, it should be quoted at the same rate of Rs. 42.4000 at New York. But under imperfect conditions prevailing, the rates in different centers may be different. Thus at New York Indian rupees may be quoted at Rs. 42.4800 per dollar. In such a case, it would be advantageous for a bank in Mumbai to buy US dollars locally and arrange to sell them at New York. Assuming the operation to involve Rs. 10 lakhs, the profit made by the bank would be:
At Mumbai US dollars purchased for Rs. 10,00,000 at Rs. 42,4000 would be (10,00,000 ÷ 42.4000) USD 23,584.90.
Amount in rupees realized on selling USD 23,584.90 at New York at Rs. 42.4800 would be Rs. 10,01,887.
Therefore, the gross profit made by the bank on the transaction is Rs, 1,887. The net profit would be after deducting cable charges, etc., incurred for the transaction.
The purchase and sale of a foreign currency in different centers to take advantage of the rate differential is known as ‘arbitrage operations’.
When the arbitrage operation involves only two currencies, as in our illustration, it is known as ‘simple’ or ‘direct’ arbitrage.
Sometimes the rate differential may involve more than two currencies. For example, let us say that these rates are prevailing:
- Mumbai on New York Rs. 42.4000
- New York on London USD 1.5100
- Mumbai on London Rs. 64.0600
Based on quotation for dollar in Mumbai and for sterling in New York, the sterling rate in Mumbai should be Rs. 64,0250 while the prevailing rate is Rs. 64.0600. The bank can buy dollar locally and utilize it in New York to acquire sterling there. The sterling thus purchased may be disposed of locally. Let us say the transaction in undertaken for Rs. 10,00,000.
- The bank buys dollars for Rs. 10,00,000 at Mumbai. Amount realized in dollars is (10,00,000 ÷ 42.4000) USD 23,584.90.
- The bank sells USD 23,584.90 at New York and acquires pound sterling. Amount realized in pound sterling at USD 1.5100 per pound is (23,584.90 ÷ 1.5100) GBP 15,619.14.
- The bank sells GBP 15,619.14 at Bombay at Rs. 64.0600 and realizes Rs. 10,00,562.
Therefore, the gross profit on the combined transaction is Rs. 562.
Such an arbitrage operation which involves more than two currencies is known as ‘compound’ or ‘indirect’ arbitrage.
Currency arbitrage transactions also explain why such profitable opportunities are fleeting. In the process of taking advantage of an arbitrage opportunity the buying and selling of currencies tends to move rates in a manner that eliminates profit opportunity in the future. When profitable arbitrage opportunities disappear, we say that the no arbitrage condition holds.