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Arbitrage is the process of simultaneous buying and selling of an asset from different platforms, exchanges or locations to cash in on the price difference (usually small in percentage terms). While getting into an arbitrage trade, the quantity of the underlying asset bought and sold should be the same. Only the price difference is captured as the net pay-off from the trade. The pay-off should be large enough to cover the costs involved in executing the trades (i.e. transaction costs). Else, it won’t make sense for the trader to initiate the trade in the first place.

The exchange rate between any two currencies is kept the same in different monetary centers by arbitrage. This refers to the purchase of a currency in the monetary center where it is cheaper, for immediate resale in the monetary center where it is more expensive, in order to make a profit.

For example, if the dollar price of the euro was $0.99 in New York and $1.01 in Frankfurt, an arbitrageur (usually a foreign exchange dealer of a commercial bank) would purchase euros at $0.99 in New York and immediately resell them in Frankfurt for $1.01, thus realizing a profit of $0.02 per euro. While the profit per euro transferred seems small, on ¤1 million the profit would be $20,000 for only a few minutes work. From this profit must be deducted the cost of the electronic transfer and the other costs associated with arbitrage. Since these costs are very small, we shall ignore them here.

As arbitrage takes place, however, the exchange rate between the two currencies tends to be equalized in the two monetary centers. Continuing our example, we see that arbitrage increases the demand for euros in New York, thereby exerting an upward pressure on the dollar price of euros in New York. At the same time, the sale of euros in Frankfurt increases the supply of euros there, thus exerting a downward pressure on the dollar price of euros in Frankfurt. This continues until the dollar price of the euro quickly becomes equal in New York and Frankfurt (say at $1 = ¤1), thus eliminating the profitability of further arbitrage.When only two currencies and two monetary centers are involved in arbitrage, as in the preceding example, we have two-point arbitrage. When three currencies and three monetary centers are involved, we have triangular, or three-point, arbitrage. While triangular arbitrage is not very common, it operates in the same manner to ensure consistent indirect, or cross, exchange rates between the three currencies in the three monetary centers. For example, suppose exchange rates are as follows:

$1 = ¤1 in New York

¤1 = £0.64 in Frankfurt

£0.64 = $1 in London

These cross rates are consistent because

$1 = ¤1 = £0.64

and there is no possibility of profitable arbitrage. However, if the dollar price of the euro were $0.96 in New York, with the other exchange rates as indicated previously, then it would pay to use $0.96 to purchase ¤1 in New York, use the ¤1 to buy £0.64 in Frankfurt, and exchange the £0.64 for $1 in London, thus realizing a $0.04 profit on each euro so transferred.

On the other hand, if the dollar price of the euro was $1.04 in New York, it would pay to do just the opposite—that is, use $1 to purchase £0.64 in London, exchange the £0.64 for ¤1 in Frankfurt, and exchange the ¤1 for $1.04 in New York, thus making a profit of $0.04 on each euro so transferred.

As in the case of two-point arbitrage, triangular arbitrage increases the demand for the currency in the monetary center where the currency is cheaper, increases the supply of  the currency in the monetary center where the currency is more expensive, and quickly eliminates inconsistent cross rates and the profitability of further arbitrage. As a result, arbitrage quickly equalizes exchange rates for each pair of currencies and results in consistent cross rates among all pairs of currencies, thus unifying all international monetary centers into a single market.

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