Arbitrage can be loosely defined as capitalizing on a discrepancy in quoted prices by making a riskless profit. In many cases, the strategy does not require an investment of funds to be tied up for a length of time and does not involve any risk.
Two coin shops buy and sell coins. If shop A is willing to sell a particular coin for $120, while Ship B is willing to buy that same coin for $130, a person can execute arbitrage by purchasing the coin at Ship A for $120 and selling it to Shop B for $130. The prices at coin ships can vary because demand conditions may vary among shop locations. If two coin shops are not aware of each other’s prices, the opportunity for arbitrage may occur. The act of arbitrage will cause prices to realign. In our example, arbitrage would cause Shop A to raise its price (due to high demand for the coin). At the same time, Shop B would reduce its bid price after receiving a surplus of coins as arbitrage occurs. The type of arbitrage discussed in this chapter is primarily international in scope; it is applied to foreign exchange and international money markets and takes three common forms:
- Locational arbitrage
- Triangular arbitrage
- Covered interest arbitrage.
Each form will be discussed in turn.
Commercial banks providing foreign exchange services normally quote about the same rates on currencies, so shopping around may not necessarily lead to a more favorable rate. If the demand and supply conditions for a particular currency vary among banks, the banks may price that currency at different rates, and market forces will force realignment
When quoted exchange rates vary among locations, participants in the foreign exchange market capitalize on the discrepancy. Specifically, they can use locational arbitrage, which is the process of buying a currency at the location where it is prices cheap and immediately selling it at another location where it is priced higher.
Akron Bank and Zyn Bank serve the foreign exchange market by buying and selling currencies. Assume that there is no bid/ask spread. The exchange rate quoted at Akron Bank for a British pound is $1.60, while the exchange rate quoted at Zyn Bank is $1.61. You could conduct locational arbitrage by purchasing pounds at Akron Bank for $1.60 per pound and then selling them at Zyn Bank for $1.61 per pound. Under the condition that there is no id/ask spread and there are no other costs to conducting this arbitrage strategy, your gain would be $.01 per pound. The gain is risk free in that you knew when you purchased the pounds how much you could sell them for. Also, you did not have to tie your funds up for any length of time. Locational arbitrage is normally conducted by banks or other foreign exchange dealers whose computers can continuously monitor the quotes provided by other banks. If other banks noticed a discrepancy between Akon Bank and Zyn Bank, they would quickly engage in locational arbitrage to earn an immediate risk-free profit. Since banks have a bid/ask spread on currencies, this next example accounts for the spread.
Cross exchange rates represent the relationship between two currencies that are different from one’s base currency. In the United States, the termcross exchange rates refers to the relationship between two non-dollar currencies.
If the British pound (£) is worth $1.60, while the Canadian dollar (C$) is worth $.80, the value of the British pound with respect to the Canadian dollar is calculated as follows:
Value of £ in units of C$ = $1.60/$.80 = 2.0
The value of the Canadian dollar in units of pounds can also be determined by cross exchange rate formula:
Value of C$ in units of £ = $.80/ $1.60= .50
Notice that the value of a Canadian dollar in units of pounds is simply the reciprocal of the value of a pound in units of Canadian dollars. If a quoted across exchange rate differs from the appropriate cross exchange rate (as determined by the preceding formula), you can attempt to capitalize on the discrepancy. Specifically, you can use triangular arbitrage in which currency transactions are conducted in the spot market to capitalize on a discrepancy in the cross exchange rate between two currencies.
Assume that a bank has quoted the British pound £ at $1.60, the Malaysian ringgit (MYR) at $.20, and the cross exchange rate at £ = MYR8.1. Your first task is to use the pound value in U.S. dollars and Malaysian ringgit. The cross rate formula in the previous example reveals that the pound should be worth MYR8.0.
When quoting a cross exchange rate of £1 –MYR8.0, the bank is exchanging too many ringgits for a pound and is asking for too many ringgits in exchange for a pound. Based on this information, you can exchange in triangular arbitrage by purchasing pounds with dollars, converting the pounds to ringgit, and then exchanging the ringgit for dollars. If you have $10,000, how many dollars will you end up with if you implement this triangular arbitrage strategy? To answer the question, consider the following steps illustrated
- Determine the number of pounds received for your dollars: $10,000 = £6,250, based on the bank’s quote of 1.60 per pound.
- Determine how many ringgit you will receive in exchange for pounds: £6,250 = MYR50, 625, based on the bank’s quote of 8.1 ringgit per pound.
- Determine how many U.S. dollars you will receive in exchange for the ringgit: MRY50, 625 = $10,125 based on the bank’s quote of $.20 per ringgit (5 ringgit to the dollar). The triangular arbitrage strategy generates $10,125, which is $125 more than you started with.
Like locational arbitrage, triangular arbitrage does not tie up funds. Also, the strategy is risk free since there is no uncertainty about the prices at which you will buy and sell the currencies.
Accounting for the Bid/Ask Spread. The previous example is simplified in that it does not account for transaction costs. In reality, there is a bid and ask quote for each currency, which means that the arbitrageur incurs transaction costs that can reduce or even eliminate the gains from triangular triangle.