Daily trading volume in the foreign exchange markets often exceeds $1 trillion. Participants trade in the spot currency markets, forward markets, and futures markets. In addition, currency options, currency swaps, and other derivative contracts are traded. For simplicity, this case focuses on the spot currency market only. A spot currency transaction is simply an agreement to buy some amount of one currency using another currency.14 For example, a British company might need to pay a Japanese supplier 150 million yen. Suppose that the spot yen/pound rate is 134.33. Then the British company could use the spot currency market to buy 150 million yen at a cost of 1,116,653 (150,000,000 134.33) British pounds. A sample of todays cross-currency spot rates is given in the file Currency Rates.xlsx. To continue the example, suppose the company canceled the order from the supplier and wanted to convert the 150 million yen back into British pounds. If the pound/yen spot rate is 0.00743, the company could use the 150 million yen to buy 1,114,500 (150,000,000 0.00743) pounds. Note that the 1,114,500 pounds is less than the original 1,116,653 pounds. The difference is the result of the bid-offer spread: The price to buy yen (the bid price) is greater than the price to sell yen (the offer price). The bid-offer spread represents a transaction cost to the company. CASE 4.4 FOREIGN CURRENCY TRADING Occasionally, market prices may become out of line in the sense that there are arbitrage opportunities. In this context, arbitrage means that there is a set of spot currency transactions that creates positive wealth but does not require any funds to initiatethat is, it is a money pump. When such pure arbitrage opportunities exist, supply and demand forces will generally move prices to eliminate the opportunities. Hence, it is desirable to quickly identify arbitrage opportunities when they do exist and to take advantage of them to the greatest extent possible.

Questions

1. Develop an LP model to determine whether there are any arbitrage opportunities with the spot currency rates given in the file. Note that an arbitrage opportunity could involve several currencies. If there is an arbitrage opportunity, your model should specify the exact set of transactions to achieve it.

2. Find the cross-currency rates in a recent newspaperfor example, in the Wall Street Journalor on the Web at http://www.oanda.com/ convert/classic. Check the numbers for an arbitrage opportunity. If you find one, do you think it represents a real arbitrage opportunity? Why or why not?