Question

Problem 2.(35 points) Suppose that the current Japan/US exchange rate is Eyys - 120, while the current Japan/Euro exchange rate is Eyje = 130 and the Euro/US exchange rate is Ee/s-0.7. Suppose your bank can exchange dollars, yen and euros freely and without extra charge at the current exchange rate. Now consider the following scheme. 1. Suppose you take out $100 from your savings account and convert them into yen at the current exchange rate. How many yen would you have? 2. You next take the yen you just obtained and convert them into euros. How many euros would you have? 3. You next take the euros and convert them back to dollars. How many dollars would you get? 1. What is your revenue from running this scheme?

Answer 1

1. If you take 100 Dollars and convert to yen at the exchange rate of 120 yen per dollar, you will get 100*120=12,000 Yen

2. If you take these 12,000 yen and convert to euros at the exchange rate of 130 yen per euro, you will get 12,000/130=92.308 Euros

3. If you take 92.308 Euros and convert it back to US dollars at an exchange rate of 0.7 Euros/Dollar, you will get 92.308/0.7=131.87 Dollars.

4. The revenue from running the scheme will be 131.87-100= 31.87$ gained per 100$ used for the scheme.

5. This scheme is not feasible in real life as due to use of high speed computers and high-speed trading systems, large scale traders often catch the differences and close the gap quickly. The exchange rates are really close, for example in this example the exchange rate in the stage 3 between Euros and dollar will be close to 0.92 Euros per dollar so the total dollars in the end is only very slightly greater than 100 and the difference is small enough to not make it worthwhile to run small amounts through the scheme due to transaction costs. Thus it is only possible for large scale traders with high speed systems to profit from the minor differences and so the gaps close very soon.

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