Solution to Problem Set 3 Fall 04 - Arkansas State University

[Pages:2]Problem Set 3 International Trade

SOLUTION

1. (a) Explain how foreign exchange arbitrage will take place if $1.98 = ?1 in New York and at the same time $2.00 = ?1 in London. (b) What happens as arbitrage takes place? (5 points)

Answer: (a) Foreign exchange arbitrageurs will buy pounds in New York at $1.98 per pound and immediately resell them in London for $2.00, making a profit of $0.02 or 1% on each pound so exchanged (minus the interest charge on the money during the time it is tied up in arbitrage and the cost of the telegraphic transfer[transaction costs]--both of which are very small). This profit margin may seem very small indeed, but on a transaction of $1million, it means a gain of almost $10,000 for only a few minutes work. It is important to note that if this transaction is carried out correctly, the arbitrageur incurs no risk. (b) As arbitrage continues, the dollar price of the pound tends to increase in New York (because of the increase in demand for pounds) and to fall in London (because of the increased supply of pounds). This tends to reduce the profitability of arbitrage and to result in approximately the same dollar price for the pound in New York, London and every other monetary center where the two currencies are traded for each other. When foreign exchange arbitrage does not occur either because of lack of knowledge or because it is forbidden, wide differences can exist in different monetary centers in the exchange rate between two currencies.

2. Suppose that the spot rate of the pound today is $2.00 while the 3-month forward rate is $2.02. (a) How can a U.S. importer who has to pay ?10,000 in 3 months hedge his foreign exchange risk? (b) What happens if the U.S. importer does not hedge and the spot rate of the pound in 3 months is $2.22? $1.95? (5 points)

Answer: (a) The U.S. importer can hedge by buying ?10,000 today for delivery in 3 months at today's 3-month forward rate of the pound of $2.02. Thus, he willingly pays on his forward contract $0.02 more per pound (or $200 for the ?10,000) than today's spot rate in order to insure himself against the risk that the spot rate of the pound in 3 months will be much higher than $2.02. After 3 months, when his payment becomes due, the U.S. importer will pay $20,200 and get the ?10,000 he needs to make the payment, regardless of what the spot rate of the pound is at that time. (b) If the U.S. importer does not hedge and the spot rate of the pound in 3 months is $2.22, he has to pay $22,200, or $2000 more than if he had hedged, to get the ?10,000 he needs to make the payment. On the other hand, if the spot rate of the pound in 3 months is instead $1.95, he has to pay only $19,500 or $700 less than if he had hedged to get the ?10,000 he needs. Thus, by hedging, the U.S. importer will not only avoid the risk of having to pay more in terms of dollars than he anticipated, but he will also (and at the same time) forgo the chance that he will have to pay less. However, since he is not a speculator, he is satisfied with this situation.

3. Suppose that a speculator believes that the spot rate of the pound in 3 months will be lower than today's 3-month forward rate of the pound of $1.98. (a) How can the speculator use dollars for speculation in the forward exchange market? (b) What happens if the spot rate of the pound in 3 months is $1.90? $2.10? $1.98? (5 points)

Answer: (a) The speculator should sell pounds today for delivery in 3 months at today's forward rate of $1.98 per pound. (b) If after 3 months, the spot rate of the pound is $1.90, the speculator buys pounds at the price of $1.90 each and delivers them for the previously contracted price of $1.98 per pound earning $0.08 per pound. If the spot rate is $2.10 in 3 months, the speculator must buy each pound for $2.10 and sell each pound for 1.98 losing $0.12 per pound. If the spot rate for pounds in 3 months is $1.98, the speculator makes no profit or loss (except for the loss of transaction costs).

4. Suppose that the rate on 3-month treasury bills is (on a yearly basis) 10% in London and 6% in New York and the spot rate of the pound is $2.00. (a) How can a U.S. investor undertake uncovered interest arbitrage? (b) What happens if the spot rate of the pound in 3 months is $1.99? $1.98? $1.96? (c) How can the U.S. investor undertake covered interest arbitrage if the pound is at a 3 month forward discount of 1% (per year)and the spot rate of the pound is $2.00? How much would the U.S. investor earn on his foreign investment? What would be expected to happen to the dollar price of pounds? (10 points)

Answer: (a) The U.S. investor can exchange dollars for pounds at today's spot rate of $2.00 per pound and then use these pounds to buy 3-month British treasury bills in London and earn 4% more per year or 1% more for the 3 months than if U.S. treasury bills had been purchased in New York. (b) If in 3 months the spot rate of the pound is $1.99, the U.S. investor will earn an extra 1% interest for the 3 months, but since the pounds were originally purchased at $2.00 and are being resold at $1.99 a loss of one-half of 1% will be made on the transaction:

$2.00 - $1.99 = $0.01 = 0.005 or one - half of 1%

$2.00

$2.00

Thus, about one-half of 1% more is earned on the investment than if U.S. treasury bills had been purchased in New York. If in 3 months the spot rate is $1.98, 1% will be lost on the transaction and no profit will be earned by investing in British treasury bills. Finally, if the spot rate in 3 months is $1.96, 2% is lost on the foreign exchange transaction and is only partially offset by the 1% additional interest earned. This is why interest arbitrage is usually covered. (c) the U.S. investor can undertake covered interest arbitrage by (1) exchanging dollars for pounds at today's spot rate of the pound of $2.00, (2) using these pounds to buy 3-month British treasury bills in London and (3) engaging today in a forward sale of an equal amount of pounds (plus the amount of interest earned) for dollars at today's 3-month forward rate of the pound. The result is that an extra 1% of interest will be earned but one-fourth of 1% will be lost on the forward contract, for a net riskless gain of about three-fourths of 1% on the investment. There is an incentive for covered interest arbitrage as long as the positive interest differential in favor of London exceeds the forward discount on the pound (on a yearly basis).

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