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CHAPTER 6 INTERNATIONAL PARITY RELATIONSHIPS AND FORECASTING FOREIGN
EXCHANGE RATES
ANSWERS & SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS
QUESTIONS
1. Give a full definition of arbitrage.
Answer: Arbitrage can be defined as the act of simultaneously buying and selling the same or
2. Discuss the implications of the interest rate parity for the exchange rate determination.
Answer: Assuming that the forward exchange rate is roughly an unbiased predictor of the future
spot rate, IRP can be written as:
The exchange rate is thus determined by the relative interest rates, and the expected future
spot rate, conditional on all the available information, It, as of the present time. One thus can say
3. Explain the conditions under which the forward exchange rate will be an unbiased predictor
of the future spot exchange rate.
Answer: The forward exchange rate will be an unbiased predictor of the future spot rate if (i) the
4. Explain the purchasing power parity, both the absolute and relative versions. What causes
the deviations from the purchasing power parity?
Answer: The absolute version of purchasing power parity (PPP):
The relative version is:
5. Discuss the implications of the deviations from the purchasing power parity for countries’
competitive positions in the world market.
Answer: If exchange rate changes satisfy PPP, competitive positions of countries will remain
unaffected following exchange rate changes. Otherwise, exchange rate changes will affect
6. Explain and derive the international Fisher effect.
Answer: The international Fisher effect can be obtained by combining the Fisher effect and the
relative version of PPP in its expectational form. Specifically, the Fisher effect holds that
Assuming that the real interest rate is the same between the two countries, i.e., $ = £, and
substituting the above results into the PPP, i.e., E(e) = E($)- E(£), we obtain the international
7. Researchers found that it is very difficult to forecast the future exchange rates more
accurately than the forward exchange rate or the current spot exchange rate. How would you
interpret this finding?
Answer: This implies that exchange markets are informationally efficient. Thus, unless one has
8. Explain the random walk model for exchange rate forecasting. Can it be consistent with the
technical analysis?
Answer: The random walk model predicts that the current exchange rate will be the best
predictor of the future exchange rate. An implication of the model is that past history of the
*9. Derive and explain the monetary approach to exchange rate determination.
Answer: The monetary approach is associated with the Chicago School of Economics. It is
S($/£) = (M$/M£)(V$/V£)(y£/y$),
where M denotes the money supply, V the velocity of money, and y the national aggregate
output. The theory holds that what matters in exchange rate determination are:
10. Explain the following three concepts of purchasing power parity (PPP):
a. The law of one price.
b. Absolute PPP.
c. Relative PPP.
Answer:
a. The law of one price (LOP) refers to the international arbitrage condition for the standard
b. Absolute PPP holds that the price level in a country is equal to the price level in another
c. Relative PPP holds that the rate of exchange rate change between a pair of countries is
11. Evaluate the usefulness of relative PPP in predicting movements in foreign exchange rates
on:
a. Short-term basis (for example, three months)
b. Long-term basis (for example, six years)
Answer.
a. PPP is not useful for predicting exchange rates on the short-term basis mainly because
PROBLEMS
1. Suppose that the treasurer of IBM has an extra cash reserve of $100,000,000 to invest for
six months. The six-month interest rate is 8 percent per annum in the United States and 7
percent per annum in Germany. Currently, the spot exchange rate is €1.01 per dollar and the
six-month forward exchange rate is €0.99 per dollar. The treasurer of IBM does not wish to bear
any exchange risk. Where should he/she invest to maximize the return?
Solution: The market conditions are summarized as follows:
If $100,000,000 is invested in the U.S., the maturity value in six months will be
Alternatively, $100,000,000 can be converted into euros and invested at the German interest
rate, with the euro maturity value sold forward. In this case the dollar maturity value will be
2. While you were visiting London, you purchased a Jaguar for £35,000, payable in three
months. You have enough cash at your bank in New York City, which pays 0.35% interest per
month, compounding monthly, to pay for the car. Currently, the spot exchange rate is $1.45/£
(a) Keep the funds at your bank in the U.S. and buy £35,000 forward.
(b) Buy a certain pound amount spot today and invest the amount in the U.K. for three months
Solution: The problem situation is summarized as follows:
A/P = £35,000 payable in three months
Option a:
When you buy £35,000 forward, you will need $49,000 (= £35,000 × $1.40/£) in three months
Thus, the cost of Jaguar as of today is $48,489.
Option b:
The present value of £35,000 is £34,314 = £35,000/(1.02). To buy £34,314 today, it will cost
3. Currently, the spot exchange rate is $1.50/£ and the three-month forward exchange rate is
$1.52/£. The three-month interest rate is 8.0% per annum in the U.S. and 5.8% per annum in
the U.K. Assume that you can borrow as much as $1,500,000 or £1,000,000.
a. Determine whether the interest rate parity is currently holding.
b. If the IRP is not holding, how would you carry out covered interest arbitrage? Show all the
steps and determine the arbitrage profit.
c. Explain how the IRP will be restored as a result of covered arbitrage activities.
Solution: Let’s summarize the given data first:
a. (1+i$) = 1.02
b. (1) Borrow $1,500,000; repayment will be $1,530,000.
(2) Buy £1,000,000 spot using $1,500,000.
c. Following the arbitrage transactions described above,
The dollar interest rate will rise;
The pound interest rate will fall;
4. Suppose that the current spot exchange rate is €0.80/$ and the three-month forward
exchange rate is €0.7813/$. The three-month interest rate is 5.60 percent per annum in the
United States and 5.40 percent per annum in France. Assume that you can borrow up to
$1,000,000 or €800,000.
a. Show how to realize a certain profit via covered interest arbitrage, assuming that you want to
realize profit in terms of U.S. dollars. Also determine the size of your arbitrage profit.
b. Assume that you want to realize profit in terms of euros. Show the covered arbitrage process
and determine the arbitrage profit in euros.
Solution:
a. (1+ i$) = 1.014 < (F/S) (1+ i €) = 1.0378. Thus, one has to borrow dollars and invest in euros
to make arbitrage profit.
1. Borrow $1,000,000 and repay $1,014,000 in three months.
2. Sell $1,000,000 spot for €800,000.
b. Follow the first three steps above. But the last step, involving exchange risk hedging, will be
different. Specifically, for the euro-based investor, the source of currency risk is the dollar
5. In the issue of October 23, 1999, the Economist reports that the interest rate per annum is
5.93% in the United States and 70.0% in Turkey. Why do you think the interest rate is so high in
Turkey? Based on the reported interest rates, how would you predict the change of the
exchange rate between the U.S. dollar and the Turkish lira?
Solution: A high Turkish interest rate must reflect a high expected inflation in Turkey. According
6. As of November 1, 1999, the exchange rate between the Brazilian real and U.S. dollar is
R$1.95/$. The consensus forecast for the U.S. and Brazil inflation rates for the next 1-year
period is 2.6% and 20.0%, respectively. What would you forecast the exchange rate to be at
around November 1, 2000?
Solution: Since the inflation rate is quite high in Brazil, we may use the purchasing power parity
to forecast the exchange rate.
R$ is expected to depreciate by about 17.4% against the US dollar. Thus, the expected
exchange rate would be
7. (CFA question) Omni Advisors, an international pension fund manager, uses the concepts of
purchasing power parity (PPP) and the International Fisher Effect (IFE) to forecast spot
exchange rates. Omni gathers the financial information as follows:
Base price level 100
Current U.S. price level 105
Current South African price level 111
Calculate the following exchange rates (ZAR and USD refer to the South African rand and U.S.
dollar, respectively).
a. The current ZAR spot rate in USD that would have been forecast by PPP.
b. Using the IFE, the expected ZAR spot rate in USD one year from now.
c. Using PPP, the expected ZAR spot rate in USD four years from now.
Solution:
a. ZAR spot rate under PPP = [1.05/1.11](0.175) = $0.1655/rand.
8. Suppose that the current spot exchange rate is €1.50/₤ and the one-year forward exchange
rate is €1.60/₤. The one-year interest rate is 5.4% in euros and 5.2% in pounds. You can borrow
at most €1,000,000 or the equivalent pound amount, i.e., ₤666,667, at the current spot
exchange rate.
a. Show how you can realize a guaranteed profit from covered interest arbitrage. Assume that
you are a euro-based investor. Also determine the size of the arbitrage profit.
b. Discuss how the interest rate parity may be restored as a result of the above
transactions.
c. Suppose you are a pound-based investor. Show the covered arbitrage process and
determine the pound profit amount.
Solution:
a. First, note that (1+i €) = 1.054 is less than (F/S)(1+i €) = (1.60/1.50)(1.052) = 1.1221.
You should thus borrow in euros and lend in pounds.
1) Borrow €1,000,000 and promise to repay €1,054,000 in one year.
2) Buy ₤666,667 spot for €1,000,000.
b. As a result of the above arbitrage transactions, the euro interest rate will rise, the pound
c. The pound-based investor will carry out the same transactions 1), 2), and 3) in a. But to
