CHAPTER 5 INTERNATIONAL PARITY RELATIONSHIPS AND FORECASTING
FOREIGN EXCHANGE RELATIONSHIPS
SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER
QUESTIONS AND PROBLEMS
1. Give a full definition of arbitrage.
Answer: Arbitrage involves the simultaneous purchase and sale of the same or equivalent assets or
commodities – buying at a low price, selling at a high price – thus making a riskless profit.
2. Discuss the implications of the interest rate parity for the exchange rate determination.
Answer: Assuming the forward exchange rate is an unbiased predictor of the future spot rate, IRP
between dollars and pounds can be written as:
S = [(1 + i£)/(1 + $ )]E[St+1 t
The exchange rate is thus determined by relative interest rates and the expected future spot rate
conditional on available information, I, ts of the present time. The expectation is self-fulfilling.
Since the information set is continuously updated as news hit the market, the exchange rate
exhibits a dynamic, random behavior.
4. Explain purchasing power parity, both the absolute and relative versions. What causes deviations
from the purchasing power parity?
Answer: Absolute (or static) purchasing power parity (PPP) is S = P /P where S$is£the spot
exchange rate, P i$ the price level in the dollar country (Canada) and P is t£e price level in the
pound country (Britain). Relative (or dynamic) PPP is e = π - π where e is the rate of change of
the spot exchange rate, π i$ the expected change of price level (expected inflation) in the dollar
country (Canada) and π .is£the expected change of price level (expected inflation) in the pound
PPP can be violated by barriers to trade – such as tariffs or transportation costs – or cross-country
IM-1 differences in tastes. PPP is the law of one price applied to a standard consumption basket.
5. Discuss the implications of the deviations from purchasing power parity for countries’ competitive
positions in the world market.
Answer: If exchange rate changes satisfy PPP, the competitive positions of countries remain
unaffected by the exchange rate changes. Such exchange rate changes are strictly “nominal”.
Otherwise, exchange rate changes affect relative the competitiveness of industries in the countries
involved. If a country’s currency appreciates (depreciates) by more than is warranted by PPP, that
country’s real exchange rate rises. The effect is to raise the relative price of that country’s
exported goods while reducing (for domestic use or consumption) the relative price of that
country’s imports. Exporters are hurt. Importers are helped.
6. Explain and derive the International Fisher Effect.
Answer: The International Fisher Effect combines domestic Fisher effects in two countries and the
relative version of PPP in its expectational form. Specifically, the country-specific Fisher effect
for a dollar country and a pound country is, respectively …
E(π )$= i -$ρ $ where E(π ) $s the expected rate of inflation, i is t$e nominal interest rate
and ρ $s the real rate of interest in the dollar country, and likewise,
E(π £ = i -£ρ . £n the pound country.
Assuming the real interest rate is the same in the two countries, i.e., ρ = ρ , and substituting the
above results into the PPP, i.e., E(e) = E(π )- $(π ), t£e international Fisher effect is: E(e) = i - i . $ £
7. Researchers found that it is very difficult to forecast future exchange rates more accurately than the
forward exchange rate or the current spot exchange rate. How would you interpret this finding?
Answer: Foreign exchange markets are informationally efficient. Unless one has private
information that is not yet reflected in the current market rates, which is the case for virtually all
participants in foreign exchange markets, all new relevant information is truly new. New
information that can either raise the exchange rate or lower it is equally likely to raise or lower the
exchange rate. The random flow of new information generates random movements of the exchange
IM-2 8. Explain the random walk model for exchange rate forecasting. Can itbe consistent with the
Answer: If exchange rates follow a random walk, the current exchange rate is the best predictor of
the future exchange rate. In that case the past history of the exchange rate is of no value in
predicting future exchange rate. A random walk model is inconsistent with technical analysis
which tries to use past history to predict future exchange rate.
9. Derive and explain the monetary approach to exchange rate determination.
Answer: The monetary approach to exchange rate movements is based on two tenets: purchasing
power parity and the quantity theory of money. Combining these two theories suggests the $/£ spot
exchange rate as: S($/£) = (M /$ )(£ /V $(y£/y £,$
where M denotes the rate money supply, V is the velocity of money (essentially national income
divided by money supply) and y is national income. What matters in exchange rate determination are:
i. relative money supply,
ii. relative velocities of money, and
iii. relative national incomes.
10. [CFA question: 1997, Level 3.] Explain the following three concepts of purchasing power parity
a. The law of one price
b b. Absolute PPP
c. Relative PPP
a. The Law of One Price (LOP) maintains that the same good (or basket of goods) must have the
same price in two places. Otherwise, arbitrage – arbitragers buying at the low-priced site and
selling at the higher priced site – will ensue until the prices are the same in the two sites.
b. Absolute Purchasing Power Parity (absolute PPP) holds that the price level in a country is equal
to the price level in another country times the exchange rate between the two countries. i.e., P /P 1 2
= S 1/2re is virtually no empirical evidence to support Absolute Purchasing Power Parity.
IM-3 c. Relative Purchasing Power Parity (relative PPP) holds that the rate of exchange rate change
between a pair of countries is equal to the difference in expected inflation rates between the two
11. [CFA question: 1997, Level 3.] 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)
a. PPP is not useful for predicting exchange rates on the short-term basis mainly because
international commodity arbitrage is a costly process.
b. PPP is at most useful for predicting exchange rates on the long-term basis.
1. Suppose that the treasurer of Weston’s has an extra cash reserve of $10 million to invest for six
months. The six-month interest rate is 4 percent per annum in Canada and 5 percent per annum in
Germany. Currently, the spot exchange rate is €0.65 per dollar and the six-month forward
exchange rate is €0.66 per dollar. The treasurer of Weston’s does not wish to bear any exchange
risk. Where should he invest?
Solution: The market conditions are summarized as follows:
i$= 4%; i =€5%; S = €0.65/$; F = €0.66/$.
If $10 million is invested in Canada, the maturity value in six months will be
$10,200,000 = $10,000,000 (1 + (.04/2)).
Alternatively, $10 million can be converted into euro and invested at the European interest rate,
with the euro maturity value sold forward for forward cover. In this case the dollar maturity value
will be … $10,094,700 = ($10,000,000 x 0.65)(1 + (.05/2))(1/0.66)
Clearly it is better to invest $10 million in Canada. Even though the European interest rate exceeds
the interest rate in Canada, the expected depreciation of the euro vis-à-vis the Canadian dollar that
is built into the relation between the spot and forward rates more than offsets the international
2. While you were visiting Paris you purchased a Renault for €10,000 payable in three months. You
have enough cash at your bank in Vancouver, earning interest of 0.35 percent per month
compounded monthly, to pay for the car. Currently, the spot exchange rate is $1.45/€ and the 3-
month forward exchange rate is $1.40/€. In Paris the money market interest rate is 2.0 percent for
a 3-month investment.
There are two alternative ways of paying for your Renault.
a. Keep the funds at your bank in Canada and buy €10,000 forward.
b. Buy a certain euro amount spot today and invest the amount in Europe for three months so that
the maturity value become equal to €10,000. Evaluate each payment method. Which method would
you prefer? Why?
IM-5 Solution: The problem situation is summarized as follows:
Obligation = €10,000 payable in 3 months
$ = 0.35 percent per month compounded monthly
€ = 2.0 percent for 3 months
S = $1.45/€
F = $1.40/€
To buy €10,000 forward, you will need 10,000*1.40 or $14,000 in 3 months to fulfill the forward
contract. The present value of $14,000 discounted at the dollar interest rate is:
$14,000/(1.0035) = $13,854
Thus, the cost of the car as of today is $13,854.
The present value of €10,000 is €9,804 = €10,000/(1.02). To buy €9,804 today will cost $14,216
= $9,804 x1.45. Thus the dollar cost of the Renault as of today is $14,216.
Option “a” is preferred. The difference between Options “a” and “b” is $362, or $14,216 minus
3. Currently, the spot exchange rate is $1.50/€ and the 3-month forward exchange rate is $1.49/€. The
3-month interest rate is 4 percent per annum in Canada and 5 percent per annum in Europe.
Assume you can borrow as much as $1,500,000 or €1,000,000.
a. Determine whether interest rate parity is currently holding.
a. If IRP is not holding, how would you carry out covered interest arbitrage? Show all the
steps and determine the arbitrage profit.
c. Explain how IRP will be restored as a result of covered arbitrage activities.
Solution: First, summarize the given data:
S = $1.50/€; F = $1.49/€; i$= 4 %; i€= 5 %
Credit = $1,500,000 or €1,000,000
a. In Canada investment: (1+i ) =$(1 + (0.04/4)) = 1.0100
Covered investment in Europe: (1+i )(F/€) = (1 + (0.05/4))*(1.49/1.50) = 1.00575
IM-6 Thus, IRP is not holding exactly.
The arbitrager will borrow in Euro and invest in Canadian dollar securities.
b. 1. Borrow €1,000,000; repayment will be €1,012,500 = €1,000,000 *(1.0125)
2. Buy $1,500,000 spot using €1,000,000.
3. Invest $1,500,000 at $ interest rate; maturity value will be $1,515,000
4. Buy €1,012,500 forward for $1,508,625 = €1,012,500 * 1.49
Arbitrage profit will be $6,375.
c. In the process of the arbitrage transactions described above,
The dollar interest rate will fall. ( Canadian securities prices rise. )
The euro interest rate will rise. ( European securities prices fall. )
The spot exchange rate (in $/€ ) will fall. ( Up from S = $1.50/ € )
The forward exchange rate (in $/€ ) will rise. ( Down from F = $1.49/€ )
These adjustments continue until IRP holds.
4. Suppose that the current spot exchange rate is €0.65/$ and the three-month forward exchange rate
is €0.64/$. The three-month interest rate is 5.6 percent per annum in Canada and 5.4 percent per
annum in France. Assume that you can borrow up to $1,000,000 or €1,060,000.
a. Show how to realize a certain profit via covered interest arbitrage, assuming that you
want to realize profit in terms of dollars. Also determine the size of your arbitrage
b. Assume that you want to realize profit in terms of euros. Show the covered arbitrage
process and determine the arbitrage profit in euros.
Solution: The market data are summarized as follows:
S = €0.65/$ = $1.5385/€;
F = €0.64/$ = $1.5625/€;
On a 3-month basis: i = $0.056/4) = 0.014; i = (0.0€4/4) = 0.0135
(1+i $ = 1.014 < (1+i )(F€S) = (1.0135)*(0.65/0.64) = 1.029336
a. 1. Borrow $1,000,000; repayment will be $1,014,000
2. Buy €650,000 spot for $1,000,000.
3. Invest in France at 5.4 % for 3 months; maturity value will be €658,775
IM-7 4. Sell €658,775 forward for $1,029,336 = €658,775* ($1.5625/€)
Arbitrage profit will be $15,336 = $1,029,336 - $1,014,000
b. 1. Borrow $1,000,000; repayment will be $1,014,000.
2. Buy €650,000 spot for $1,000,000.
3. Invest in France at 5.4 % for 3 months; maturity value will be €658,775
4. Buy $1,014,000 forward for €648,960 = $1,014,000 / ($1.5625/€)
Arbitrage profit will be €9,815 = €658,775 - €648,960
Note that only step (4) is different.
5. The Economist reports that the interest rate per annum is 5 percent in Canada and 50 percent in
Turkey. Why do you think the interest rate is so high in Turkey? On the basis of the reported
interest rates, how would you predict the change of the exchange rate between the Canadian
dollar and the Turkish lira?
Solution: The high Turkish interest rate reflects high expected inflation in Turkey. According to
international Fisher effect (IFE), we ha