Homework Assignment 6
Chapter 15 – Questions
1. When the Euro appreciates, are you more likely to drink California or French
wine?
You are more likely to drink California wine because the euro
appreciation makes French wine relatively more expensive than
California wine.
2. “A country is always worse off when its currency is weak (falls in value).” Is
the statement true, false or uncertain? Explain your answer.
False. Although a weak currency has the negative effect of making it
more expensive to buy foreign goods or to travel abroad, it may help
domestic industry. Domestic goods become cheaper relative to foreign
goods, and the demand for domestically produced goods increases.
The resulting higher sales of domestic products may lead to higher
employment, a beneficial effect on the economy.
3. In a newspaper, chose one exchange rate from each of the regions listed in
Following the Financial News box on p347. Which of these currencies have
appreciated, and which have depreciated since June 23, 2010?
4. If the Japanese price level rises by 5% relative to the price level in the United
States, what does the theory of purchasing power parity predict will happen
to the value of the Japanese Yen in terms of US dollars?
It predicts that the value of the yen will fall 5% in terms of dollars.
5. If the demand for a country’s exports falls at the same time that tariffs on
imports are raised, will the country’s currency tend to appreciate or
depreciate in the long run?
In the long run, the fall in the demand for a country’s exports leads to
a depreciation of its currency, but the higher tariffs lead to an
appreciation. Therefore, the effect on the exchange rate is uncertain.
6. In the mid-to-late 1970’s, the yen appreciated relative to the dollar even
though Japan’s inflation rate was higher than America’s. How can this be
explained by an improvement in the productivity of Japanese industry
relative to American industry?
Even though the Japanese price level rose relative to the American,
the yen appreciated because the increase in Japanese productivity
relative to American productivity made it possible for the Japanese to
continue to sell their goods at a profit due to the high value of the yen.
Predicting the future
7. The president of the United States announces that he will reduce inflation
with a new anti-inflation program. If the public believes him, predict what
will happen to the exchange rate for the U.S. dollar vs. other currencies.
The dollar will appreciate. Because expected U.S. inflation falls as a
result of the announcement, there will be an expected appreciation of
the dollar and so the expected return on dollar assets will rise. As a
result, the demand curve will shift to the right and the equilibrium
value of the dollar will rise.
8. If the Bank of England prints money to reduce unemployment, what will
happen to the value of the pound in the short run and the long run?
The pound depreciates but overshoots, declining by more in the short
run than in the long run. Consider Britain to be the domestic country.
The rise in the money supply leads to a higher domestic price level in
the long run, which leads to a lower expected future exchange rate. In
addition, the rise in the money supply lowers the domestic interest
rate on pound assets. Both of these changes lower the expected return
on pound assets at any given exchange rate, shifting the demand curve
to the left. The short-run outcome is a lower value of the pound.
However, in the long run, the domestic interest rate returns to its
previous value, and the demand curve shifts back to the right
somewhat. The exchange rate rises to some extent, but still remains
below its initial level.
9. If the Indian government unexpectedly announces that it will be imposing
higher tariffs on foreign goods one year from now, what will happen to the
value of the Indian rupee today?
The Indian rupee will appreciate. The announcement of tariffs will
raise the expected future exchange rate for the rupee and so increase
the expected appreciation of the rupee. This means that the demand
for rupee-denominated assets will increase, shifting the demand curve
to the right, and the rupee exchange rate therefore rises.
10. If nominal interest rates in the US rise but real interest rates fall, predict
what will happen to the US exchange rate.
The dollar will depreciate. A rise in nominal interest rates but a
decline in the real rate implies a rise in expected inflation that
produces an expected depreciation of the dollar that is larger than the
increase in the domestic interest rate. As a result, the expected return
on dollar assets falls at any exchange rate, shifting the demand curve
to the left and leading to a fall in the exchange rate.
11. If American auto companies make a breakthrough in automobile technology
and are able to produce a car that gets 60 miles to the gallon, what will
happen to the US exchange rate?
The dollar will appreciate. The increase in U.S. productivity raises the
expected future exchange rate and thus raises the expected return on
dollar assets at any exchange rate. The resulting rightward shift of the
demand curve leads to a rise in the equilibrium exchange rate.
12. If Mexicans go on a spending spree and buy twice as much French perfume,
Japanese TVs, English sweaters, Swiss watches and Italian wine, what will
happen to the value of the Mexican Peso.
The peso will depreciate. Consider Mexico to be the domestic country.
An increased demand for imports would lower the expected future
exchange rate and result in a lower expected appreciation of the peso.
The resulting lower expected return on peso assets at any given
exchange rate would then shift the demand curve to the left, leading to
a fall in the peso exchange rate.
13. If expected inflation drops in Europe so that interest rates fall there, predict
what will happen to the exchange rate for the US dollar vs. the Euro.
The dollar will depreciate. The drop of expected inflation in Europe,
which leads to a decline in the foreign interest rate (which is smaller
than the drop in expected inflation), leads to a decline in the relative
expected return on dollar assets, because the expected euro
appreciation is greater than the decline in the foreign interest rate.
The result of the decline in the relative expected return on dollar
assets, a leftward shift of the demand curve, and the equilibrium U.S.
exchange rate falls.
14. If the European Central Bank decides to contract the money supply to fight
inflation, what will happen to the value of the US dollar vs. the Euro?
The contraction of the European money supply will increase
European interest rates and raise the future value of the euro, both of
which will decrease the relative expected return on dollar assets. The
demand curve will then shift to the left, and the dollar will depreciate.
15. If there is a strike in France, making it harder to buy French goods, what will
happen to the value of the Euro?
Consider France to be the domestic country. Because it is harder to
get French goods, people will buy more foreign goods and the value of
the euro in the future will fall. The expected depreciation of the euro
lowers the expected return on euro assets at any exchange rate, so the
demand curve shifts to the left and the value of the euro will fall.
Chapter 15 – Quantitative Problems
1. A German sports car is selling for 70,000 euros. What is the dollar price in
the United States for the German car if the exchange rate is 0.90 euros per
dollar?
70,000 euros  ($1/0.90 euros)  $77,777.77.
2. An investor in England purchased a 91-day T-bill for $987.65. At that time,
the exchange rate was $1.75 per pound. At maturity, the exchange rate was
$1.83 per pound. What was the investor’s holding period return in pounds?
The bond cost $987.65/$1.75 = £564.37.
At maturity, the $1,000 is worth $1,000/$1.83 = £546.45.
The holding period return is (546.45 − 564.37)/564.37 = −0.0317.
3. An investor in Canada purchased 100 shares of IBM on January 1 at $93.00
per share. IBM paid an annual dividend of $0.72 on December 31st. The
stock was sold that day as well for $100.25. The exchange rate was $0.68 per
Canadian Dollar on January 1 and $0.71 per Canadian dollar on December 31.
What is the investor’s total return in Canadian dollars?
The price of each share is $93.00/$0.68 = 136.76 Canadian dollars.
The dividend is $0.72/$0.71 = 1.014 Canadian dollars
The sale price is $100.25/$0.71 = 141.20 Canadian dollars
The return = (141.20 + 1.014 − 136.76)/136.76 = 0.03988
4. The current exchange rate is 0.75 euro per dollar, but you believe that the
dollar will decline to 0.67 euro per dollar in 1-years time. If a eurodenominated bond is yielding 2%, what return do you expect in US dollars?
If one takes 100 dollars and converts it into euros one has 75 euros.
One can then invest this in a euro-denominated bond yielding 2%.
Thus one has 76.5 euros at the end of 1 year. One can then exchange
this back into US dollars at an exchange rate of 0.67 euro/dollars.
This gives a value of 114.18. Thus the return in US dollars is 14.18%.
5. The six-month forward rate between the British pound and the US dollar is
$1.75 per pound. If six-month interest rates are 3% in the United States and
150 basis points higher in England, what is the current exchange rate?
Spot rate  1.75  (1.045/1.03)^0.5  $1.762/£
6. If the Canadian dollar to the U.S. dollar exchange rate is 1.28 CAD/USD and
the British Pound to US dollar exchange rate is 0.62 GBP/USD, what must the
Canadian dollar to British Pound exchange rate be?
Spot rate  1.28  (1/0.62)  2.0645 Canadian dollars/pound
7. The NZ dollar to US dollar exchange rate is 1.36 NZD/USD, and the British
Pound to US dollar exchange rate is 0.62 GBP/USD. If you find that the
British Pound to New Zealand dollar exchange rate is 0.49 GBP/NZD, what
would you do to earn a riskless profit?
Exchange $1.00 into 1.36 New Zealand dollars.
Exchange the 1.36 New Zealand dollars into 0.6664 British pounds.
Exchange the 0.6664 British pounds into $1.0748.
8. In 1999, the Euro was trading at $0.90 per euro. If the euro is now trading at
$1.16 per euro, what is the percentage change in the Euro’s value? Is this an
appreciation or depreciation?
% Change = (1.16 – 0.90)/0.90 = 28.88%
The dollar has depreciated by 28.88%
9. The Brazilian Real is trading at 0.375 real per US dollar. What is the US
dollar per real exchange rate?
2.6667 USD per real
10. The Mexican peso is trading at 10 pesos per dollar. If the expected US
inflation rate is 2% while the expected Mexican inflation rate is 23% over the
next year, what is the expected exchange rate in one year?
Expected rate = 10 × (1.23/1.02) = 12.059 pesos per dollar
11. The current exchange rate between the US and Britain is $1.825 per pound.
The six-month forward rate between the British Pound and the US dollar is
$1.79. If British interest rates are 5% then what are US interest rates?
Assume interest rates are of the form (1 + 𝑟)𝑡 .
NOTE I REWROTE THIS PROBLEM BECAUSE AS STATED THERE WAS
NOT A UNIQUE SOLUTION. You need to use the relationship between
spot and forward rates
1𝐺𝐵𝑃 = 1.825𝑈𝑆𝐷
1 × (1 + 5%)0.5 𝐺𝐵𝑃 = 1.825 × (1 + 𝑟)0.5 𝑈𝑆𝐷
(1 + 𝑟)0.5
1𝐺𝐵𝑃 = 1.825 ×
𝑈𝑆𝐷 = 1.79𝑈𝑆𝐷
(1 + 5%)0.5
1.79
(1 + 𝑟)0.5 =
(1 + 5%)0.5
1.825
2
1.79
(1 + 5%)0.5 ) − 1
𝑟=(
1.825
𝑟 = 1.01%
12. The current exchange rate between the Japanese yen and the US dollar is 120
yen per dollar. If the dollar is expected to depreciate by 10% relative to the
yen, what is the new expected exchange rate?
120*.9=108 yen per dollar
13. If the price level recently increased by 20% in England while falling by 5% in
the United States, how much must the exchange rate change if PPP holds?
Assume that the current exchange rate is 0.55 pounds per dollar.
0.55*1.25 =0.6875 pounds per dollar.
14. A one-year CD in Europe is currently paying 5%, and the exchange rate is
0.99 euros per dollar. If you believe that the exchange rate will be 1.04 euros
per dollar one year from now, what is the expected return in terms of
dollars?
If you start with 1 dollar. This turns into 0.99 euros. You then invest
the euros in the one-year CD. At maturity this yields 1.0395 euros.
You then turn this back into dollars which yields 0.9995 dollars. The
1-year expected return is thus 1-0.9995=-0.0005 dollars.
15. One-year interest rates are 2% in Japan and 4% in the United States. The
current exchange rate is 120 yen per dollar. If you can enter into a one
forward exchange contract of 115 yen per dollar, how can you arbitrage the
situation?
The first thing to do is figure out what the correct forward rate should
be. The forward rate should be 120*1.02/1.04 = 117.69 yen/dollar.
Thus you want to exchange yen for dollars at 115 rather than the
implied 117.69. If you start with no money then you need to borrow 1
dollar at 4% exchange them into 120 yen and invest the yen at 2%.
The yen will grow to be 120*1.02 = 122.4 so you enter into a forward
exchange agreement to exchange 122.4 yen into dollars at an
exchange rate of 115. This will yield 1.064 dollars. You need to repay
your dollar borrowing which will cost 1.04 dollars. Thus you make a
risk-less profit of 0.024 dollars.
16. The interest rate in the United States is 4% and the Euro is trading at 1 euro
per dollar. The euro is expected to depreciate to 1.1 euros per dollar in oneyears time. Calculate the interest rate in Europe.
The correct formula to use is
(1 + 𝑟𝑒𝑢𝑟𝑜 )
1 𝑒𝑢𝑟𝑜⁄𝑑𝑜𝑙𝑙𝑎𝑟 ×
= 1.1 𝑒𝑢𝑟𝑜⁄𝑑𝑜𝑙𝑙𝑎𝑟
(1 + 𝑟𝑈𝑆𝐷 )
𝑟𝑒𝑢𝑟𝑜 = 1.1 × (1.04) − 1 = 14.4%
Chapter 15 – Additional Problems
1. Choose an exchange rate that you looked at in problem 3. Go back 3 months
from today and find:
a. The exchange rate that was valid for that date.
b. The exchange rate valid for today.
c. A measure of government 3-month interest rates in that country from
3 months ago.
d. The relevant 3-month T-bill rate from 3 months ago.
Given all of this information would you have expected that the foreign
currency would have strengthened versus the dollar over the past three
months or weakened? Explain your answer. What actually happened?
There will be lots of answers for this question
2. The spot rate for British Pounds (GBP) into Swiss Francs (CHF) is 1.4966
CHF/GBP. The 3-month forward point is quoted as -28.
a. What is the 3-month forward rate?
1.4936
b. Are interest rates higher in the UK or Switzerland?
UK interest rates are higher.
c. If interest rates in the UK are 0.5% then what are interest rates in
Switzerland? Assume rates are of the form (1 + 𝑟)𝑡
We use the relationship
(1 + 𝑟𝐶𝐻𝐹 )0.25
1.4966 𝐶𝐻𝐹⁄𝐺𝐵𝑃 ×
= 1.4936 𝐶𝐻𝐹⁄𝐺𝐵𝑃
(1 + 𝑟𝐺𝐵𝑃 )0.25
1.4936
𝑟𝐶𝐻𝐹 = (
1.4966
4
× (1.005)0.25 ) − 1 =-.7498%
3. The spot rate for British Pound (GBP) into South African Rand (ZAR) is 14.06
ZAR/GBP. 6-month interest rates in the UK are 0.75% and 6-month interest
rates in South Africa are 5.5%. Assume rates are of the form (1 + 𝑟)𝑡
a. Would you expect that the forward FX rate to be higher or lower than
today?
Higher than today
b. What is the 6-month forward FX rate?
1.0550.5
𝑍𝐴𝑅
14.06
⁄𝐺𝐵𝑃
= 14.3876
1.00750.5
c. What is the quote for the 6-month forward point?
3276