Foreign Exchange and Interest Rates Arbitrage

This assignment provides a series of problems related to foreign exchange and interest rates, covering topics such as forward contracts, arbitrage opportunities, and currency exchange rate calculations. Students are required to calculate interest rates, determine correct forward exchange rates, and identify arbitrage opportunities based on given information about interest rates and exchange rates in different countries.

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 euro-denominated 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
1 GBP=1.825 USD
1 × ( 1+5 % )0.5 GBP=1.825 × ( 1+r )0.5 USD
1 GBP=1.825 × ( 1+r )0.5
( 1+5 % )0.5 USD=1.79 USD
( 1+r )0.5 = 1.79
1.825 ( 1+5 % )0.5

r =( 1.79
1.825 ( 1+5 % ) 0.5
)
2
−1
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 one-years time. Calculate
the interest rate in Europe.
The correct formula to use is