Transcript Chapter 2 – Problem 1

Chapter 2 – Problem 1

1. On August 8, 2000, Zimbabwe changed the value
of the Zim dollar from Z$38/UD$ to Z$50/USD.

a. What was the original U.S. dollar value of the Zim
dollar? What is the new U.S. dollar value of the Zim
dollar?
•
•
Prior to devaluation was $0.0263 (1/38).
Subsequent to devaluation, the Zim dollar was worth $0.02
(1/50).
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Chapter 2 – Problem 1

b. By what percent has the Zim dollar
devalued (revalued) relative to the U.S. dollar?
•
The U.S. dollar value of the Zim dollar has changed
by:
(0.02 - 0.0263)/0.0263 = -24%.
•
Thus, the Zim dollar has devalued by 24% against the
U.S. dollar.
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Chapter 2 – Problem 5

5. At the time Argentina launched its new exchange rate
scheme, the euro was trading at $0.85.
Exporters and importers would be able to convert between
dollars and pesos at an exchange rate that was an average of
the dollar and the euro exchange rates, that is,
P1 = $0.50 + €0.50.

a. How many pesos would an exporter receive for one dollar
under the new system?
•
•
P1 = $0.50 + €0.50 = $0.50 + $0.85/2 = $0.925. The peso
value of a dollar is thus 1/0.925, or $1 = P1.081.
This exchange rate is equivalent to dollar appreciation of
8.1% against the peso.
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Chapter 2 – Problem 5

b. How many dollars would an importer
receive for one peso under the new
system?

As shown in the answer to Part a, P1 =
$0.925. This exchange rate is equivalent
to peso devaluation against the dollar of
7.5%.
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Chapter 3 – Problem 1

1. As mentioned in the chapter, during the currency crisis of
September 1992, the Bank of England borrowed DM 33 billion
from the Bundesbank when a pound was worth DM 2.78 or
$1.912. It sold these DM in the foreign exchange market for
pounds in a futile attempt to prevent a devaluation of the
pound. It repaid these DM at the post-crisis rate of DM 2.50/£1.
By then, the dollar/pound exchange rate was $1.782/£1.

a. How much had the pound sterling devalued in the interim
against the Deutsche mark? Against the dollar?
•
During this period, the pound depreciated by 10.1% against the
mark and by 6.8% against the dollar
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Chapter 3 – Problem 1

b. What was the cost of intervention to the Bank of England in
pounds? In dollars?
•

The Bank of England borrowed DM 33 billion and must repay DM
33 billion. When it borrowed these DM, the DM was worth
£0.3597, valuing the loan at £11.87 billion (DM 33 billion x 0.3597).
• After devaluation, the DM was worth £0.4000. The Bank of
England's cost of repaying the DM loan was £13.20 billion (DM 33
billion x 0.4). Thus, the cost of intervention was £1.33 billion.
In dollar terms, intervention cost $825 million.
• DM's initial value of $0.6878 (1.912/2.78) - ending value of
$0.7128 (1/2.50) = $0.025
• $0.025 x 33,000,000,000 = $825 million.
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Chapter 4 – Problem 4


4. In early 1996, the short-term interest rate in France
was 3.7%, and forecast French inflation was 1.8%. At the
same time, the short-term German interest rate was 2.6%
and forecast German inflation was 1.6%.
a. Based on these figures, what were the real interest
rates in France and Germany?
• The French real interest rate was:
1.037/1.018 - 1 = 1.87%. The corresponding real
rate in Germany was 1.026/1.016 - 1 = 0.98%.
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Chapter 4 – Problem 4

b. To what would you attribute any discrepancy
in real rates between France and Germany?
• Inclusion of a higher inflation risk component in the
French real interest rate than in the German real rate.
• Other possibilities are the perceived effects of currency
risk or transactions costs that could offset this arbitrage
opportunity.
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Chapter 4 – Problem 5


5. In July, the one-year interest rate is 12% on
British pounds and 9% on U.S. dollars.
a. If the current exchange rate is $1.63/£1, what
is the expected future exchange rate in one year?
• According to the international Fisher effect, the
spot exchange rate expected in one year equals
1.63 x 1.09/1.12 = $1.5863.
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Chapter 4 – Problem 5

b. Suppose a change in expectations regarding
future U.S. inflation causes the expected future
spot rate to decline to $1.52/£1. What should
happen to the U.S. interest rate?
• Assuming that the British interest rate stayed at
12% (because there has been no change in
expectations of British inflation),
• then according to the IFE,
1.52/1.63 = (1+r)/1.12 or r = 4.44%.
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Chapter 4 – Problem 13


13. Suppose that three-month interest rates (annualized)
in Japan and the United States are 7% and 9%,
respectively. If the spot rate is ¥142/$1 and the 90-day
forward rate is ¥139/$1:
a. Where would you invest?
• Dollar return from an investment in Japan: convert
dollars to yen at the spot rate, invest the yen at 1.75%
(7% x 3/12), and then sell the proceeds forward for
dollars.
• This yields a dollar return: 142 x 1.0175/139 = 1.0395
or 3.95%. It exceeds the 2.25% (9% x 3/12) return from
the United States.
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Chapter 4 – Problem 13

b. Where would you borrow?
• The flip side of a lower return in the United States
is a lower borrowing cost. Borrow in the United
States at 2.25%.
Borrow in Japan:
1 JPY / 142 – (1 + 0.07 x 3/12) / 139 = 0.0002779
Cost of debt = 0.0002779 x 142 / 1 = 3.95%
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Chapter 4 – Problem 13

c.
What arbitrage opportunity do these figures present?
• It makes sense to borrow dollars in New York at 2.25%
and invest them in Tokyo at 3.95% (but transaction
costs could wipe out the yield differential).

d. Assuming no transaction costs, what would be your
arbitrage profit per dollar or dollar-equivalent borrowed?
• The profit would be a 1.7% (3.95% - 2.25%) return per
dollar.
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Chapter 4 – Problem 14

14. Here are some prices in the international money markets:
Spot rate
= $0.95 /€
Forward rate (one year)
= $0.97 /€
Interest rate (€)
= 7% per year
Interest rate ($)
= 9% per year
 a.
Assuming no transaction costs or taxes exist, do covered arbitrage
profits exist in the above situation? Describe the flows.
• Arbitrage profits can be earned by borrowing dollars, buying euros in
the spot market, investing the euros at 7%, and selling the euro
interest and principal forward for one year for dollars.
• The annual dollar return on dollars invested in Germany is
(1.07 x 0.97)/0.95 - 1 = 9.25%.
• This return exceeds the 9% return on dollars invested in the United
States by 0.25% per annum.
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Chapter 4 – Problem 14

b. Suppose now that transaction costs in the foreign
exchange market equal 0.25% per transaction. Do
unexploited covered arbitrage profit opportunities still exist?
• In this case, the return on arbitraging dollars falls to:
1/0.95 x (1-0.0025) x 1.07 x 0.97 (1-0.0025) – 1.09 =
- 0.293%
• Thus, arbitraging from dollars to euros has now
become unprofitable and no capital flows will occur.
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Chapter 4 – Problem 14

c. Suppose no transaction costs exist. Let the capital
gains tax on currency profits equal 25%, and the ordinary
income tax on interest income equal 50%. In this situation,
do covered arbitrage profits exist? How large are they?
Describe the transactions required to exploit these profits.
•
•
In this case, the after-tax interest differential in favor of the
U.S. is (1 + 0.09 x 0.50 – 1 + 0.07 x 0.50)/(1 + 0.07 x .50) =
0.97%, while the after-tax forward premium on the euro is
0.75x(0.97 - 0.95)/0.95 = 1.58%.
Since the after-tax forward premium exceeds the after-tax
interest differential, dollars will continue to flow to Germany
as before.
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Chapter 4 – Problem 15


15. Suppose today's exchange rate is $0.90/€. The 6month interest rates on dollars and euros are 6% and 3%,
respectively. The 6-month forward rate is $0.8978. A
foreign exchange advisory service has predicted that the
euro will appreciate to $0.9290 within six months.
a. How would you use forward contracts to profit in the
above situation?
•
Buying euro forward for six months and selling it in the spot
market, you expect a profit of $0.0312 (0.9290 - 0.8978) per
euro bought forward. This is a semiannual return of 3.48%
(0.0312/0.8978). Whether this profit materializes depends
on the accuracy of the advisory service's forecast.
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Chapter 4 – Problem 15

b. How would you use money market instruments
(borrowing and lending) to profit?
•
•

By borrowing dollars at 6% (3% semiannually), converting
them to euros in the spot market, investing the euros at 3%
(1.5% semiannually), selling the euro proceeds at an
expected price of $0.9290/ Є, and repaying the dollar loan,
you will earn an expected semiannual return of 1.77%:
Return per dollar borrowed = (1/0.90) x 1.015 x 0.9290 - 1.03
= 1.77%
c. Which alternatives (forward contracts or money market
instruments) would you prefer? Why?
•
The return per dollar in the forward market is substantially
higher than the return using the money market speculation.
Other things being equal, therefore, the forward market
speculation would be preferred.
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Chapter 7 – Problem 4

4. An investor wishes to buy euros spot (at
$0.9080) and sell euros forward for 180 days
(at $0.9146).
a. What is the swap rate on euros?

b. What is the premium on 180-day euros?

• A premium of 66 points.
• The 180-day premium is (0.9146 - 0.9080)/0.9080
x 2 = 1.45%.
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Chapter 7 – Problem 5



5. Suppose Credit Suisse quotes spot and 90-day forward
rates of $0.7957-60, 8-13.
a. What are the outright 90-day forward rates that Credit
Suisse is quoting?
• The outright forwards are:
bid rate = $0.7965 = (0.7957 + 0.0008)
and ask rate = $0.7973 = (0.7960 + 0.0013).
b. What is the forward discount or premium associated with
buying 90-day Swiss francs?
• The forward premium = [(0.7973 - 0.7960)/0.7960]x 4
=0.65%
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Chapter 7 – Problem 5

c. Compute the percentage bid-ask spreads on spot
and forward Swiss francs.
Percent
spread
=
Ask
price - Bid
Ask
•
•
price
x 100
price
The spot bid-ask spread is:
(0.7960 - 0.7957)/0.7960 = 0.04%.
The corresponding forward bid-ask spread is
(0.7973 - 0.7965)/0.7973 = 0.10%.
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Chapter 7 – Problem 7


7. Suppose the euro is quoted at 0.6064-80 in
London, and the pound sterling is quoted at
1.6244-59 in Frankfurt.
a. Is there a profitable arbitrage situation?
Describe it.
• Buy euros for £0.6080. Use the euros to buy
pounds for €1.6259. This is equivalent to selling
euros for £0.6150. There is a net profit of £0.0070
per euro bought and sold–a percentage yield of
1.16% (0.0070/0.6080).
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Chapter 7 – Problem 7

b. Compute the percentage bid-ask spreads on the
pound and euro.
• The percentage bid-ask spreads on the pound and
euro are calculated as follows:
• £ bid-ask spread =
(1.6259 - 1.6244)/1.6259 = 0.09%
• euro bid-ask spread =
(0.6080 - 0.6064)/0.6080 = 0.26%
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Chapter 7 – Problem 8
8. As a foreign exchange trader at Sumitomo Bank, one of your
customers would like a yen quote on Australian dollars. Current
market rates are:
Spot
30-day
30-day outright forward
rates
¥101.37-85/U.S.$1
15-13
¥101.22-72/U.S.$1
A$1.2924-44/U.S.$1
20-26
A$1.2944-70/U.S.$1
a. What bid and ask yen cross rates would you quote on spot
Australian dollars?


•
•
By means of triangular arbitrage, we can calculate the market
quotes for the Australian dollar in terms of yen as ¥78.31-81/A$1
As a foreign exchange trader, you would try to buy Australian
dollars at slightly less than ¥78.31 and sell them at slightly more
than ¥78.81.
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Chapter 7 – Problem 8

•
•
•
b. What outright yen cross rates would you quote on
30-day forward Australian dollars?
By means of triangular arbitrage, we can then calculate the market
quotes for the 30-day forward Australian dollar in terms of yen as
¥78.04-58/A$1
For the yen bid price for the forward Australian dollar, we need to first
sell Australian dollars forward for U.S. dollars and then sell the U.S.
dollars forward for yen. It costs A$1.2970 to buy U.S.$1 forward. With
U.S.$1 we can buy ¥101.22. Hence, A$1.2970 = ¥101.22, or A$1 =
¥78.04. This is the yen bid price for the forward Australian dollar.
The yen ask price for the Australian dollar can be found by first selling
yen forward for U.S. dollars and then using the U.S. dollars to buy
forward Australian dollars. Given the quotes above, it costs ¥101.72 to
buy U.S.$1, which can be sold for A$1.2944. Hence, A$1.2944 =
¥101.71, or A$1 = ¥78.58. This is the yen ask price for the forward A$.
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Chapter 7 – Problem 8

c. What is the forward premium or discount on buying
30-day Australian dollars against yen delivery?

The ask rate for 30-day forward Australian dollars is ¥78.58 and the
spot ask rate is ¥78.81. Thus, the Australian dollar is selling at a
forward discount to the yen. The annualized discount equals 3.43%, computed as follows:
Forward
premium
or discount
=
Forward
rate Spot rate
Spot rate
x
360
Forward
contract
=
78.58 - 78.81
78.81
x
360
30
number of days
26
= - 3.43%
Chapter 7 – Problem 10
10.
On checking the Telerate screen, you see the following exchange
rate and interest rate quotes:
Currency
90-day interest rates annual
Spot rates
Dollar
Swiss franc
4.99% - 5.03%
3.14% - 3.19%
$0.711 - 22



90-day forward rates
$0.726 - 32
a.
Can you find an arbitrage opportunity?
• Two possibilities: Borrow dollars and lend in Swiss francs or borrow Swiss
francs and lend in dollars. The profitable arbitrage opportunity is: Lend
Swiss francs financed by borrowing U.S. dollars.
b.
What steps must you take to capitalize on it?
• Borrow dollars at 1.2575% for 90 days (5.03%/4), convert these dollars into
francs at the ask rate of $0.722, lend the francs at 0.785% for 90 days
(3.14%/4), and sell the francs forward for dollars at the buy rate of $0.726.
c.
What is the profit per $1,000,000 arbitraged?
• The profit is $1,000,000 x [(1.00785/0.722) x 0.726 - 1.012575] = $858.66.
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