1. (10 points) Suppose that one year interest rates in the US are 0.01 (1%) and .03
(3%) in Europe. The current spot rate is $1.35/€, calculate the forward rate
consistent with covered interest rate parity. Explain your answer.
𝐹=𝑆∗
1 + 𝑟𝑑
1 + .01
= 1.35 ∗
= 1.3238
1 + 𝑟𝑓
1 + .03
Investors will still be indifferent among the available interest rates in two countries because the
forward exchange rate sustains equilibrium such that the dollar return on dollar deposits is equal
to the dollar return on foreign deposit, thereby eliminating the potential for covered interest
arbitrage profits.
2. Suppose that one year interest rates in the US are 0% and that one year interest
rates in Europe are 4%. The current $/€ exchange rate is 1.2. Suppose that you
have $100 to invest.
a. (10 points) Use the uncovered interest rate parity (UIP) condition (the
approximation) and solve for the expected exchange rate, one year hence,
that is consistent with UIP. Show that with this particular exchange rate,
the returns in 'like' currencies are approximately the same.
∆𝐸𝑡 (𝑆𝑡 )
𝑆𝑡
= 𝑆𝑡 (𝑖$ − 𝑖€ ) = ∆𝐸𝑡 (𝑆𝑡 )
𝑖$ = 𝑖€ +
= 1.2(0 − .04) = −.048
$100 ∗
1
= $100 ∗ .8333 €⁄$ = €83.33
$
1.2 ⁄€
83.33 ∗ (1 + .04) = €86.66
€86.66 ∗ (1.2 − .048) = €86.66 ∗ 1.152 = $99.83 ~ $100
$100 ∗ (1 + 0) = $100
b. (10 points) Explain the intuition underlying your results.
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Uncovered interest rate parity asserts that an investor with dollar deposits will earn the interest
rate available on dollar deposits, while an investor holding euro deposits will earn the interest rate
available in the euro-zone, but also a potential gain or loss on euros depending on the rate of
appreciation or depreciation of the euro against the dollar. If uncovered interest rate parity holds,
such that an investor is indifferent between dollar versus euro deposits, then any excess return
on euro deposits must be offset by some expected loss from depreciation of the euro against the
dollar. Conversely, some shortfall in return on euro deposits must be offset by some expected
gain from appreciation of the euro against the dollar.
3. Suppose you have $1000 that serves as margin for a $9000 one year loan where
the interest rate is 1%. You invest the total = $10,000 in Europe where the
exchange rate is $1.25 $/€. The one year interest rate in Europe is 4%.
a. (10 points) According to UIP, what is the expected exchange rate one year
from now?
Consider the following two scenarios:
Scenario #1: The $/€ exchange rate remains constant over the holding
period = 1 year
(1 + 𝑖$ ) =
= 1.01 =
𝐸𝑡 (𝑆𝑡+𝑘 )
(1 + 𝑖€ )
𝑆𝑡
𝐸𝑡 (𝑆𝑡+𝑘 )
∗ 1.04
1.25
1.2625 = 𝐸𝑡 (𝑆𝑡+𝑘 ) ∗ 1.04
𝐸𝑡 (𝑆𝑡+𝑘 ) = 1.2139
Scenario #2: The exchange rate after one year is 1.3 $/€
𝑆𝑡 = 𝐸𝑡 (𝑆𝑡+𝑘 ) ∗
𝑆𝑡 = 1.3 ∗
(1 + 𝑖$ )
(1 + 𝑖€ )
1.01
1.04
𝑆𝑡 = 1.2625
1.01 =
𝐸𝑡 (𝑆𝑡+𝑘 )
∗ 1.04
1.2625
2
𝐸𝑡 (𝑆𝑡+𝑘 ) = 1.2261
b. (10 points) Assuming scenario #1, what is your profit / loss and your rate
of return in $ when you close your position?
$10,000 ∗ 1.01 = $10,100
$100 profit
c. (10 points) Assuming scenario #2, what is your profit / loss and your rate
of return in $ when you close your position?
. 04 +
1.3 − 1.25
= .08
1.25
10000 ∗ 1.08 = 10800
$800 profit
4. Suppose that you have the following information:
The inflation rate in the US is 2% and -2% in Japan (deflation in Japan)
The real exchange rate ($/yen) is appreciating by 2%.
a. (10 points) What is the implied change in the nominal exchange rate
($/yen)? Please show work. Explain the intuition of your result.
∆𝐸𝑡 (𝑆𝑡+𝑘 )
= 𝜋𝑢𝑠 − 𝜋𝑗𝑝 = .02 − (−.02) = .04 = 4%
𝑆𝑡
Implied change in nominal exchange rate = 4%
The real exchange rate tries to take relative changes in countries' inflation rates
into account
b. (10 points) Suppose that Bank of Japan (BOJ) successfully rids the
economy of deflation so that the new rate of inflation is 2%, same as the
US. Assuming all else constant, what is the implication on the nominal
exchange rate? Explain the intuition of your result.
∆𝐸𝑡 (𝑆𝑡+𝑘 )
= 𝜋𝑢𝑠 − 𝜋𝑗𝑝 = .02 − .02 = 0
𝑆𝑡
The nominal exchange rate shouldn’t change.
1.
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Covered interest rate parity is more likely to hold in a world where countries impose
significant capital controls.
A) True
B) False
2.
In terms of the terminology regarding the carry trade, the cost of carry is the rate of
interest in the high interest rate country.
A) True
B) False
3.
UIP, strictly speaking, implies that the carry trade strategy of borrowing in the low
interest rate country and investing in the high interest rate country will result in zero
profits.
A) True
B) False
4.
If good X costs $150 in the US and €100 in Europe and the current exchange rate is
1.3$/€ , then according to PPP, the $ is undervalued.
A) True
B) False
5.
The existence of trade barriers is one reason that APPP does not hold.
A) True
B) False
6.
According to the Balassa-Samuelson Model, one reason APPP does not hold in the data
is due to the existence of non-tradable goods and services.
A) True
B) False
7.
According to the Balassa-Samuelson Model, non-tradable services are cheaper in
developing countries relative to developed countries.
A) True
B) False
8.
According to relative PPP, if inflation is higher in Europe than it is in the US, the Euro
should appreciate so that the law of one price holds.
A) True
B) False
9.
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Suppose APPP holds so that the real exchange rate =1. According to relative purchasing
power parity, if prices are rising in Japan and remaining constant in the US, then the US $
will appreciate against the Japanese yen.
A) True
B) False
10.
One reason that we see deviations from PPP in the data is due to 'sticky' prices.
A) True
B) False
1.
(75 points total) Monetary Approach to the Exchange Rate. For the following
questions imagine a world in which the assumptions of the monetary approach to the
exchange rate hold at all times. There are two countries the U.S. and Mexico (treat
Mexico as the home country). Suppose that the real interest rate is 2%. In Mexico, the
expected money supply growth rate is 8 percent and the expected real GDP growth rate is
2 percent. In the United States the expected money supply growth rate is 4 percent and
the expected real GDP growth rate is 1 percent.
a.
(5 points) What is the nominal interest rate in Mexico? In the United States?
𝜋𝑀 = ∆𝑀𝑠𝑀 − ∆𝐺𝐷𝑃𝑀 = .08 − .02 = .06
𝑖𝑀 = 𝑟 + 𝜋𝑀 = .02 + .06 = .08
𝜋𝑈𝑆 = ∆𝑀𝑠𝑈𝑆 − ∆𝐺𝐷𝑃𝑈𝑆 = .04 − .01 = .03
𝑖𝑈𝑆 = 𝑟 + 𝜋𝑈𝑆 = .02 + .03 = .05
b.
(5 points) What is the expected change in the exchange rate in Mexican terms
Epeso/$?
. 06 − .03 = .03 = 3%
The peso should be selling at a forward discount of 3%
Suppose at time T, the money supply in Mexico increases by 50% unexpectedly. Nothing
else changes (including expectations for the future). Please answer the following
questions:
c.
(5 points) What happens to the Mexican interest rate at time T? Explain your
answer.
𝜋𝑀 = ∆𝑀𝑠𝑀 − ∆𝐺𝐷𝑃𝑀 = .50 − .02 = .48
𝑖𝑀 = 𝑟 + 𝜋𝑀 = .02 + .48 = .50
An increase to the money supply causes inflation to skyrocket, driving nominal rates up
significantly
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d.
(5 points) What happens to the exchange rate written in Mexican terms at time T?
. 48 − .03 = .45 = 45%
The peso should be selling at a forward discount of 45%
e.
(20 points) Draw 4 times series diagrams as we did in the lesson (all referring to
Mexican economic variables) with the log of the Mexican money supply on the top left,
real money balances and nominal interest rates on the top right, the log of the price level
on bottom left, and the log of the exchange rate: Mexican pesos per $ on bottom right.
Please show exactly what happens to these time series variables at time T using real
numbers when possible. Please label graph completely (levels, growth rates, etc)
Now suppose instead (go back to the original conditions) that the expected rate of growth
of the Mexican real GDP increases from 2 percent to 4 percent at time T. Nothing else
changes (including the levels of all other variables).
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f.
(5 points) What happens to the Mexican interest rate at time T? (Give numbers)
𝜋𝑀 = ∆𝑀𝑠𝑀 − ∆𝐺𝐷𝑃𝑀 = .08 − .04 = .04
𝑖𝑀 = 𝑟 + 𝜋𝑀 = .02 + .04 = .06
g.
(5 points) What happens to the level of the exchange rate written in Mexican
terms at time T?
. 04 − .03 = .01 = 1%
The peso should be selling at a forward discount of 1%
h.
(5 points) What happens to the rate of depreciation/appreciation of the Mexican
peso, whichever applies?
The rate of depreciation declines
i.
(20 points) Just like you did in part e), draw 4 times series diagrams as we did in
the lesson (all referring to Mexican economic variables) with the log of the Mexican
money supply on the top left, real money balances and nominal interest rates on the top
right, the log of the price level on bottom left, and the log of the exchange rate: Mexican
pesos per $ on bottom right. Please show exactly what happens to these time series
variables at time T using real numbers when possible. Please label graph completely
(levels, growth rates, etc)
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2.
(15 points total) Given Europe and the US and assuming that relative PPP and
UIP holds, you are given the following information: The nominal interest rate in the US
is 1% and 2% in Europe. The inflation rate in Europe is 2%.
a.
(5 points) What is the inflation rate in the US?
(𝑖$ − 𝑖€ ) = (𝜋𝑢𝑠 − 𝜋€ )
. 01 − .02 = 𝜋𝑢𝑠 − .02
𝜋𝑢𝑠 = .01 = 1%
b.
(5 points) What is the rate of appreciation/depreciation, whichever applies, of the
$ relative to the €?
. 01 − .02 = −.01 = −1%
c.
(5 points) What is the real interest rate in both countries?
𝑖 = 𝑟 + 𝜋𝑢𝑠
. 01 = 𝑟 + .01
𝑟=0
3.
(15 points total) You are the central banker for a country (Turkey) that is
considering the adoption of a new nominal anchor. When you take the position as
chairperson, the inflation rate is 4% and your position as the central bank chairperson
requires that you achieve a 2.5% inflation target within the next year. The economy’s
growth in real output is currently 3%. The world real interest rate is currently 1.5%. The
currency used in your country is the lira. Assume prices are flexible.
a.
(5 points) What is the growth rate of the money supply in this economy? If you
choose to adopt a money supply target, what is the money supply growth rate that will
achieve your inflation target?
𝑀 = 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 + 𝑟𝑒𝑎𝑙 𝐺𝐷𝑃 𝑔𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒
𝑀 = .04 + .03 = .07 = 7%
𝑀𝑡𝑎𝑟𝑔𝑒𝑡 = .025 + .03 = .055 = 5.5%
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b.
(5 points) Suppose the inflation rate in the United States is currently 2% and you
adopt an exchange rate target relative to the U.S. dollar. Calculate the percent
appreciation/depreciation in the lira needed for you to achieve your inflation target. Will
the lira appreciate or depreciate relative to the U.S. dollar?
. 025 − .02 = .005 = 0.5%
The lira should depreciate 0.5% relative to the dollar
c.
(5 points) Your final option is to achieve your inflation target using interest rate
policy. Using the Fisher equation, calculate the current nominal interest rate in your
country. What nominal interest rate will allow you to achieve the inflation target?
𝑖 = 𝑟 + 𝜋
𝑖𝑡0 = .015 + .04 = .055 = 5.5%
𝑖𝑡1 = .015 + .025 = .035 = 3.5%
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