Instructor: Yuan Liu
ECON160B,SSII 2013
Internationl Macroeconomics
Assignment 1
Due Aug 13th in class
1. Refer to the exchange rates given in the following table:
Table 1: Exchange rate measured in foreign currency per $ (EF X/$ )
Country
Canada
Japan
Mexico
Euro
Trade Share
36%
16%
20%
28%
Currency
Jul 31st 2012
Canadian dollar
1.00
Japanese yen
78.1
Mexico Peso
13.3
Euro
0.81
Jul 31st 2013
1.03
98.1
12.8
0.75
Source: The Economist
Based on the table provided, answer the following questions:
(a) Compute the Canadian dollar-Japanese yen exchange rate (EC$/Y en ) on Ju1 31st
2012 and Jul 31st 2013. Did Canadian dollar appreciate or depreciate against
Japanese yen?
EC$/$
1
On Jul 31st 2012, EC$/yen = Eyen/$
= 78.1
= 0.0128.
E
C$/$
= 1.03
= 0.0105
On Jul 31st 2013, EC$/yen = Eyen/$
98.1
Canadia dollar appreciated against Japanese yen.
(b) Compute the Mexico Peso-Euro exchange rate (Epeso/euro ) on Jul 31st 2012 and
Jul 31st 2013. Did Euro appreciate or depreciate against Mexico peso?
Epeso/$
On Jul 31st 2012, Epeso/euro = Eeuro/$
= 13.3
= 16.42.
0.81
E
peso/$
On Jul 31st 2013, Epeso/euro = Eeuro/$
=
Euro appreciated against Mexico peso.
12.8
0.75
= 17.067
(c) Compute the U.S. dollar-Euro exchange rate (E$/euro ) on Jul 31st 2012 and Jul
31st 2013. Did U.S. dollar appreciate or depreciate against Euro? Calculate the
precentage change of exchange rate (E$/euro ).
1
1
On Jul 31st 2012, E$/euro = 0.81
= 1.2346; On Jul 31st 2013, E$/euro = 0.75
= 1.33.
1.33 − 1.2346
= 7.73%
1.2346
Dollar depreciate against Euro by 7.73%.
(d) Convert all the rest exchange rates to be measured as U.S. dollar per foreign
currency (E$/F X ) as what you did with dollar-euro exchange rate in the previous
question. Calculate the precentage change of exchange rate.
(e) Suppose U.S. only trade with Canada, Japan, Mexico and European Union. Trade
share of each country/region in U.S. trade is given in the table. Use the trade
1
E$/C$
E$/yen
E$/peso
E$/euro
Jul 31st 2012
1
0.0128
0.075
1.2346
Jul 31st 2013
0.97
0.0102
0.078
1.33
percentage change
-3%
-20.3%
4%
7.73%
shares as weights to compute the percentage change in the nominal effective exchange rate for the U.S. between 2012 and 2013 (in dollar per foreign currency).
Did dollar appreciate or depreciate against the basket of currencies?
−3%(36%) + (−20.3%)(16%) + 4%(20%) + 7.73%(28%) = −1.36%
Dollar appreciate relative to a basket of currencies.
2. Suppose quotes for the dollar-euro exchange rate E$/euro are as follows: in N.Y. $1.5
per euro, and in Tokyo $1.55 per euro. Describe how investors use arbitrage to take
advantage of the difference in exchange rates. Explain how this process will affect the
dollar price of the euro in N.Y. and Tokyo. (This is problem 5 in chapter 2 in the
textbook.)
Investors will buy euros in N.Y. at a price of $1.5 each and then sell these euros in
Tokyo at a price of $1.55, earning a $0.05 profit on each euro. With the influx of buyers
in N.Y., the price of euros in N.Y. will increase. With the influx of traders selling euros
in Toyko, the price of euros in Tokyo will decrease. This price adjustment continues
until the exchange rates are equal in both markets.
3. Apple is expecting a payment of 10 million Japanese yen for iphones sold in Japan in
5 months. The cost of producing and shipping these iphones is $80,000. The current
spot rate is 100 yen per U.S. dollar. Apple is concerned that U.S. dollar is going to
appreciate against Japanese yen over the next 5 months.
(a) Suppose exchange rate remains unchanged, how much does Apple expect to receive in U.S. dollars? Compute Apple’s profit under this scenario.
Apple expect to receive $100,000. ( 10,000,000/100 ). Profit is $20,000.
(b) How much would Apple receive if the dollar appreciated to 110 yen per U.S.
dollar? Compute Apple’s profit under this scenario
10,000,000/110 =$90,909. Profit is $10,909.
(c) Describe how Apple could use a forward contract to avoid the risk of losses associated with the potential appreciation in the U.S. dollar. Suppose the 5 month
forward exchange rate between dollar and yen is 102 yen per dollar.
Lock in the rate at which Apple will sell the yens and buy dollars in 5 months
using a forward contract. This would ensure the firm’s yen receipts will sell for
$98,039. The profit is locked at $18,039.
4. Suppose you have $10,000 you wish to invest. For each of the following scenarios
explain whether you would be better off putting your money in the foreign or domestic
alternative presented.
2
(a) You know you will need your money in 1 year. The annual interest rate on bank
deposits is 4% in the U.S. and 10% in Chili. The current exchange rate is 3.52
Chilean peso per dollar. You expect that in one year the exchange rate will be
4.78 chilean peso per dollar.
Deposit in the U.S.: $10, 000(1 + 4%) = $10, 400.
1
= $8100.4
Deposit in Chili: $10, 000(3.52peso/$)(1 + 10%) 4.78peso/$
Better off depositing your money in the U.S..
(b) You konw you will need your money in 1 year. The annual intereat rate on bank
deposits is 5.5% in the U.S. and 6.5% in EU. The currenct exchange rate is 0.9
euros per dollar. The 1 year forward exchange rate is 0.98 euros per dollar.
Deposit in the U.S.: $10, 000(1 + 5.5%) = $10550
1
= $9780.6
Deposit in EU: $10, 000(0.9euro/$)(1 + 6.5%) 0.98euro/$
Better off depositing your money in the U.S..
5. Assume both CIP and UIP hold when you answer the following questions:
(a) Interest rate on bank deposit is 4% in South Africa and 6% in the U.S.. If the
expected future spot exchange rate one year from now is 6.05 Rand per dollar,
what must be the current spot exchange rate be in order to clear the foreign
exchange market? Which no arbitrage condition did you use to compute the
equilibrium current spot exchange rate?
Treat South Africa as the home country. According to UIP:
1 + irand =
e
Erand/$
Erand/$
(1 + i$ )
Plug in numbers given in the question:
1 + 4% =
6.05
(1 + 6%)
Erand/$
Solve for the spot exchange rate: Erand/$ = 6.17
(b) Suppose the current spot exchange rate is indeed what you computed in part a,
what would be the equilibrium forward exchange rate using interest rate informations in part a? Which no arbitrage condition did you use to compute the
equilibrium forward exchange rate?
If both UIP and CIP hold,
e
= 6.05
Frand/$ = Erand/$
(c) Interest rate on bank deposit is still 4% in South Africa and 6% in the U.S..
Suppose that the expected future spot rate is 6.25 rather than 6.05. How does
this change your answer to part a?
6.25
(1 + 6%)
Erand/$
Solve for the spot exchange rate: Erand/$ = 6.37 As expected ex-rate increases,
equilibrium spot ex-rate increases. Expectation is self-fullfilling.
1 + 4% =
3
(d) Suppose your expectation remains at 6.25, and interest rate in South Africa is
now 6.7%. How does this change your answer to part c?
1 + 6.7% =
6.25
(1 + 6%)
Erand/$
Solve for the spot exchange rate: E$/rand = 6.21 As intereat rate increases in
South Africa, bank deposit in rand is more attractive. Compared with part c,
spot exchange rate decreases, rand appreciates against dollar.
6. Suppose annual intereat rate on bank deposit is 2% in the US and 4% in the UK. If UIP
holds, what is the expected appreciation of U.S. dollar against pound over one year?
If the current spot exchange rate is E$/£ = 0.6, what is the expected spot exchange
rate one year from now?
i$ − i£ =
e
∆E$/£
E$/£
Expected appreciation of U.S. dollar is 2%. Expected future spot rate is 0.6(1 − 2%) =
0.588
4