Download Purchasing Power Parity

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Commerce 260306
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Commerce 260508
Handout #6
International Parity Conditions
Purchasing Power Parity
Yee-Tien “Ted” Fu
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4-2
Reading Assignments for This Week
Scan
Read
Chaps 3-5
Pages
Luenberger
Chap
Pages
Solnik
Chap
Pages
Levich
Blanchard
Chap 18
Pages
Openness in Goods and Financial Markets
Wooldridge
Chap 4
Pages
Multiple Regression Analysis: Inference
4-3
World Interest Rates Table
Major Central Banks Overview
Next Meeting
Last Change
Current
Interest Rate
Bank of
Canada
Jul 15 2008
Apr 22 2008
3%
Bank of
England
Jul 10 2008
Apr 10 2008
5%
Bank of Japan
Jul 15 2008
Feb 21 2007
0.5%
European
Central Bank
Aug 07 2008
Jul 03 2008
4.25%
Federal
Reserve
Aug 05 2008
Apr 30 2008
2%
Swiss National
Bank
Sep 18 2008
Sep 13 2007
2.75%
The Reserve
Bank of
Australia
Aug 05 2008
Mar 04 2008
7.25%
Central Bank
http://www.fxstreet.com/fundamental/interest-rates-table/
4-4
How do you like the 8 months Liquid CD with a minimum
required balance of $10,000 and a ceiling of $500,000?
CERTIFICATES OF DEPOSIT AS OF JULY 7, 2008
Minimum
Annual
Interest
Term
Balance* Percentage Yield*
Rate
5 years
$5,000+
5.00%
4.88%
4 years
$5,000+
4.25%
4.16%
3 years
$5,000+
3.50%
3.44%
2 years
$5,000+
3.40%
3.34%
18 months
$5,000+
3.75%
3.68%
12 months
$5,000+
2.75%
2.71%
9 months Special $5,000+
3.50%
3.44%
8 month Liquid
$10,000+
3.25%
3.20%
6 months
$5,000+
2.65%
2.62%
3 months
$5,000+
2.60%
2.57%
30 day Special*
$25,000+
2.50%
2.47%
*The 30-day CD has a minimum opening balance of $25,000.
*The 8 Month Liquid CD Maintains a minimum balance of $10,000,
and a maximum opening balance of $500,000.
4-5
http://finance.mapsofworld.com/financial-market/world-inflation.html
http://inflationdata.com/inflation/Inflation_Rate/InternationalSites.asp
4-6
Exchange Rates Table
http://www.x-rates.com/
4-7
July 2007
http://www.eco
nomist.com/ma
rkets/bigmac/
4-8
June 24, 2008
4-9
Feb 04, 2009
4-10
International Parity Relations Linear Approximation
where Spot Rate S are in indirect quote (FC/DC or FC/$)
Forward Rate
Unbiased
FRU Property
Purchasing Power
Parity (relative
PPP
version)
FIE
Uncovered Interest Parity
or Fisher International
Effect
Solnik 2.1
IRP
Interest Rate
Parity
4-11
It takes three to five years to see a significant
(+)(-)valuation to be cut in half.
Source: Page 129 of Levich 2E
4-12
Foreign Exchange Markets
International Parity Conditions
Purchasing Power Parity
MS&E 247S International Investments
Yee-Tien (Ted) Fu
“Under the skin of any international economist
lies a deep-seated belief in some variant of
the PPP theory of the exchange rate.”
- Dornbusch and Krugman (1976)
4-14
Parity Conditions
• Parity or equilibrium conditions can be thought
of as international financial “benchmarks” or
“break-even values”.
¤ They are the defining points where the decisionmaker in a private enterprise is indifferent
between the two strategies summarized by the
two halves of the parity relation.
¤ Such decisions include :
– to borrow in one currency or another?
– to locate a plant in one country or another?
– to measure exposure to currency risks using one
formula or another?
4-15
Parity Conditions
• Parity conditions are the most intriguing when
they are false. Why is this so?
¤ Because the parity conditions rely heavily on
arbitrage, a violation of parity often implies that
a direct or indirect profit opportunity (or cost
advantage) is available to the decision-maker.
¤ These times present the greatest opportunities
but not necessarily the greatest risks.
¤ So, the decision-maker should be most
interested in knowing the direction and duration
of such departures from parity.
4-16
Analysis of Parity Conditions
For each parity condition :
Step 1: Assume a perfect capital market setting.
- no transaction costs
- no taxes
- complete certainty
Step 2: Relax the key assumptions underlying
the parity condition.
Step 3: Review the empirical evidence under the
parity condition.
We will begin with purchasing power parity (PPP) by
developing its theory and reviewing the empirical
evidence related to it.
4-17
Purchasing Power Parity
• When goods become expensive in one
•
country (relatively high inflation rate), exports
decrease and imports increase due to
arbitrage across the goods markets. So, the
demand for foreign currencies increases and
the domestic currency value is depressed.
The result is that currencies will fluctuate
until the relative purchasing power of each
country is the same, that is, reaches parity.
4-18
Purchasing Power Parity
• The theory of purchasing power parity (PPP)
•
focuses on this inflation - exchange rate
relationship.
The absolute form is the “Law of One Price”.
It suggests that similar products in different
countries should be equally priced when
measured in the same currency.
• The relative form of PPP accounts for market
imperfections like transportation costs,
tariffs, and quotas.
4-19
Absolute PPP
The Law of One Price is the principle that in a
perfect capital market setting, homogeneous
goods will sell for the same price in two
markets, taking into account the exchange rate.
Example:
If the price of wheat is $4.50/bushel in the US
and the $/£ exchange rate (S) is $1.50/£,
then the price of wheat in the UK should be
$4.50/bushel / $1.50/£ = 3.00£/bushel.
4-20
Absolute PPP
The price of a market basket of U.S. goods
equals the price of a market basket of U.K.
goods when multiplied by the exchange rate:
PUS, t = S$/£, t x PUK, t
Driving Force: Arbitrage in goods
PUS = PUK x Spot
4-21
Relative PPP
The percentage change in the exchange rate
equals the percentage change in U.S. goods
prices less the percentage change in foreign
goods prices.
Driving Force: Arbitrage in goods
%Δ Spot = %Δ PUS - %Δ PUK
4-22
Relative PPP
Assume that the following hold only with K:
a
b
PUS, t+1 = K x S$/£, t+1 x PUK, t+1
PUS, t = K x S$/£, t x PUK, t
(4.3a)
(4.3b)
(1 + pUS) = (1 + s) x (1 + pUK )
= 1 + s + pUK + s x pUK
(4.4)
where p = P t+1 - P t , s = S t+1 - S t
Pt
St
(% change)
Rearranging terms, we have:
pUS = s + pUK + s x pUK
4-23
Relative PPP
Example:
If UK prices rose by 20% (from 100 to 120),
and the US$ depreciated by 10% (from $1.50
to $1.65), then US prices need to rise by 32%
(from 100 to 132) to maintain the relative PPP.
That is, pUS = 10% + 20% + 10% X 20% = 32%
4-24
Relative PPP
Assuming small % changes in prices and
exchange rates, we can ignore the crossproduct term (s x pUK) :
s = pUS - pUK
% exchange
% change in _ % change in
rate change = US prices
UK prices
i.e.
%Δ Spot = %Δ PUS - %Δ PUK
4-25
Relative PPP
What if we are interested in the level of the
exchange rate that satisfies PPP?
• PPP spot rate is the spot rate that
reestablishes PPP relative to some base
period, or the exchange rate that would just
offset the relative inflation between a pair of
countries since the base period.
4-26
Relative PPP
PUS, t+1 = K x S$/£, t+1 x PUK, t+1
PUS, t = K x S$/£, t x PUK, t
4.3a
4.3b
(4.3a)
(4.3b)
S$/£, t+1
PUS, t+1 / PUK, t+1
S$/£, t =
PUS, t / PUK, t
SPPP, t+1 = S$/£, t
or SPPP, t+1 = S$/£, t
PUS, t+1 / PUK, t+1
PUS, t / PUK, t
(4.7a)
PUS, t+1 / PUS, t
PUK, t+1 / PUK, t
(4.7b)
4-27
Relative PPP
Example:
Assume that the nominal exchange rate in the
base period was $1.50 and that the prices of US
goods had risen by 8%, while the prices of UK
goods had risen by 4%.
The PPP spot rate is $1.50/£ X 1.08/1.04
= $1.5577/£
A nominal exchange rate of $1.5577/£ would reestablish PPP in comparison with the base period.
Nominal exchange rates > $1.5577/£
represent £ "overvaluation" ($ undervaluation).
4-28
Relative PPP
Note that purchasing power conditions
do not imply anything about causal
linkages between prices and exchanges
rates or vice versa.
Both prices AND exchange rates are jointly
determined by other variables in the economy.
A nation's money supply policy, tax (fiscal)
policy, or commercial (tariff) policy may affect
BOTH domestic prices and the exchange
rates.
4-29
Relative PPP - Another Derivation
• When inflation occurs and PPP holds, the
exchange rate will adjust to maintain the parity:
Pf (1 + If ) (1 + ef ) = Ph (1 + Ih )
where Ph = price index of goods in the home country
Pf = price index of goods in the foreign country
Ih = inflation rate in the home country
If = inflation rate in the foreign country
ef = % change in the foreign currency’s value
• Since Ph = Pf , solving for ef gives:
ef = (1 + Ih ) _ 1
(1 + If )
Madura
4-30
Relative PPP - Another Derivation
• The relationship can be simplified as follows:
ef ≈
_
Ih
If
This formula is appropriate only when the inflation
differential is small.
Old Data, Old Data, Old Data
Example:
Suppose that the inflation rate in U.S. is 9%, while
U.K.’s rate is 5%. Then PPP suggests that the
exchange rate should appreciate by about 4%.
U.S. will import more, while U.K. will import less, until
the exchange rate has risen by about 4%. At this
point, U.K. goods will cost 5+4=9% more to U.S.
consumers, while U.S. goods will cost 9-4=5% more
to U.K. consumers.
Madura
4-31
Graphic Analysis of Purchasing Power Parity
Inflation Rate Differential (%)
home inflation rate - foreign inflation rate
4
PPP line
2
-3
-1
1
-2
-4
Madura
3
%Δ in the
foreign
currency
spot rate
4-32
Graphic Analysis of Purchasing Power Parity
Inflation Rate Differential (%)
home inflation rate - foreign inflation rate
4
PPP line
Increased
purchasing
power of
2
foreign
goods
-3
-1
1
-2
-4
Madura
3
Decreased
purchasing
power of
foreign
goods
%Δ in the
foreign
currency
spot rate
4-33
Purchasing Power Parity
• If the actual inflation differential and exchange
•
rate % change for two or more countries
deviate significantly from the PPP line over
time, then PPP does not hold.
A statistical test can be developed by applying
regression analysis to the historical exchange
rates and inflation differentials:
ef = a0 + a1 { (1+Ih)/(1+If) - 1 } + μ
The appropriate t-tests are then applied to a0
and a1, whose hypothesized values are 0 and
1 respectively.
Madura
4-34
Purchasing Power Parity
• PPP may not occur consistently due to:
the existence of other influential factors like
differentials in income levels and risk, as well
as government controls; and
¤ the lack of substitutes for traded goods.
A limitation in testing PPP is that the results
may vary according to the base period used.
PPP can also be tested by assessing a “real”
exchange rate over time. If this rate reverts to
some mean level over time, this would
suggest that it is constant in the long run.
¤
•
•
Madura
4-35
The Real Exchange Rate
• For a country which relies heavily on trade to
•
maintain living standards, it is arguable that
the exchange rate that is important is not the
rate at which the country’s currency
exchanges for another, but the rate at which
the country’s goods exchange in
international trade.
One such calculation of this is the real
exchange rate, which relates the effective
exchange rate to the price of domestic goods
relative to the price of foreign goods.
International Business Economics: Piggott and Cook
4-36
The Effective Exchange Rate
• Since a currency varies against other currencies, it
sometimes makes little sense to refer to one
particular bilateral rate intended to represent the
foreign exchange value of that currency.
• What is needed is some kind of average foreign
currency value, of, say, the pound or Deutsche mark
against several other currencies, and indeed this is
what is currently computed for all major currencies.
• These “average exchange rates” are termed effective
exchange rates and are calculated as an index.
International Business Economics: Piggott and Cook
4-37
The Effective Exchange Rate
Effective exchange rates (1991=100)
Sterling
US$
DM
81.2
130.6
107.4
1985
89.8
113.9
99.5
1986
96.0
97.9
105.2
1987
100.1
95.8
103.8
1988
102.8
95.1
100.6
1989
100.4
99.1
101.0
1990
100.0
100.0
100.0
1991
103.8
96.5
98.6
1992
100.7
107.9
88.4
1993
89.2
100.1
109.7
1994
85.4
101.0
116.8
1995
115.0
87.3
107.6
1996
International Business Economics: Piggott and Cook
Yen
68.3
89.9
97.5
106.5
99.9
91.8
100.0
105.4
126.6
136.3
143.9
125.5
4-38
The Effective Exchange Rate
• The effective exchange rate is an index of the
weighted-average foreign exchange value of
a currency against a basket of other
currencies.
¤ This index summarizes in one number the
value of the currency against a number of
other currencies.
• The weights are usually based on a country’s
trade against its trading partners.
Extra-Man
4-39
The Effective Exchange Rate
Example
Suppose the U.S. only trades with Japan and Germany.
Year 1 yen 100/$ index 100
Year 2 yen 105/$ index 105
Year 3 yen 110/$ index 110
DM 1.50/$ index 100
DM 1.65/$ index 110
DM 1.65/$ index 110
Total U.S. trade = $1000 billion
with Japan
$ 600 billion weight: 60%
with Germany
$ 400 billion weight: 40%
Effective exchange rate for the $:
Extra-Man
Year 1: 100
Year 2: 107
Year 3: 110
4-40
Openness in Goods and Financial Markets
Opening the Economy to International Transactions
Two dimensions of openness:
1. Openness in Goods Markets
2. Openness in Financial Markets
4-41
Openness in Goods Markets
4-42
Openness in Goods Markets
Observations of U.S. Exports and Imports
• Exports and imports in the U.S. were 5% of GDP in
•
•
1960, are 12% (11.2% exports, 13% imports) of GDP
today.
Decline in exports and imports from 1929-1936 was
due in large part to the Smoot-Hawley Act of 1930,
which led to sharp increases in tariffs with the hope
of increasing the demand for domestic goods,
thereby helping the U.S. economy recover from the
Great Depression.
Large trade surpluses occurred in the 1940s, while
large trade deficits occurred in the 1980s.
4-43
Openness in Goods Markets
Measuring the Degree of Openness
• Volume of Trade: Ratio of exports or imports to
•
GDP (U.S. = 12%)
Tradable Goods Ratio: Percent of output that
competes in foreign markets
(U.S. = 60%)
4-44
Openness in Goods Markets
A Look Around the World
Country
Export Ratio (%)
United States
12
Japan
10
Germany
23
United Kingdom 29
Country Export Ratio (%)
Switzerland
40
Austria
38
Belgium
73
Luxembourg
91
4-45
Openness in Goods Markets
What Do You Think...
Can exports exceed GDP?
The trick is to realize that exports and imports may be
exports and imports of intermediate goods.
E.g., a country imports intermediate good for $1 billion
and transfers them into final goods using only labor,
which costs $200 million. Assume that there is no profit.
The value of final goods is thus equal to $1,200 million.
Assume that $1 billion worth of goods is exported and the
rest is consumed in the country. Recall that GDP is value
added in the economy ($200 million here), so that the ratio
of exports to GDP is equal to 5.
4-46
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
Real Exchange Rates: Price of foreign goods in terms of
domestic goods
Nominal Exchange Rates: The relative prices of
currencies
4-47
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
Nominal Exchange Rates: Two Views
1.
The price of domestic currency in terms of foreign
currency.
2.
The price of foreign currency in terms of domestic
currency.
For Example:
December 1998: Nominal exchange between U.S. dollar
and German Deutschemark (DM)
$ in terms of DM: 1$ = 1.67 DM
DM in terms of $s: 1DM = 0.60 $
4-48
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
Nominal Exchange Rates--Choosing a Definition:
Nominal exchange rates (E): price of foreign
currency in terms of
domestic currency
For Example:
E between the U.S. (domestic) and Germany (foreign)
is the price of DM in terms of $
E = .60 (December 1998)
4-49
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
Measuring Changes in the Nominal Exchange Rate (E)
• Appreciation of domestic currency corresponds to
a decrease in E
• Depreciation of domestic currency corresponds to
an increase in E
4-50
Openness in Goods Markets
The Nominal Exchange Rate, Appreciation, &
Depreciation: Germany and the United States*
Nominal Exchange Rate, E (Price of DM in terms of dollars)
Appreciation of the dollar
Price of dollars in DM increases
Equivalently:
Price of DM in dollars decreases
Equivalently:
Exchange rate decreases: E↓
Depreciation of the dollar
Price of dollars in DM decreases
*Note that E is in the
Equivalently:
form of “American
Price of DM in dollars increases
Quote” or “Direct
Quote” here.
Equivalently:
Exchange rate increases: E↑
4-51
4-52
Openness in Goods Markets
The Nominal Exchange Rate between the DM and the Dollar
1978 - 1998
A sharp dollar appreciation
in the first half of the 1980s
was followed by an equally
sharp dollar depreciation in
the second half of the
1980s.
4-53
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
Observations on E between U.S. and Germany:
1.
The trend increase in E
1975 DM = 40 cents
1998 DM = 60 cents
2.
The large fluctuations in E
Early 1980s the value of DM dropped 57 cents
to 30 cents
Late 1980s the value of DM rose to 60 cents
4-54
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
Question:
Does a decrease in E of U.S. $s for DMs necessarily
mean U.S. citizens can buy more German goods with
their dollars?
Hint: What is the inflation rate in Germany?
4-55
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
Calculating Real Exchange Rates
The price of one German good (Mercedes SL) in terms of
one U.S. Good (Cadillac Seville)
1.
Convert the price of the Mercedes from DM to $s
PDM = 100,000
DM = .60$s
P$s = 100,000 x .60 = $60,000
2.
Compute the ratio of the $ price of the Mercedes to the
Cadillac (Cadillac price = $40,000)
Real exchange rate between U.S. & Germany =
$60,000
= 1 .5
$40,000
4-56
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
Expanding the Real Exchange Rate Calculation to the
Entire Economic System
If:
P = U.S. GDP Deflator
P* = German GDP Deflator
E = DM-dollar nominal exchange rate
Then: Price of German goods in US$ = EP*
Real exchange rate (ε ) = EP*
P
NOTE:
Real exchange rates (ε ) are index numbers and
measure only relative change.
4-57
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
The Construction of the Real Exchange Rate
Price of German
goods in DM
P*
Price of German
goods in dollars
EP*
Price of U.S.
goods in dollars
P
Real exchange
rate
ε = EP*
P
4-58
Openness in Goods Markets
The Real Exchange Rate and Real
Appreciation and Real Depreciation*
Real Exchange Rate, ε (Price of German goods in terms of U.S. goods)
Real Appreciation
Price of U.S. goods in terms of German goods increases
Equivalently:
Price of German goods in terms of U.S. goods decreases
Equivalently:
Real exchange rate decreases: ε ↓
Real Depreciation
Price of U.S. goods in terms of German goods decreases
Equivalently:
Price of German goods in terms of U.S. goods increases
Equivalently:
Real exchange rate decreases: ε ↑
*From the view of United States looking at Germany
4-59
4-60
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
Real and Nominal Exchange Rates
Between Germany and the U.S., 1975-1998
4-61
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
The Real and Nominal Exchange Rates Between Germany
and the U.S. 1975-1998
Observations:
•
The real 1998 exchange 0.60 was the same as 1975.
P * remained unchanged.
E and P both rose, so
∈= E
•
P
Movements in ε are driven primarily by change in E
4-62
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
The Country Composition of U.S. Merchandise Trade, 1998
Countries
Canada
Western Europe
Japan
Mexico
Asia*
OPEC**
Others
Total
Exports to
Imports from
$ BillionsPercent $ BillionsPercent
156
159
57
78
126
15
80
671
23
24
8
12
19
2
11
100
177
193
121
95
247
19
67
919
*Not including Japan.
**OPEC: Organization of Petroleum Exporting Countries.
19
21
13
11
27
2
7
100
4-63
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
Country Composition of U.S. Merchandise Trade, 1998
Observations:
• Canada and Western Europe account for 40-47%
of U.S. trade.
• Large trade deficit with Japan:
Exports to = $57 Billion
Imports from = $121 Billion
4-64
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
Real Multilateral Exchange Rates
• The real exchange rate when considering many
countries
• Calculate by using each country’s share of
trade as the weight for that country
4-65
Openness in Goods Markets
The Choice Between Domestic and Foreign Goods
The U.S. Effective Real Exchange Rate
1975 - 1998
The multilateral real U.S.
exchange rate is also
called the U.S. tradeweighted real exchange
rate, and the U.S.
effective real exchange
rate.
4-66
The Real Exchange Rate
Real magnitudes are constructed from nominal
magnitudes by adjusting for the appropriate
price levels (P) or inflation rates.
nominal income
Real income =
$ per market basket
$55,000/year
=
$250/market basket
= 220 market baskets/year in 1990
(define this as 100)
So, real income is measured in terms of real
goods and services.
4-67
The Real Exchange Rate
In 1991, nominal income rises by 10%
(to $60,500) while the price of a market basket
rises by 8% (to $270).
To express real income in 1991 as an index:
index (1991) = real income (1991)
real income (1990)
= (60,500/270)
220
= 1.0185
Real income has increased by 1.85%.
4-68
The Real Exchange Rate
The nominal exchange rate (e.g., S=$0.60/DM)
measures the rate of exchange between the
currencies of two countries.
Currency traders quote nominal exchange rates.
The real exchange rate is calculated by
correcting the nominal exchange rate for the
price levels in two countries.
4-69
The Real Exchange Rate
Assuming the case that absolute purchasing
power parity holds:
($600 Price/USgood)
$0.60/DM =
(DM 1000 Price/GermanGood)
LHS = 1 = US good / German good
RHS
In other words, when PPP holds, identical US
goods and German goods exchange for each
other on a one-for-one basis; and the
real exchange rate is constant.
4-70
The Real Exchange Rate
Spot (Real, t) = Spot (Nominal, t)
Spot (PPP, t)
If real exchange rate index = $0.60/DM / $0.50/DM
= 1.2
=> DM is "overvalued" on a PPP basis,
since DM 1 exchanges for $0.60 > PPP spot exchange
$0.50 or 1.0 German good can be exchanged for 1.2
US goods
and sellers of German goods have lost
competitiveness.
4-71
Evidence: The Law of One Price
• One test of the Law of One Price is the Big Mac index,
which has been published annually in The Economist
since 1986.
http://www.economist.com/markets/Bigmac/Index.cfm
• The Big Mac index (burgernomics) was devised as a
•
•
light-hearted guide to whether currencies are at their
“correct” level, based on PPP – the notion that a
dollar should buy the same amount in all countries.
Thus in the long run, the exchange rate between two
countries should move towards the rate that
equalizes the prices of an identical basket of goods
and services in each country.
In other words, a dollar should buy the same amount
everywhere.
The Economist
4-72
Evidence: The Law of One Price
¤
¤
¤
Our “basket” is a McDonalds’ Big Mac, which is
produced and consumed in 120 countries
around the world.
The Big Mac PPP is the exchange rate that
would leave hamburgers costing the same in
America as abroad.
Comparing actual exchange rates with PPPs
signals whether a currency is under- or overvalued.
The Economist
4-73
Evidence: The Law of One Price
• The result of the 2000 survey suggested that the
•
average price of a Big Mac in the U.S. was $2.51, but
was as little as $1.19 in Malaysia, and as much as
$3.58 in Israel.
Hence the Israeli shekel is the most overvalued
currency (by 43%), while the Malaysian ringgit is the
most undervalued (by 53%).
The Economist
4-74
Big Mac foreign-currency price
PPP rate =
US($) price
(of the
US$)
The Economist
convert into dollars at the spot rate
25/04/00
4-75
25/04/00
The Economist
4-76
The first column of the table shows local-currency prices
of a Big Mac, while the second converts them into
dollars. The third column calculates PPPs.
Big Mac PPP rate
=
(of the US$)
foreign currency price
US($) price
Big Mac PPP rate
(of the foreign =
currency)
US($) price
foreign currency price
spot rate
– Big Mac PPP rate
Under (-) / Over (+)
(of foreign currency) (of the foreign currency)
x 100
valuation against =
Big Mac PPP rate
the dollar, %
(of the foreign currency)
4-77
Evidence: The Law of One Price
Example 1. Canada
Purchasing power of C$2.85
= Purchasing power of $2.51
= a Big Mac
Hence Big Mac PPP implies 1 C$ = $ (2.51/2.85)
However from the market spot rate, 1 C$ = $ (1/1.47)
(-)/(+) valuation against $, % (based on Big Mac PPP)
(1/1.47) - (2.51/2.85)
(1/1.47)
=
= (2.51/2.85) - 1
(2.51/2.85)
= - 22.8%
4-78
Evidence: The Law of One Price
Example 2. Denmark
Purchasing power of 24.75 DKr
= Purchasing power of $2.51
= a Big Mac
Hence Big Mac PPP implies 1 DKr = $ (2.51/24.75)
However from the market spot rate, 1 DKr = $ (1/8.04)
(-)/(+) valuation against $, % (based on Big Mac PPP)
(1/8.04) - (2.51/24.75)
(1/8.04)
=
= (2.51/24.75) - 1
(2.51/24.75)
= + 22.6%
4-79
17/04/01
4-80
17/04/01
4-81
The average price of a Big Mac in the U.S. is $2.54
(including sales tax). In Japan, Big Mac scoffers have to
pay ¥294, or $2.38 at current exchange rates. Dividing the
yen price by the dollar price gives a Big Mac PPP of ¥116.
Comparing that with this week’s rate of ¥124 implies that
the yen is 6% undervalued.
(1/124 - 1/116)/(1/116) = -0.0645 = -6%
The cheapest Big Macs are found in China, Malaysia, the
Philippines and South Africa, and all cost less than
$1.20 – these countries have the most undervalued
currencies, by more than 50%.
The most expensive Big Macs are found in Britain,
Denmark and Switzerland – they have the most
overvalued currencies. Sterling, for example is 12%
overvalued against the dollar – less than two years ago,
it was overvalued by 26%.
4-82
Overall, the dollar has never looked so overvalued during
15 years of burgernomics. In the mid 1990s the dollar was
cheap against most currencies; now it looks dear against
all but three. The most undervalued of the rich-world
currencies are the Australian and New Zealand dollars,
which are both 40-45% below McParity. They need to
ketchup.
All the emerging-market currencies are undervalued
against the dollar on a Big Mac PPP basis. That, in turn,
means that a currency such as Argentina’s peso, which is
undervalued only a tad against the dollar, is massively
overvalued compared with other currencies, such as the
Brazilian real and virtually all of the East Asian
currencies.
4-83
25/04/02
4-84
25/04/02
4-85
The average American price has fallen slightly over the
past year, to $2.49. The cheapest Big Mac is in Argentina
(78 cents), after its massive devaluation; the most
expensive ($3.81) is in Switzerland. By this measure, the
Argentine peso is the most undervalued currency and the
Swiss franc the most overvalued.
The euro is only 5% undervalued relative to its Big Mac
PPP, far less than many economists claim. The euro area
may have a single currency, but the price of a Big Mac
varies from euro2.15 in Greece to euro2.95 in France.
However, that range has narrowed from a year ago.
The Australian dollar is the most undervalued rich-world
currency, 35% below McParity. No wonder the Australian
economy was so strong last year. Sterling, by contrast, is
one of the few currencies that is overvalued against the
dollar, by 16%; it is 21% too strong against the euro.
4-86
Overall, the dollar looks overvalued. Over half the
emerging-market currencies are more than 30%
undervalued. That implies that any currency close to
McParity (eg, the Argentine peso last year, or the
Mexican peso today) will be overvalued against other
emerging-market rivals.
Adjustment back towards PPP does not always come
through a shift in exchange rates. It can also come
about through price changes. In 1995 the yen was 100%
overvalued. It has since fallen by 35%; but the price of a
Japanese burger has also dropped by one-third.
In the early 1990s the Big Mac index repeatedly
signalled that the dollar was undervalued, yet it
continued to slide for several years until it flipped
around. Our latest figures suggest that, sooner or later,
the mighty dollar will tumble...
4-87
Apr 24th 2003
4-88
4-89
4-90
4-91
Evidence: The Law of One Price
• Some find the Big Mac index hard to swallow. Not
•
•
•
only does the PPP theory hold only for the very long
run, but hamburgers are a flawed measure of PPP.
Local prices may be distorted by trade barriers on
beef, sales taxes, local competition and changes in
the cost of non-traded inputs such as rents.
But despite its flaws, the Big Mac index produces
PPP estimates close to those derived by more
sophisticated methods.
A currency can deviate from PPP for long periods,
but several studies have found that the Big Mac PPP
is a useful predictor of future movements – “betting
on the most undervalued of the main currencies each
year is a profitable strategy.”
The Economist
4-92
Evidence: The Law of One Price
¤
¤
¤
Indeed, the Big Mac has had several forecasting
successes.
When the euro was launched at the start of 1999,
most forecasters predicted that it would rise against
the dollar. But the euro has instead tumbled – exactly
as the Big Mac index had signaled. At the start of
1999, euro burgers were much dearer than American
ones, suggesting that the euro had started off
significantly overvalued.
One of the best-known hedge funds, Soros Fund
Management, admitted that it chewed over the sell
signal given by the Big Mac index when the euro was
launched, but then decided to ignore it. The euro
tumbled, and Soros was cheesed off.
The Economist
4-93
Year 2000
2.51/2.56 = 0.98
(0.93-0.98)/0.98 = -5%
€ is undervalued by 5%
Year 2001
2.54/2.57 = 0.99
(0.88-0.99)/0.99 = -11%
€ is undervalued by 11%
The average price today in the 12 euro countries is
euro2.57, or $2.27 at current exchange rates. The
euro’s Big Mac PPP against the dollar is
euro1=$0.99, which shows that it has now undershot
McParity by 11%. That, in turn, implies that sterling
is 26% overvalued against the euro.
Please update the Big Mac Index at
http://www.economist.com/PrinterFriendly.cfm?Story_ID=2708584
(also appear in this week’s reading list).
4-94
July 2007
4-95
July 2007
*
*
4-96
July 2007
4-97
The price of a burger depends
heavily on local inputs such as rent
and wages, which are not easily
arbitraged across borders and tend
to be lower in poorer countries. For
this reason PPP is a better guide to
currency misalignments between
countries at a similar stage of
development.
4-98
The most overvalued currencies are found
on the rich fringes of the European Union:
in Iceland, Norway and Switzerland.
Indeed, nearly all rich-world currencies are
expensive compared with the dollar. The
exception is the yen, undervalued by 33%.
This anomaly seems to justify fears that
speculative carry trades, where funds
from low-interest countries such as Japan
are used to buy high-yield currencies,
have pushed the yen too low. But broader
measures of PPP suggest the yen is close
to fair value.
4-99
Carry Trade: borrow money at a cheaper rate
than you can earn on an investment elsewhere
2007
The biggest risk is generally that the exchange rate moves
against you – the higher-interest rate currency rapidly
devalues, reducing the value of your assets relative to your
borrowing. That's why these trades are often described as
“picking up nickels in front of a steamroller”
4-100
2008
http://www.centralbankrates.com/
4-101
2009
http://www.centralbankrates.com/
4-102
Japan’s low Interest Rate
The savings rates of Japanese
households have been among the
highest in the world, and high savings
rates push down the interest rate.
In addition, Japanese investment was
low in 2002 because of the weak
economy at that time. Low investment
also reduced real interest rates.
http://www.worthpublishers.com/ballpreview/casestudy1.PDF
4-103
About the CFA Program
• The Chartered Financial Analyst (CFA) Program is a
•
•
•
globally recognized standard for measuring the
competence and integrity of financial analysts.
Its curriculum develops and reinforces a fundamental
knowledge of investment principles.
Three levels of examination measure a candidate’s
ability to apply these principles at a professional level.
The CFA exam is administered annually in more than 70
nations worldwide.
• http://www.aimr.org/cfaprogram/
4-104
CFA (level III, 1997)
a. Explain the following three concepts of
purchasing power parity (PPP):
i. The law of one price.
ii. Absolute PPP.
iii. Relative PPP.
b. Evaluate the usefulness of relative PPP in
predicting movements in foreign exchange
rates on a:
i. Short-term basis (e.g., three months).
ii. Long-term basis (e.g., six years).
4-105
CFA (level III, 1997)
i. The law of one price is that, assuming competitive markets
and no transportation costs or tariffs, the same goods
should have the same real prices in all countries after
converting prices to a common currency.
ii. Absolute PPP, focusing on baskets of goods and services,
states that the same basket of goods should have the same
price in all countries after conversion to a common currency.
Under absolute PPP, the equilibrium exchange rate
between two currencies would be the rate that equalizes the
prices of a basket of goods between the two countries. This
rate would correspond to the ratio of average price levels in
the countries. Absolute PPP assumes no impediments to
trade and identical price indexes that do not create
measurement problems.
4-106
CFA (level III, 1997)
iii. Relative PPP holds that exchange rate movements reflect
differences in price changes (inflation rates) between
countries. A country with a relatively high inflation rate will
experience a proportionate depreciation of its currency’s
value vis-à-vis a country with a lower rate of inflation.
Movements in currencies provide a means for maintaining
equivalent purchasing power levels among currencies in
the presence of differing inflation rates.
Relative PPP assumes prices adjust quickly and price
indexes properly measure inflation rates. Because relative
PPP focuses on changes and not absolute levels, relative
PPP is more likely to be satisfied than the law of one price
or absolute PPP.
4-107
CFA (level III, 1997)
i. Short-term basis (e.g., three months). Relative PPP is not
consistently useful in the short run because: (1)
Relationships between month-to-month movements in
market exchange rates and PPP are not consistently strong,
according to empirical research. Deviations between the
rates can persist for extended periods; (2) exchange rates
fluctuate minute by minute because they are set in the
financial markets. Price levels, in contrast, are sticky and
adjust slowly; and, (3) many other factors can influence
exchange rate movements rather than just inflation.
ii. Long-term basis (e.g., six years). Research suggests that
over the long term a tendency exists for market and PPP
rates to move together, with market rates eventually moving
toward levels implied by PPP.
4-108
CFA (level III, 1998)
Even though the investment community generally
believes that country M’s recent budget deficit
reduction is “credible, sustainable, and large,”
analysts disagree about how it will affect country M’s
foreign exchange rate. Juan DaSilva, CFA, states
“the reduced budget deficit will lower interest rates,
which will immediately weaken country M’s foreign
exchange rate.”
a. Discuss the direct (short-term) effects of a
reduction in country M’s budget deficit on:
i. Demand for loanable funds.
ii. Nominal interest rates.
iii. Exchange rates.
4-109
CFA (level III, 1998)
b. Helga Wu, CFA, states, “Country M’s foreign
exchange rate will strengthen over time as a
result of changes in expectations in the private
sector in country M.” Support Wu’s position that
country M’s foreign exchange rate will strengthen
because of the changes a budget deficit
reduction will cause in:
i. Expected inflation rates.
ii.Expected rates on return on domestic
securities.
4-110
CFA (level III, 1998)
i. Demand for loanable funds. The immediate effect of
reducing the budget deficit is to reduce the demand for
loanable funds because the government needs to borrow
less to bridge the gap between spending and taxes.
ii. Nominal interest rates. The reduced public sector demand
for loanable funds has the direct effect of lowering nominal
interest rates because lower demand leads to lower cost of
borrowing.
iii. Exchange rates. The direct effect of the budget deficit
reduction is a depreciation of the domestic currency and the
exchange rate. As investors sell lower yielding country M
securities to buy the securities of other countries, country
M’s currency will come under pressure and country M’s
currency will depreciate.
4-111
CFA (level III, 1998)
i. Expected inflation rates. In the case of a credible,
sustainable, and large reduction in the budget deficit,
reduced inflationary expectations are likely because the
central bank is less likely to monetize the debt by printing
money. Purchasing power parity and international Fisher
relationships suggest that a currency should strengthen
against other currencies when expected inflation
declines.
ii. Expected rates on return on domestic securities. A
reduction in government spending would tend to shift
resources into private sector investments, where
productivity is higher. The effect would be to increase the
expected return on domestic securities.
4-112
CFA (level III, 1996)
The HFS Trustees have decided to invest in
international equity markets and have hired Jacob
Hind, a specialist manager, to implement this
decision. He has recommended that an unhedged
equities position be taken in Japan, providing the
following comment and data to support his views:
“Appreciation of a foreign currency increases
the returns to a U.S. dollar investor. Since
appreciation of the yen from 100¥/$ to 98 ¥/$
is expected, the Japanese stock position
should not be hedged.”
4-113
CFA (level III, 1996)
Market Rates and Hind’s Expectations
Spot rate (direct quote)
Hind’s 12-month currency forecast
1-year Eurocurrency rate (% per annum)
Hind’s 1-year inflation forecast (% per annum)
U.S.
Japan
n/a
n/a
6.00
3.00
100
98
0.80
0.50
Assume that the investment horizon is one year
and that there are no costs associated with
currency hedging. State and justify whether Hind’s
recommendation should be followed. Show any
calculations.
4-114
CFA (level III, 1996)
Appreciation of a foreign currency will, indeed, increase
the dollar returns that accrue to a U.S. investor.
However, the amount of the expected appreciation must
be compared with the forward premium or discount on
that currency in order to determine whether hedging
should be undertaken or not.
In the present example to yen is forecast to appreciate
from 100 to 98 (2 percent). However, the forward
premium on the yen as given by the differential in oneyear eurocurrency rates, suggests an appreciation of
over 5 percent:
Forward premium = [(1.06)/(1.008)] -1 = 5.16%
4-115
CFA (level III, 1996)
Thus, the manager’s strategy to leave the yen
unhedged is not appropriate. The manager should
hedge because by doing so, a higher rate of yen
appreciation can be locked in. Given the on-year
eurocurrency rate differentials, the yen position
should be left unhedged only if the yen is forecast
to appreciate to over 95 yen per US dollar.
4-116
Measuring the Cost of Living
•
•
Inflation refers to a situation in which the
economy’s overall price level is rising.
The inflation rate is the percentage change
in the price level from the previous period.
4-117
The GDP Deflator versus the
Consumer Price Index
•
•
Economists and policymakers monitor
both the GDP deflator and the consumer
price index to gauge how quickly prices
are rising.
There are two important differences
between the indexes that can cause
them to diverge.
4-118
The GDP Deflator versus the
Consumer Price Index
•
•
The GDP deflator reflects the prices of
all goods and services produced
domestically, whereas...
…the consumer price index reflects the
prices of all goods and services bought
by consumers.
4-119
The GDP Deflator versus the
Consumer Price Index
•
•
The consumer price index compares the price of a
fixed basket of goods and services to the price of
the basket in the base year (only occasionally
does the BLS change the basket)...
…whereas the GDP deflator compares the price of
currently produced goods and services to the
price of the same goods and services in the base
year.
4-120
Contrasting the CPI and GDP Deflator
Imported
Imported consumer
consumer goods:
goods:
ƒƒ included
included in
in CPI
CPI
ƒƒ excluded
excluded from
from GDP
GDP deflator
deflator
Capital
Capital goods:
goods:
ƒƒ excluded
excluded from
from CPI
CPI
ƒƒ included
included in
in GDP
GDP deflator
deflator (if
(if
produced
produced domestically)
domestically)
The
The basket:
basket:
ƒƒ CPI
CPI uses
uses fixed
fixed basket
basket
ƒƒ GDP
GDP deflator
deflator uses
uses basket
basket of
of
currently
currently produced
produced goods
goods && services
services
This
This matters
matters ifif different
different prices
prices are
are
changing
changing by
by different
different amounts.
amounts.
4-121
Two Measures of Inflation
15
Percent
15
Percent
per Year
per Year
10
10
5
0
5
0
-5
-5
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
CPI
CPI GDP
GDPdeflator
deflator
4-122
CPI vs. GDP deflator
In each scenario, determine the effects on the
CPI and the GDP deflator.
A. Starbucks raises the price of Frappuccinos.
B. Caterpillar raises the price of the industrial
tractors it manufactures at its Illinois factory.
C. Armani raises the price of the Italian jeans it
sells in the U.S.
4-123
Answers
A. Starbucks raises the price of Frappuccinos.
The CPI and GDP deflator both rise.
B. Caterpillar raises the price of the industrial
tractors it manufactures at its Illinois
factory.
The GDP deflator rises, the CPI does not.
C. Armani raises the price of the Italian jeans it
sells in the U.S.
The CPI rises, the GDP deflator does not.
4-124
MEASURING THE COST OF LIVING
Consumer Price Index
• The consumer price index (CPI) is a measure
of the overall cost of the goods and services
bought by a typical consumer.
• It is used to monitor changes in the cost of
living over time.
• It reports the movement of prices using an
index number.
• When the CPI rises, the typical family has to
spend more dollars to maintain the same
standard of living.
4-125
How the Consumer Price Index Is
Calculated
• Fix the Basket: Determine what goods are
most important to the typical consumer.
Ê The Bureau of Labor Statistics (BLS)
identifies a market basket of goods and
services the typical consumer buys.
Ê The BLS conducts monthly consumer
surveys to determine what they buy and how
much they pay.
• Find the Prices: Find the prices of each of the
goods and services in the basket for each
point in time.
4-126
How the Consumer Price Index Is
Calculated
• Compute the Basket’s Cost: Use the data on
prices to calculate the cost of the basket of
goods and services at different times.
• Choose a Base Year and Compute the Index:
Ê Designate one year as the base year, which is the
benchmark used for comparison.
Ê Compute the index by dividing the price of the basket
in one year by the price in the base year and
multiplying by 100.
4-127
How the Consumer Price Index Is
Calculated
• Compute the inflation rate: The inflation rate
is the percentage change in the price index
from the preceding period.
4-128
Calculating the Consumer Price Index and the
Inflation Rate
•
•
•
•
•
Base Year is 1990
Basket of goods in 1990 cost $1,200
The same basket in 1991 costs $1,236
CPI = ($1,236/$1,200) X 100 = 103
Prices increased 3 percent between 1990 and
1991
4-129
Calculating the Consumer Price Index and the
Inflation Rate: Another Example
•
•
•
•
•
Base Year is 1998.
Basket of goods in 1998 costs $1,200.
The same basket in 2000 costs $1,236.
CPI = ($1,236/$1,200) X 100 = 103.
Prices increased 3 percent between 1998
and 2000.
4-130
What’s in the CPI’s Basket (in year 2000)?
5%
6%
6% 5% 5%
Housing
Food/Beverages
Transportation
40%
17%
16%
Medical Care
Apparel
Recreation
Other
Education and
communication
4-131
What’s in the CPI’s Basket (in year 2004)?
4%
4%
Housing
6%
Transportation
6%
Food & Beverages
42%
6%
Medical care
Recreation
Education and
communication
Apparel
15%
17%
Other
4-132
The Measurement of GDP
GDP is the market value of all
final goods and services
produced within a country in a
given period of time.
4-133
GDP and Its Components (1998)
Total
(in billions of dollars)
Per Person
(in dollars)
% of Total
Gross domestic product, Y
$8,511
$31,522
100 percent
Consumption, C
5,808
21,511
68
Investment, I
1,367
5,063
16
Government purchases, G
1,487
5,507
18
Net exports, NX
-151
-559
-2
4-134
…some people dispute the validity of GDP as a
measure of well-being. When Senator Robert
Kennedy was running for president in 1968, he gave
a moving critique of such economic measures:
[Gross domestic product] does not allow for the
health of our children, the quality of their education,
or the joy of their play. It does not include the
beauty of our poetry or the strength of our
marriages, the intelligence of our public debate or
the integrity of our government officials. It
measures neither our courage, nor our wisdom, nor
our devotion to our country. It measures
everything, in short, except that which makes life
worthwhile, and it can tell us everything about
America except why we are proud that we are
Americans.
4-135
Real versus Nominal GDP
•
•
Nominal GDP values the production of
goods and services at current prices.
Real GDP values the production of
goods and services at constant prices.
4-136
Real versus Nominal GDP
An accurate view of the economy
requires adjusting nominal to real
GDP by using the GDP deflator.
4-137
GDP Deflator
•
•
The GDP deflator measures the current
level of prices relative to the level of
prices in the base year.
It tells us the rise in nominal GDP that is
attributable to a rise in prices rather than a
rise in the quantities produced.
4-138
GDP Deflator
The GDP deflator is calculated as follows:
Nominal GDP
GDP deflator =
× 100
Real GDP
4-139
Converting Nominal GDP to Real
GDP
Nominal GDP is converted to real
GDP as follows:
(Nominal GDP20xx )
Real GDP20xx =
X 100
(GDP deflator20xx )
4-140
Real and Nominal GDP
Year
Price of
Hot dogs
Quantity of
Hot dogs
Price of
Hamburgers
Quantity of
Hamburgers
2001
$1
100
$2
50
2002
$2
150
$3
100
2003
$3
200
$4
150
4-141
Real and Nominal GDP
Calculating Nominal GDP:
2001
($1 per hot dog x 100 hot dogs) + ($2 per hamburger x 50 hamburgers) = $200
2002
($2 per hot dog x 150 hot dogs) + ($3 per hamburger x 100 hamburgers) = $600
2003
($3 per hot dog x 200 hot dogs) + ($4 per hamburger x 150 hamburgers) = $1200
4-142
Real and Nominal GDP
Calculating Real GDP (base year 2001):
2001
($1 per hot dog x 100 hot dogs) + ($2 per hamburger x 50 hamburgers) = $200
2002
($1 per hot dog x 150 hot dogs) + ($2 per hamburger x 100 hamburgers) = $350
2003
($1 per hot dog x 200 hot dogs) + ($2 per hamburger x 150 hamburgers) = $500
4-143
Real and Nominal GDP
Calculating the GDP Deflator:
2001
($200/$200) x 100 = 100
2002
($600/$350) x 100 = 171
2003
($1200/$500) x 100 = 240
4-144
Inflation Rate Calculation
Calculating the inflation rates with GDP
Deflators
2001
2002
( 171 - 100) / 100 = 71%
2003
( 240 - 171) / 171 = 40%
4-145
Real GDP in the United States
Billions of
1992 Dollars
8,000
(Periods of falling real GDP)
7,000
6,000
5,000
4,000
3,000
1970
1975
1980
1985
1990
1995
2000
4-146
Correcting Variables for Inflation:
Comparing Dollar Figures from Different Times
• Inflation makes it harder to compare dollar
amounts from different times.
• We can use the CPI to adjust figures so that
they can be compared.
4-147
EXAMPLE: The High Price of Gasoline
• Price of a gallon of regular unleaded gas:
$1.42 in March 1981
$2.50 in August 2005
• To compare these figures, we will use the CPI
to express the 1981 gas price in “2005
dollars,”
what gas in 1981 would have cost if the
cost of living were the same then as in 2005.
• Multiply the 1981 gas price by
the ratio of the CPI in 2005 to the CPI in 1981.
4-148
EXAMPLE: The High Price of Gasoline
date
Price of gas
CPI
Gas price in
2005 dollars
3/1981
$1.42/gallon
88.5
$3.15/gallon
8/2005
$2.50/gallon
196.4
$2.50/gallon
• 1981 gas price in 2005 dollars
= $1.42 x 196.4/88.5
= $3.15
• After correcting for inflation, gas was more
expensive in 1981.
4-149
Correcting Variables for Inflation:
Indexation
A dollar amount is indexed for inflation
if it is automatically corrected for inflation
by law or in a contract.
For example, the increase in the CPI
automatically determines
¤
the cost-of-living allowances (COLAs) in
many multi-year labor contracts
¤
the adjustments in Social Security payments
and federal income tax brackets
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Assignment for Chapter 4
Exercises 5, 6, 7.
Question: How to measure inflation "financially"?
Answer: Yields of TIPS "minus" Yields of regular treasury
securities
Note that TIPs are Treasury Inflation Protected
Securities. Investors may purchase TIPs at
http://www.publicdebt.treas.gov/sec/seciis.htm
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5.
Suppose the current spot rate is $ 1.55/£ on the first of January. By
year's end, the US CPI is expected to climb from
144 to 150 and
the UK CPI is expected to climb from 120 to 130. According to PPP,
what is the expected spot rate on December 31?
SOLUTIONS:
SPPP,t+1 = St,$/£ * (CPIt+1,US/CPIt,US)/(CPIt+1,UK/CPIt,UK);
SPPP,Dec = $1.55/£ * (150/144)/(130/120) = $ 1.4904/£
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6.
Consider the following data for the U.S. and Surlandia for the years 1975 - 1980.
1975
1976
1977
1978
1979
1980
Pengo/$
8.5
17.4
28.0
34.0
39.0
39.0
Surlandia CPI
100
312
599
838
1118
1511
U.S. CPI
161.2
170.5
181.5
195.4
217.4
246.8
a.
According to the Purchasing Power Parity Theory, by how much is the Pengo
over- or under-valued at the end of 1980?
b.
On what basis could someone refute your calculation?
SOLUTIONS:
a.
One way to calculate the PPP rate in 1980 is SPPP, 1980 = S1975 * [ PSUR,
1980 / PU.S., 1980] / [ PSUR, 1975 / PU.S., 1975] = 8.5 peso/$ * [1511/246.8]
/ [ 100/161.2] = 83.89 peso/$
[1/39.0 - 1/83.89] / [1/83.89] = 2.15 ===> 2.15 -1 = 1.15 Î peso is 115%
overvalued at 39.00 peso/$
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7.
In the above table of numbers for Surlandia and the US, the
nominal bi-lateral exchange rate at the end of 1980 was
reported as 39.0 Pengos/$. What was the real bi-lateral
exchange rate? Hint:
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