Lecture 4 (b)
Foreign Exchange Rates and International Parity
(outline)
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What We Mean and Why It Matters
Purchasing Power Parity
International Fisher Effects
Interest Rate Parity
Parity and Forecasting
What Determines the Exchange Rate? A Review
• We have already seen how, in the end, money is just a commodity and so
the FX rate will be determined by supply and demand.
• Supply and demand will depend on
– Relative inflation rates (note the importance of monetary policy)
– Relative interest rates (same note)
– Other factors that influence trade (e.g., productivity)
Now We’re Going to Try and More Carefully Describe How
These Fundamentals Shape Price
But before going there, let’s note a couple of things
• Exchange rates are often much more volatile than the
underlying fundamentals
– FX rates sometimes change by 10% a day. Inflation rates
and interest rates aren’t nearly that volatile
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Brazilian Real to USD daily % change
15
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0
But before going there, let’s note a couple of things
• Exchange rates are often much more volatile than the
underlying fundamentals
– FX rates sometimes change by 10% a day. Inflation rates
and interest rates aren’t nearly that volatile
• The volume of FX trading is far in excess of the amount
demanded for transactions purposes.
The Magnitude of the Global Foreign Exchange Market
Average Daily Turnover in billions of US dollars
Notional Amounts for Derivatives
3500
3000
2500
Spot Transactions
Outright Forwards & Swaps
OTC Derivative Instruments
2000
1500
1000
500
1292
959
853
688
1260
900
670
520
0
April 1995
810
590
590
April 1998
820
390
April 2001
Source: Bank for International Settlements Central Bank Survey 2004
620
April 2004
• This must mean that the hour-to-hour/day-to-day prices for FX
are being shaped by speculators and arbitragers who are trying
to anticipate changes and take profits.
• But this certainly doesn’t mean the market is being manipulted
• Nor is it to say that the market is being “set” (in the long term)
by forces other than these fundamentals.
The parity conditions give us a starting point to
answer some important questions:
– Are changes in exchange rates predictable?
– How are exchange rates related to interest rates?
– What, at least theoretically, is the “proper”
exchange rate?
What is, at least theoretically, the “proper” exchange
rate?
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This is given by our first “parity” relationship
PURCHASING POWER PARITY (PPP)
Provides a benchmark to suggest the levels that
exchange rates should achieve.
Starts with the “Law of One Price”
The law of one price
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A identical good should cost the same in all markets
Absolute Purchasing Power Parity
• Suppose that
– gold is selling in the US for P$/oz=$300
– gold is selling in Europe for P€/oz=€240.
– the spot exchange rate is S$/€ =1.25
– This means the dollar price of gold purchased in Europe is
S$/€ P€/oz = $300
• The law of one price says that the dollar price of a good like
gold should be same no matter where you buy it (except
maybe for some differences due to transactions costs that we’ll
talk about later). Thus
S$/€ P€/oz = P$/oz
Relative Purchasing Power Parity, Inflation and Exchange
Rates
• Suppose that in December, 2000 gold was selling for $300 and €240
– Formally P0$/oz=$300 and P0€/oz = € 300.
• Suppose that the US inflation rate in 2001 was 5% and the European
inflation rate was 10%.
– Formally Ius=5% and Ieurope=10%
• This means we expect that in 2001 gold should sell for $315=300x(1+.05)
• €262=240x(1+.1)
– Formally, P1$/oz =P0$/oz (1+IUS) and P1€/oz= P0€/oz (1+Ieurope)
• A bit of algebra shows that
S1d/f/S0d/f = (1+Id)/(1+If)
Or very nearly
$ change in Spot rate = Id - If
Relative Purchasing Power Parity
Stated another way
Rate of change in S = Domestic inflation – Foreign Inflation
e=
ΠU.S. - ΠFor
• Key insight: Relative PPP focus on changes in
the exchange rate, not levels
• Key Prediction: Relative PPP says domestic
and foreign inflation determine the dynamics of
the spot exchange rate.
Who came up with PPP and why?
• Our First Famous Dead Guy: Gustav Cassel
• He popularized PPP in the 1920s to explain
what was going on in the world at that time
• In those years, many countries (Germany,
Hungary, and the Soviet Union) had experienced
Hyperinflation.
• As the purchasing power of these countries sharply declined,
the same currencies also depreciated sharply against stable
currencies like the U.S. dollar
• PPP became popular then, how about now (think Latin
America)
Purchasing Power Parity: Caveats
• PPP conditions do not imply anything about causal
linkages between prices and exchange rates or vice
versa.
• Both prices and exchange rates are jointly
determined by other variables in the economy.
• PPP is an equilibrium condition that must be
satisfied when the economy is at its long-term
equilibrium.
• It does, however, give us a powerful tool if it holds!
Does PPP hold?
• Let’s test absolute PPP first.
• How would devise a test of absolute PPP?
• The most famous test of absolute PPP is The
Economist magazine's
Big Mac Index
Burgernomics: The Big Mac Index
• The Economist’s Big Mac index was first launched in
1986 as a gastronome’s guide to whether currencies
were at their correct exchange rate.
• Examines the price of a common good (the Big Mac)
worldwide.
Burgernomics: The Big Mac Index
• Before we get serious, some little known Big Mac
Triva
– By 1996, you could get one in 80 countries
– In China, it is know as Juwuba, “big with no
equal”
– In Moscow and Beijing, the McDonalds has over
700 seats and 30 registers
$3.06: Average
of NY, Chicago,
SF
2.92 Euros: Price of
Big Mac in Euro
member countries, which
at current FX rate of
1.22 is 3.58
S=3.06/2.92=1.05
However, actual
exchange rate is 1.22, so
Euro is overvalued 17%
Overall, we can get a Big
Mac for really cheap in
countries like China,
Malaysia, Thailand,
Philippines
However, it costs 5.05
USD for one in
Switzerland
So, it implies that
Switzerland has the most
overvalued currency and
the others the most
undervalued
For a short video on the Big Mac index
• http://www.economist.com/media/audio/burgernomics.ram
That’s just one good: Can you think of another item that is
available just about anywhere?
The Tall-Latte Index
Available in 32 countries.
Average price in US (2004) was $2.80 (about the
same as a big mac)
Burgers or Beans?
• Do we see the same story?
• The tall-latte index tells broadly
the same story as the Big Mac
index for most main currencies
• Where the two measures differ
is in Asia: In China, it is 56%
undervalued according to the
Big Mac, but spot on its dollar
PPP according to our Starbucks
index. If so, American
manufacturers have no grounds
to complain about the yuan. The
pricing differences probably
reflect different competition in
the markets for the two products.
Even more fun with
Burgernomics
• Working time needed to buy a Big Mac
• It aims to measure well-being by
estimating how many minutes workers in
various countries must toil to buy a Big
Mac.
• In Kenya, UBS says that it takes just
over three hours of labor for a typical
worker to afford one of McDonald's
hefty burgers.
• Americans, lucky for them, need to work
for only ten minutes. Such differences
reflect variations in productivity as well
as disparities in local costs of ingredients.
Another application: The Big Mac Index of Cigarette
Affordability
• In calling for increases in tobacco tax, tobacco control
advocates often find it useful to compare cigarette prices
internationally with those in their own country.
• To do this, they must somehow convert prices in other
countries using a standard measure, most commonly the price
in $US. Exchange rates, however, may be influenced by many
factors including inflation differentials, monetary policy,
balance of payments, and market expectations
• The Big Mac index of cigarette affordability provides a
reasonable estimation of relative affordability of cigarettes
The Big Mac Index of Cigarette Affordability
Burgernomics (cont.)
•
While originally introduced as a bit of fun, it has
inspired several serious studies
Burgernomics (cont.)
Pakko and Pollard (1996) conclude that
Big Mac PPP holds in the long run, but currencies
can deviate from it for lengthy period. They note
several reasons why the Big Mac index may be
flawed
1. The absolute version of PPP assumes
there are no barriers to trade.
• High prices in Europe, Japan and
South Korea partly reflect high tariff’s
on beef. Differences in transport costs
also matter: shipping lettuce and beef is
expensive
Burgernomics (cont.)
2. Prices are distorted by taxes
High rates of VAT in countries such as
Denmark and Sweden exaggerate the degree to
which their currencies are overvalued
3. Profit margins vary amount countries
according to competition
In the US, we have the Whopper, other
countries do not have a close substitute
Testing PPP
Currencies with the largest relative decline (gain) in
purchasing power saw the sharpest erosion
(appreciation) in their foreign exchange rate
As measured by relative inflation rates
The Final Word on PPP
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2
Despite often lengthy departures from PPP, there
is a clear correspondence between relative
inflation rates and changes in nominal exchange
rates
Next , we look at other parity relationships that
provide insights into what determines FX rates
Real Exchange Rates
• The “real” value of any price is just the actual value (nominal
value) adjusted for inflation. That is, you can tell whether the
relative value of the price has gone up or down
• The “real” exchange rate accounts for the relative inflation in
each country
Sreal = Snominalx(1+If)/(1+Id)
Real Exchange Rates (an Example)
Mexico
US
Year
Price Index
Inflation
Rate
Price Index
1999
100
2000
115
15%
105
2001
124.2
8%
109.2
Spot Rate
Inflation
Rate
Nominal
Real
0.1
0.1
5%
0.09
0.0986
4%
0.09
0.1024
100
•Suppose that in 1999, a week in Aqcupulco cost MXP 10,000 and week in Miami
cost $1000. The two trips cost the same (MXP 10,000 = $1000)
•Suppose in 2000, the cost of the two trips rose by the inflation rates within each
country. The Mexican vacation costs MXP 11,500 and the US vacation cost
$1,050.
•In fact the Mexican trip has actually gone down in price (MXP
11,500=11,500x.09=$1,035). This is consistent with the decline in the real
exchange rate (from .10 to .0986).
•See if you can show why the trip has gone up in price in 2001.)
Fisher Equation:
• Nominal interest rate ( r ) compensates for “real” time value of
money (r*) plus Inflation (I)
• Thus, if there were no inflation a unit of currency invested
today should grow by the r* to become (1+r*)
• If there were inflation, that amount should grow by the
inflation rate (1+r)=(1+r*)(1+I) (note: if r and I are fractions,
this is very close to saying r = r*+I)
• for example if the inflation rate is 10% and the real time value
is 2%, a dollar today should grow to 1.02x1.1=$1.122
Irving Fisher (1867-1947)
This Yale economist was an eccentric and colorful
figure. When Irving Fisher wrote his 1892
dissertation, he constructed a remarkable machine
equipped with pumps, wheels, levers and pipes in order to illustrate his
price theory. Socially, he was an avid advocate of eugenics and health
food diets. He made a fortune with his visible index card system known today as the rolodex - and advocated the establishment of an
100% reserve requirement banking system His fortune was lost and his
reputation was severely marred by the 1929 Wall Street Crash, when just
days before the crash, he was reassuring investors that stock prices were
not overinflated but, rather, had achieved a new, permanent plateau
International Fisher Equation
• Rearranging terms from the Fisher Equation we get
(1+rd)/(1+Id)=(1+r*)
• The Law of One Price suggests that the real value of money should be the
same anywhere
– (no matter what the nominal rate, the real rate should be r*).
• Thus, Law of One Price implies
(1+rd)/(1+Id)=(1+r*)= (1+rf)/(1+If)
or
(1+rd)/((1+rf )=(1+Id)/(1+If)
• But then the relative purchasing power relation would imply that
S1/S0=(1+Id)/(1+If)= (1+rd)/((1+rf )
• That is, the ratio between the expected future spot rate and the current spot
rate is determined by the ratio of the relative returns between the two
countries.
Question: Do We Believe in the International Fisher
Relation?
• This is really like asking real returns tend to be the same
across countries
• Yes: The world is full of greedy, grasping MBA’s. If the Law
of One Price didn’t hold, then there is a profit opportunity that
these people would spot and quickly eliminate.
• No: The world is full of blockheads and bureaucrats.
Ignorance and red tape erect all sorts of barriers that prevent
the Law of One Price from holding.
Interest Rate Parity: Simple Example
• Suppose you want to invest $100,000 for one year.
• Option I: Buy a $100,000 certificate of deposit from a US bank that pays
rus
• Option II. Convert your $100,000 into Canadian $’s and buy a CD from a
Canadian bank that pays rc.
– The two options are hard to compare since you don’t know what the
exchange rate will be in one year, when you cash in the Canadian CD.
But
• To eliminate the uncertainty about the future exchange rate, sell the C$’s on
the forward market.
• Suppose S$/c$=.80
– F$/C$1=.80.
– rus = 5%
– rcan=10%
• This is a no-brainer. Why?
Interest Rate Parity: Conclusion
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– If US rates are 5%, $100,000 will yield $105,000 in one year
Option 2 (Invest abroad):
– Convert at the spot rate to obtain 1/Sd/f units of the foreign currency
– ( if S$/c$ = .80 , then $100,000=100,000/.80= C$125,000 )
– Investing that amount in the foreign country, will yield (1/Sd/f)x(1+rf) in
one year
– If Canadian rates are 10%, you will have C$137,500=125,000x1.1 in
one year
– Sell the amount of the currency you expect to receive in the forward
market, thereby guaranteeing that you will end up with
Fd/f(1/Sd/f)x(1+rf) units of the domestic currency.
– If F$/C$=.7636, you will have $105,000=.7636x137,500
All things equal, the two amounts must be the same. That is
(Fd/f/Sd/f)=(1+rd)/(1+rf)
if F$/C$=.80, investing in Canada would have yielded
$110,000=.8x137,500.
Interest Rate Parity
in a Perfect Capital Market
• IRP draws on the principle that in equilibrium, two
investments exposed to the same risks must have the
same returns.
• Suppose an investor puts $1 in a US$ security. At the
end of one period, wealth = $1  (1 + i$)
• Alternatively, the investor can put the $1 in a UK£
security and cover his or her exposure to UK£
exchange rate changes. At the end of one period,
wealth =
1.0
$1
 1  i£   Ft ,1
St
Interest Rate Parity
in a Perfect Capital Market
• In a perfect world, the two investments would yield
the same return and so
1.0
$1
 1  i£   Ft ,1  $1 1  i$ 
St

Ft ,1  St
St
i$  i£

1  i£
forward premium = % interest differential
Why Do We Think IRP Might Be True?
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•
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Think about what happens in the first example given above (rus=5%, rcan=10%,
S$/C$ = F$/C$ =.80).
As we’ve already seen, investors will start to favor investments in Canada. As this
happens:
– Canadian interest rates fall and US rates go up (the ratio of the relative discount
factors gets bigger)
– The spot rate goes up as investors sell US dollars and buy Canadian dollars.
– The Forward rate goes down (remember the investors would be selling C$’s in
the forward market)
Notice how all of these market forces would drive the various factors back into the
alignment described by the interest rate parity condition.
But this isn’t exactly an “arbitrage” condition since we haven’t seen how someone
could make an instant profit by taking advantage of the imbalance. If there were
such an arbitrage condition, it would be true that the IRP condition would almost
continually hold. (If not, the arbitrageur would take a profit..) In fact, there is an
arbitrage condition
Covered Interest Arbitrage. (Example)
• Suppose you got an e-mail from your broker advising that you could
borrow or lend in US dollars at rus=5% or borrow or lend in euros
reuro=8%.
• You are further advised that you can you can buy or sell currency at a spot
rate of S=1.25 and a one-period forward rate of F =1.2125.
• Good News!!!
• Borrow 1 euro at 8%, noting that this obligates you to pay 1.08 euro in one
year.
• Since you know you will owe the euro, buy this amount in the forward
market (obligating you to pay 1.08x1.2125 = $1.3095)
• Convert that 1 euro into $1.25
• Lend at 5% (claiming $1.3125)
• In one year you will have $1.3125-1.3095 = .0030
• Repeat several billion times
The Forward Rate Unbiased Condition
Forward Rate Unbiased
Today’s forward premium (for delivery in n days)
equals the expected percentage change in the spot rate
(over the next n days).
Ft  St 
  
~
S t  E S t  n  St S t
Driving force: Market players monitor the difference between
today’s forward rate (for delivery in n days)
and their expectation of the future spot rate
(n days from today).
Foreign Rate as Unbiased Predictor of Future Spot
Rate
The Forward Rate Unbiased Condition
If UIP does not holds:
• Positions in different currencies can lead to
profit opportunities
– Could imply market inefficiency
Empirical Evidence:
•Early studies were supportive
•Recent studies are not
•People are willing to pay for FX advisors
•More when we get to Market Efficiency
OK, ENOUGH ALREADY: What are the takeaways from
the Parity Conditions?
1. When IRP holds, the covered cost of funds is identical
across all currencies and the covered return on funds is
identical across all currencies; there are neither
bargains or nor bad deals on a covered basis.
2. When the International Fisher Effect Holds, the
expected cost of borrowed funds is identical across
currencies and the expected return on invested funds is
identical across currencies on an uncovered basis.
1. Some currencies may have high nominal interest
rates and others may have low nominal interest
rates, but when the expected exchange rate change
is taken into account, all currencies return the same
nominal interest rate.