International Finance
Chapter 5
Part 1: International Parity
Relationships
FORWARD RATES
• Involves contracting today for the future
purchase or sale of foreign exchange.
– Forward rate is set today!
• Forward rate can be:
– Equal to spot (flat)
– Worth more than spot (premium)
– Worth less than spot (discount)
EXAMPLES OF FORWARD
RATES
• Wednesday, June 4, 2004
• American Terms
– U.K. (Pound)
• 1 month forward
$1.8343
$1.8289
• European Terms
– Japan (yen)
• 1 month forward
110.07
109.95
FORWARD DISCOUNTS AND
PREMIUMS
• Is the pound selling at a forward discount
or forward premium?
– U.K. (Pound)
• 1 month forward
$1.8343
$1.8289
• Answer:
– Discount: 1 month forward is less than the
spot by $.0054
FORWARD PREMIUMS AND
DISCOUNTS
• Is the Japanese yen selling at a forward
premium or forward discount?
– Japan (yen)
• 1 month forward
110.07
109.95
• Answer:
– Premium: Dollar is selling at a discount; with the 1
month forward less than the spot by .12 yen.
– Convert to American terms (110.07 = $.009085;
109.95 = $.009095). Yen 1 month forward is worth
$.000010 more than the spot.
WHAT DETERMINES THE
FORWARD RATE?
• What does NOT determine forward rate:
– Market’s expectation about where spot rate
will be in the future.
• What does determine forward rate:
– Assuming no capital controls, in equilibrium
the rate represents the difference in interest
rates between the two currencies in question.
INTEREST RATE PARITY
• Interest rate parity theory provides a linkage
(and explanation) between international money
markets and (forward) foreign exchange
markets.
• The theory states that the difference in the
national interest rates for securities of similar risk
and maturity should be equal to, but opposite in
sign to, the forward rate discount or premium for
the foreign currency (except for transaction
costs)
EXAMPLE
• Assume a US dollar-based investor has $1 million to
invest for 90 days and can select from two
investments:
– Invest in the U.S. and earn 4.0% p.a.
– Invest in Switzerland and earn 8.0% p.a.
• Problem with Swiss franc investment:
– Uncertainty about the future spot rate, or what if the franc
depreciates against the dollar!
• Solution for investor:
– Cover the Swiss franc investment by selling the Swiss francs
anticipated from the investment forward 90 days.
– But what will the forward rate be?
FORWARD RATE UNDER
INTEREST RATE PARITY
• In equilibrium, the forward rate must settle
at a rate to offset the interest rate
differential between the two currencies in
question.
• This is to insure that the two investments
will yield similar returns.
– To prevent covered interest arbitrage
opportunities!!!
COVERED INTEREST ARBITRIGE
• Assume:
– 90 day Interest rate in U.S. is 4%
– 90 day Interest rate in Switzerland is 8%
• Assume the spot rate and the 90 day forward
rate are the same
• A U.S. investor could invest in Switzerland, and
cover (sell francs forward) and obtain a (foreign
exchange) riskless return of 8% which is 400
basis points greater than investing in the U.S.
• This is covered interest arbitrage!
EQUILIBRIUM
• In equilibrium the forward rate will price the
currency to offset the interest rate differential.
• In the previous example, the “correct” 90 day
forward Swiss franc rate will be at a discount of
4% of its spot.
• When the U.S. investor covers, the 8% Swiss
return is reduced by the 4% discount, resulting in
a covered return of 4%.
VIEWING IRP
i $ = 4.00 % per annum
(1.00 % per 90 days)
Start
$1,000,000
S = SF 1.4800/$
End
 1.01
$1,010,000
Dollar money market
$1,010,000
90 days
F90 = SF ?/$
Swiss franc money market
SF 1,480,000
 1.02
i SF = 8.00 % per annum
(2.00 % per 90 days)
SF 1,509,600
EQUILIBRIUM
i $ = 4.00 % per annum
(1.00 % per 90 days)
Start
$1,000,000
S = SF 1.4800/$
End
 1.01
$1,010,000
Dollar money market
$1,010,000
90 days
F90 = SF 1.49465/$
Swiss franc money market
SF 1,480,000
 1.02
i SF = 8.00 % per annum
(2.00 % per 90 days)
SF 1,509,600
HOW IS THE FORWARD RATE
CALCULATED?
• The forward rate is calculated from three
observable elements:
– The (current) spot rate
– The foreign currency deposit rate
– The home (U.S.) currency deposit rate
FORWARD RATE FORMULA
FnFC/$  SFC/$

N 
 FC
 1   i x 360 



x

N 
 $
 1   i x 360 



• Where:
Fn = forward rate (FC/$), n business days in the future.
S = spot rate (FC/$)
N = number of days in forward contract
iFC = interest rate on foreign currency deposit
i$ = interest rate on U.S. dollar deposit
EXAMPLE
• Assume:
– Current Yen Spot rate = ¥120.0000
– 90 day dollar rate = 2.0%
– 90 day yen rate = .5%
• Calculate the 90-day yen forward rate
FC/$
90
F
S
FC/$

90 
 FC
 1   i x 360 



x

90 
 $
 1   i x 360 



SOLUTION
  FC 90 
 1   i x 360 



FC/$
FC/$
F90  S x
  $ 90 
 1   i x 360 

 
FC/$
90
F
S
120/$
x
 1.00125
 1.005
F90FC/$

90 

1

.005x



360


 S120/$ x 

90 

 1   .020 x 360 



FC/$
90
F
 119.5522
SOLUTION TO SWISS FRANC
EXAMPLE
• Recall, the following information about the Swiss
franc example:
– Swiss franc spot rate of Sfr1.4800/$,
– a 90-day Swiss franc deposit rate of 8.00%
– a 90-day dollar deposit rate of 4.00%.






FSfr/$  Sfr1.4800x 
90











1  0.08 x 90
360






















1  0.04 x 90
360
 Sfr1.4800x 1.02  Sfr1.4947/$
1.01
COVERED INTEREST
ARBITRAGE
• If the forward rate is not correct, the
chance of covered interest arbitrage
exists.
• Generally, these situations will not last
long
• As the market takes advantage of them,
equilibrium will be restored.
EXAMPLE
i $ = 4.00 % per annum
(1.00 % per 90 days)
Start
$1,000,000
S = SF 1.4800/$
End
 1.01
$1,010,000
Dollar money market
$1,020,000*
90 days
F90 = SF 1.4800/$
Swiss franc money market
SF 1,480,000
 1.02
SF 1,509,600
i SF = 8.00 % per annum
(2.00 % per 90 days)
•Assume the forward rate is 1.48. Then, the covered Swiss investment yields $1,020,000,
$10,000 more than the U.S. investment.
USING IRP TO FORECAST
• While the forward rate under the
assumption of the Interest Rate Parity
model assumes:
– The forward rate simply represents interest
rate differentials
– And NOT the market’s view of the future spot
rate.
• Some forecasters do use this model to
forecast future spot rates.
Forward Rates as an
Unbiased Predictor
• Some forecasters believe that the forward rate is
an “unbiased” predictor of the future spot rate.
• This is roughly equivalent to saying that the
forward rate can act as a prediction of the future
spot exchange rate, but
– it will generally “miss” the actual future spot
rate
– and it will miss with equal probabilities
(directions) and magnitudes (distances) which
offset the errors of the individual forecasts!
Forward Rates: Unbiased Predictor
Exchange rate
F2
S2
Error
Error
S1
F1
F3
Error
S3
S4
Time
t1
t2
t3
t4
The forward rate available today (Ft,t+1), time t, for delivery at future time t+1, is used as a
“predictor” of the spot rate that will exist at that day in the future. Therefore, the forecast spot
rate for time St2 is F1; the actual spot rate turns out to be S2. The vertical distance between the
prediction and the actual spot rate is the forecast error. When the forward rate is termed an
“unbiased predictor,” it means that the forward rate over or underestimates the future spot rate
with relatively equal frequency and amount, therefore it misses the mark in a regular and orderly
manner. Over time, the sum of the errors equals zero.
Other Parity Models
• Two other important parity models are:
• Purchasing Power Parity
– Exchange rate between two countries should be
equal to the ratio of the two countries price level.
– The change in the exchange rate will be equal to the
difference in inflation.
• International Fisher Effect
– The change in the exchange rate will be equal to the
difference in the nominal interest rate between two
countries.
LAW OF ONE PRICE
• The Purchasing Power Parity model is
based on the Law of One Price:
– The Law of one price states that all else
being equal (i.e., no transaction costs or other
frictions) a product’s price should be the same
in all markets (countries).
– Why? The principle of competitive markets
assumes that prices will equalize if costs of
moving such goods does not exist.
LAW OF ONE PRICE
• When prices for a particular product are
expressed in different currencies, the law
of one price states that after adjusting for
exchange rates, prices will be the same.
• Example (U.S. and Japan):
– The price of a product in US dollars (P$), multiplied by
the spot exchange rate (S = yen per dollar), equals
the price of the product in Japanese yen (P¥), or:
P$  S = P¥
EXAMPLE
• If a Big Mac costs $2.00 in the United
States and if the current spot rate is ¥110,
then the Law of One Price would suggest
a price in Japan of:
• $2.00 x ¥111 = ¥222.00
PPP EXCHANGE RATE
• Conversely, if the prices for similar goods
were known in local currencies, the
appropriate (PPP) spot exchange rate (S)
could be calculated from relative product
prices, or
• Spot PPP rate = Foreign Price/Home Price
PPP Example: Sept 11, 2003
•
•
•
•
•
Big Mac: Boulder, Colorado: $2.29
Big Mac: Osaka, Japan:
¥250
PPP Exchange Rate = Yen Price/Dollar Price
PPP Exchange Rate = ¥250/$2.29 = ¥109.17
The PPP rate can be compared to the actual rate,
and if:
–
–
–
–
Actual > PPP = currency may be undervalued!
Actual < PPP = currency may be overvalued!
Rate on September 11, 2003 = 117.1240
Thus, this model suggested the yen was undervalued at
that time (or dollar was overvalued).
ABSOLUTE PPP
• The “absolute” PPP measures the
“correctness” of the current spot rate on
the bases of similar goods in different
countries.
• A popular version of the absolute PPP
technique is found in the Economist “Big
Mac” index.
Big Mac Index: Explanation From
the Economist Magazine
• “Burgernomics is based on the theory of purchasingpower parity, 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.
• The Economist "basket" is a McDonald's Big Mac, which
is produced in about 120 countries.
• The Big Mac PPP is the exchange rate that would mean
hamburgers cost the same in America as abroad.
• Comparing actual exchange rates with PPPs indicates
whether a currency is under- or overvalued.”
Big Mac Index Web Site
• The Economist Magazine publishes their Big
Mac Index twice a year.
– http://www.economist.com/markets/Bigmac/Index.cfm
• Currently the index (May 27, 2004) suggests:
– Swiss franc: PPP = 2.19; actual = 1.25
• World’s most overvalued currency!
– Philippine peso: PPP = 23.8; actual = 55.8
• World’s most undervalued currency!
OECD PPP MEASURES
• A more comprehensive measure of a country’s
PPP is provided by the OECD for 30 member
countries. It can be found on the following website:
• http://www.oecd.org/home/
• Or:
• http://www.oecd.org/department/0,2688,en_264
9_34357_1_1_1_1_1,00.html
RELATIVE PPP
• The relative Purchasing Power Parity
model is concerned with the “rate of
change” in the exchange rate.
• Model suggests that the percent change in
the exchange rate should be equal to the
difference in the rates of inflation between
countries, or
% change in FX rate = Home inflation rate –
Foreign inflation rate.
RELATIVE PPP EXAMPLE
• Assume the following:
– Annual rate of inflation in U.S. = 2.0%
– Annual rate of inflation in U.K. = 3.0%
• The British pound should depreciate 1%
per year against the U.S. dollar.
• If the current rate is $1.80, then
– 1 year from now the rate should be: $1.7820
– 2 years from now the rate should be: $1.7642
– Etc….
TESTS OF THE PPP
• The existing empirical tests of the PPP
have proved disappointing.
• Generally the results do not support the
PPP.
• However, PPP can still provide us with a
“benchmark” test of whether a currency is
overvalued or undervalued against other
currencies.
INTERNATIONAL FISHER
EFFECT
• The last major parity model is the
International Fisher Effect.
• Begins with the Fisher Effect:
– A change in the expected rate of inflation will
result in a direct and proportionate change in
the market rate of interest.
FISHER EFFECT
• Market rate of interest is comprised of two
components:
– Real rate requirement
• Relates to the real growth rate in the economy
– Expected rate of inflation
• Real rate requirement is assumed to be
relatively stable
• Thus, changes in market interest rates occur
because of changes in expected inflation!
FISHER EFFECT EXAMPLE
• Assume the following:
– real rate requirement is 3.0%
– Expected rate of inflation is 1.0%
• Under these conditions, the market
interest rate would be 4%
• If the expected rate of inflation increases
to 2.0%, the market interest rate would
rise to 5%.
FISHER EFFECT DATA
Country
CPI Forecast
2004 2005
2 Year Gov’t
Bond Rate
Australia
U.S.
Switzerland
Japan
+2.2%
+1.9%
+0.7%
-0.1%
5.27%
2.45%
1.13%
0.14%
+2.5%
+1.8%
+0.4%
nil
Forecast: The Economist Poll,
Date: May 29, 2004
FISHER EFFECT ASSUMPTIONS
• Model assumes that the real rate requirement is
the same across countries.
• Thus market interest rate differences between
counties is accounted for on the basis of
differences in inflation expectations.
• If the interest rate is 5% in the U.S. and 7% in
the U.K. then:
– The expected rate of inflation is 2% higher in the U.K.
INTERNATIONAL FISHER
EFFECT
• Changes in exchange rates will be driven by
differences in market interest rates between
countries.
• Because differences in interest rates capture
differences in expected inflation.
– High interest rate countries (due to high expected
rates of inflation) will experience currency
depreciation.
– Low interest rate countries (due to low expected rates
of inflation) will experience currency appreciation.
INTERNATIONAL FISHER
EFFECT EXAMPLE
• Using interest rate data from Bloomberg’s
web site (rates and bonds):
– http://www.bloomberg.com/markets/index.html
• 2 year U.S. Government rate
2.65%
• 2 year Japanese Government rate: 0.14%
• Higher U.S. rate is accounted for on the basis of
higher expected U.S. inflation:
• 2.65 – 0.14 = 2.51
EXCHANGE RATE CHANGE
• Given the expected inflation differences,
the yen will appreciate 2.51% per year.
• Current spot rate 110.
• Spot rate 1 year from now: 107.239
• Spot rate 2 years from now: 104.547
• Etc…