INTERNATIONAL PARITY CONDITIONS
Remember, an indirect quote is the foreign currency over the domestic currency. This is
the “normal form” for the formulas we will cover.
indirect quote 
Pf
Pd
The “Law of One Price” states that a product sold in two different markets should be the
same price.
If 1) the products are identical and 2) there are no frictions (i.e. transportation costs or
government restrictions).
Law of one price : P d x S  P f
Pf
where, the spot rate ( S ) is d
P
Purchasing Power Parity (PPP) takes the law of one price a step further. It states that
since the prices should be the same across countries, the exchange rate between two
countries should be the ratio of the prices in each country.
PPP :
Price of a product in Country A
 Spot rate ( S )
Price of a product in Country B
where, the spot rate ( S ) is
PA
PB
Example: If a hamburger is $2.54 in the United States and 3.60 real (R$) in Brazil, then
the PPP spot rate should be:
S
3.60 R$
1.42 R$
, which reduces to 
$2.54
1$
If the actual exchange rate is S 
2.19 R$
, then according to the PPP theory the Brazilian
1$
real is undervalued by 35%.

 1.42 R$ 
 2.19 R$  
 PPP implied rate  1$   Actual exchange rate  1$    1  % over (or under )valued





FYI McDonalds' Big Mac is produced locally in almost 120 countries!1
1
Source: The Economist, “Food for thought,” May 27, 2004.
1
Relative Purchasing Power Parity (RPPP) takes things a step further. This theory
states that if inflation is higher in Country A than in Country B, then Country A’s
currency will fall.
Why? Because inflation causes goods to become more expensive (and therefore less
competitive) in a country; this will lead to a deficit in the current account (more imports
then exports).
Remember from your homework in Chapter 3:
If the currency is fixed, a deficit in the current account will cause an initial decrease in
the country’s foreign exchange reserves2 caused by increased flight from the local
currency to stronger foreign currencies… if this continues, the country will have to
devalue its currency.
And if the currency is floating, deficit in the current account will cause private parties to
judge the economy as being weak; and the currency will probably drop in value in the
free exchange markets. This drop might be self-correcting because a cheaper local
currency will encourage more exports and make imports more expensive. (Note: No
specific reason exists to expect foreign exchange reserves to change.)
Example: If inflation in Colombia is 2% and inflation in the United States is 6%, then
RPPP would predict that the peso would appreciate by 4% relative to the dollar.
% ∆ in the spot exchange rate = (-) % ∆ in expected rates of inflation
According to PPP the expected spot rate (S2) is derived from the following formula:
1  ( E )i 
x
1  ( E )i 
f
( E ) S2  S1
d
where, the spot rate ( S ) is
Pf
 E (S2 )  is the expected spot rate and  ( E )i  is expected inflation
Pd
Sometimes it is better to compare one country to a group of countries to get a better feel
for a currency’s position (i.e. over/under valuation). This is done with an index.
A nominal effective exchange rate index uses actual exchange rates to create an index and
a real effective exchange rate index uses the purchasing power parity exchange rate to
create an index.
2
As the Central Bank buys local currency with foreign exchange reserves to support the currency, the
foreign exchange reserves will decrease—“supporting” a currency means decreasing the supply –the
money in circulation—so that the “price”—the exchange rate—increases.
2
To find the real effective exchange rate for Country A (versus Country B) use the
following formula:
ERA  ENA x
CA
CB
Pass-through is the degree to which the prices of imported and exported goods change as
a result of exchange rate changes.
Remember according to “the law of one price” a product sold in two different markets
should be the same price. But this is not always the case due to factors such as
component costs, lags in exchange rate changes, and the price elasticity of demand.
Price elasticity of demand is the percentage change (% ∆) in the quantity of the good
demanded as a result of a % ∆ in the price. Here is the formula:
price elasticity of demand  e p 
%Qd
%P
Note: If the absolute value of ep is < 1.0, then the good is relatively “inelastic.” An
absolute value of greater than 1.0 indicates a relatively “elastic” good.
A product that is relatively “inelastic” means that the quantity demanded is relatively
unresponsive to price changes.
Example: Inelastic product - textbooks in the U.S. market
If the price of textbooks increases by 10% (from $100 to $110), the same number of
books will be sold.
Note: this theory holds for most high-priced items. Most people who have the money to
buy something for $15,000 will be less likely to notice a price increase of 10%.
A product that is relatively “elastic” means that the quantity demanded is responsive to
price changes.
Example: Elastic product - computers in the U.S. market
If the price of a computer increases, people will wait to purchase. (Instead of buying a
computer in two years a percentage of consumers will wait a third year to update their
computer)
3
Pass through steps
Step 1: Find the price at the end of the period (P2).
P1 x expected inflation = P2
Step 2: Find S2. Assuming PPP, you can find S2 with the following formula:
1  ( E )i 
x
1  ( E )i 
f
( E ) S2  S1
d
where, the spot rate ( S ) is
Pf
 E (S2 )  is the expected spot rate and  ( E )i  is expected inflation
Pd
Step 3: Find the % ∆ in exchange rates.
S1  S2
x 100  % 
S2
Pf
where, the spot rate ( S ) is d and (% ) is the percent change
P
Step 4: Using the pass through rate, discount the % ∆.
pass through rate x % ∆ = discounted rate
Step 5: Insert the discounted rate into the following formula to find the effective
exchange rate.
S1
 effective rate
1  discounted rate 
Pf
where, the spot rate and the effective rates are d
P
Step 6: Divide P2 by the effective exchange rate to get the price at the end of the period.
P2 / effective rate = price after pass through
4
The Fisher effect states that the nominal interest rate (i) in a country should be equal to
the real rate of interest (r) plus expected inflation (π). Here is the formula:
i=r+π
Remember, the nominal exchange rate is the actual spot rate while the real exchange rate
is adjusted for inflation.
The International Fisher effect extends this to account for differences in interest rates
across borders. Here is the formula:
S1  S2 d f
 i i
S2
Pf
where, the spot rate (S ) is d
P
Example:
U.S. bond earning 5% interest
Turkish bond earning 20% interest
If an investor in Turkey is indifferent and would invest in either of the above bonds, then
she expects the dollar to appreciate by 15% against the Turkish lira over the next ten
years.
1) If she chooses the U.S. bond, she expects the dollar to appreciate by more
than 15% over the ten year period.
2) If she chooses the Turkish bond, then she expects the dollar to appreciate
by less than 15% against the Turkish lira over the ten year period.
If she invests in the U.S. bond and the dollar appreciates by 18% over the ten year period,
she will earn an extra 3% when she converts her income into the local currency (lira).
Forward rate: An exchange rate quoted today for settlement at a future date. Note: with
forwards no money changes hands until settlement. Here is the formula for the forward
rate:
  f days  
1   i x 360  
F


Fdays 
S x 
F
  d days  
1   i x 360  

 
Pf
where, the spot rate ( S ) is d and (i ) is the annual interest rate
P
f
days
d
days
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The forward premium (or discount) is the percentage difference between the spot
exchange rate and the forward exchange rate. Here is the formula:
ff 
S  Fdays
Fdays
x
360
x 100
days
where, the spot rate ( S ) is
f
Fdays
Pf
and
the
forward
rate
(
F
)
is
days
d
Pd
Fdays
Note: the forward premium is an annual figure.
Futures contracts: exchange-traded agreements that call for the future delivery of a
standard amount of any good (i.e. foreign currency) at a fixed time, place, and price.
Interest rate parity (IRP) states the difference in national interest rates for securities of
similar risks and maturities should be equal to, (but have the opposite sign), the forward
rate discount or premium for the foreign currency (without considering transaction
costs3).
1  i   S x 1  i  x F1
d
days
f
days
days
where,  idays  is the annual rate x
Also, the spot rate ( S ) is
days
360
f
Fdays
Pf
and
the
forward
rate
(
F
)
is
days
d
Pd
Fdays
Exhibit 6.6 Interest Rate Parity
i $ = 8.00 % per annum
(2.00 % per 90 days)
Start
$1,000,000
End
x 1.02
$1,020,000
$1,019,993*
Dollar money market
S = SF 1.4800/$
90 days
F90 = SF 1.4655/$
Swiss franc money market
SF 1,480,000
x 1.01
SF 1,494,800
i SF = 4.00 % per annum
(1.00 % per 90 days)
3
You could expect transaction costs to be about 0.18% to 0.25% of the total transaction.
6
Covered Interest Rate Arbitrage (CIA) is the idea that an imbalance in parity
conditions can create a “risk less” opportunity for an arbitrager.
Exhibit 6.7 Covered Interest Arbitrage (CIA)
Eurodollar rate = 8.00 % per annum
Start
End
$1,000,000
x 1.04
$1,040,000
$1,044,638
Arbitrage
Potential
Dollar money market
180 days
S =¥ 106.00/$
F180 = ¥ 103.50/$
Yen money market
¥ 106,000,000
x 1.02
¥ 108,120,000
Euroyen rate = 4.00 % per annum
Example:
Step 1: Convert $1,000,000 at the spot rate of ¥106.00/$ to ¥106,000,000
Step 2: Invest the proceeds, (¥106,000,000), in a euroyen account for six months, earning
4% per annum, or 2% for 180 days.
Step 3: Simultaneously sell the future yen proceeds (¥108,120,000) forward for dollars at
the 180-day forward rate of ¥103.50/$. Note: at this point you have “locked in” the
amount of $1,044,638 in 180 days (or 6 months).
Step 4: Out of the $1,044,638 you have to repay the loan (plus interest), this is called
your opportunity cost of capital. To do this, calculate the interest rate for the period (8%
per year is 4% for 180 days)4. So to borrow $1,000,000 you have to pay $40,000 in
interest at the end of 6 months. Subtract the $1,040,000 from the $1,044,638 that you
will receive from your forward contract for a “risk less” profit of $4,638.
Notice that these activities should help the currencies return to equilibrium.
4
To use our formula: 8% x
180
 4%
360
7
Uncovered Interest Arbitrage (UIA)
Uncovered interest arbitrage is great when you are dealing with fixed exchange
currencies, because the profit at the end of the period is dependant of the exchange rate
(and since this is “uncovered” it is a very risky investment).
Exhibit 6.7 Uncovered Interest Arbitrage
Investors borrow yen at 0.40% per annum
Start
¥ 10,000,000
End
x 1.004
Japanese yen money market
S =¥ 120.00/$
360 days
¥ 10,040,000 Repay
¥ 10,500,000 Earn
¥
460,000 Profit
S360 = ¥ 120.00/$
$83,333.33
and
$87,500.00
US dollar money market
$ 83,333,333
x 1.05
Note: there
is a typo in
the book.
The correct
figures are:
$ 87,500,000
Since there are men and women making a killing in this business, the opportunities for
smaller investors are almost impossible… It is these two types of arbitrage that keep
exchange rates more or less in equilibrium.
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Definitions:
Unbiased Predictor – means that “on average” the estimation will be wrong on the up
side or the downside with equal frequency and degree. In other words, the errors are
normally distributed.
-∞%
0%
+∞%
Note: if you can find something to be right about >50% of the time, you could make a
fortune (or if you could be right only about the side-positive or negative) with certainty.
So if you knew for certain only that a stock would go down (but not by how much), you
could short the currency5 for a profit.
Market efficiency – is the theory that states you cannot know for certain anything about
the future price (side or percentage). The assumptions behind this theory are that 1) all
relevant information is quickly reflected in both the spot and forward exchange markets,
2) there are no transaction costs (or they are trivial), and 3) instruments denominated in
different currencies are perfect substitutes for one another (i.e. that you would be just as
happy with a - Eastern Caribbean dollar denominated bond, a gourde bond from Haiti, or
a U.S. dollar denominated bond).
Global developments such as technology and regulations are making market efficiency
more and more possible.
5
Shorting a currency means selling it at a high price and then buying it back later (hopefully at a lower
price).
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Final Project
Session 1
The World Factbook: http://www.cia.gov/cia/publications/factbook/index.html
Potential value drivers (destroyers) Chapter 1
Session 2
The World Bank: http://www.worldbank.org/data/countrydata/countrydata.html
Session 3
www.countryreports.org
International Finance Corporation: www.ifc.org
Resources for Finance Courses
Session 1
www.investopedia.com
Session 3
www.wikipedia.org
Resources for your Career
Session 1
LIFA Exam: www.the-ira.org
CFA Exam: www.cfainstitute.org
Session 2
www.jobsinthemoney.com
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