Universidad Autónoma de Madrid
International Finance
2024/25
Topic 4: Determining exchange rates
and exchange rate policies
www.uam.es
Determining exchange rates and exchange rate policies
4.1 Introduction
4.2 Purchasing Power Parity (PPP)
4.3 Balance of Payments (BOP) Theory
4.4 Monetary Approach
4.5 Interest Rate Parity
www.uam.es
Theories explaining exchange rate movements
PPP
(Purchasing Power Parity)
The demand for the foreign currency is derived from
the demand for foreign goods and services
Balance of Payments Approach
All the elements in the Balance of Payments have
influence on supply and demand for the foreign
currency
Monetary Approach
This approach combines the PPP one and the
Quantity Theory of Money
www.uam.es
Determining exchange rates and exchange rate policies
4.1 Introduction
4.2 Purchasing Power Parity (PPP)
4.3 Balance of Payments (BOP) Theory
4.4 Monetary Approach
4.5 Interest Rate Parity
www.uam.es
Key ideas and approaches
 The theory of purchasing power parity (PPP) explains the behaviour of
exchange rates as a function of the price level across countries.
 The central idea of this theory is that the value of a currency is
determined by the amount of goods and services one may buy with
one currency unit;
 Therefore, exchange rates are linked to inflation rates;
 There are three approaches to this theory:
 Commodity Price Parity (CPP);
 Absolute Purchasing Power Parity (A-PPP);
 Relative Purchasing Power Parity (R-PPP).
www.uam.es
Commodity Price Parity (CPP) (1)
Let’s consider a good (“i”) and two countries (USA and China)
In accordance with this theory:
At moment “0”:
Pi ,0 (CHN )  S0 (CNY ,1USD)  Pi ,0 (USA)
At moment “1”:
Pi ,1 (CHN )  S1 (CNY ,1USD)  Pi ,1 (USA)
P: price
S: spot exchange rate
CNY: Chinese yuan
USD: US Dollar
At any time, the
price of “i” is
the same in
both countries
The yuan price of a good in China must be
equal to the yuan price of the same good in
USA.
Thus, the exchange rate between yuan and dollar must be equal to the
ratio of the countries’s price levels.
At moment “0”:
S 0 (CNY ,1USD ) 
P0 (CHN )
At moment “1”:
S1 (CNY ,1USD ) 
P1 (CHN )
P1 (USA)
P0 (USA)
www.uam.es
Commodity Price Parity (CPP) (1)
Appreciation and depreciation

S (CNY , 1USD ) 
+ : USD’s appreciation
CNY’s depreciation
S1 (CNY, 1USD ) - S0 (CNY, 1USD )
S0 (CNY, 1USD )
- : USD’s depreciation
CNY’s appreciation
www.uam.es
CPP (2)
 In accordance with the Commodity PP theory, what will it happen if the
equality is not held?
 Arbitrage transactions are carried out. One can buy the good in the
cheaper place and then sell it in the more expensive place.
 As a consequence, prices are getting equal
One example:
Pi ,0 (CHN )  S0 (CNY ,1USD)  Pi ,0 (USA)
i = trousers
40 CNY <
6 CNY
1 USD
10 USD
60 CNY
People in US
with USD
They travel
to China
They go back
to US
They buy CNY
by selling USD
They buy
trousers
CNY
Ptrousers (CHN)
USD
They sell
Chinese
trousers
Ptrousers (USA)
www.uam.es
CPP (3)
 What are the requirements so that arbitrage transactions may be
implemented and prices be balanced?
 Freedom of commerce: There must be an absence of tariffs and
quantitative restrictions on trade.
 Non existence of transaction costs: The costs of transport and
insurance of the goods must be zero. Difficult to comply even for
large sales volumes.
 The good should be marketable: That is, a consumer can buy a good
and then sell it to other consumers. Example: industrial inputs or
the case of gold, crude oil and other commodities. It is not the case
for services.
 The supply conditions must be equalised. If this is not the case, it is
because the exchange rate is influenced by variables other than
prices.
www.uam.es
CPP (3)
 If unbalances are persistent, this is one cause to explain:
 International trade growth. International trade develops between
countries because some countries exploit their cost advantages and
others exploit their quality advantages. These advantages cannot
be adopted by other countries in the short term.
 Multinational firm expansion. Multinational companies locate and
relocate subsidiaries according to the cost and quality advantages
of the factors of production.
 Workers’ migration. The different labour costs between countries
favour the migration of workers from countries with lower costs to
countries with higher costs. Example: Some Chinese people go to
these countries and offer a service at a higher price than in their
country of origin but lower than the usual price in the host country.
www.uam.es
THE BIG MAC INDEX
• The Big Mac Index was invented in 1986 by the Economist.
• It is based in the PPP theory.
• Equalised the Price of a Burger in any country to the Price of a Burger in
US.
www.uam.es
Absolute Purchasing Power Parity (A-PPP)
Let’s consider a basket of goods and two countries (USA and China)
In accordance with this theory:
At moment “0”:
P0 (CHN )  S 0 (CNY ,1USD)  P0 (USA)
At moment “1”:
P1 (CHN )  S1 (CNY ,1USD )  P1 (USA )
………………………………
At any time, the
price of the
basket
is the same in
both countries
Analogue comments on arbitrage
www.uam.es
Relative Purchasing Power Parity (R-PPP) (1)
We consider inflation rates instead of prices of a basket of goods. We use the
percentage change in prices of the basket, as inflation rate.
I CHN 
P1 (CHN )  P0 (CHN )
IUSA 
P0 (CHN )
P1 (USA)  P0 (USA)
P0 (USA)
The price of a basket of goods in “1” is defined as:
P1 (USA)  P0 (USA)  (1  IUSA )
P1 (CHN )  P0 (CHN )  (1  I CHN )
Thus,
P1 (CHN )  P0 (CHN )  (1  I CHN )
P1 (USA)  P0 (USA)  (1  IUSA )
where: S1 (CNY ,1USD ) 
P (CHN )
P1 (CHN )
and S 0 (CNY ,1USD )  0
P0 (USA)
P1 (USA)
Then, S1 (CNY ,1 USD )  S 0 (CNY ,1 USD ) 
S1 (CNY ,1 USD ) (1  I CHN )

S 0 (CNY ,1 USD ) (1  IUSA )

(1  I CHN )
(1  IUSA )
1  S (CNY ,1 USD ) 
(1  I CHN )
(1  IUSA )
www.uam.es
Relative Purchasing Power Parity (R-PPP) (1)

1  S (CNY , 1USD ) 
I
 I USA
S (CNY , 1USD )  CHN
1  I USA

1  I CHN
1  I USA

I CHN  I USA  S (CNY , 1USD)
www.uam.es
Relative Purchasing Power Parity (R-PPP) (1)
Conclusion
The currency of a country with higher (lower) inflation rate tends
to depreciate (appreciate). Empirical evidence support this
statement, although not in the exact extent indicated by the
formula.
www.uam.es
Page 15
R-PPP (2)
Adjustment process
1.
Let’s consider a country with higher inflation rate than other country
2.
Residents in that country will be encouraged to replace purchasing in
their country by doing it in the other country. The effects would be:

An increase on foreign currency demand and consequently an
appreciation of it (national currency depreciation).

An increase on foreign goods demand and therefore an increase
in those prices.

A combination of the two above effects.
3. The adjustment is not perfect due to transaction costs as well as other
imperfections.
www.uam.es
Determining exchange rates and exchange rate policies
4.1 Introduction
4.2 Purchasing Power Parity (PPP)
4.3 Balance of Payments (BOP) Theory
4.4 Monetary Approach
4.5 Interest Rate Parity
www.uam.es
Balance of Payments and Currency Markets
• A BOP is the statistical record of a country’s international transactions
over a certain period of time.
• In this double-entry bookkeeping system, any receipt from a foreigner is
recorded as a credit and payments to foreigners are recorded as debits.
• The three major divisions of a BOP are:
• Current account: includes the exports and imports of goods and
services. The current account is further subdivided into merchandise
trade, services, factor income, and unilateral transfers.
• Financial account: includes all purchases and sales of financial assets
such as stocks, bonds, bank accounts, real estate and businesses.
• Capital account: consists of capital transfers and the cross-border
acquisition and disposal of nonproduced non-financial assets such as
natural resources and marketing assets.
• Official reserves account: consists of a country’s reserve assets such
as gold, foreign exchange reserves, and SDRs (Financial support from
IMF).
www.uam.es
Balance of Payments and Currency Markets
Let´s assume a country with a non-internationally accepted currency
Incoming foreign reserves
GOODS AND SERVICES
EXPORTS
FINANCIAL CAPITAL
IMPORTS
CURRENCY
MARKETS
GOODS AND SERVICES
IMPORTS
Exchange
rate
FINANCIAL CAPITAL
EXPORTS
Outgoing foreign reserves
They depend on:
• P: Prices in home country
• P*: Prices in foreign country
• GDP: in home country
• GDP*: in foreign country
They depend on:
• r: Interest rate in home country
• r*: Interest rate in foreign
country
• Risk and expectation
www.uam.es
How changes in prices may affect exchange rate
 Demand - Foreign Curr.
 Supply - National Curr.
M
S
P
X
Foreign currency appreciated
National currency depreciated
 Supply - Foreign Curr.
 Demand - National Curr.
 Demand - Foreign Curr.
 Supply - National Curr.
M
P*
X
M: Imports
S
Foreign currency depreciated
National currency appreciated
 Supply - Foreign Curr.
 Demand - National Curr.
X: Exports
www.uam.es
How changes in GDP may affect exchange rate
 Demand - Foreign Curr.
 Supply - National Curr.
GDP
M
X?
Improving
expectations
in the country
GDP*
National currency depreciated
 Supply - Foreign Curr.
 Demand - National Curr.
Usually they improve
Incoming
financial
capitals
S
Foreign currency depreciated
National currency appreciated
 Supply - Foreign Curr.
 Demand - National Curr.
M?
S
X
Improving
expectations
in the other
country
S
Foreign currency appreciated
Outgoing
financial
capitals
S
Foreign currency depreciated
National currency appreciated
Foreign currency appreciated
National currency depreciated
 Demand - Foreign Curr.
 Supply - National Curr.
www.uam.es
How changes in interest rates may affect exchange rate
 Supply - Foreign Curr.
 Demand - National Curr.
r
r*
Incoming financial
capitals
Outgoing financial
capitals
Incoming financial
capitals
Outgoing financial
capitals
Risk and expectations constant
S
Foreign currency depreciated
National currency appreciated
 Demand - Foreign Curr.
 Supply - National Curr.
 Supply - Foreign Curr.
 Demand - National Curr.
S
Foreign currency appreciated
National currency depreciated
 Demand - Foreign Curr.
 Supply - National Curr.
www.uam.es
Determining exchange rates and exchange rate policies
4.1 Introduction
4.2 Purchasing Power Parity (PPP)
4.3 Balance of Payments (BOP) Theory
4.4 Monetary Approach
www.uam.es
Monetary Approach
M: Monetary
offer
Y: Real output
V: velocity of
money, this is,
speed at which
money changes
hands.
P: level of prices
This approach is based on the Quantity Theory of Money
In the base country: M ·v = P · Y
P=
In the foreign country: M* ·v* = P* · Y*
P* =
In accordance
with A-PPP
S=
M·v
Y
M* · v*
Y*
M · v · Y*
P
S=
P*
M* · v* · Y
1 currency unit of the foreign country = currency units of the base country
P0 (CHN )  S 0 (CNY ,1USD)  P0 (USA)
P = S0 · P*
Foreign currency appreciated
M
S
Foreign currency depreciated
M*
National currency depreciated
S
National currency appreciated
www.uam.es
Determining exchange rates and exchange rate policies
4.1 Introduction
4.2 Purchasing Power Parity (PPP)
4.3 Balance of Payments (BOP) Theory
4.4 Monetary Approach
4.5 Interest Rate Parity
4.6 Overview of the FX market
www.uam.es
Interest Rate Parity
• Interest rate parity (IRP) is an arbitrage condition that must
hold when international financial markets are in equilibrium.
• Let us derive IRP using a simple example with just $1.
 Suppose that you have $1 to invest over one-year.
 Consider two alternative ways of investing your fund:
i. Invest domestically at the U.S. interet rate
ii. Invest in a foreign country (U.K.) at the foreign
interest rate and hedge the Exchange risk by selling
it through a foward.
 Consider only risk-free investments like a U.S. Treasury
note.
www.uam.es
Interest Rate Parity
• First alternative: if you invest $1 domestically at the U.S.
interest rate iUSA , the maturity value in one year will be
$1
$11  iUSA 
0
1 year
www.uam.es
Interest Rate Parity
• Second alternative: to invest in the U.K. For that, you carry out the
following sequence of transactions:
1.
F and S are
expressed as the
amount of
dollars per
foreign currency
Exchange $1 for a pound amount £(1 / S0 ) at the spot exchange
rate (S0).
2.
Invest the pound amount at the U.K. interest rate iGBP  , with
the maturity value of $1(1 /S 0 )(1  iGBP ) in one year.
3.
$1(1 /S 0 )
$1(1 /S 0 )(1  iGBP )
0
1 year
Sell the maturity value of the U.K. investment in exchange for a
predetermined dollar amount, this is, using a forward exchange
rate.
 $1(1 /S 0 )(1  iGBP )F
www.uam.es
Interest Rate Parity
• The domestic (U.S.) and foreign (U.K.) investments are two equivalent
investments: same initial investment, same risk, and same length of
investment period (one year).
• Under arbitrage equilibrium, for two equivalent investments the
profit must be the same:
(1  iUSD ) 
F0 ,1
S0
(1  iGBP )
or
 (1  iUSD ) 
F0 ,1  S0 

(
1

i
)
GBP 

• The dollar interest rate from the UK investment is given by :
F
iUSD  0 ,1 (1  iGBP )  1
S0
www.uam.es
Interest Rate Parity
• The IRP relationship is sometimes also approximated as follows:
 F S 
 F S 
(iUSD  iGBP )   0 ,1 0 (1  iGBP )   0 ,1 0 
 S0 
 S0 
When IRP hold, you will be indifferent between investing your money in
the United States and investing in the U.K. with forward hedging.
However, if IRP is violated:
•
•
F
(1  iUSD )  0 ,1 (1  iGBP ) , better investing in US and borrowing in UK.
S0
(1  iUSD ) 
(See example)
F0 ,1
S0
(1  iGBP ) , better investing in UK and borrowing in US.
www.uam.es