Foreign Exchange
BA 282
Macroeconomics
Class Notes - Part 3
Foreign Exchange
1
Foreign Exchange Rates


The exchange rate is the price of one country’s
currency in terms of another country’s currency
Quoted exchange rates can be either direct or
indirect, one method is usually the convention

Direct: home currency per unit of foreign currency


Examples from US perspective:
1.676 US Dollars (USD) per British Pound (GBP)
1.152 US Dollars (USD) per Euro (EUR)
Indirect: foreign currency per unit of home currency

Examples from US perspective:
109.58 Japanese Yen (JPY) per US Dollar (USD)
1.3664 Swiss Francs (CHF) per US Dollar (USD)
Foreign Exchange
2
Prices in Foreign Currency

Use the exchange rate in direct terms
Example 1: How much does a €100 sweater cost an
American if the exchange rate is 1.15 $/€?
Price in $ = €100 * 1.15 $/€ = $115.00
Example 2: How much does a 100 CHF sweater cost an
American if the exchange rate is 1.37 CHF/$?
Price in $ = 100 CHF * (1 / 1.37 CHF/$) = $72.99
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3
Depreciation and Appreciation

A depreciation of the local currency means that it
takes more local currency to buy a unit of foreign
currency


An appreciation of the local currency is the opposite
Example:

If the $/€ exchange rate goes up from 1.10 to 1.20 the
dollar has depreciated against the euro

but, the euro has appreciated against the dollar.
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4
Depreciation and the Price of Imports


A depreciation of a country’s currency makes its
goods cheaper for foreigners and makes foreign
goods more expensive.
Example: Consider a bottle of French wine that
costs $20 when the $/€ exchange rate is 0.85.
Now what is the $ price of the bottle of wine if the
dollar depreciates to 0.95 $/€ ?
Price in € before depreciation = $20 (1/0.85 $/€ ) = € 23.53
Price in $ after depreciation = € 23.53 (0.95 $/€ ) = $ 22.35
or
Price in $ after depreciation = $20 (0.95/0.85) = $ 22.35
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5
Foreign Exchange Trading

The vast majority of foreign exchange (FX) trading
is done over-the-counter (OTC)

Most transactions have the USD on one side

Dollar is called a vehicle currency

Trading is centered at major multinational banks
(called dealers) such as Citibank, Bank of America,
Deutsche Bank, HSBC, etc.

By volume, it is the largest market in the world

Average daily turnover is about 1.5 trillion USD
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6
Foreign Exchange Trading

Trading takes place 24 hours a day during the
business week

Trading moves around the globe:
London => New York => Tokyo => London

Other important participants are



Corporations
Nonbank financial institutions
Central banks
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7
For current rates see: http://online.wsj.com/documents/mktindex.htm?worldval.htm
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8
Spot vs. Forward rates

Spot Rate: the exchange rate that is applicable
today


The settlement or value date for a spot transaction (the
date on which the parties actually exchange assets)
occurs two business days after the deal is made
Forward Rate: the exchange rate agreed on today
for a transaction at a future date.


Most commonly quoted 30, 90, or 180 days in the future.
The forward exchange rate is set so that no money
changes hands today.
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9
Forward Example

Boeing plans to deliver a 777 to KLM in six months
and receive 110 million Euros. Boeing calls
Citibank and enters into a 180-day forward contract
at a forward rate of 0.8700 $/€.

This obligates Boeing to deliver €110m to Citibank
in 180 days in exchange for
€ 110m * 0.8700 $/€ = $ 95.700m
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10
Why Use Forwards

Suppose that Boeing did not enter into a forward
agreement. What would be the dollar proceeds
from the sale if in 6 months the Euro ends up
trading at:
USD/EUR
0.82
0.87
0.92
Foreign Exchange
USD Proceeds
0.82 * 110m = $ 90.2m
0.87 * 110m = $ 95.7m
0.92 * 110m = $ 101.2m
11
Derivative Securities

A forward contract is the simplest form of a
derivative security

Definition: A derivative security is a financial
contract that derives its value from the price of
another underlying asset.

Other common examples:



Swaps
Put and call options
Futures contracts (exchange-traded forwards)
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FX Trading Statistics
Average Daily Volume
(USD Billions)
Transaction Type
Spot Transactions
Forwards and Forex Swaps
Currency Swaps
Options
Correction for reporting errors
Estimated Total
April 2004
621
1,152
21
117
-31
1,880
Source: Bank for International Settlements
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FX Derivative Market Stats
The Global Foreign Exchange Derivatives Markets
Notional Amounts Outstanding in Billions of US Dollars
December 2003
Total contracts
24,475
with other reporting dealers
with other financial institutions
with non-financial customers
8,660
9,450
6,365
up to one year
between one and five years
over five years
18,840
3,901
1,734
Memorandum Item:
Exchange-traded Contracts
132
Source: Bank for International Settlements
Foreign Exchange
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JPY/USD
400
350
300
250
200
150
100
50
Foreign Exchange
15
20
05
20
00
19
95
19
90
19
85
19
80
19
75
19
70
0
Trade-Weighted USD Exchange Rate
160
140
120
100
80
20
03
19
98
19
93
19
88
19
83
19
78
19
73
60
The index is a weighted average of the foreign exchange values of the U.S. dollar against other major
currencies. The index weights, which change over time, are derived from U.S. export shares. The index is
calculated in indirect terms so higher values imply a stronger USD.
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Foreign Exchange
17
-05
-05
Jul
Jan
-04
-04
Jul
Jan
-03
-03
Jul
Jan
-02
-02
Jul
Jan
-01
-01
Jul
Jan
-00
-00
Jul
Jan
-99
-99
Jul
Jan
USD/EUR
1.40
1.30
1.20
1.10
1.00
0.90
0.80
The Law of One Price

In competitive markets free of transportation costs
and other barriers to trade, identical goods sold in
different countries must sell for the same price
(when expressed in the same currency).

Why?
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18
The Law of One Price

We can write an equation for the law of one price
as,
PiLC = PiFC * E
where
PiLC is the local currency price of good i
PiFC is the foreign currency price of good i
E is the dollar to euro exchange rate

Or we can rearrange the equation to get
E = PiLC / PiFC
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Purchasing Power Parity (PPP)
PPP looks just like the law of one price except the
prices are for a “basket” of goods rather than for a
particular good so
E = PLC / PFC
or
PLC = PFC * E
where
PLC is the local currency aggregate price level
PFC is the foreign currency aggregate price level

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Invented in 1986 as a light-hearted guide to
whether currencies are at their “correct” level,
burgernomics is based on the theory of purchasingpower parity (PPP). This says that, in the long run,
exchange rates should move toward rates that would
equalise the prices of an identical basket of goods
and services in any two countries. To put it simply: a
dollar should buy the same everywhere. Our basket
is a McDonald's Big Mac, produced locally to roughly
the same recipe in 118 countries. The Big Mac PPP
is the exchange rate that would leave burgers
costing the same as in America. Comparing the PPP
with the actual rate is one test of whether a currency
is undervalued or overvalued.
The first column of the table shows
local-currency prices of a Big Mac. The second
converts them into dollars. The average price of a
Big Mac in four American cities is $2.71. The
cheapest burgers are in China ($1.20); the dearest
are in Switzerland ($4.52). In other words, the yuan
is the most undervalued currency, the Swiss franc
the most overvalued. The third column calculates Big
Mac PPPs. Dividing the local Chinese price by the
American price gives a dollar PPP of 3.65 yuan. The
actual exchange rate is 8.28 yuan, implying that the
Chinese currency is undervalued by 56% against the
dollar.
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21
Purchasing Power Parity (PPP)

PPP asserts that all countries’ price levels are
equal when measured in terms of the same
currency


Note: In practice the basket of goods is the same as the
one used for the CPI
PPP predicts that a decline (increase) in a
currency’s domestic purchasing power will be
associated with a proportional currency
depreciation (appreciation) in the foreign exchange
market
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22
Absolute PPP vs. Relative PPP

Absolute PPP (PLC = PFC * E) represents the
relationship between the level of the exchange rate
and the level of prices in the two economies

Relative PPP states that the percentage change in
the exchange rate will be equal to the difference in
the percentage change in the price levels in the two
countries
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23
Absolute PPP vs. Relative PPP

We can write an equation for Relative PPP as
(Et - Et-1)/ Et-1 = pLC,t – pFC,t
where
pi,t is the inflation rate (Pi,t - Pi,t-1)/ Pi,t-1 in country i between
time t-1 and t
Et is the exchange rate at time t
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24
Empirical Evidence on PPP

To test absolute PPP, we measure the price level of
a basket of goods in various countries.


For example, The Economist’s Big Mac Index
To test relative PPP we can look at the correlation
between exchange rates and relative price levels

Typically correlations are low

Empirically, PPP theory does poorly in predicting
exchange rate movements for developed countries

Why is it hard to test these theories?
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25
Problems with PPP

Transport costs and trade barriers



If it costs a substantial amount to transport goods, then
this prevents the ability to do “arbitrage”
In some industries transport costs are effectively infinite
(e.g., housing). These are called nontradable goods.
Governments usually have import tariffs, etc.

Monopolistic or oligopolistic practices

Measurement differences

“Sticky” prices
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26
Demand for Foreign Currency

If we think of foreign currency as a financial asset
then the demand for foreign currency will depend
on the investment properties of foreign currency

For example, we might consider the following
properties




Expected Return
Risk
Liquidity
Inflation
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Demand for Foreign Currency

For now we are going to concentrate on only one of these
 Expected Return

Notation
RLC
Interest rate in local currency (e.g., USD)
RFC
Interest rate in foreign currency (e.g., EUR)
Et
Actual exchange rate at time t in LC/FC
Ee
Expected exchange rate in one year
(this is the expectation of a random variable)
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28
Demand for Foreign Currency

Definition: The annual rate of depreciation of LC
relative to FC is the percentage increase in E over
one year,
rate of depreciation = (E1 - E0) / E0

The LC rate of return on FC deposits is
approximately RFC plus the rate of depreciation

Today we do not know what E1 will be, only what
we expect it to be (Ee). So,
expected rate of return on FC = RFC + (Ee - E0) / E0
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29
FX Market Equilibrium

Equilibrium in the foreign exchange market is
defined as
difference in rate of return = RLC - RFC - (Ee - E0) / E0 = 0

This is also called the interest parity condition and
can be written as
RLC = RFC + (Ee - E0) / E0
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30
Graphing Interest Parity

We can rearrange this equation so that
E0 = Ee / (1 + RLC - RFC)

Example: Suppose R€=5.2% and Ee=0.95 $/€, what
is the exchange rate today (E0) for the following
USD interest rates?
R$
E0
2%
4%
6%
8%
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31
Plot the Points
Exchange Rate
($/€)
0.9814
0.9615
0.9425
Expected Return
on € Deposits
0.9241
2%
Foreign Exchange
4%
6%
8%
Rate of Return ($)
32
Graphical Equilibrium
Exchange Rate
(LC/FC)
E0’’
E0*
2
1
E0’
3
RLC
Foreign Exchange
Expected Return
on FC Deposits
Rate of Return (LC)
33
Changing LC Interest Rates and
Exchange Rate Equilibrium
Exchange Rate
(LC/FC)
E0
1
LC Appreciates
2
E0’
RLC
Foreign Exchange
1’
R’LC
Expected Return
on FC Deposits
Rate of Return (LC)
34
Changing FC Interest Rates and
Exchange Rate Equilibrium
Exchange Rate
(LC/FC)
Rise in FC
Interest Rate
E0’
2
E0
1
LC Depreciates
RLC
Foreign Exchange
Expected Return
on FC Deposits
Rate of Return (LC)
35
Money, Interest Rates, & Exchange Rates

We can combine what we learned previously about
the demand for money with what we now know
about exchange rates

This gives a more integrated picture of how money,
interest rates, and exchange rates interact

For convenience let’s rotate the money market
graph clockwise 90o and combine it with the FX
market graph
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36
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37
Money Market / Exchange Rate Linkages
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38
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39
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40
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41
Time path of US economic variables after a
permanent increase in the US money supply
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42
FX & Currency Swaps



A swap is an agreement between two parties to
exchange a predefined set of cashflows for a
specified period.
A FX swap is the spot sale of a currency combined
with a forward repurchase agreement (like a repo)
A simple currency swap is when one counterparty
would agree to pay €10 million each year for five
years. The other counterparty would agree to pay
$8 million each year for five years.

Note that this currency swap is just a set of five forward
contracts.
Foreign Exchange
43
FX & Currency Swap facts

Most currency swaps entail an up-front exchange of
principal (unlike interest rate swaps)

Like FX forwards, most FX swaps have one side in
USD

Currency swaps tend to be traded at longer
maturities than forwards or options (> 1 year)
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44
FX Options

A call (put) option gives the owner the right but not the
obligation to buy (sell) foreign currency at a prespecified
exchange rate (called the strike) at a prespecified date.

An option allow the owner to participate in exchange rate
changes in one-direction only

Consequently, options always have an upfront cost (called
the premium)

For a US investor,


call options payoff when the USD/FCU exchange rate increases
put options payoff when the USD/FCU exchange rate decreases
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45
Calls and Puts
Put Option
X = Strike
P0 = Put Premium
Net Payoff = max(X-E,0) - P0
Call Option
X = Strike
C0 = Call Premium
Net Payoff = max(E-X,0) - C0
Payoff
Payoff
X
C
0
Foreign Exchange
USD/FCU
at Maturity
X
USD/FCU
at Maturity
P0
46
Put Option Example


Put options are frequently used to “hedge” foreign
exchange revenues
Back to Boeing example,

Recall Boeing expects to receive 110 million Euros in six
months. Boeing calls Citibank and buys a 180-day put
option with a strike of 0.85 $/€ for a premium of $2 million
today.

When does Boeing exercise the put option?
Would the put option premium be more or less if the
strike was 0.80 $/€?

Foreign Exchange
47
Changes in E0 and Expected Returns

How does a change in E0 (all else held constant)
change the LC expected return of FC deposits?

Example:


E0 equals 1.00$/€ and Ee equals 1.05$/€.

Now suppose E0 increases to 1.03$/€

What happens to the dollar return on euros?
In general, a depreciation of the local currency
results in a decrease in the local currency return of
foreign currency deposits
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