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Foreign Exchange Markets
Dr Bryan Mills
Based on http://faculty.washington.edu/karpoff/FIN%20509/FIN509_session7.ppt
Outline of these slides
• The foreign exchange (FX) market
• Basic questions and definitions
• Four theories
– Purchasing Power Parity
– Interest Rate Parity
– Fisher condition for capital market equilibrium
– Expectations theory of forward rates
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1. The Foreign Exchange Market
Sell
Reuters 19/4/2010
buy
Currency
Last
Day High Day Low % Change Bid
Ask
Euro/US $
1.3489
1.3489
1.3489
+0.01%
1.3489
1.3494
UK £/US $
1.5338
1.5339
1.5338
+0.01%
1.5338
1.5342
US $/¥en
92.450
92.460
92.420
+0.06%
92.450
92.5
US $/SFranc 1.0625
1.0632
1.0628
-0.03%
1.0625
1.0631
US $/Can $ 1.0144
1.0152
1.0146
+0.02%
1.0144
1.0149
Aust $/US $ 0.92400
0.92410 0.92370 +0.03%
0.92400 0.92440
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The Foreign Exchange Market...
Some forward currency rates as of May 24,
2004:
U.S. dollars per Euro (bid prices):
Spot rate
1.2017
One-month forward
1.20062
3 months forward
1.19898
6 months forward
1.19789
12 months forward
1.19854
24 months forward
1.19804
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2. Some basic questions
• Why aren’t FX rates all equal to one?
• Why do FX rates change over time?
• Why don’t all FX rates change in the same
direction?
• What drives forward rates – the rates at which
you can trade currencies at some future date?
5
Definitions
• r$ : dollar rate of interest (r¥, rHK$,…)
• i$ : expected dollar inflation rate
• f€/$ : forward rate of exchange
• s€/$ : spot rate of exchange
– “Indirect quote”:
s€/$ = 0.83215
– “Direct quote”:
s$/€ = 1.2017
 1 $ buys 0.83215 €
 1 € buys $1.2017
6
3. Four theories
.
Difference in
interest rates
1 + r€
1 + r$
Fisher
Theory
Interest
Rate
parity
Exp. difference in
inflation rates
1 + iSFr
1 + i$
Relative PPP
Difference between
forward & spot rates
F€/$
Exp. Theory
s€/$
of forward
rates
Expected change
in spot rate
E(s€/$)
S€/$
7
Theory #1: Purchasing power parity
Law of One Price
Versions of
PURCHASING
POWER
PARITY
Absolute PPP
Relative PPP
8
The Law of One Price
• A commodity will have the same price in
terms of common currency in every country
– In the absence of frictions (e.g. shipping costs,
tariffs,..)
– Example
Price of wheat in France (per bushel): P€
Price of wheat in U.S. (per bushel): P$
P€ = s€/$  P$
S€/$ = spot exchange
rate
9
The Law of One Price, continued
• Example:
Price of wheat in France per bushel (p€) = 3.45 €
Price of wheat in U.S. per bushel (p$) = $4.15
S€/$ = 0.83215 (s$/€ = 1.2017)
Dollar equivalent price
of wheat in France= s$/€ x p€
= 1.2017 $/€ x 3.45 € = $4.15
 When law of one price does not hold, supply
and demand forces help restore the equality
10
Absolute PPP
• Extension of law of one price to a basket of goods
• Absolute PPP examines price levels
– Apply the law of one price to a basket of goods with
price P€ and PUS (use upper-case P for the price of the
basket):
S€/$ = P€ / PUS
where P€ = i (wFR,i  p€,i )
PUS = i (wUS,i  pUS,i )
11
Absolute PPP
• If the price of the basket in the U.S. rises
relative to the price in Euros, the U.S. dollar
depreciates:
May 21 :
s€/$ = P€ / PUS
= 1235.75 € / $1482.07 = 0.8338 €/$
May 24:
s€/$ = 1235.75 € / $1485.01 = 0.83215 €/$
12
Relative PPP
Absolute PPP:
P€ = s€/$  P$
For PPP to hold in one year:
P€ (1 + i€) = E(s€/$)  P$ (1 + i$),
or:
P€ (1 + i€) = s€/$ [E(s€/$)/s€/$ )]  P$ (1 + i$)
Using absolute PPP to cancel terms and rearranging:
Relative PPP:
1 + i€ = E(s€/$)
1 + i$
s€/$
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Relative PPP
• Main idea – The difference between
(expected) inflation rates equals the
(expected) rate of change in exchange rates:
1 + i€ = E(s€/$)
1 + i$
s€/$
14
What is the evidence?
• The Law of One Price frequently does not
hold.
• Absolute PPP does not hold, at least in the
short run.
– See The Economist’s Big McCurrencies
• The data largely are consistent with Relative
PPP, at least over longer periods.
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Deviations from PPP
Simplistic model
Why does
PPP
not
hold?
Imperfect Markets
Statistical difficulties
16
Deviations from PPP
Simplistic model
Imperfect Markets
Statistical difficulties
Transportation costs
Tariffs and taxes
Consumption patterns differ
Non-traded goods & services
Sticky prices
Markets don’t work well
Construction of price indexes
- Different goods
- Goods of different qualities
17
Summary of theory #1:
.
Exp. difference in
inflation rates
1 + i€
1 + i$
Relative PPP
Expected change
in spot rate
E(s€/$)
S€/$
18
Theory #2: Interest rate parity
• Main idea: There is no fundamental advantage to
borrowing or lending in one currency over
another
• This establishes a relation between interest rates,
spot exchange rates, and forward exchange rates
– Forward market: Transaction occurs at some point in future
– BUY: Agree to purchase the underlying currency at a predetermined
exchange rate at a specific time in the future
– SELL: Agree to deliver the underlying currency at a predetermined
exchange rate at a specific time in the future
19
Example of a forward market transaction
• Suppose you will need 100,000€ in one year
• Through a forward contract, you can commit to
lock in the exchange rate
• f$/€ : forward rate of exchange
Currently, f$/€ = 1.19854
 1 € buys $1.19854
 1 $ buys 0.83435 €
• At this forward rate, you need to provide
$119,854 in 12 months.
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Interest Rate Parity
START (today)
$117,228
END (in one year)
r$=2.24%
$117,228  1.0224 = $119,854
(Invest in $)
s€/$=0.83215
$117,228  0.83215 = 97,551€
One year
(Invest in €)
f€/$=0.83435
97,551€  1.0251 = 100,000€
r€=2.51%
21
Interest rate parity
• Main idea: Either strategy gets you the
100,000€ when you need it.
• This implies that the difference in interest
rates must reflect the difference between
forward and spot exchange rates
Interest
Rate Parity:
1 + r€ = f€/$
1 + r$
s€/$
22
Interest rate parity example
• Suppose the following were true:
12 month interest
rate
U.S Dollar
Euro
2.24%
2.70%
Spot rate
1.2017 € / $
Forward rate
1.19854 € / $
– Does interest rate parity hold?
– Which way will funds flow?
– How will this affect exchange rates?
23
Evidence on interest rate parity
• Generally, it holds
• Why would interest rate parity hold better
than PPP?
– Lower transactions costs in moving currencies
than real goods
– Financial markets are more efficient that real
goods markets
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Summary of theories #1 and #2:
.
Difference in
interest rates
1 + r€
1 + r$
Interest
Rate
parity
Difference between
forward & spot rates
f€r/$
s€/$
Exp. difference in
inflation rates
1 + i€
1 + i$
Relative PPP
Expected change
in spot rate
E(s€/$)
s€/$
25
Theory #3: The Fisher condition
• Main idea: Market forces tend to allocate
resources to their most productive uses
• So all countries should have equal real rates of
interest
• Relation between real and nominal interest rates:
(1 + rNominal) = (1 + rReal)(1 + i )
(1 + rReal) = (1 + rNominal) / (1 + i )
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Example of capital market equilibrium
• Fisher condition in U.S. and France:
(1 + r$(Real)) = (1 + r$) / (1 + i$)
(1 + r€(Real)) = (1 + r€) / (1 + i€)
• If real rates are equal, then the Fisher condition
implies:
1 + r€ =
1 + r$
1 + i€
1 + i$
• The difference in interest rates is equal to the
expected difference in inflation rates
27
Summary of theories 1-3:
.
Difference in
interest rates
1 + r€
1 + r$
Interest
Rate
parity
Difference between
forward & spot rates
f€/$
s€/$
Fisher
Theory
Exp. difference in
inflation rates
1 + i€
1 + i$
Relative PPP
Expected change
in spot rate
E(s€/$)
s€/$
28
Theory #4: Expectations theory of forward
rates
• Main idea:
– The forward rate equals expected spot exchange
f€/$ = E(s€/$)
rate
Expectations theory
of forward rates:
f€/$ = E(s€/$ )
s€/$
s€/$
29
Expectations theory of forward rates
• With risk, the forward rate may not equal the spot rate
Group 1: Receive €
in six months, want $
Group 2: Contracted to
pay out € in six months
• Wait six months and
convert € to $
• Wait six months and
convert $ to €
• Sell € forward
• Buy € forward
or
or
• If Group 1 predominates, then E(s€/$) < f€/$
• If Group 2 predominates, then E(s€/$) > f€/$
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Takeaway: Summary of all four theories
.
Difference in
interest rates
1 + r€
1 + r$
Fisher
Theory
Interest
Rate
parity
Exp. difference in
inflation rates
1 + i€
1 + i$
Relative PPP
Difference between
forward & spot rates
f€/$
Exp. Theory
s€/$
of forward
rates
Expected change
in spot rate
E(s€/$)
s€/$
31