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Foreign Exchange Markets
Dr Bryan Mills
Based on http://faculty.washington.edu/karpoff/FIN%20509/FIN509_session7.ppt
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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
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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
Reuters 19/4/2010 Sell buy
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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?
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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 1 $ buys 0.83215 €– “Direct quote”: s$/€ = 1.2017 1 € buys $1.2017
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3. Four theories
.
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Difference ininterest rates
1 + r€
1 + r$
Exp. difference ininflation rates
1 + iSFr
1 + i$
Difference betweenforward & spot rates
F€/$
s€/$
Expected changein spot rate
E(s€/$)S€/$
FisherTheory
Relative PPPInterest
Rateparity
Exp. Theory of forward
rates
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Theory #1: Purchasing power parity
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Versions ofPURCHASING
POWERPARITY
Versions ofPURCHASING
POWERPARITY
Law of One Price
Absolute PPP
Relative PPP
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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,..)
– ExamplePrice of wheat in France (per bushel): P€
Price of wheat in U.S. (per bushel): P$
S€/$ = spot exchange rate9
P€ = s€/$ P$
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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$/€ = 1.2017)
Dollar equivalent priceof wheat in France = s$/€ x p€
= 1.2017 $/€ x 3.45 € = $4.15
When law of one price does not hold, supply and demand forces help restore the equality
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Absolute PPP• Extension of law of one price to a basket of goods
• Absolute PPP examines price levels– Apply the law of one price to a basket of goods with
price P€ and PUS (use upper-case P for the price of the basket):
where P€ = i (wFR,i p€,i )PUS = i (wUS,i pUS,i )
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S€/$ = P€ / PUS
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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 € / $1485.01 = 0.83215 €/$
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Relative PPP
Absolute PPP:
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$)
Using absolute PPP to cancel terms and rearranging:
Relative PPP:13
P€ = s€/$ P$
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:
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1 + i€ = E(s€/$)1 + i$ s€/$
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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
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Why doesPPPnot
hold?
Why doesPPPnot
hold?
Simplistic model
Imperfect Markets
Statistical difficulties
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Deviations from PPP
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Simplistic model
Imperfect Markets
Statistical difficulties
Transportation costsTariffs and taxesConsumption patterns differNon-traded goods & services
Sticky pricesMarkets don’t work well
Construction of price indexes- Different goods- Goods of different qualities
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Summary of theory #1:
.
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Exp. difference ininflation rates
1 + i€
1 + i$
Expected changein spot rate
E(s€/$)S€/$
Relative PPP
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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
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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$/€ : forward rate of exchangeCurrently, f$/€ = 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 ParitySTART (today) END (in one year)
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$117,228 $117,228 1.0224 = $119,854
r$=2.24%
$117,228 0.83215 = 97,551€
s€/$=0.83215
r€=2.51%
97,551€ 1.0251 = 100,000€
f€/$=0.83435One year
(Invest in $)
(Invest in €)
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Interest rate parity
• Main idea: Either strategy gets you the 100,000€ when you need it.
• This implies that the difference in interest rates must reflect the difference between forward and spot exchange rates
Interest Rate Parity:
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1 + r€ = f€/$
1 + r$ s€/$
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Interest rate parity example
• Suppose the following were true:
– Does interest rate parity hold?– Which way will funds flow?– How will this affect exchange rates?
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U.S Dollar Euro
12 month interest rate
2.24% 2.70%
Spot rate 1.2017 € / $
Forward rate 1.19854 € / $
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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:
.
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Difference ininterest rates
1 + r€
1 + r$
Exp. difference ininflation rates
1 + i€
1 + i$
Difference betweenforward & spot rates
f€r/$
s€/$
Expected changein spot rate
E(s€/$)s€/$
Relative PPPInterest
Rateparity
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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$)(1 + r€(Real)) = (1 + r€) / (1 + i€)
• If real rates are equal, then the Fisher condition implies:
• The difference in interest rates is equal to the expected difference in inflation rates
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1 + r€ = 1 + i€1 + r$ 1 + i$
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Summary of theories 1-3:
.
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Difference ininterest rates
1 + r€
1 + r$
Exp. difference ininflation rates
1 + i€
1 + i$
Difference betweenforward & spot rates
f€/$
s€/$
Expected changein spot rate
E(s€/$)s€/$
FisherTheory
Relative PPPInterest
Rateparity
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Theory #4: Expectations theory of forward rates
• Main idea:– The forward rate equals expected spot exchange
rate
Expectations theory of forward rates:
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f€/$ = E(s€/$)
f€/$ = E(s€/$ ) s€/$ s€/$
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Expectations theory of forward rates• With risk, the forward rate may not equal the spot rate
• If Group 1 predominates, then E(s€/$) < f€/$ • If Group 2 predominates, then E(s€/$) > f€/$ 30
Group 1: Receive € in six months, want $
• Wait six months and convert € to $
or• Sell € forward
Group 1: Receive € in six months, want $
• Wait six months and convert € to $
or• Sell € forward
Group 2: Contracted to pay out € in six months
• Wait six months and convert $ to €
or• Buy € forward
Group 2: Contracted to pay out € in six months
• Wait six months and convert $ to €
or• Buy € forward
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Takeaway: Summary of all four theories.
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Difference ininterest rates
1 + r€
1 + r$
Exp. difference ininflation rates
1 + i€
1 + i$
Difference betweenforward & spot rates
f€/$
s€/$
Expected changein spot rate
E(s€/$)s€/$
FisherTheory
Relative PPPInterest
Rateparity
Exp. Theory of forward
rates