1 1. the foreign exchange market some currency rates as of may 21, 2004: per u.s. dollar: brazil...

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1. The Foreign Exchange MarketSome currency rates as of May 21, 2004:

Per U.S. dollar:

Brazil (Real) 3.1939

Mexico (Peso) 11.5754

Japan (Yen) 112.2839

Indonesia (Rupiah) 89066

South Africa (Rand) 6.7295

United Kingdom (Pound) 0.5593

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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




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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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Definitionsr$ : 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.

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

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 rate

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 PPPExtension 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 )

S€/$ = P€ / PUS

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Absolute PPPIf 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:

P€ = s€/$ P$

1 + i€ = E(s€/$)1 + i$ s€/$

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Relative PPPMain idea – The difference between (expected) inflation rates equals the (expected) rate of change in exchange rates:

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

Why doesPPPnot

hold?

Why doesPPPnot

hold?

Simplistic model

Imperfect Markets

Statistical difficulties

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Deviations from PPP

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:.


1 + i€

1 + i$


E(s€/$)S€/$

Relative PPP

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Theory #2: Interest rate parityMain 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 futureBUY: Agree to purchase the underlying currency at a predetermined exchange rate at a specific time in the futureSELL: 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 transactionSuppose 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)$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 parityMain 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€/$

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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?

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 parityGenerally, 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:.


1 + r€

1 + r$


1 + i€

1 + i$


f€r/$

s€/$


E(s€/$)s€/$


Rateparity

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Theory #3: The Fisher conditionMain 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

1 + r€ = 1 + i€1 + r$ 1 + i$

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Summary of theories 1-3:.


1 + r€

1 + r$


1 + i€

1 + i$


f€/$

s€/$


E(s€/$)s€/$

FisherTheory


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:

f€/$ = E(s€/$)

f€/$ = E(s€/$ ) s€/$ s€/$

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Expectations theory of forward ratesWith 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€/$) > f€/$

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.


1 + r€

1 + r$


1 + i€

1 + i$


f€/$

s€/$


E(s€/$)s€/$

FisherTheory


Rateparity

Exp. Theory of forward

rates

1 1. the foreign exchange market some currency rates as of may 21, 2004: per u.s. dollar: brazil...

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