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Foreign Exchange MarketsPowerPoint Presentation

Foreign Exchange Markets

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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

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

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?

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

- “Indirect quote”:

3. Four theories

.

Fisher

Theory

Difference in

interest rates

1 + r€

1 + r$

Exp. difference in

inflation rates

1 + iSFr

1 + i$

Interest

Rate

parity

Relative PPP

Difference between

forward & spot rates

F€/$

s€/$

Expected change

in spot rate

E(s€/$)

S€/$

Exp. Theory

of forward

rates

Theory #1: Purchasing power parity

Law of One Price

Versions of

PURCHASING

POWER

PARITY

Absolute PPP

Relative PPP

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$

S€/$ = spot exchange rate

P€ = s€/$ P$

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

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 )

- 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

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 € / $1485.01 = 0.83215 €/$

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$s€/$

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$s€/$

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.

Deviations from PPP

Simplistic model

Why does

PPP

not

hold?

Imperfect Markets

Statistical difficulties

Deviations from PPP

- 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

Simplistic model

Imperfect Markets

Statistical difficulties

Summary of theory #1:

.

Exp. difference in

inflation rates

1 + i€

1 + i$

Relative PPP

Expected change

in spot rate

E(s€/$)

S€/$

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

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.

Interest Rate Parity

START (today)END (in one year)

r$=2.24%

$117,228

$117,228 1.0224 = $119,854

(Invest in $)

One year

s€/$=0.83215

f€/$=0.83435

(Invest in €)

$117,228 0.83215 = 97,551€

97,551€ 1.0251 = 100,000€

r€=2.51%

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$s€/$

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?

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

Summary of theories #1 and #2:

.

Difference in

interest rates

1 + r€

1 + r$

Exp. difference in

inflation rates

1 + i€

1 + i$

Interest

Rate

parity

Relative PPP

Difference between

forward & spot rates

f€r/$

s€/$

Expected change

in spot rate

E(s€/$)

s€/$

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 )

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$

Summary of theories 1-3:

.

Fisher

Theory

Difference in

interest rates

1 + r€

1 + r$

Exp. difference in

inflation rates

1 + i€

1 + i$

Interest

Rate

parity

Relative PPP

Difference between

forward & spot rates

f€/$

s€/$

Expected change

in spot rate

E(s€/$)

s€/$

Theory #4: Expectations theory of forward rates

- Main idea:
- The forward rate equals expected spot exchange rate
Expectations theory

of forward rates:

- The forward rate equals expected spot exchange rate

f€/$ = E(s€/$)

f€/$ = E(s€/$ )

s€/$s€/$

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€/$) > f€/$

- 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

Takeaway: Summary of all four theories

.

Fisher

Theory

Difference in

interest rates

1 + r€

1 + r$

Exp. difference in

inflation rates

1 + i€

1 + i$

Interest

Rate

parity

Relative PPP

Difference between

forward & spot rates

f€/$

s€/$

Expected change

in spot rate

E(s€/$)

s€/$

Exp. Theory

of forward

rates

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