1 chapter 4 parity conditions and currency forecasting

1

CHAPTER 4

PARITY CONDITIONS AND

CURRENCY FORECASTING

PART I. ARBITRAGE AND THE LAW OF ONE PRICE

I. THE LAW OF ONE PRICEA. Law states:

Identical goods sell for the same price worldwide.

ARBITRAGE AND THE LAW OF ONE PRICE

B. Theoretical basis:

If the price after exchange-rate

adjustment were not equal,

arbitrage in the goods worldwide ensures

eventually it will.


C. Five Parity Conditions Result From These Arbitrage Activities

1. Purchasing Power Parity (PPP)2. The Fisher Effect (FE)3. The International Fisher Effect

(IFE)4. Interest Rate Parity (IRP)5. Unbiased Forward Rate (UFR)


D. Five Parity Conditions Linked by

The adjustment of variousrates and prices to inflation.


E. Inflation and home currency depreciation:

1. jointly determined by the growth of domestic money supply;

2. Relative to the growth of

domestic money demand.


F. THE LAW OF ONE PRICE

- enforced by international

arbitrage.

PART II. PURCHASING POWER PARITY

I. THE THEORY OF PURCHASING

POWER PARITY: states that spot exchange rates between currencies will change to the differential in inflation rates between countries.

PURCHASING POWER PARITY

II. ABSOLUTE PURCHASING POWER PARITY

A. Price levels adjusted for

exchange rates should be

equal between countries


II. ABSOLUTE PURCHASING POWER PARITY

B. One unit of currency has same purchasing

power globally.


III. RELATIVE PURCHASING POWER PARITY

A. states that the exchange rate of one currency against another will adjust to

reflect changes in the price levels of the two countries.


1. In mathematical terms:

where et = future spot rate

e0 = spot rate

ih = home inflation

if = foreign inflation t = the time period

tf

tht

i

i

e

e

1

1

0


2. If purchasing power parity is expected to hold, then the bestprediction for the one-periodspot rate should be

tf

th

ti

iee

1

10


3. A more simplified but less precise relationship is

that is, the percentage change should be approximately equal to the inflation rate differential.

fht iie

e

0


4. PPP says

the currency with the higher inflation rate is expected to depreciate relative to the

currency with the lower rate of inflation.


B. Real Exchange Rates:the quoted or nominal rate adjusted for a country’s inflation rate is

th

tf

tt i

iee

)1(

)1('


C. Real exchange rates1. If exchange rates adjust to inflation differential, PPP states that real exchange rates stay the same.

PART III.THE FISHER EFFECT (FE)

I. THE FISHER EFFECTstates that nominal interest rates (r) are a function of the real interest rate (a) and a premium (i) for inflation expectations.

R = a + i

THE FISHER EFFECT

B. Real Rates of Interest1. Should tend toward equality

everywhere through arbitrage.

2. With no government interference nominal rates vary by inflation differential or

rh - rf = ih - if

PART IV. THE INTERNATIONAL FISHER EFFECT (IFE)

I. IFE STATES:A. the spot rate adjusts to the interest rate differential between two countries.

THE INTERNATIONAL FISHER EFFECT

IFE = PPP + FE

tf

tht

r

r

e

e

)1(

)1(

0


B. Fisher postulated1. The nominal interest rate

differential should reflect the inflation rate differential.


B. Fisher also postulated that2. Expected rates of return are

equal in the absence of

government

intervention.


C. Simplified IFE equation:

(if rf is relatively small)

1 0

0h f

e er r

e


D. Implications of IFE1. Currency with the lower

interest rate is expected to appreciate relative to the one

with a higher rate.


D. Implications of IFE

2. Financial market arbitrage:

insures interest rate differential is an unbiased predictor of change in

future spot rate.

PART VI. INTEREST RATE PARITY THEORY

I. INTRODUCTION

A. The Theory states:

the forward rate (F) differs from the spot rate (S) at equilibrium by an amount

equal to the interest differential (rh - rf) between two countries.

INTEREST RATE PARITY THEORY

2. The forward premium or

discount equals the interest

rate differential.

(F - S)/S = (rh - rf)

where rh = the home rate

rf = the foreign rate


3. In equilibrium, returns oncurrencies will be the samei. e. No profit will be realizedand interest parity existswhich can be written

1

1h

f

rF

S r


B. Covered Interest Arbitrage

1. Conditions required:

interest rate differential does

not equal the forward

premium or discount.

2. Funds will move to a country

with a more attractive rate.


3. Market pressures develop:a. As one currency is more demanded

spot and sold forward.

b. Inflow of fund depresses interest rates.

c. Parity eventually reached.


C. Summary:Interest Rate Parity states:

1. Higher interest rates on a

currency offset by forward discounts.

2. Lower interest rates are

offset by forward premiums.

PART VI. THE RELATIONSHIP BETWEEN THE

FORWARD AND THE FUTURE SPOT RATE

I. THE UNBIASED FORWARD RATEA. States that if the forward rate is unbiased, then it should reflect the expected future spot rate.

B. Stated asft = et

1 chapter 4 parity conditions and currency forecasting

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