chapter 4 nd


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3

Inflation

Changes in

Exchange

rates

Changes in

Interest

rates

PPPFE

Changes in

Forward

Rates

IRPUFR

IFE


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4

ARBITRAGE AND THE

LAW OF ONE PRICEA. Five Parity Conditions Linked by

the adjustment of

rates and prices

to inflation


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5

INFLATION

(Ms) > (MD)


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ARBITRAGE AND THE

LAW OF ONE PRICEB. Inflation and home currency

depreciation are:

1. jointly determined by thegrowth of domestic moneysupply (Ms) and

2. relative to the growth ofdomestic money demand (MD).


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PART II.PURCHASING POWER

PARITY

I. THE THEORY OF PURCHASING

POWER PARITY

states that spot exchange ratesbetween currencies will change tothe differential in inflation ratesbetween countries.


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Purchasing Power Parity:

ConditionsIn order to exist PPP we assume:

1. All goods and services are tradable

2. Transportation and other Trading costs

are zero

3. Consumers in all countries consume thesame proportions of goods and services


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PART I.ARBITRAGE AND THE LAW

OF ONE PRICEII. THE LAW OF ONE PRICE

A. Law states:

Identical goods sell for thesame price worldwide.

B. Theoretical basis:If the price after exchange-rate

adjustment was not equal,arbitrage worldwide ensures thateventually it will.

C. Absolute Purchasing Power Parity


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PURCHASING POWER

PARITYIII. RELATIVE PURCHASING

POWER PARITY

A. states that the exchange rate of

one currency against anotherwill adjust to reflect changesin

the price levels of the twocountries.


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PURCHASING POWER

PARITY1. In mathematical terms:

where et = future spot ratee0 = spot rateih = home inflation expectedif = foreign inflation exp

t = time period

01

1

t

ht

t

f

iee i


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PURCHASING POWER

PARITY2. If purchasing power parity is

expected to hold, then thebest

prediction for the one-periodspot rate should be

0

1

1

t

h

t t

f

i

e e i


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13

PURCHASING POWER

PARITY3. A more simplified but less precise

relationship is

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

0

0

th f

e ei i

e


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PURCHASING POWER

PARITY4. PPP says

the currency with the higherinflation rate is expected todepreciate relative to the

currency with the lower rate ofinflation.


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Sample Problem

Projected inflation rates for the U.S. and Germanyfor the next twelve months are 10% and 4%,respectively. If the current exchange rate is

$.50/dm, what should the future spot rate be at theend of next twelve months?

0

1

1

t

h

t t

f

ie e

i

1

1 1

1.10.50

1.04

e

1 .50(1.0577)e

1$.529e


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16

PART III.

THE FISHER EFFECTI. THE FISHER EFFECT

states that nominal interest rates(r) are a function of the realinterest rate (a) and a premium (i)

for inflation expectations.R = a + i


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PART IV. THEINTERNATIONAL FISHER

EFFECTA. Real Rates of Interest

1. Should tend toward equality

everywhere through arbitrage.

2. With no government interference

nominal rates vary by inflation

differential or

rh - rf = ih - if


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THE INTERNATIONAL

FISHER EFFECTB. According to the IFE,

countries with higherexpected inflation rateshave higher interest rates.


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THE INTERNATIONAL

FISHER EFFECTII. IFE STATES:

A. the spot rate adjusts to the interest rate

differential between two countries.

B. IFE = PPP + FE

01

1

t

ht

t

f

re

e r


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THE INTERNATIONAL

FISHER EFFECTC. Fisher postulated

1. The nominal interest rate

differential should reflectthe inflation rate differential.


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THE INTERNATIONAL

FISHER EFFECTD. Simplified IFE equation:

0

0

th f

e er re


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THE INTERNATIONAL

FISHER EFFECTE. Implications if IFE is at work:

1. Currency with the lowerinterest rate expected toappreciate relative to onewith a higher rate.

The International Fisher


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The International FisherEffect

If the /$ spot rate is 108/$ and the interestrates in Tokyo and New York are 6% and 12%,

respectively, what is the future spot rate two

years from now?

0

1

1

t

h

t t

f

re er

2

2 21.061081.12

e

2

1.1236108

1.2544

e

296.74 / $e

PART V


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PART V.INTEREST RATE PARITY

THEORY

I. INTRODUCTION

A. The Theory states:

the forward rate (F) differs fromthe spot rate (S) at equilibrium

by an amount equal to the interestdifferential (rh - rf) between two

countries.


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INTEREST RATE PARITY

THEORYB. The forward premium or discount equals

the interest rate differential.

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

where rh = the home raterf = the foreign rate

F = the forward rate

S = the spot rate


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THEORYC. In equilibrium, returns on currencies willbe the same

i. e. No profit will be realized andinterest rate parity exists which can be written

1

1

h

f

rFS r


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THEORYD. Covered Interest Arbitrage

1. Conditions required:

interest rate differential doesnot equal the forwardpremium or discount.

2. Funds will move to a countrywith a more attractive rate.


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THEORY3. Market pressures develop:

a. As one currency is more

demanded spot and soldforward.

b. Inflow of funds depressesinterest rates.

c. Parity eventually reached.


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INTEREST RATE PARITYIf the Swiss franc is $.68/SF on the spot market and

the annualized interest rates in the U.S. and Switzerland,respectively, are 7.94% and 2%, what is the 180 day

forward rate under parity conditions?

01

1

ht

f

rf er

180

.07941

2

.68 .021

2

f

180 $.70/f SF


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THEORYE. Summary:

Interest Rate Parity states

1. Higher interest rates on acurrency offset by forwarddiscounts.

2. Lower interest rates are offsetby forward premiums.


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PART VI. THE RELATIONSHIPBETWEEN THE FORWARD AND THE

FUTURE SPOT RATE

I. THE UNBIASED FORWARD RATE

A. States that if the forward rate is

unbiased, then it should reflect the

expected future spot rate.

B. Stated asft = et

chapter 4 nd

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