١

Parity Conditions in

International Finance and

Currency Forecasting

Chapter 4

٢

ARBITRAGE AND THE LAW

OF ONE PRICE

Five Parity Conditions Result From 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)

٣

PART I. ARBITRAGE AND THE LAW OF

ONE PRICE

I. THE LAW OF ONE PRICE

A. Law states:Identical goods sell for the same price worldwide.

B. Theoretical basis:If the price after exchange-rate adjustment were not equal, arbitrage in the goods worldwide ensures eventually it will.

٤

ARBITRAGE AND THE LAW

OF ONE PRICE

C. Five Parity Conditions Linked by

The adjustment of rates and prices to inflation

٥

ARBITRAGE AND THE LAW

OF ONE PRICE

D. Inflation and home currency depreciation are:

1. Jointly determined by the growth of domestic money supply (Ms) and

2. Relative to the growth ofdomestic money demand.

٦

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.

٧

PURCHASING POWER PARITY

II.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.

٨

PURCHASING POWER PARITY

1. In mathematical terms:

et = (1 + ih)t

e0 (1 + if)t

where et = future spot ratee0 = spot rateih = home inflationif = foreign inflationt = time period

٩

PURCHASING POWER PARITY

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

et = e0(1 + ih)t

(1 + if)t

١٠

PURCHASING POWER PARITY

3. A more simplified but less precise

relationship is

et - e0 = ih - ife0

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

١١

PURCHASING POWER PARITY

4. PPP says

the currency with the higher inflation rate is expected to depreciate relative to the currency with the lower rate of inflation.

١٢

Sample Problem

� Projected inflation rates for the U.S. and Germany for 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 the end of next twelve months?

( )( )0

1

1

t

h

t t

f

ie e

i

+=

+

( )( )

1

1 1

1 . 1 0. 5 0

1 . 0 4e =

1 .50(1.0577)e =

1 $.529e =

١٣

PART III.

THE FISHER EFFECT

I. THE FISHER EFFECT

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

R = a + i

١٤

PART IV. THE INTERNATIONAL

FISHER EFFECT

A. 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

١٥

THE INTERNATIONAL FISHER

EFFECT

B. According to the IFE,

countries with higher inflation rates have higher interest rates.

C. Due to capital market integration globally, interest rate differentials are eroding.

١٦

THE INTERNATIONAL FISHER

EFFECT

I. IFE STATES:

A. the spot rate adjusts to the interest rate differential between two countries.

B. IFE = PPP + FE

et = (1 + rh)t

e0 (1 + rf)t

١٧

THE INTERNATIONAL FISHER

EFFECT

B. Fisher postulated:

1. The nominal interest rate differential should reflect the inflation rate differential.

2. Expected rates of return are equal in the absence of government intervention.

١٨

THE INTERNATIONAL FISHER

EFFECT

C. Simplified IFE equation:

rh - rf = et - e0

e0

١٩

THE INTERNATIONAL FISHER

EFFECT

D. Implications if IFE1. Currency with the lower

interest rate expected to appreciate relative to onewith a higher rate.

2. Financial market arbitrage:insures interest rate differential

is an unbiased predictor of change in future spot rate.

٢٠

The International Fisher Effect

If the ¥/$ spot rate is ¥108/$ and the interest

rates 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 e

r

+=

+

( )( )

2

2 2

1.06108

1.12e =

( )( )2

1 .1236108

1 .2544e =

2 ¥96.74 / $e =

٢١

PART V.

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.

٢٢

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

٢٣

INTEREST RATE PARITY

THEORY

3. In equilibrium, returns on

currencies will be the same

i. e. No profit will be realizedand interest parity existswhich can be written(1 + rh) = F(1 + rf) S

٢٤

INTEREST RATE PARITY

THEORY

B. Covered Interest Arbitrage

1. Conditions required:interest rate differential does not equal the forward premium or discount.

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

٢٥

INTEREST RATE PARITY

THEORY

3. Market pressures develop:

a. As one currency is moredemanded spot and soldforward.

b. Inflow of funds depressesinterest rates.

c. Parity is eventually reached.

٢٦

INTEREST RATE PARITY

If 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? ( )( )0

1

1

h

t

f

rf e

r

+=

+

1 8 0

. 0 7 9 41

2. 6 8

. 0 21

2

f

+ =

+

180 $.70/f SF=

٢٧

INTEREST RATE PARITY

THEORY

C. Summary:

Interest Rate Parity states:

1. Higher interest rates on a currency offset by forwarddiscounts.

2. Lower interest rates are offsetby forward premiums.

٢٨

PART VI.

THE RELATIONSHIP BETWEEN 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 as

ft = et