chapter 4 nd
TRANSCRIPT
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Parity Conditions in
International Financeand Currency
Forecasting
Chapter 4
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ARBITRAGE AND THE
LAW OF ONE PRICEFive 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)
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Inflation
Changes in
Exchange
rates
Changes in
Interest
rates
PPPFE
Changes in
Forward
Rates
IRPUFR
IFE
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ARBITRAGE AND THE
LAW OF ONE PRICEA. Five Parity Conditions Linked by
the adjustment of
rates and prices
to inflation
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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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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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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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INTEREST RATE PARITY
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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INTEREST RATE PARITY
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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INTEREST RATE PARITY
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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INTEREST RATE PARITY
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