parity condition in international finance · five parity conditions result from arbitrage...
TRANSCRIPT
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١
Parity Conditions in
International Finance and
Currency Forecasting
Chapter 4
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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)
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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.
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ARBITRAGE AND THE LAW
OF ONE PRICE
C. Five Parity Conditions Linked by
The adjustment of rates and prices to inflation
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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.
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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.
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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.
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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
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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
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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.
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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.
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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 $.529e =
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PART III.
THE FISHER EFFECT
I. THE FISHER EFFECT
states that nominal interest rates (r) are a function of the real interest rate (a) and a premium (i) for inflation expectations.
R = a + i
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١٤
PART IV. THE INTERNATIONAL
FISHER EFFECT
A. Real Rates of Interest
1. Should tend toward equality
everywhere through arbitrage.
2. With no government interference
nominal rates vary by inflation
differential or
rh - rf = ih - if
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١٥
THE INTERNATIONAL FISHER
EFFECT
B. According to the IFE,
countries with higher inflation rates have higher interest rates.
C. Due to capital market integration globally, interest rate differentials are eroding.
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١٦
THE INTERNATIONAL FISHER
EFFECT
I. IFE STATES:
A. the spot rate adjusts to the interest rate differential between two countries.
B. IFE = PPP + FE
et = (1 + rh)t
e0 (1 + rf)t
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١٧
THE INTERNATIONAL FISHER
EFFECT
B. Fisher postulated:
1. The nominal interest rate differential should reflect the inflation rate differential.
2. Expected rates of return are equal in the absence of government intervention.
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١٨
THE INTERNATIONAL FISHER
EFFECT
C. Simplified IFE equation:
rh - rf = et - e0
e0
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THE INTERNATIONAL FISHER
EFFECT
D. Implications if IFE1. Currency with the lower
interest rate expected to appreciate relative to onewith a higher rate.
2. Financial market arbitrage:insures interest rate differential
is an unbiased predictor of change in future spot rate.
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٢٠
The International Fisher Effect
If the ¥/$ 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 =
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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.
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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
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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
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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.
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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.
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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=
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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.
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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