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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.
ARBITRAGE AND THE LAW OF ONE PRICE
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)
ARBITRAGE AND THE LAW OF ONE PRICE
D. Five Parity Conditions Linked by
The adjustment of variousrates and prices to inflation.
ARBITRAGE AND THE LAW OF ONE PRICE
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.
ARBITRAGE AND THE LAW OF ONE PRICE
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
PURCHASING POWER PARITY
II. ABSOLUTE PURCHASING POWER PARITY
B. One unit of currency has same purchasing
power globally.
PURCHASING POWER PARITY
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.
PURCHASING POWER PARITY
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
PURCHASING POWER PARITY
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
PURCHASING POWER PARITY
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
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.
PURCHASING POWER PARITY
B. Real Exchange Rates:the quoted or nominal rate adjusted for a country’s inflation rate is
th
tf
tt i
iee
)1(
)1('
PURCHASING POWER PARITY
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
THE INTERNATIONAL FISHER EFFECT
B. Fisher postulated1. The nominal interest rate
differential should reflect the inflation rate differential.
THE INTERNATIONAL FISHER EFFECT
B. Fisher also postulated that2. Expected rates of return are
equal in the absence of
government
intervention.
THE INTERNATIONAL FISHER EFFECT
C. Simplified IFE equation:
(if rf is relatively small)
1 0
0h f
e er r
e
THE INTERNATIONAL FISHER EFFECT
D. Implications of IFE1. Currency with the lower
interest rate is expected to appreciate relative to the one
with a higher rate.
THE INTERNATIONAL FISHER EFFECT
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
INTEREST RATE PARITY THEORY
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
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 country
with a more attractive rate.
INTEREST RATE PARITY THEORY
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.
INTEREST RATE PARITY THEORY
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