Parity Conditions in
International Finance and
Currency Forecasting
Chapter 8
1
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.
2
ARBITRAGE AND THE LAW OF
ONE PRICE
C. Five Parity Conditions Result From
These Arbitrage Activities
1.
2.
3.
4.
5.
Purchasing Power Parity (PPP)
The Fisher Effect (FE)
The International Fisher Effect
(IFE)
Interest Rate Parity (IRP)
Unbiased Forward Rate (UFR)
3
ARBITRAGE AND THE LAW OF
ONE PRICE
D. Five Parity Conditions Linked by
1.
The adjustment of various
rates and prices to inflation.
2.
The notion that money should
have no effect on real
variables (since they have been
adjusted for price changes).
4
ARBITRAGE AND THE LAW OF
ONE PRICE
E. Inflation and home currency
depreciation are:
jointly determined by the
growth of domestic money
supply relative to the growth of
domestic money demand.
5
PART II.
PURCHASING POWER PARITY
I. THE THEORY OF PURCHASING
POWER PARITY
is based on law of one price,
and the no-arbitrage condition
(internationally)
6
PURCHASING POWER PARITY
II.
ABSOLUTE PURCHASING
POWER PARITY
A.
Price levels (adjusted for
exchange rates) should be
equal between countries
B.
One unit of currency has same
purchasing power globally.
7
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.
B.
Real exchange rate stays the
same.
8
PURCHASING POWER PARITY
1. In mathematical terms:
et
e0
where et
e0
ih
if
t
= (1 + ih)t
(1 + if)t
= future spot rate
= spot rate
= home inflation
= foreign inflation
= time period
9
PURCHASING POWER PARITY
2. If purchasing power parity is
expected to hold, then the best
prediction for the one-period
spot rate should be
e1
= e0(1 + ih)1
(1 + if)1
10
PURCHASING POWER PARITY
3. A more simplified but less precise
relationship is
e1 - e0 = i h - if
e0
that is, the percentage change
should be approximately equal to
the inflation rate differential.
11
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.
12
PURCHASING POWER PARITY
B. Real Exchange Rates:
the quoted or nominal rate adjusted
for it’s country’s inflation rate
e’t
= et (1 + if)t = e0
(1 + ih)t
*real exchange rate remains constant
13
PURCHASING POWER PARITY
C. Real exchange rates
1.
If exchange rate adjust to
inflation differential, PPP
states that real exchange rates
stay the same.
2.
Competitive positions of
domestic and foreign firms
are unaffected.
14
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
15
THE FISHER EFFECT
B. 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
16
THE FISHER EFFECT
C.
D.
E.
According to the Fisher Effect,
countries with higher inflation
rates have higher interest rates.
Due to capital market
integration globally, interest
rate differentials are eroding.
Real interest rate differences
can exists due to currency risk
and country risk.
17
PART IV.
THE INTERNATIONAL FISHER
EFFECT
I. IFE STATES:
A. the spot rate adjusts to the interest
rate differential between two
countries.
B. PPP & FE ---> IFE
et
e0
= (1 + rh)t
(1 + rf)t
18
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.
19
THE INTERNATIONAL FISHER
EFFECT
C. Simplified IFE equation:
rh - rf = e 1 - e 0
e0
interest rate differential is equal to
change in the exchange rate
20
THE INTERNATIONAL FISHER
EFFECT
D. Implications if IFE
1.
Currency with the lower
interest rate expected to
appreciate relative to one
with a higher rate.
2.
Financial market arbitrage
insures interest rate differential
is an unbiased predictor of
change in future spot rate.
3.
Holds if the IR differential is
due to differences in expected
inflation.
21
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
rate differential (rh - rf) between
two countries.
22
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
23
INTEREST RATE PARITY THEORY
3.
In equilibrium, returns on
currencies will be the same
i. e. No profit will be realized
and interest rate parity
exits which can be written
(1 + rh) = F
(1 + rf)
S
24
INTEREST RATE PARITY THEORY
Interest rate parity is assured by the noarbitrage condition.
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.
25
INTEREST RATE PARITY THEORY
3. Market pressures develop:
a.
As one currency is more
demanded spot and sold
forward.
b. Inflow of funds depresses
interest rates.
c.
Parity eventually reached.
26
INTEREST RATE PARITY THEORY
C. Interest Rate Parity states:
1.
Higher interest rates on a
currency offset by forward
discounts.
2.
Lower interest rates are offset
by forward premiums.
Deviations from IRP are small and
short-lived.
Deviations may be caused by taxes,
transaction costs, capital controls.
27
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
f0(t) = et
C. Usually holds, at least in terms of the
direction (not necessarily the
magnitude).
28
PART VII.
CURRENCY FORECASTING
I. FORECASTING MODELS
A. have been created to forecast exchange
rates in addition to parity conditions.
B. Two types of forecast:
1.
Market-based
2.
Model-based
29
CURRENCY FORECASTING
1. MARKET-BASED FORECASTS
Derived from market indicators.
A. the current forward rate contains implicit
information about exchange rate
changes for one year.
B. Interest rate differentials may be used to
predict exchange rates beyond one year.
30
CURRENCY FORECASTING
2. MODEL-BASED FORECASTS
Employ fundamental and technical
analysis.
A. Fundamental relies on key
macroeconomic variables and policies
which most like affect exchange rates.
B. Technical relies on use of
1. Historical volume and price data
2. Charting and trend analysis
31