Parity Conditions in
International Finance and
Currency Forecasting
Chapter 4
١
ARBITRAGE AND THE LAW
OF ONE PRICE
Five Parity Conditions Result From
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)
٢
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.
٣
ARBITRAGE AND THE LAW
OF ONE PRICE
C. Five Parity Conditions Linked by
The adjustment of rates and prices
to inflation
٤
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 of
domestic money demand.
٥
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.
٦
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.
٧
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
٨
PURCHASING POWER PARITY
2. If purchasing power parity is
expected to hold, then the best
prediction for the one-period
spot rate should be
et
= e0(1 + ih)t
(1 + if)t
٩
PURCHASING POWER PARITY
3. A more simplified but less precise
relationship is
et - e0 = ih - i f
e0
that is, the percentage change
should be approximately equal to
the inflation rate differential.
١٠
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.
١١
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?
et = e0
(1 +
(1 +
e1 = .5 0
ih
)
if
)
t
t
(1 . 1 0 )
1
(1 . 0 4 )
1
e1 = .50(1.0577)
e1 = $.5 29
١٢
PART III.
THE FISHER EFFECT
I. THE FISHER EFFECT
states that nominal interest rates (r) are
a function of the real interest rate (a)
and a premium (i) for inflation
expectations.
R = a + i
١٣
PART IV. THE INTERNATIONAL
FISHER EFFECT
A. Real Rates of Interest
1. Should tend toward equality
everywhere through arbitrage.
2. With no government interference
nominal rates vary by inflation
differential or
rh - rf = ih - if
١٤
THE INTERNATIONAL FISHER
EFFECT
B.
According to the IFE,
countries with higher inflation
rates have higher interest rates.
C.
Due to capital market
integration globally, interest
rate differentials are eroding.
١٥
THE INTERNATIONAL FISHER
EFFECT
I. IFE STATES:
A. the spot rate adjusts to the interest
rate differential between two countries.
B. IFE = PPP + FE
et
e0
= (1 + rh)t
(1 + rf)t
١٦
THE INTERNATIONAL FISHER
EFFECT
B. Fisher postulated:
1. The nominal interest rate
differential should reflect the
inflation rate differential.
2. Expected rates of return are
equal in the absence of
government intervention.
١٧
THE INTERNATIONAL FISHER
EFFECT
C. Simplified IFE equation:
rh - rf = et - e 0
e0
١٨
THE INTERNATIONAL FISHER
EFFECT
D. Implications if IFE
1. Currency with the lower
interest rate expected to
appreciate relative to one
with a higher rate.
2.
Financial market arbitrage:
insures interest rate differential
is an unbiased predictor of
change in future spot rate.
١٩
The International Fisher Effect
If the ¥/$ 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?
et = e0
(1 +
rh
)
(1 + r )
t
f
1 .0 6 )
(
= 108
2
(1 .1 2 )
2
e2
t
e2
1 .1 2 3 6 )
(
= 108
(1 .2 5 4 4 )
e2 = ¥96.74 / $
٢٠
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.
٢١
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
٢٢
INTEREST RATE PARITY
THEORY
3.
In equilibrium, returns on
currencies will be the same
i. e. No profit will be realized
and interest parity exists
which can be written
(1 + rh) = F
(1 + rf)
S
٢٣
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.
٢٤
INTEREST RATE PARITY
THEORY
3. Market pressures develop:
a.
b.
c.
As one currency is more
demanded spot and sold
forward.
Inflow of funds depresses
interest rates.
Parity is eventually reached.
٢٥
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
1 + rh )
(
conditions?
f = e
0
t
f
1 8 0
=
(1
.6 8
f180 = $.70/ SF
+ r
f
)
.0 7 9 4 

1
+


2


.0 2 

1
+


2


٢٦
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.
٢٧
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
٢٨