International Parity
Relationships and Forecasting
Foreign Exchange Rates
6
Chapter Six
Chapter Objective:
This chapter examines several key international
parity
p
y relationships,
p , such as interest rate parity
p y and
purchasing power parity.
6-0
Chapter Outline
Interest
InterestRate
RateParity
Parity

Covered Interest
Arbitrage
Purchasing
Purchasing
Power
Power
Parity
Parity
IRP and Exchange Rate
Determination
the Real
Exchange Rate
Reasons
for
Deviations
from
IRP
Evidence on Purchasing Power
Parity

PPP
Deviations
and
Fisher
The
The
Fisher
Fisher
Effects
Effects
Effects



International
Forecasting
ForecastingExchange
Fisher
Exchange
Effects
Rates
Rates

Purchasing
Power
Parity
 The
Fisher Market
EffectsApproach
 Efficient



The
Fisher
F Fundamental
Forecasting
i Effects
E
Exchange
h
Rates
R
Approach
Forecasting
Exchange Rates
 Technical Approach

Performance of the Forecasters
6-1
1
Interest Rate Parity




Interest Rate Parity Defined
Covered Interest Arbitrage
Interest Rate Parity & Exchange Rate
Determination
Reasons for Deviations from Interest Rate Parity
6-2
Interest Rate Parity Defined



IRP is an “no arbitrage” condition.
If IRP did not hold, then it would be possible for a
trader to make unlimited amounts of money
exploiting the arbitrage opportunity.
Since we don’t typically observe persistent
arbitrage conditions,
conditions we can safely assume that
IRP holds.…almost all of the time!
6-3
2
Variable Definitions
iH : Interest Rate in the home country
iF : Interest Rate in the foreign country
S = Current spot rate for the foreign currency (in direct quote)
F = 1 year forward rate for the foreign currency (in direct quote)
FPH = one year forward premium from the home country’s
viewpoint = (F-S) / S
FPF = one year forward premium from the foreign country’s
viewpoint = (S- F) / F or (1/ FPH – 1)
iCH : Covered rate of interest, from the home country’s viewpoint
iCF : Covered rate of interest, from the foreign country’s
viewpoint
(1 + i )
F$/£ = S$/£ × (1 + i$)
£
6-4
Interest Rate Parity Carefully Defined
Consider two alternative one-year investments for $1
1.
You could invest in the US at iH. Future value of this investment
in $ will be: $1 × (1 + iH) = (1 + iH)
2.
Or you could convert $1 into the foreign currency at the going
spot rate (S) and invest 1/S in the foreign country at iF whose
future value will be: [1/S × (1 + iH)]. In order to eliminate any
exchange rate risk, you will have to sell this amount at forward
rate (F) to get you money back in $: F x [1/S × (1 + iH)]
Since these investments have the same risk, they must have
the same future value (otherwise an arbitrage would exist)
(1 + i$)
F
F
=
S
×
$/
£
$/
£
(1 + iF) ×
= (1 + iH)
(1 + i£)
6-5
S
3
Interest Rate Parity Defined
Formally,
y,
1 + iH F
=
S
1 + iF
1 + iH
1 + iF
Or
-1
=
F–S
S
= FP
IRP is sometimes approximated as
iH – i F ≈ F – S
S
6-6
Interest Rate Parity Carefully Defined

Depending upon how you quote the exchange
rates, direct (S, F) or indirect (SI, FI), we have:
1 + iF
FI
=
1 + iH
SI
or
1 + iH F
=
1 + iF
S
…so
so be a bit caref
carefull about
abo t that.
that
6-7
4
Interest Rate Parity Carefully Defined

No matter how you quote the exchange rate (direct or
indirect) to find a forward rate, increase the dollars
by the dollar rate and the foreign currency by the
foreign currency rate:
FI = SI ×
1 + iF
1 + iH
or
F= S×
1 + iH
1 + iF
…be careful—it’s easy to get this wrong.
6-8
Covered Rate of Interest
Home Country’s viewpoint (iCH) =
(1 + iF) x (1 + FPH ) - 1
F i Country’s
Foreign
C
’ viewpoint
i
i (i
( CF) =
(1 + iH) x (1 + FPFF$/)£ -=1S$/£ × (1 + i$)
6-9
(1 + i£)
5
IRP & Covered Interest Arbitrage (CIA)
CIA is possible when:
iCH > iH
iCF > iF
When CIA is possible, iH, iF , and FP will have
to adjust to eliminate arbitrage.
IRP holds when CIA is not possible:
iCH = iH
(1 + i$)
iCF = iF F$/£ = S$/£ × (1
+i )
£
6-10
IRP and Covered Interest Arbitrage
If IRP failed to hold,, an arbitrage
g would exist. It is
easiest to see this in the form of an example.
Consider the following set of foreign and domestic
interest rates and spot and forward exchange rates.
Spot exchange rate for GBP
S = $2.0000
$2 0000
360-day forward rate for GBP
F = $1.9700
US interest rate
iH = 5.00%
British interest rate
iF =
8.00%
6-11
6
IRP and Covered Interest Arbitrage
If IRP failed to hold,, an arbitrage
g would exist. It is
easiest to see this in the form of an example.
Consider the following set of foreign and domestic
interest rates and spot and forward exchange rates.
Spot exchange rate for GBP
S = $2.0000
$2 0000
360-day forward rate for GBP
F = $1.9100
US interest rate
iH = 5.00%
British interest rate
iF =
8.00%
6-12
IRP and Covered Interest Arbitrage
6-13
7
IRP and Covered Interest Arbitrage
If IRP failed to hold,, an arbitrage
g would exist. It is
easiest to see this in the form of an example.
Consider the following set of foreign and domestic
interest rates and spot and forward exchange rates.
Spot exchange rate for BP
S = $2.0000
$2 0000
360-day forward rate for BP
F = $2.0400
US interest rate
iH = 8.00%
British interest rate
iF =
4.00%
6-14
IRP and Covered Interest Arbitrage
If IRP failed to hold,, an arbitrage
g would exist. It is
easiest to see this in the form of an example.
Consider the following set of foreign and domestic
interest rates and spot and forward exchange rates.
Spot exchange rate for BP
S = $2.000
$2 000
360-day forward rate for BP
F = $2.090
US interest rate
iH = 8.00%
British interest rate
iF =
4.00%
6-15
8
Reasons for Deviations from IRP
Transactions Costs


The interest rate available to an arbitrageur for borrowing,
ib may exceed the rate he can lend at, il.
There may be bid-ask spreads to overcome, Fb/Sa < F/S
Capital Controls

Governments sometimes restrict import and export of
money through taxes or outright bans.
6-16
Reasons for Deviations from IRP
6-17
9
Purchasing Power Parity





The concept of Absolute and Relative Purchasing
Power Parity (PPP)
PPP and Exchange Rate Determination
PPP Deviations and the Real Exchange Rate
Consequences of PPP Violations
Evidence on PPP
6-18
Absolute Purchasing Power Parity




A dollar should buy the same quantities of goods
and services in all countries
According to absolute PPP, in the long run,
currencies should move towards the rate which
equalizes the prices of an identical basket of
goods and services in each country
The exchange rate (direct quote) between two (S)
currencies should equal the ratio of the countries’
price levels in the home (PH) and foreign (PF)
country: S = (PH / (PF)
Examples
6-19
10
Absolute Purchasing Power Parity and
Exchange Rate Determination
PH
PF
For example, if an ounce of gold costs $1200 in
the U.S. and € 800 in Europe, then the price of
one euro in terms of dollars should be:
$1200
$1 50/ €
S = € 800 = $1.50/
S=
What happens if S = 1.25 or S = 1.75?
6-20
Does PPP Hold? More Examples
6-21
11
Evidence on Absolute PPP

Absolute PPP probably doesn’t hold precisely in
the
h reall world
ld for
f a variety
i off reasons:

Tradable and non-tradable factors of production




Haircuts cost 10 times as much in the developed world as in
the developing world.
Film, on the other hand, is a highly standardized commodity
that is actively traded across borders.
Shipping costs, as well as tariffs and quotas can lead to
deviations from PPP.
Relative PPP-determined exchange rates can
provide a more valuable benchmark.
6-22
PPP: Evidence
6-23
12
Does PPP Hold? The Case of Big Mac
6-24
Relative Purchasing Power Parity


Even if the dollar does not buy the same basket of
goods in other countries, the purchasing power of
the
h ddollar
ll in
i these
h
countries
i could
ld remain
i stable
bl
over time.
We can show that according to Relative PPP:


If two countries have different inflation rates, then the
exchange rates between the two countries will adjust to
maintain equality of relative purchasing power for the
citizens of both countries.
The “real” exchange rate will remain constant
6-25
13
Variable Definition
S= Current spot rate (price of foreign currency) in direct quote
S1 = Actual spot rate, 1 year from now
F = 1-year forward rate
FP = the forward premium = [(F-S) / S] = [(F/S) - 1]
H = Inflation rate in the home country
F = Inflation rate in the foreign country
E(S1) = Expected spot rate, 1 year from now, based on PPP
E(e) = [E(S1)/S] – 1 = The expected percentage change, or
rate of change, in the spot rate, based on PPP
e = (S1/S) – 1 = The actual percentage change, or rate of
change, in the spot rate
Sr= real spot rate
6-26
Absolute Purchasing Power Parity and
Exchange Rate Determination
PH
PF
For example, if an ounce of gold costs $1200 in
the U.S. and € 800 in Europe, then the price of
one euro in terms of dollars should be:
$1200
$1 50/ €
S = € 800 = $1.50/
S=
What happens if S = 1.25 or S = 1.75?
6-27
14
Purchasing Power Parity and
Exchange Rate Determination



Suppose the spot exchange rate (S) is $1.50 = €1.00
If the inflation rate in the U.S. (H) is expected to
be 5% in the next year and 3% in the euro zone(F),
Then the expected exchange rate in one year E(S)
should be such that $1.50×(1.05) = €1.00×(1.03)
$1.50×(1.05)
50 (1 05)
$1.575
$1
575 = $1.5291
E(S1) = $1
=
€1.00×(1.03)
€1.03
E(e) = [E(S1)/S – 1] = $1.5291 - 1 = .019 = 1.94%
$1.50
6-28
Purchasing Power Parity and
Exchange Rate Determination

Because of the inflation differential, the euro is expected to
appreciate by 1.94% in the spot market by the end of the year:
E(S1)
=
S
$1.50×(1.05)
€1.00×(1.03)
$1.50
€1.00
=
1.05 1 + H
=
1.03
1 + F
Relative PPP states that the rate of change in the exchange rate
is equal to differences in the rates of inflation—roughly 2%
Also remember that E(S1) = F
So that: expected rate of change in the exchange rate = forward
premium, or E(e) = FP
6-29
15
Relative Purchasing Power Parity

According to Relative PPP:
E(S1)
1 + H
=
S
1 + F
1 + H
E(e) =
1 + F
Approximately:
pp
y E(e)
( ) =
-1
H - F
E(S1) = S [1 + E(e)]
6-30
“Real” Exchange Rate
Real exchange rate is the spot rate adjusted for inflation, let
us call it Sr . It is supposed to tell us if a foreign currency
has appreciated or depreciated, after adjusting for inflation.
Sr
=
S1
Under PPP, real exchange rates should remain constant
Suppose the US the current spot rate for € is 1.50 and US
inflation rate is 5% while the inflation rate is 3% in the euro
zone If the spot rate next year turns out to be 1.52,
zone.
1 52 the real
exchange rate is: 1.52*(1.03/1.05) = $1.491
• We can say that although the spot rate for € appreciated in “nominal”
terms from $1.50 to $1.54, it actually depreciated in “real” terms from
$1.50 to $1.491
• This would weaken the US’s competitive position against Europe
6-31
16
PPP & Competitiveness
We can also use PPP to determine the competitiveness of the
home country’s currency
q
=
=
=
E(S1)/S1
q = 1: Competitiveness of home country is unchanged
q < 1: Competitiveness of home country has improved
q > 1: Competitiveness of home country has deteriorated
6-32
PPP Conditions Summarized
PPP is Violated
PPP Holds Foreign
g currencyy has
Foreign
g currencyy has
appreciated (USD has depreciated (USD has
depreciated) in “real” appreciated) in “real”
terms
terms
No Change
S1 = E(S1)
e = E(e)
S = Sr
q=1
US exports more competitive US exports less competitive
S1 > E(S1)
e > E(e)
S > Sr
q<1
S1 < E(S1)
e < E(e)
S< Sr
q>1
6-33
17
PPP: EXAMPLE 1





Inflation rate in the US is 5%; H = 0.05
Inflation rate in the Europe is 3%; F = 0.03
Current spot rate for € is $1.50; S = 1.50
To maintain relative PPP
PPP, the expected percentage change in the spot
exchange rate for €, E(e) = (1.05) / (1.03) - 1 = 1.9417 %
To maintain relative PPP, the expected spot exchange rate for €, at the
end of the year, E(S1) = $1.50 ( 1 + 0.019417)= $1.5291 per €
If, 1 year latter the actual spot rate, S1 for € turns out to be
$1.54
$1.52
Compared to E(S1) of $1.5291, S1 is
higher
lower
Actual % change in S: e = (S1/S) -1
1
2 027 %
2.027
1 333 %
1.333
The “real” rate for €, Sr = S1 *[1.03/1.05]
$1.5107
$1.4910
q is equal to: [1+E(e)] / [1 + e ] = E(S1)/S1
0.9929
1.0060
The “real” rate (Sr) has:
increased
decreased
In real terms, € has:
appreciated
depreciated
US’s competitiveness has:
improved
deteriorated
6-34
PPP: EXAMPLE 2





Inflation rate in the US is 5%; H = 0.05
Inflation rate in the Switzerland is 2%; F = 0.08
Current spot rate for SF is $0.90; S = 0.90
Too maintain relative
e ve PPP,, thee expected pe
percentage
ce tage cchange
a ge iin tthee spot
exchange rate for SF, E(e) = (1.05) / (1.08) - 1 = - 2.778 %
To maintain relative PPP, the expected spot exchange rate for SF, at the
end of the year, E(S1) = $0.90 ( 1 + 0.02941)= $0.875 per SF
If, 1 year latter the actual spot rate, S1 for SF turns out to be $0.86
$0.88
higher
Compared to E(S1) of $0.875, S1 is
lower
Actual % change in S: e = (S1/S) -1
1
- 4.444
4 444 %
- 2.222
2 222 %
The “real” rate for SF, Sr =S1*[1.08/1.05]
$0.8846
$0.9051
q is equal to: [1+E(e)] / [1 + e ] = E(S)/S1
1.017
0.994
The “real” rate (Sr) has:
decreased
increased
In real terms, SF has:
depreciated
appreciated
US’s competitiveness has:
deteriorated
improved
6-35
18
Purchasing Power Parity
and Interest Rate Parity

Notice that the PPP & IRP equations are equal
because E(S) = F or E(e) = FP:
IRP
PPP
F
1 + iH
E(S)
1 + H
=
= 1+i =
S
S
1 + F
F
E(e) =
1 + H
-1 =
1 + F
1 + iH
-1 = FP
1 + iF
6-36
PPP: Evidence
6-37
19
Expected Rate of Change in Exchange
Rate as Inflation Differential

We could also reformulate
our equations as inflation
or interest rate differentials:
F($/€)
1 + $
=
S($/€)
1 + €
F($/€) – S($/€)
1 + $
1 + $ 1 + €
=
–1=
–
S($/€)
1 + €
1 + € 1 + €
E(e) =
F($/€) – S($/€)
 – €
≈ $ – €
= $
S($/€)
1 + €
6-38
Fisher Effect
The nominal interest rate is composed of a real
interest rate and an expected inflation rate.
Nominal interest rate: i; Real rate: ρ; Expected inflation: 
(1 + i) = (1 + ρ) (1 + )
i = ρ +  + ρ
Approximately: i = ρ + 
If real rates are equal across countries, or: ρH = ρF
Then: (1 + iH) / (1 + iF) = (1 + H) / (1 + F)
Approximately : iH - iF = H - F
6-39
20
International Fisher Effect (IFE)



The concept of IEF
IFE Conditions
Deviations of from IFE: uncovered rates of
interest: from the home and foreign country’s
view point
6-40
International Fisher Effect (IFE)

In an integrated global money and capital
markets:
(1) Domestic fisher effect holds in each country.
(2) All investors have the same real rate of return
worldwide.
(3) Therefore all nominal interest rate differences
must be due to inflation differences
6-41
21
International Fisher Effect (IFE)

The exchange rate of a country with a
higher (lower) interest rate than its trading
partner should depreciate (appreciate) by
the amount of the interest rate difference
to maintain equality of real rates of return.
6-42
IFE: Terminology
iH = Nominal interest rate for the home country
g country
y
iF = Nominal interest rate for the foreign
S = Current spot rate (direct quote) for the foreign
currency (in home currency units)
S1 = Next year’s spot rate (direct quote) for the
foreign currency
6-43
22
Uncovered Rate: Home County’s View
point


The uncovered rate from the home county’s point of view (iUH) is the rate earned by the
holders of dollars by:
1. Converting DOLLARS into FOREIGN CURRENCY today at the current spot exchange
rate (S), and
2. Investing the FOREIGN CURRENCY at the FOREIGN INTEREST RATE (iF), and
3. Converting FOREIGN CURRENCY back into DOLLARS at maturity using the future
spot exchange rate (S1)
This return is affected by two factors:
 whether the foreign currency appreciates or depreciates against the dollar = % change
in direct quote (DQ) = (S1 - S) / S
 The rate of interest you earn in the foreign country = iF
You calculate it as:
iUH = (1 + % change in DQ)*(1 + iF) – 1
Profit making Strategy:
If iUH > iH then borrow in dollars and invest in foreign currency
If iUH < iH then borrow in foreign currency and invest in dollars
If iUH = iH then you cannot make any profit
6-44
Uncovered Rate: Foreign County’s
View point


The uncovered rate from the foreign county’s point of view (iUF) is the rate earned by
the holders of foreign currency by:
1. Converting FOREIGN CURRENCY into DOLLARS today at the current spot
exchange rate (S),
(S) and
2. Investing the DOLLARS at the US INTEREST RATE (iH), and
3. Converting DOLLARS back into FOREIGN CURRENCY at maturity using the
future spot exchange rate (S1)
This return is affected by two factors:
 whether the US Dollars appreciates or depreciates against the foreign currency = %
change in indirect quote (IQ) = (S0 - S1) / S1
 The rate of interest you earn in the home country (US) = iH
You calculate it as:
iUF = (1 + % change in IQ)*(1 + iH) – 1
Profit making strategy :
If iUF > iF then borrow in foreign currency and invest in dollars
If iUF < iF then borrow in dollars and invest in foreign currency
If iUF = iF then you cannot make any profit
6-45
23
IFE Conditions




According to IFE one should not be able to make money by
consistently borrowing in one country and investing in
another
These conditions are met when: iUH = iH or iUF = iF
According to IFE the above conditions will hold only when
the expected percentage change in the spot rate, E(e):
E(e)= (1 + iH) / (1 + iF) – 1
Approximately: E(e)= iH - iF
According to IFE
IFE, the expected spot rate 1 year from now,
now
E(S1), should be:
E(S1) = S [1 + E(e)]
6-46
Uncovered Rate and IFE: Summarized
If iUH > iH or iUF < iF then investors will profit if they:
•
•
•
•
•
borrow in the home country (US)
convert the $ loan amount into foreign currency
invest in the foreign capital market
at the
h end
d off the
h bborrowing/investment
i /i
period
i d convert the
h foreign
f i currency back
b k
into domestic currency ($) and pay off the domestic (US) loan
If this continues then: S↑, E(S1)↓, iH↑, iF↓, until iUH = iH or iUF = iH, or IFE holds
If iUF > iF or iUH < iH then investors will profit if they:
•
•
•
•
•
borrow in the foreign country
convert the loan amount from foreign currency into domestic currency ($)
invest in the domestic (US) capital market
at the end of the borrowing/investment period convert the domestic currency ($)
back into foreign currency and pay off the foreign loan
If this continues then: S↓, E(S1)↑, iH↓, iF↑, until iUH = iH or iUF = iH, or IFE holds
6-47
24
IFE : Example 1






Interest rate in US, iH = 7 % & Euro zone interest rate, iF = 9 %
Current spot rate for €, S = $1.40
According to IFE, the percentage change in exchange rate, based on
direct quote,
quote for € should be:
E(e) = (1.07) / (1.09) - 1 = - 1.83486%
According to IFE, the expected spot rate for € at the end of the year
should be:
E(S1) = $1.40 ( 1 - 0.0183) = $ 1.37 / €
What happens if you believe (predict) that S1 will be $1.39 ?
 You could make money by borrowing in $ and investing in €
 Can you show how?
What happens if you believe (predict) that S1 will be $1.35 ?
 You could make money by borrowing in € and investing in $
 Can you show how?
6-48
IFE : Example 2






Interest rate in US, iH = 7% & Interest rate in Switzerland, iF = 3%
Current spot rate for SF (S)= $0.85
According to IFE, the percentage change in exchange rate, based on
direct quote,
quote SF should be:
E(e) = (1.06) / (1.03) - 1 = 3.8845%
According to IFE, the expected spot rate for SF at the end of the year
should be:
E(S1) = $0.85 ( 1 + 0.0288) = $0.883 / SF
What happens if you believe (predict) that S1 will be $0.90 ?
 You could make money by borrowing in $ and investing in FF
 Can
C you show
h how?
h ?
What happens if you believe (predict) that S1 will be $0.87 ?
 You could make money by borrowing in SF and investing in $
 Can you show how?
6-49
25
Approximate Equilibrium Exchange
Rate Relationships
E(e)
( )
≈ IFE
(iH – iF)
≈ FEP
≈ PPP
F–S
≈ IRP
S
E(H – F)
6-50
Exact Equilibrium Exchange Rate
Relationships
IFE
1 + iH
1 + iF
E ( S1 )
S
PPP
IRP
FEP
F
S
E(1 + H)
E(1 + F)
6-51
26
Variable Definitions
S= Current spot rate (price of foreign currency) in direct quote
S1 = Actual spot rate, 1 year from now
F = 1-year forward rate
FPH = the forward premium = [(F-S) / S] = [(F/S) - 1] from the home
country’s view point
FPF = the forward premium = [(S-F) / F] = [(S/F) - 1] from the foreign
country’s view point
H = Inflation rate in the home country
F = Inflation rate in the foreign country
ρ = Real rate of interest
E(S1) = Expected spot rate,
rate 1 year from now
now, based on PPP
E(e) = [E(S1)/S] – 1 = The expected percentage change, or rate of
change, in the spot rate, based on PPP
e = (S1/S) – 1 = The actual percentage change, or rate of change, in the
spot rate
Sr= real spot rate
iH = Nominal interest rate for the home country
iF = Nominal interest rate for the foreign country
Formula: Purchasing Power Parity
(PPP)
Exact relationship:
E(e) =(1
(1 + πH) / (1 + πF) - 1
Approximate relationship:
E(e) = πH - πF
S1 = S0 * [ 1 + E(e) ]
SR = S1 *(1 + πF) / (1 + πH)
Fisher
i
Equation:
i
(1 + i) = (1 + ρ)) (1 + ))
i = ρ +  + ρ
Approximately: i = ρ + 
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Formula: International Fisher Effect
(IFE)
Fisher Equation: (1 + i) = (1 + ρ) (1 + )
i = ρ +  + ρ
Approximately: i = ρ + 
iuh : Uncovered rate of return, home country’s viewpoint
iuf : Uncovered rate of return, foreign country’s viewpoint
iuh = (1 + if) (1 + % change in DQ ) – 1
iuf = (1 + ih) (1 + % change in IQ ) – 1
% change
h
iin DQ (direct
(di t quote)=
t ) (S1 - S0) / S0
% change in IQ (indirect quote) = [1 /(1+ % change in DQ] - 1
The IFE relationship holds when:
E(e)= (1 + iH) / (1 + iF) – 1
Approximately: E(e)= iH – iF
S1 = S0 * [1 + E(e)]
Formula: Interest Rate Parity (IRP)
Calculating the covered rate of returns (home & foreign country’s view point)
ich= Covered rate of return, home country’s view point
icf= Covered rate of return, foreign country’s view point
ich = (1 + if) (1 + FPh) – 1
icf = (1 + ih) (1 + FPf) – 1
The IRP relationship holds when the expected forward premium from the
home country’s point of view (FPh ):
FPh = (1 + ih)/(1 + if) – 1
S1= S0 * ( 1 + FPh)
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The Hamburger Standard: Further
Discussion
6-56
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