International Parity
Relationships & Forecasting
Chapter Six
Foreign Exchange Rates
INTERNATIONAL
FINANCIAL
Chapter Objective:
MANAGEMENT
6
INTERNATIONAL
FINANCIAL
MANAGEMENT
Seventh Edition
This chapter examines several key international
parity relationships, such as interest rate parity and
Fourth Edition
purchasing power parity.
EUN / RESNICK
6-0
EUN / RESNICK
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6-1
Chapter Outline
Interest Rate Parity
Purchasing Power Parity
l  The Fisher Effects
l  Forecasting Exchange Rates
l
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
l
Interest Rate Parity
Covered Interest Arbitrage
IRP and Exchange Rate Determination
n  Reasons for Deviations from IRP
n
l
n
Purchasing Power Parity
The Fisher Effects
l  Forecasting Exchange Rates
l
l
6-2
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6-3
Chapter Outline
l
l
Interest Rate Parity
Purchasing Power Parity
PPP Deviations and the Real Exchange Rate
n  Evidence on Purchasing Power Parity
n
The Fisher Effects
l  Forecasting Exchange Rates
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Chapter Outline
Interest Rate Parity
Purchasing Power Parity
l  The Fisher Effects
l  Forecasting Exchange Rates
l
l
l
6-4
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6-5
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1
Chapter Outline
Interest Rate Parity
Interest Rate Parity
l  Purchasing Power Parity
l  The Fisher Effects
l  Forecasting Exchange Rates
l
Efficient Market Approach
Fundamental Approach
n  Technical Approach
n  Performance of the Forecasters
n
n
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
6-6
Interest Rate Parity
Interest Rate Parity Defined
Interest Rate Parity Defined
Covered Interest Arbitrage
l  Interest Rate Parity & Exchange Rate
Determination
l  Reasons for Deviations from Interest Rate Parity
(Covered) IRP is an arbitrage condition.
If IRP did not hold, then it would be possible for
an astute trader to make unlimited amounts of
money exploiting the arbitrage opportunity.
l  Since we don’t typically observe persistent
arbitrage conditions, we can safely assume that
IRP holds.
l
l
l
l
n
Interest Rate Parity Carefully Defined
Consider alternative one year investments for $100,000:
1.
Invest in the U.S. at i$. Future value = $100,000 × (1 + i$)
2.
Trade your $ for £ at the spot rate, invest $100,000/S$/£ in
Britain at i£ and get rid of any exchange rate risk by selling
the future value of the British investment forward.
Future value = $100,000(1 + i£)×
F$/£
S$/£
Since these investments have the same risk, they must have
the same future value (otherwise an arbitrage would exist)
(1 + i£) ×
6-10
F$/£
= (1 + i$)
S$/£
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Exception in periods of financial market stress? Why?
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6-9
Alternative 2:
Send your $ on a
round trip to
Britain
$1,000
S$/£
$1,000
Alternative 1:
invest $1,000 at i$
$1,000×(1 + i$) =
IRP
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6-8
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6-7
Step 3: repatriate
future value to the
U.S.A.
IRP
Step 2:
Invest those
pounds at i£
Future Value =
$1,000
× (1+ i£)
S$/£
$1,000
× (1+ i£) × F$/£
S$/£
Since both of these investments have the same risk, they must
Copyright © 2007 by The McGraw-Hill
Companies,
Inc. All rights
reserved.
have6-11
the same future value—otherwise
an arbitrage
would
exist
2
Interest Rate Parity
Interest Rate Parity Defined
l
$100,000
$1,000×(1 + i$) =
$100,000(1 + i$)
1.  Trade $100,000 for £ at S
$100,000(F/S)(1 + i£)
(1 + i$) =
3.  One year later,
trade £ for $ at F
2.  Invest £100,000 at i£
S
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6-12
The scale of the project is unimportant
Interest Rate Parity Defined
Formally,
6-13
F$/£
S$/£
× (1+ i£)
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Interest Rate Parity Carefully Defined
l
(F/S)(1 + i¥) = (1 + i$)
or if you prefer,
1 + i$
F
=
1 + i¥
S
$1,000 × (1+ i ) × F
£
$/£
S$/£
Depending upon how you quote the exchange rate
($ per ¥ or ¥ per $) we have:
1 + i¥
F¥/$
=
1 + i$
S¥/$
or
1 + i$
F$/¥
=
1 + i¥
S$/¥
IRP is sometimes approximated as
i$ – i¥ = F – S
S
6-14
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6-15
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IRP and Covered Interest Arbitrage
IRP and Covered Interest Arbitrage
If IRP failed to hold, an arbitrage would exist. It’s
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.
A trader with $1,000 to invest could invest in the
U.S., in one year his investment will be worth
$1,071 = $1,000×(1+ i$) = $1,000×(1.071)
Alternatively, this trader could exchange $1,000 for
£800 at the prevailing spot rate, (note that £800 =
$1,000÷$1.25/£) invest £800 at i£ = 11.56% for
one year to achieve £892.48. Translate £892.48
back into dollars at F360($/£) = $1.20/£, the
£892.48 will be exactly $1,071.
Spot exchange rate
360-day forward rate
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S($/£) = $1.25/£
F360($/£) = $1.20/£
U.S. discount rate
i$ = 7.10%
British discount rate
i£ =
11.56%
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6-17
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3
Interest Rate Parity
& Exchange Rate Determination
Interest Rate Parity
$1,000
1.  Trade $100,000 for £800
2.  Invest £800 at 11.56% = i£
$1,071
According to IRP only one 360-day forward rate,
F360($/£), can exist. It must be the case that
F360($/£) = $1.20/£
$1,071
Why?
3.  One year later, trade
£892.48 for $ at
F360($/£) = $1.20/£
If, say, F360($/£) ≠ $1.20/£, an astute trader could
make money with one of the following strategies:
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6-18
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6-19
Arbitrage Strategy I
Arbitrage Strategy II
If F360($/£) > $1.20/£
i. Borrow $1,000 at t = 0 at i$ = 7.1%.
If F360($/£) < $1.20/£
i. Borrow £800 at t = 0 at i£= 11.56% .
ii. Exchange $1,000 for £800 at the prevailing spot
rate, (note that £800 = $1,000÷$1.25/£) invest
£800 at 11.56% (i£) for one year to achieve
£892.48
ii. Exchange £800 for $1,000 at the prevailing spot
rate, invest $1,000 at 7.1% for one year to
achieve $1,071.
iii. Translate £892.48 back into dollars, if
F360($/£) > $1.20/£ , £892.48 will be more than
enough to repay your dollar obligation of $1,071.
iii. Translate $1,071 back into pounds, if
F360($/£) < $1.20/£ , $1,071 will be more than
enough to repay your £ obligation of £892.48.
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6-20
Reasons for Deviations from IRP
l
Transactions Costs
The interest rate available to an arbitrageur for
borrowing, ib, may exceed the rate he can lend at, il.
n  There may be bid-ask spreads to overcome, Fb/Sa < F/S
n  Thus
“Problems” with Covered IRP
l
n
(Fb/Sa)(1 + i$a) - (1 + i¥ b) ≤ 0
l
Capital Controls
n
6-22
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6-21
It is an arbitrage relation
n
l
What if we want to forecast future FX rates, or to
explain past FX rate changes
Where is inflation?
n
Shouldn’t inflation affect exchange rates?
n
If so, what is the connection with IRP?
u For
example, why did the dollar depreciate in March 2008
against the € despite news of an unexpected drop in US
inflation and Eurozone inflation at a 14-year high?
Governments sometimes restrict the import/export
of currency by means of taxes or outright bans.
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6-23
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4
Purchasing Power Parity
Purchasing Power Parity
l
Purchasing Power Parity and Exchange Rate
Determination
Law of One Price
Absolute version of PPP
n  Relative version of PPP
n
n
u The
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Absent transactions costs, goods should cost the
same in any pair of countries: P$ = P£ . S($/£), i.e.,
P$
S($/£) =
P£
l  Example: if an ounce of gold costs $600 in the
U.S. and £300 in the U.K., then the price of one
pound in terms of dollars should be:
P$ $600
S($/£) =
=
= $2/£
P£ £300
l
6-26
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PPP and Exchange Rate Determination
(“Relative” Version of PPP)
l
l
Idea: “Relative PPP” states that the rate of change
in the exchange rate, denoted e, should be equal
to the differences between inflation rates (why?):
(st+T – st)
(π$ – π£)
≈ π$ – π£
e=
=
st
(1 + π£ )
If U.S. inflation is π$ = 5% and U.K. inflation is
π£ = 8%, then the pound should depreciate by
2.78%, i.e., lose about 3% of its value in dollars
6-28
l
PPP Deviations and the Real Exchange Rate
l
Evidence on PPP
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PPP and Exchange Rate Determination
(“Law of One Price” Version of PPP)
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latter is the most frequently used (“default”)version
6-25
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PPP and Exchange Rate Determination
(“Absolute” Version of PPP)
l
The exchange rate between two currencies should
equal the ratio of the countries’ price levels:
P$
S($/£) =
P£
l  For
example, if the price of a “reference basket”
is $300 in the U.S. and £150 in the U.K., then the
price of 1£ in terms of the dollar should be:
P$ $300
S($/£) =
=
= $2/£
P£ £150
6-27
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PPP Deviations and the
Real Exchange Rate (RER Index)
Define the U.S. RER index = q =
(1 + π$)
(1 + e)(1+ π£)
(1 + π$ )
so q = 1.
If PPP holds, then (1 + e) =
(1 + π£ )
If q < 1 competitiveness of domestic country (U.S.)
improves; (Example: The Economist_07a)
If q > 1 competitiveness of domestic country (U.S.)
worsens.
6-29
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5
PPP Deviations and the
Real Exchange Rate (RER Level)
The RER at time t is, by definition, s’t = st
The RER at time t+T = s’t+T = st+T [(1+ π*)/(1+ π)]
PPP Deviations and the
Real Exchange Rate (RER Index)
Foreign country’s RER index
=
If s’t+T < s’t
If s’t+T > s’t
6-30
: U.S. competitiveness worsens.
: U.S. competitiveness improves.
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6-31
PPP Deviations and the
Real Exchange Rate (Example)
PPP Deviations and the
Real Exchange Rate (Example)
Question 2, PS#4: Intuitive Answer.
The ¥/$ exchange rate moved from ¥105/1$ in March 1994 to ¥90/1$ in
March 1995;
During the same period, the U.S. consumer price index (CPI) rose from
130 to 133.6, and the corresponding Japanese index moved
from 110 to 110.7;
What was the real appreciation of the ¥ during the relevant year (3-94
to 3-95)? Explain, intuitively and formally.
6-32
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Intuitively, notice that 1$ buys in 3-95 about 14.3% (15/105)
fewer ¥ than it did 1 year earlier, yet the inflation differential between
the US and Japan was only 2.2% (133.6/130 - 110.7/110). Hence, the
real depreciation of the $ must have been about 12% (14.3%-2.2%).
We can look at the same situation from the alternative point of
view of the real appreciation of the Japanese ¥. In nominal terms, the ¥
appreciated against the $ by 16.7% (from 0.009524$/1¥ to 0.011111$/
1¥), yet the inflation differential was only 2.2%. Hence, the real
appreciation of the ¥ must have been about 14.5% (16.7%-2.2%).
.
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6-33
PPP Deviations and the
Real Exchange Rate (Example)
Evidence on PPP
l
Question 2, PS#4: Formal Answer.
s’(beginning of last year) = s’(March 94) = s’(t) = 0.009524 $/¥
PPP probably doesn’t hold precisely in the real world for a
variety of reasons.
n
1+µ* ⎞
s't+T = st+T ⎛⎜
⎟ = (0.011111 $/ 1¥) 1.006
⎝ 1+µ ⎠
1.028
(
cost 10 times as much in OECD countries as in the developing
world (Economist alternative? # of minutes to buy a Big Mac, 08-2009).
) = .010873 $/¥
n
-1 =
s't+T
s't
memory, on the other hand, is a standardized commodity that
is actively traded across borders.
u  Even for such tradables, though, there may be deviations from PPP due
to shipping costs, tariffs, quotas, etc.
-1 = 0.010873 -1 = 14.17 %
0.009524
Note: The difference between the formal (14.17%) and intuitive (14.5%) answers
comes from discounting.
6-34
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vs. Tradables (TGS):
u  Computer
Hence, the real appreciation of the ¥ is:
s‘(beginning of last year)
Non-Tradables (NTG, NTGS):
u  Haircuts
s’(beginning of this year) = s’(March 95) = s’(t+T)
s‘(beginning of this year)
s’t
q* < 1 à foreign country’s competitiveness
improves (and U.S. competitive position worsens);
q* > 1 à foreign country’s competitiveness worsens
(and U.S. competitiveness improves).
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Question 2, PS#4.
s’t+T
If PPP holds, then s’t+T = s’t so q* = 1
If PPP holds, then st+T = st [(1+ π)/(1+ π*)], so
s’t+T = st [(1+ π)/(1+ π*)][(1+ π*)/(1+ π )]= st = s’t
q* =
l
PPP-determined exchange rates still provide a valuable
benchmark.
6-35
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6
Evidence on PPP
l
The Fisher Effects
Big Mac index
n
Law of One Price in Practice
n
Empirical evidence
u  Examples:
u Country
Big Mac parities for many countries (Economist site)
specificities:
n  Is the Big Mac really a commodity in India?
n  Are fast-food restaurants an everyday experience everywhere?
n  How much time does it take to buy a Big Mac?
u How
l
about a latte? Starbuck index, anyone?
Trade-weighted real exchange rate (Economist_07d)
6-36
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6-37
The Fisher Effects
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The Fisher Effects
An increase (decrease) in the expected rate of inflation will
cause a proportionate increase (decrease) in the interest
rate in the country.
l  For the U.S., the Fisher effect is written as:
1 + i$ = (1+ ρ$)(1 + E[π$]) = 1 + ρ$ + E[π$] + ρ$E[π$]
i$ = ρ$ + E(π$) + ρ$E[π$] ≈ ρ$ + E[π$]
Where
ρ$
is the equilibrium expected “real” U.S. interest rate
E[π$] is the expected rate of U.S. inflation
i$
is the equilibrium expected nominal US int. rate
l
l
Domestic Fisher effect
n
l
International Fisher effect
n
l
Link between a country’s nominal int. rate and its inflation rate
If FF is a reality in every country, what does it say about exchnage
rates
Can the Fisher effects tell us anything
n
6-38
about when forward rates can help predict future spot rates?
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6-39
Expected Inflation
l
implies that the expected inflation rate is
approximated as the difference between the
nominal and real interest rates in each country, i.e.
E[π$] =
6-40
International Fisher Effect
If the Fisher effect holds in the U.S.
The Fisher effect
i$ = ρ$ + (1 + ρ$)E[π$] ≈ ρ$ + E[π$]
l
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
(i$ – ρ$)
(1 + ρ$)
≈ i$ – ρ$
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
i$ = (1+ ρ$)(1 + E[π$]) ≈ ρ$ + E[π$]
and if the Fisher effect holds in Japan,
i¥ = (1+ ρ¥ )(1 + E[π¥]) ≈ ρ¥ + E[π¥]
and if the real rates are the same in each country
(i.e. ρ$ = ρ¥ ), then we get the International Fisher
(i$ – i¥)
Effect:
E(e) =
≈ i$ – i¥
(1 + i¥)
6-41
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7
Approximate Equilibrium Exchange
Rate Relationships
International Fisher Effect
If the International Fisher Effect holds,
(i$ – i¥)
E(e) =
(1 + i¥)
and “if” IRP also holds
F–S
S
=
E(e)
≈ IFE
(i$ – i¥)
(i$ – i¥)
(1 + i¥)
≈ PPP
F–S
F–S
≈ IRP
S
≈ FE
then “forward parity” holds: E(e) =
≈ FRPPP
E(π$ – π£)
S
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6-42
≈ FEP
6-43
Approximate Equilibrium Exchange
Rate Relationships
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
The Exact Fisher Effects
An increase (decrease) in the expected rate of inflation
will cause a proportionate increase (decrease) in the
interest rate in the country.
l  For the U.S., the Fisher effect is written as:
1 + i$ = (1 + ρ$ ) × E(1 + π$)
Where
ρ$ is the equilibrium expected “real” U.S. interest rate
E(π$) is the expected rate of U.S. inflation
i$ is the equilibrium expected nominal U.S. interest rate
l
E(e)
≈ UIRP
(i$ – i¥)
≈ FP
≈ PPP
F–S
≈ IRP
S
≈ FE
≈ FRPPP
E(π$ – π£)
6-44
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6-45
International Fisher Effect
If the Fisher effect holds in the U.S.
1 + i$ = (1 + ρ$ ) × E(1 + π$)
and the Fisher effect holds in Japan,
1 + i¥ = (1 + ρ¥ ) × E(1 + π¥)
and if the real rates are the same in each country
ρ$ = ρ¥
then we get the
E(1 + π¥)
1 + i¥
International Fisher Effect: 1 + i = E(1 + π )
$
$
6-46
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
International Fisher Effect
If the International Fisher Effect holds,
E(1 + π¥)
1 + i¥
=
1 + i$
E(1 + π$)
and “if” IRP also holds
1 + i¥
F¥/$
=
1 + i$
S¥/$
then forward rate PPP holds:
6-47
F¥/$
E(1 + π¥)
=
S¥/$
E(1 + π$)
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
8
Exact Equilibrium Exchange Rate
Relationships
E (S ¥ / $ )
S¥ / $
IFE
1 + i¥
1 + i$
FEP
PPP
UIRP
F¥ / $
S¥ /$
IRP
FE
Exact Equilibrium Exchange Rate
Relationships
1 + i¥
1 + i$
FRPPP
FP
PPP
F¥ / $
S¥ /$
IRP
FE
E(1 + π¥)
E(1 + π$)
6-48
E (S ¥ / $ )
S¥ / $
FRPPP
E(1 + π¥)
E(1 + π$)
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6-49
Forecasting Exchange Rates
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Forecasting Exchange Rates
Efficient Markets Approach
Fundamental Approach
l  Technical Approach
l  Performance of the Forecasters
l
l
6-50
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6-51
Currency Carry Trade
Efficient Markets Approach
Financial Markets are efficient if prices reflect all
available and relevant information.
l  If this is so, exchange rates will only change when
new information arrives, thus:
St = E[St+1]
and
Ft = E[St+1| It]
l  Predicting exchange rates using the efficient
markets approach is affordable – but is it good?
l
6-52
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Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
l
If UIRP does not hold, then…
n
n
Currency carry trade buy a currency with a high rate of interest and fund the purchase by borrowing a currency with low rates of interest, without any hedging.
Carry trade profitable if the int. rate diff. exceeds the appreciation of the funding currency against the target currency.
l  Risk?
l
6-53
6-­‐‑53
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9
Fundamental Approach
l
Uses econometrics to develop models that use a variety of
explanatory variables. Involves 3 steps:
n
step 1: Estimate the structural model
n
step 2: Estimate future parameter values
n
step 3: Use the model to develop forecasts
n  What variables should be included – macro, order flow?
n  Why is this any easier than forecasting the FX rate itself?
n  Why should past relations between variables hold in the future?
l
Downside
n
6-54
Technical Approach
Technical analysis looks for patterns in the past
behavior of exchange rates.
l  Clearly it is based upon the premise that history
repeats itself.
l  Thus it is at odds with the EMH
l  Short-term vs. Long-term differences?
l
n
In the short run at least, fundamental models seem not to work any
better than the forward rate model or the random walk model.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
n
6-55
Performance of the Forecasters
l
In the long run, fundamentals do matter
In the short run, trader prophecies may be self-fulfilling
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
End Chapter Six
Forecasting is difficult, especially with regard to
the future.
n
Still, the evidence suggests that UIRP does pretty well
at horizons of 5 to 10 years (in contrast to short term)
As a whole, forecasters appear not to do a much
better job of forecasting future exchange rates
than does the forward rate
l  The founder of Forbes Magazine once said:
“You can make more money selling financial
advice than following it”
l
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