Management 3460
Institutions and Practices in
International Finance
Fall 2003
Greg Flanagan
Chapter 5
International Parity
Relationships and Forecasting
FX Rates
Chapter Objectives
The student will be able to:
Define Interest Rate Parity
State and apply the IRP equation
Explain and calculate covered Interest
Arbitrage
Give reasons for Deviations from IRP
Explain the adjustment process when IRP
does not hold that brings it to equilibrium.
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Oct 9-14, 2003
Chapter Objectives
The student will be able to:
Define Purchasing Power Parity (PPP)
Explain why there are PPP Deviations
and the Real Exchange Rate
Discuss the Evidence for Purchasing
Power Parity
Explain the Fisher Effect
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Chapter Objectives
The student will be able to:
Explain the different approaches to
forecasting exchange rates:
Efficient Market
Fundamental
Technical
Discuss the performance of
forecasters.
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Interest Rate Parity (IRP)
Definition: IRP is the situation where the forward
FX premium (discount) of one currency just offsets
the higher (lower) interest rate in another country.
It is an arbitrage equilibrium condition.
If IRP did not hold, then it would be possible for a
trader to make a profit exploiting the arbitrage
opportunity.
persistent arbitrage conditions rarely exist
suggesting that we can assume that IRP holds.
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Oct 9-14, 2003
Interest Rate Parity (IRP)
Return in country j = ij
Covered interest return
(1 + ik) F(j/k)
S(j/k)
or: (1 + ik)(F/S)
IRP equilibrium:
(1 + ij) = (F/S)(1 + ik)
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Oct 9-14, 2003
Interest Rate Parity Example
j = US
k =UK
Suppose you have $100,000 to invest for one year.
You can either
1.
invest in the U.S. at i$. Future value = $100,000(1 + i$)
or
2. trade your dollars for pounds at the spot rate, invest in UK
at i£ and hedge your exchange rate risk by selling the future
value of the British investment forward. The future value =
$100,000(F/S)(1 + i£)
Since both of these investments have the same risk, they must
have the same future value—otherwise an arbitrage would
exist, therefore (F/S)(1 + i£) = (1 + i$)
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Interest Rate Parity
$100,000
1. Trade $100,000 for £ at S
2. Invest £100,000 at i£
S
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$100,000(1 + i$)
$100,000(F/S)(1 + i£)
3. One year later,
trade £ for $ at F
Oct 9-14, 2003
Interest Rate Parity
(F/S)(1 + ik ) = (1 + ij)
1 + ij
F
=
1 + ik
S
or
IRP is sometimes approximated as
ij – ik = F – S
S
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Oct 9-14, 2003
IRP and Covered Interest
Arbitrage
If IRP failed to hold, an arbitrage would exist.
Example:
Spot exchange rate
S($/£)
360-day forward rate F360($/£)
U.S. discount rate
i$
British discount rate
i£
10
=
=
=
=
$1.25/£
$1.20/£
7.10%
11.56%
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IRP and Covered Interest Arbitrage
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 $1,071.
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IRP & Exchange Rate
Determination
According to IRP only one 360-day forward
rate, F360($/£), can exist. It must be the case
that F360($/£) = $1.20/£
Why?
If F360($/£)  $1.20/£, an astute trader could
make money with one of the following
strategies:
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Arbitrage Strategy I
If F360($/£) > $1.20/£
i. Borrow $1,000 at t = 0 at i$ = 7.1%.
ii. Exchange $1,000 for £800 at the prevailing
spot rate, (note that £800 = $1,000÷$1.25/£)
invest £800 at 11.56% (i£) for one year to
achieve £892.48
iii. Translate £892.48 back into dollars, if
F360($/£) > $1.20/£ , £892.48 will be more than
enough to repay your dollar obligation of
$1,071.
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Arbitrage Strategy II
If F360($/£) < $1.20/£
i. Borrow £800 at t = 0 at i£= 11.56% .
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 $1,071 back into pounds, if
F360($/£) < $1.20/£ , $1,071 will be more than
enough to repay your £ obligation of £892.48.
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Oct 9-14, 2003
IRP adjustment process
If the covered interest return was
greater in another country, then
(F/S)(1 + ik ) > (1 + iCdn$)
A trader will borrow locally and invest
in the foreign country and pocket the
difference without risk.
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IRP adjustment process
The interest rate in Canada ij h
interest rate in the other country ik will i
Sk h
Fk i
i.e. arbitrage will occur as interest rates
approach and Forward and Spot markets
differences decrease.
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(F-S)/S(%)
4
IRP line
3
2
1
-5 -4 -3 -2
-1
1
2
3
4
5
-1
The difference in interest rates falls
(ij)- ik(%)
-2
A combination of both changes occur
-3
The difference in forward and spot rates rises
-4
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Uncovered IRP
Expectations play a considerable role
in Exchange rates
The expected rate of change in the
exchange rate is approximately equal to
the difference in the interest rates
between two countries.
E(e) = ij- ik
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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
Thus (Fb/Sa)(1 + iJl)  (1 + iJ b)  0
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(F-S)/S(%)
4
Transaction Costs
IRP line
3
2
1
-5 -4 -3 -2
-1
1
-1
2
3
4
5
(ij)- ik(%)
-2
-3
-4
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Reasons for Deviations from
IRP
Capital Controls
Governments sometimes restrict import
and export of money through taxes or
outright bans.
Political Risks
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Purchasing Power Parity
The exchange rate between two
currencies should equal the ratio of the
countries’ price levels:
Pj
S(j/k) =
Pk
i.e. Prices after exchange transactions should be
the same—the absolute version of PPP
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Purchasing Power Parity
For example, if an ounce of gold costs
$300 in the U.S. and £150 in the U.K., then
the price of one pound in terms of dollars
should be:
P$ $300
S($/£) =
= £150 = $2/£
P
£
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Purchasing Power Parity
Relative PPP states that the rate of change in
the exchange rate (e) is equal to the
differences in the rates of inflation ():
e=
($ – £)
(1 + £ )
≈ $ – £
If Cdn inflation is 5% and U.K. inflation is 8%, the
pound should depreciate by 2.78% or around 3%.
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PPP Deviations and the
Real Exchange Rate
The real exchange rate (q) is:
q=
If PPP holds, (1 + e) =
(1 + $ )
(1 + £ )
(1 + $)
(1 + e)(1+ £)
then q = 1.
If q < 1 competitiveness of domestic country
improves with currency depreciations.
If q > 1 competitiveness of domestic country
deteriorates with currency depreciations.
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Evidence on PPP
PPP doesn’t hold precisely in the real world for
a variety of reasons:
Labour: Haircuts cost 10 times as much in the
developed world as in the developing world.
Standards: Film, on the other hand, is a highly
standardized commodity that is actively traded
across borders.
Shipping costs, tariffs, and quotas can lead to
deviations from PPP.
Capital investment differences.
PPP-determined exchange rates still provide a
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valuable benchmark.
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The Fisher Effects
An increase (decrease) in the expected
rate of inflation will cause a
proportionate increase (decrease) in the
interest rate in the country.
$ is the equilibrium expected “real”
interest rate
E[$] is the expected rate of inflation
i$ is the equilibrium expected nominal
interest rate
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Expected Inflation
The Fisher effect implies that the expected
inflation rate is approximated as the
difference between the nominal and real
interest rates in each country, i.e.
i$ = $ + (1 + $)E[$] ≈ $ + E[$]
E[$] =
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(i$ – $)
(1 + $)
≈ i$ – $
Oct 9-14, 2003
International Fisher Effect
If the Fisher effect holds in the U.S.
i$ = (1+ $)(1 + E[$]) ≈ $ + E[$]
and the Fisher effect holds in Japan,
i¥ = (1+ ¥ )(1 + E[¥]) ≈ ¥ + E[¥]
and if the real rates are the same in each country
(i.e. $ = ¥ ), then we get the International
Fisher Effect
(i$ – i¥)
E(e) =
≈ i$ – i¥
(1 + i¥)
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International Fisher Effect
If the International Fisher Effect holds:
(i$ – i¥)
E(e) =
(1 + i¥)
and if IRP also holds
F–S
S
=
(i$ – i¥)
(1 + i¥)
then forward parity holds. E(e) =
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F–S
S
Oct 9-14, 2003
Approximate Equilibrium
Exchange Rate Relationships
≈ International
Fisher Effect
(i$ – i¥))
≈ PPP
≈ Forward
Expectations
Parity
≈ IRP
≈ Fisher
Effect
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E(e)
F–S
S
E($ – ¥)
≈ Forward
PPP
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Foreign Exchange Forecasting
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Efficient Markets Approach
Financial Markets are efficient if prices
reflect all available and relevant information.
If this is so, exchange rates will only change
when new information arrives, thus:
St = E[St+1]
and
Ft = E[St+1| It]
Predicting exchange rates using the is
affordable and is hard to beat.
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Fundamental Approach
Involves econometrics to develop models that
use a variety of explanatory variables. This
involves three steps:
step 1: Estimate the structural model.
step 2: Estimate future parameter values.
step 3: Use the model to develop forecasts.
The downside is that fundamental models do not
work any better than the forward rate model or
the random walk model.
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Technical Approach
Technical analysis looks for patterns in
the past behavior of exchange rates.
Clearly it is based upon the premise
that history repeats itself.
Thus it is at odds with the Efficient
Markets
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At D the short-term moving average exchange rate is
falling below the long –term moving average a depreciation of the £
At A the short-term moving average exchange rate is
rising above the long –term moving average a appreciation of the £
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Levich Analysis
MAE(S) Mean Average forecast Error
of a forecasting Service.
MAE(F) Mean Average forecast Error
of the Forward exchange rate predictor.
R = MAE(S)/MAE(F)
If the forecast service is more accurate
a R< 1.
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Only 25 out of 104 are < 1!
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Performance of the Forecasters
Forecasting is difficult, especially with
regard to the future.
As a whole, forecasters cannot do a better
job of forecasting future exchange rates than
the forward rate.
The founder of Forbes Magazine once said:
“You can make more money selling financial
advice than following it.”
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