Description
This is a presentation explains several key international parity relationships, such as interest rate parity and purchasing power parity.
INTERNATIONAL
FINANCIAL
MANAGEMENT
EUN / RESNICK
Second Edition
5
International Parity
Relationships & Forecasting
Exchange Rates
Objective:
This lecture examines several key international parity
relationships, such as interest rate parity and
purchasing power parity.
5-0
? Interest Rate Parity
? Purchasing Power Parity
? The Fisher Effects
? Forecasting Exchange Rates
5-1
? Interest Rate Parity
? Covered Interest Arbitrage
? IRP and Exchange Rate Determination
? Reasons for Deviations from IRP
? Purchasing Power Parity
? The Fisher Effects
? Forecasting Exchange Rates
5-2
? Interest Rate Parity
? Purchasing Power Parity
? PPP Deviations and the Real Exchange Rate
? Evidence on Purchasing Power Parity
? The Fisher Effects
? Forecasting Exchange Rates
5-3
? Interest Rate Parity
? Purchasing Power Parity
? The Fisher Effects
? Forecasting Exchange Rates
5-4
? Interest Rate Parity
? Purchasing Power Parity
? The Fisher Effects
? Forecasting Exchange Rates
? Efficient Market Approach
? Fundamental Approach
? Technical Approach
? Performance of the Forecasters
5-5
? Interest Rate Parity Defined
? Covered Interest Arbitrage
? Interest Rate Parity & Exchange Rate Determination
? Reasons for Deviations from Interest Rate Parity
5-6
? 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.
? Since we don’t typically observe persistent arbitrage
conditions, we can safely assume that IRP holds.
5-7
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
us
)
2. trade your dollars for yen at the spot rate, invest in
Japan at i
¥
and hedge your exchange rate risk by selling
the future value of the Japanese 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.
(F/S)(1 + i
¥
) = (1 + i
us
)
5-8
Formally,
(F/S)(1 + i
¥
) = (1 + i
us
)
or if you prefer,
5-9
S
F
i
i
=
+
+
¥
$
1
1
IRP is sometimes approximated as
S
(F- S)
) -i (i
¥
=
$
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.
5-10
Spot exchange rate S($/£) = $1.25/£
360-day forward rate F
360
($/£) = $1.20/£
U.S. discount rate i
$
= 7.10%
British discount rate i
£
= 11.56%
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÷$1.25/£) invest £800 at i
£
= 11.56% for one year to
achieve £892.48. Translate £892.48 back into dollars at
F
360
($/£) = $1.20/£, the £892.48 will be exactly $1,071.
5-11
According to IRP only one 360-day forward rate,
F
360
($/£), can exist. It must be the case that
F
360
($/£) = $1.20/£
Why?
If F
360
($/£) = $1.20/£, an astute trader could make money
with one of the following strategies:
5-12
If F
360
($/£) > $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÷$1.25/£) invest £800 at 11.56%
(i
£
) for one year to achieve £892.48
iii. Translate £892.48 back into dollars, if
F
360
($/£) > $1.20/£ , £892.48 will be more than enough to
repay your dollar obligation of $1,071.
5-13
If F
360
($/£) < $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 $1,071 back into pounds, if
F
360
($/£) < $1.20/£ , $1,071 will be more than enough to
repay your £ obligation of £892.48.
5-14
You are a U.S. importer of British woolens and have just ordered
next year’s inventory. Payment of £100M is due in one year.
5-15
IRP implies that there are two ways that you fix the cash outflow
a) Put yourself in a position that delivers £100M in one year—a long
forward contract on the pound. You will pay (£100M)(1.2/£) =
$120M
b) Form a forward market hedge as shown below.
Spot exchange rate S($/£) = $1.25/£
360-day forward rate F
360
($/£) = $1.20/£
U.S. discount rate i
$
= 7.10%
British discount rate i
£
= 11.56%
5-16
To form a forward market hedge:
Borrow $112.05 million in the U.S. (in one year you
will owe $120 million).
Translate $112.05 million into pounds at the spot
rate S($/£) = $1.25/£ to receive £89.64 million.
Invest £89.64 million in the UK at i
£
= 11.56% for
one year.
In one year your investment will have grown to
£100 million—exactly enough to pay your
supplier.
5-17
Where do the numbers come from? We owe our supplier
£100 million in one year—so we know that we need to
have an investment with a future value of £100 million.
Since i
£
= 11.56% we need to invest £89.64 million at the
start of the year.
How many dollars will it take to acquire £89.64
million at the start of the year if S($/£) = $1.25/£?
1.1156
£100
£89.64=
£1.25
$1.00
£89.64 $112.05 × =
? Transactions Costs
? The interest rate available to an arbitrageur for borrowing,
i
b
,may exceed the rate he can lend at, i
l
.
? There may be bid-ask spreads to overcome, F
b
/S
a
< F/S
? Thus
(F
b
/S
a
)(1 + i
¥
l
) ÷ (1 + i
¥
b
) s 0
? Capital Controls
? Governments sometimes restrict import and export of
money through taxes or outright bans.
5-18
? Purchasing Power Parity and Exchange Rate
Determination
? PPP Deviations and the Real Exchange Rate
? Evidence on PPP
5-19
? The exchange rate between two currencies should equal
the ratio of the countries’ price levels.
S($/£) = P
$
÷P
£
? Relative PPP states that the rate of change in an
exchange rate is equal to the differences in the rates of
inflation.
e = t
$
- t
£
? If U.S. inflation is 5% and U.K. inflation is 8%, the
pound should depreciate by 3%.
5-20
The real exchange rate is
5-21
) 1 )( 1 (
1
£
$
t
t
+ +
+
=
e
q
If PPP holds, (1 + e) = (1 + t
$
)/(1 + t
£
), 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.
? PPP probably doesn’t hold precisely in the real world for
a variety of reasons.
? 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.
? PPP-determined exchange rates still provide a valuable
benchmark.
5-22
? An increase (decrease) in the expected rate of
inflation will cause a proportionate increase
(decrease) in the interest rate in the country.
? For the U.S., the Fisher effect is written as:
i
$
= µ
$
+ E(t
$
)
Where
µ
$
is the equilibrium expected “real” U.S. interest rate
E(t
$
) is the expected rate of U.S. inflation
i
$
is the equilibrium expected nominal U.S. interest
rate
5-23
If the Fisher effect holds in the U.S.
i
$
= µ
$
+ E(t
$
)
and the Fisher effect holds in Japan,
i
¥
= µ
¥
+ E(t
¥
)
and if the real rates are the same in each country
µ
$
= µ
¥
then we get the International Fisher Effect
E(e) = i
$
- i
¥
.
5-24
If the International Fisher Effect holds,
E(e) = i
$
- i
¥
and if IRP also holds
5-25
S
(F - S)
E(e) =
S
(F- S)
-i i
¥
=
$
then forward parity holds.
5-26
S
(F - S)
E(e)
) -i (i
¥ $
t
$
- t
£
IRP
PPP
FE FRPPP
IFE FP
? Efficient Markets Approach
? Fundamental Approach
? Technical Approach
? Performance of the Forecasters
5-27
? 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:
S
t
= E[S
t+1
]
and
F
t
= E[S
t+1
| I
t
]
? Predicting exchange rates using the efficient markets
approach is affordable and is hard to beat.
5-28
? 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.
5-29
? 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 EMH
5-30
? 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 advice than
following it.”
5-31
5-32
doc_924765388.pptx
This is a presentation explains several key international parity relationships, such as interest rate parity and purchasing power parity.
INTERNATIONAL
FINANCIAL
MANAGEMENT
EUN / RESNICK
Second Edition
5
International Parity
Relationships & Forecasting
Exchange Rates
Objective:
This lecture examines several key international parity
relationships, such as interest rate parity and
purchasing power parity.
5-0
? Interest Rate Parity
? Purchasing Power Parity
? The Fisher Effects
? Forecasting Exchange Rates
5-1
? Interest Rate Parity
? Covered Interest Arbitrage
? IRP and Exchange Rate Determination
? Reasons for Deviations from IRP
? Purchasing Power Parity
? The Fisher Effects
? Forecasting Exchange Rates
5-2
? Interest Rate Parity
? Purchasing Power Parity
? PPP Deviations and the Real Exchange Rate
? Evidence on Purchasing Power Parity
? The Fisher Effects
? Forecasting Exchange Rates
5-3
? Interest Rate Parity
? Purchasing Power Parity
? The Fisher Effects
? Forecasting Exchange Rates
5-4
? Interest Rate Parity
? Purchasing Power Parity
? The Fisher Effects
? Forecasting Exchange Rates
? Efficient Market Approach
? Fundamental Approach
? Technical Approach
? Performance of the Forecasters
5-5
? Interest Rate Parity Defined
? Covered Interest Arbitrage
? Interest Rate Parity & Exchange Rate Determination
? Reasons for Deviations from Interest Rate Parity
5-6
? 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.
? Since we don’t typically observe persistent arbitrage
conditions, we can safely assume that IRP holds.
5-7
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
us
)
2. trade your dollars for yen at the spot rate, invest in
Japan at i
¥
and hedge your exchange rate risk by selling
the future value of the Japanese 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.
(F/S)(1 + i
¥
) = (1 + i
us
)
5-8
Formally,
(F/S)(1 + i
¥
) = (1 + i
us
)
or if you prefer,
5-9
S
F
i
i
=
+
+
¥
$
1
1
IRP is sometimes approximated as
S
(F- S)
) -i (i
¥
=
$
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.
5-10
Spot exchange rate S($/£) = $1.25/£
360-day forward rate F
360
($/£) = $1.20/£
U.S. discount rate i
$
= 7.10%
British discount rate i
£
= 11.56%
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÷$1.25/£) invest £800 at i
£
= 11.56% for one year to
achieve £892.48. Translate £892.48 back into dollars at
F
360
($/£) = $1.20/£, the £892.48 will be exactly $1,071.
5-11
According to IRP only one 360-day forward rate,
F
360
($/£), can exist. It must be the case that
F
360
($/£) = $1.20/£
Why?
If F
360
($/£) = $1.20/£, an astute trader could make money
with one of the following strategies:
5-12
If F
360
($/£) > $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÷$1.25/£) invest £800 at 11.56%
(i
£
) for one year to achieve £892.48
iii. Translate £892.48 back into dollars, if
F
360
($/£) > $1.20/£ , £892.48 will be more than enough to
repay your dollar obligation of $1,071.
5-13
If F
360
($/£) < $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 $1,071 back into pounds, if
F
360
($/£) < $1.20/£ , $1,071 will be more than enough to
repay your £ obligation of £892.48.
5-14
You are a U.S. importer of British woolens and have just ordered
next year’s inventory. Payment of £100M is due in one year.
5-15
IRP implies that there are two ways that you fix the cash outflow
a) Put yourself in a position that delivers £100M in one year—a long
forward contract on the pound. You will pay (£100M)(1.2/£) =
$120M
b) Form a forward market hedge as shown below.
Spot exchange rate S($/£) = $1.25/£
360-day forward rate F
360
($/£) = $1.20/£
U.S. discount rate i
$
= 7.10%
British discount rate i
£
= 11.56%
5-16
To form a forward market hedge:
Borrow $112.05 million in the U.S. (in one year you
will owe $120 million).
Translate $112.05 million into pounds at the spot
rate S($/£) = $1.25/£ to receive £89.64 million.
Invest £89.64 million in the UK at i
£
= 11.56% for
one year.
In one year your investment will have grown to
£100 million—exactly enough to pay your
supplier.
5-17
Where do the numbers come from? We owe our supplier
£100 million in one year—so we know that we need to
have an investment with a future value of £100 million.
Since i
£
= 11.56% we need to invest £89.64 million at the
start of the year.
How many dollars will it take to acquire £89.64
million at the start of the year if S($/£) = $1.25/£?
1.1156
£100
£89.64=
£1.25
$1.00
£89.64 $112.05 × =
? Transactions Costs
? The interest rate available to an arbitrageur for borrowing,
i
b
,may exceed the rate he can lend at, i
l
.
? There may be bid-ask spreads to overcome, F
b
/S
a
< F/S
? Thus
(F
b
/S
a
)(1 + i
¥
l
) ÷ (1 + i
¥
b
) s 0
? Capital Controls
? Governments sometimes restrict import and export of
money through taxes or outright bans.
5-18
? Purchasing Power Parity and Exchange Rate
Determination
? PPP Deviations and the Real Exchange Rate
? Evidence on PPP
5-19
? The exchange rate between two currencies should equal
the ratio of the countries’ price levels.
S($/£) = P
$
÷P
£
? Relative PPP states that the rate of change in an
exchange rate is equal to the differences in the rates of
inflation.
e = t
$
- t
£
? If U.S. inflation is 5% and U.K. inflation is 8%, the
pound should depreciate by 3%.
5-20
The real exchange rate is
5-21
) 1 )( 1 (
1
£
$
t
t
+ +
+
=
e
q
If PPP holds, (1 + e) = (1 + t
$
)/(1 + t
£
), 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.
? PPP probably doesn’t hold precisely in the real world for
a variety of reasons.
? 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.
? PPP-determined exchange rates still provide a valuable
benchmark.
5-22
? An increase (decrease) in the expected rate of
inflation will cause a proportionate increase
(decrease) in the interest rate in the country.
? For the U.S., the Fisher effect is written as:
i
$
= µ
$
+ E(t
$
)
Where
µ
$
is the equilibrium expected “real” U.S. interest rate
E(t
$
) is the expected rate of U.S. inflation
i
$
is the equilibrium expected nominal U.S. interest
rate
5-23
If the Fisher effect holds in the U.S.
i
$
= µ
$
+ E(t
$
)
and the Fisher effect holds in Japan,
i
¥
= µ
¥
+ E(t
¥
)
and if the real rates are the same in each country
µ
$
= µ
¥
then we get the International Fisher Effect
E(e) = i
$
- i
¥
.
5-24
If the International Fisher Effect holds,
E(e) = i
$
- i
¥
and if IRP also holds
5-25
S
(F - S)
E(e) =
S
(F- S)
-i i
¥
=
$
then forward parity holds.
5-26
S
(F - S)
E(e)
) -i (i
¥ $
t
$
- t
£
IRP
PPP
FE FRPPP
IFE FP
? Efficient Markets Approach
? Fundamental Approach
? Technical Approach
? Performance of the Forecasters
5-27
? 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:
S
t
= E[S
t+1
]
and
F
t
= E[S
t+1
| I
t
]
? Predicting exchange rates using the efficient markets
approach is affordable and is hard to beat.
5-28
? 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.
5-29
? 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 EMH
5-30
? 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 advice than
following it.”
5-31
5-32
doc_924765388.pptx