FIN 645: International
Financial Management
Lecture 3
International Parity Relationships &
Forecasting Exchange Rates
Long and Short Forward
Positions
• One can buy (take a long position) or sell (take a short
position) foreign exchange forward
• A speculative forward position
– $ will likely appreciate in value against the Swiss Franc
– The trader will short the three-month $/SF contract on January
4,2008 at F3 = $0.9077
– Assume (S)he sells SF 5,000,000 forward against dollars
– On April 4, S($/SF) = $0.9007
– The trader can buy Swiss Franc spot at $0.9007 and deliver it
under the forward contract at a price of $0.9077
– Speculative profit($0.9077- $0.9007) =$0.0070
– Total profit from the trade $35000 = (SF 5,000,000x$0.0070)
– What if the $ depreciated and S3 = $0.9107?
• Graph of long and short position
Graph of Long and Short
Forward Positions
Profit(+)
F3($/SF)
Long
position
.0070
.9107
S3=($/SF)
.9007
-.0030
-F3($/SF)
Loss
F3($/SF)= .9077
Short
position
Lecture Outline
• Forces Driving Exchange Rate Changes
• Interest Rate Parity (IRP)
– Covered Interest Arbitrage
– IRP and Exchange Rate Determination
– Reasons for Deviations from IRP
• The Law of One Price
– The two things that are equal to each other must be
selling for the same price
• Forecasting Foreign Exchange Rates?
• How are Foreign Exchange Rates Determined?
Lecture Outline
• Purchasing Power Parity (PPP)
–PPP Deviations and the Real
Exchange Rate
–Evidence on PPP
• The Fisher Effect
• Forecasting Exchange Rates
– Efficient Market Approach
– Fundamental Approach
– Technical Approach
– Performance of the Forecasters
Arbitrage Equilibrium
• The term Arbitrage can be defined as the act of
buying and selling the same or equivalent assets
or commodities for the purpose of making certain
guaranteed profit.
• As long as there are profitable arbitrage
opportunities, the market cannot be in
equilibrium
• The market is said to be in equilibrium when no
profitable arbitrage opportunities exist
• Parity relationships such as IRP and PPP, in fact,
represent arbitrage equilibrium condition
Interest Rate Parity Defined
• IRP is an arbitrage condition that must
hold when international financial markets
are in equilibrium.
• 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.
Interest Rate Parity Defined
Suppose you have $ 1 to invest for 1 yr.
You can either
1. invest in the U.S. at i$, receive future maturity value
= $1 (1 + i$); or
2. exchange your dollars for pound at the spot rate
(S), get £(1/S),
3. invest in the U.K. at interest rate i£ , with the maturity
value of £(1/S) (1 + i£).
4. hedge your exchange rate risk by selling the future
value of the U.K investment forward (for a
predetermined dollar amount). The future value =
$[(1/S)(1 + i£)] F, where F denotes the forward
exchange rate.
Interest Rate Parity Defined
• Please note that when your British investment
matures in one year, you will receive the full
maturity value, £(1/S) (1 + i£). But you have to
deliver exactly the same amount of pounds to the
counterparty of the forward contract, your net
pound position is reduced to zero. In other words,
the exchange risk is completely hedged
• You have effectively denominated the UK
investment in dollar terms
• Since both of these investments have the same
risk, they must have the same future value—
otherwise an arbitrage opportunity would exist.
(F/S)(1 + i£) = (1 + i$)
Interest Rate Parity Defined
Formally,
(F/S)(1 + i£) = (1 + i$)
or if you prefer, 1  i
$
F

1  i£ S
IRP is sometimes approximated as
(F- S)
(i$ -i£ ) 
S
IRP is a manifestation of the law of one price (LOP) to
international money market instruments.
Alternative Derivation IRP
• IRP can also be derived by constructing an
arbitrage portfolio, which involves (i) no net
investment; (ii) no risk, and then requiring that
such a portfolio should not generate any net cash
flow in equilibrium
• Consider an arbitrage portfolio consisting of three
separate positions:
– Borrow $S in the US, which is just enough to buy £1 at
the prevailing spot exchange rate (S).
– Lending £1 in the UK at the UK interest rate
– Selling the maturity value of the UK investment forward
Dollar Cash Flows to An Arbitrage
Portfolio
Transactions
CF0
CF1
1. Borrow in the U.S.
$S
-S(1+i$)
2. Lend in the U.K.
-$S
S1(1+i£)
3. Sell the £ receivable
forward*
0
(1+i£)(F-S1)
Net cash flow
0
(1+i£)F-(1+i$)S
• Selling the £ receivable “forward” will not result in any cash flow at the present
time, that is, CF0=0. But at the maturity, the seller will receive $(F-S1) for each
pound sold forward. S1 denotes the future spot exchange rate.
Dollar Cash Flows to An Arbitrage
Portfolio
• Note that:
– The Net cash flow at the time of investment is
zero; i.e. the arbitrage portfolio is self
financing; it does not cost any money to hold
this portfolio;
– The net cash flow on the maturity date is
known with certainty, because S,F, i£, and i$ are
all known.
• Since no one should be able to make certain
profits by holding this arbitrage portfolio, market
equilibrium requires that the net cash flow on the
maturity date be zero for this portfolio:
(1+i£)F-(1+i$)S=0
IRP and Interest Rates
• The IRP relationship is often approximated by:
(i$- i£) = (F-S)/S
• From the above relationship, it can be seen that
IRP provides a relationship between interest rate
of two countries.
– Interest rate will be higher in the US than in the UK
when the dollar is at a forward discount, i.e. F>S
– Interest rate will be higher in the UK than in the US
when the dollar is at a forward premium, i.e. F<S
• Forward exchange rate will deviate from the spot
rate as long as the interest rates of the two
countries are not the same.
Covered Interest Arbitrage
• When IRP holds, you will be indifferent between
investing your money in the US and investing in
the UK with forward hedging.
• If IRP is violated, you will be better off by
investing in the US(U.K) if (1 + i$) is greater
(less) than (F/S)(1 + i£).
• On the other hand, if you need to borrow, you will
choose to borrow where the dollar interest rate is
lower.
• When IRP does not hold, the situation gives rise to
covered interest arbitrage opportunities
Covered Interest Arbitrage: Cash
Flow Analysis
Transactions
CF0
CF1
1. Borrow $1,000,000
$1,000,000
-$1,050,000
2. Buy £ spot
-$1,000,000
£666,667
3. Lend £666,667
-£666,667
4. Sell 720,000 forward
Net cash flow
£720,000
£720,000
$1,065,600
0
$ 15,600
Interest Rate Parity Diagram
(F-S)/S (%)
IRP line
4
3
2
B
1
-4
-3
A
-2
-1
1
-1
-2
-3
-4
2
3
4
(i$-i£)(%)
Another CIA Example
• Three month interest rate in the US: 8.0%
per annum
• Three month interest rate in Germany:
5.0% per annum
• Current spot exchange rate: € 1.0114/$
• Three-month forward exchange rate: €
1.0101/$
• Again, we assume that the arbitrager can
borrow $1,000,000 or the equivalent €
amount, € 1,011,400
• Calculate arbitrage profit, if any.
Covered Interest Arbitrage: Cash
Flow Analysis 2
Transactions
1. Borrow € 1,011,400
2. Buy $ spot
3. Lend $1,000,000
CF0
CF1
€ 1,011,400
-€
1,024,042.50
- € 1,011,400
$1,000,000
-$1,000,000
-€ 1,024,042.50
$1,013,803
4. Buy 1,024,042.50
forward
Net cash flow
$1,020,000
0
$ 6,197
Covered Interest Arbitrage
(CIP)
• Covered Interest Arbitrage is a situation
which occurs when IRP does not hold,
thereby allowing certain arbitrage profits
to be made without the arbitrageur
investing any money out of pocket or
bearing any risk.
• To see if any CIP opportunities exist?,
Verify
 (F- S)
(i$ -i£ )
(1  i£ )

S
Deviations from IRP and
Market Adjustments
• How long will the arbitrage opportunity will last?
• As soon as deviations from IRP are detected,
informed traders will carry out CIA transactions
– Borrow in the US, interest rate in the US will rise (i$ ↑)
– Lend in the UK, interest rate will fall in the UK(i£↓)
– Buy the pound spot, the pound will appreciate in the spot
market (S↑)
– Sell the pound forward, the pound will depreciate in the
forward market (F↓)
• These adjustments will raise LHS of IRP equation and
lower the RHS until both sides are equalized,
restoring IRP
IRP and Exchange Rate
Determination
• IRP relationship can be written as
• S = [(1 + i£)/(1 + i$)]*F, i.e. given the forward
exchange rate, the spot exchange rate depends
on the relative interest rates.
• All else equal, in this example, an increase in the
US interest rate will attract capital to the US,
increasing demand for dollars and will lead to a
lower spot exchange rate -higher foreign
exchange value of the dollar.
• A decrease in the US interest rate will lower
foreign exchange value of the dollar.
IRP and Exchange Rate
Determination
• In addition to the relative interest rates,
the forward exchange rate is an important
determinant of the spot exchange rate.
• Under certain conditions, the forward
exchange rate can be viewed as the
expected future spot exchange rate
conditional on all relevant information
being available now.
F = E(St+1|It)
IRP and Exchange Rate
Determination
• S = [(1 + i£)/(1 + i$)]* E(St+1|It)
• “Expectation” plays a key role in
exchange rate determination, i.e. the
expected future exchange rate is the
major determinant of the current
exchange rate.
• Exchange rate behavior will be driven
by news events(It)
Uncovered Interest Parity
• When the forward exchange rate F is
replaced by the expected exchange rate,
E(St+1), we get the uncovered interest rate
parity relationship shown below:
(i$- i£) = E(e), where E(e) is the expected rate of
change in the exchange rate, i.e. [E(St+1)-
St]/St
• Interest rate differential between a pair of
countries is (approximately ) equal to the
expected rate of change in the exchange
rate.
Reasons for Deviations from
IRP
• Transactions Costs
– The interest rate available to an arbitrager for
borrowing, ib,may exceed the rate he can lend
at, il.
– There may be bid-ask spreads to overcome,
Fb/Sa < F/S
– Thus
(Fb/Sa)(1 + i¥l)  (1 + i¥ b)  0
• Capital Controls
– Governments sometimes restrict import and
export of money through taxes or outright bans.
Interest Rate Parity With
Transaction Costs
(F-S)/S (%)
IRP line
4
3
2
D
1
-4
C
-3
-2
-1
-1
-2
-3
Unprofitable
arbitrage
-4
1
2
3
4
(i$-i£)(%)
Deviations from Interest
Rate Parity
• Empirical evidence
– Japan imposed capital controls off and on until December 1980
– Otani and Tiwari investigated the effect of capital controls on IRP
deviations during 1978-81. They compute deviations from IRP
DIRP = [(1+i¥)S/(1+i$)F] -1
– If IRP strictly holds deviations from it would be randomly distributed,
with the expected value of zero. They found that deviations from IRP
hardly hover around zero. Highest during 1978(Japan discouraged
capital inflows to keep the yen from appreciating). As these were
removed deviations decreased in 1979. Increased again in 1980, as
Japanese financial institutions were asked to reduce FC deposits. In
December 1940, Japan liberalized FE transactions, deviations close to
zero
– Deviations from IRP, especially in 1978 and 1980, do not represent
unexploited profit opportunities, rather barriers to cross border
arbitrage.
Purchasing Power Parity
• Purchasing Power Parity and
Exchange Rate Determination
• PPP Deviations and the Real
Exchange Rate
• Evidence on PPP
Purchasing Power Parity and
Exchange Rate Determination
• Absolute PPP
– The exchange rate between two currencies should equal
the ratio of the countries’ price levels.
S(h/f) = Ph Pf
h (home currency) and f (foreign currency); Ph (home price level)
Pf (foreign price level)
• Standard commodity basket in the US is $225, in the UK
£150, the exchange rate should be $1.50 per pound.
• PPP requires that the price of the standard commodity
basket be the same across countries when measured in a
common currency.
“A Feast of Burgernomics”
“A Feast of Burgernomics”
Purchasing Power Parity and
Exchange Rate Determination
• Derivation of Relative PPP:
– Assume that price of the home country Ph and
the foreign country Pf are equal.
– Home and foreign country experiences inflation
rate of πh and πf respectively.
– Home and foreign country price indices
become Ph (1+ πh) and Pf (1+ πf ) respectively.
– If πh > πf or πf > πh, PPP does not hold.
– Exchange rate will change to maintain the
parity in purchasing power
Purchasing Power Parity and
Exchange Rate Determination
Pf(1+f )(1+ef )=Ph(1+h), where ef represents
the change in the value of the foreign currency
Solving for ef we have
(1+ef ) = Ph(1+h)/ Pf(1+f ); or ef= [(1+h)/
(1+f )]-1
-since we assumed that Ph and Pf were initially
equal in both countries.
The formula reflects the relationship between
relative inflation rate and the exchange rate.
The formula can also be expressed as e=(hf )/(1+f ) which can be approximated
by e= h- f
Purchasing Power Parity and
Exchange Rate Determination
– If h> f , ef should be positive
• foreign currency will appreciate when home country’s
inflation exceeds the foreign country’s inflation.
– If f> h, ef should be negative
• foreign currency will depreciate when foreign country’s
inflation exceeds the home country’s inflation.
• Relative PPP states that the rate of change
in an exchange rate is equal to the
differences in the rates of inflation.
e = h - f
• If U.S. inflation is 5% and U.K. inflation is
8%, the pound should depreciate by 3%.
Purchasing Power Parity and
Exchange Rate Determination
• PPP and monetary approach, associated with Chicago
School
– Based on two basic tenets: PPP and quantity theory of money
From quantity theory of money the following identity must
hold for each country
Ph=MhVh/yh, and Pf=MfVf/yf
where M denotes money supply, V the velocity of money, y
the national aggregate output, P is the general price level
• Substituting the above two equations are substituted for
the
price levels in the PPP equation, we have:
S = Ph / Pf = (Mh/Mf)(Vh/Vf)(yh/yf
Purchasing Power Parity and
Exchange Rate Determination
•
•
According to the monetary approach, what
matters in exchange rate determination are:
1. The relative money supplies
2. The relative velocity of money
3. The relative national outputs
All else equal an increase in home money supply
will



•
result in proportionate depreciation of the home
currency
so will an increase in velocity of home currency, which
is the same as increase in supply of home currency;
But increase in home output will cause appreciation of
home currency
The monetary approach can be viewed as a
long-run theory


It assumes prices adjusts fully and completely
In the short run there are price rigidities such as wage
rate set by labor contract
PPP Deviations and the
Real Exchange Rate
•If PPP holds and thus differential inflation rates
between countries are exactly offset by exchange
rate changes, countries’ competitive positions in
world export market will not be systematically
affected by exchange rate changes.
•If there are deviations, changes in the nominal
exchange rate cause changes in the real exchange
rates, affecting international competitiveness and
thus trade balances.
PPP Deviations and the
Real Exchange Rate
The real exchange rate is:
q= (1 + h)/[(1 + e)(1 + f)]
If PPP holds, (1 + e) = (1 + h)/(1 + f), then q = 1.
If q < 1 competitiveness of domestic country improves with
currency depreciations.
If q = 1 competitiveness of domestic country unaltered with
currency depreciations
If q > 1 competitiveness of domestic country deteriorates
with currency depreciations.
Evidence on PPP
• PPP probably doesn’t hold precisely in the real world for a
variety of reasons.
– Substantial barriers to international commodity arbitrage exists
– Haircuts cost 10 times as much in the developed world as in the
developing world: non-tradeables.
– Shipping costs, as well as tariffs and quotas can lead to
deviations from PPP.
• PPP-determined exchange rates still provide a valuable
benchmark
– In deciding if if a country’s currency is overvalued or
undervalued.
– Can often be used to make more meaningful international
comparisons of economic data using PPP-determined rather than
market determined exchange rates.
– Size of the economy
Comparison of GNP Per
Capita
Country
GNP per Capita
GNP per Capita
US$
PPP
Bangladesh
350
1,407
Higher PPP GNP per Capita
India
440
2,060
Higher PPP GNP per Capita
Nepal
210
1,181
Higher PPP GNP per Capita
Pakistan
470
1,652
Higher PPP GNP per Capita
Singapore
30,170
25,295
Lower PPP GNP per Capita
Japan
32,350
23,592
Lower PPP GNP per Capita
Malaysia
3,670
7,699
Higher PPP GNP per Capita
Thailand
2,160
5,524
Higher PPP GNP per Capita
China
750
3051
Higher PPP GNP per Capita
Remarks
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.
• For the home country, the Fisher effect is written as:
ih = h + E(h)
Where
h is the equilibrium expected “real” home country’s
interest rate
E(h) is the expected rate of home country’s inflation
ih is the equilibrium expected nominal home interest rate
International Fisher Effect
If the Fisher effect holds in the home country
ih = h + E(h)
and the Fisher effect holds in the foreign
country
if = f + E(f )
and if the real rates are the same in each
country
h = f
then we get the International Fisher Effect
E(e) = ih - if .
International Fisher Effect
If the International Fisher Effect holds,
E(e) = ih - if
and if IRP also holds
ih – if =(F-S)/S
then forward expectation parity holds.
(F - S)
E(e) 
S
Equilibrium Exchange Rate
Relationships
E(e)
IFE
FEP
PPP
(i$ -i¥ )
(F - S)
S
IRP
FE
FPPP
$ - £
Forecasting Exchange Rates
• Efficient Markets Approach
• Fundamental Approach
• Technical Approach
• Performance of the Forecasters
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, which is
unpredictable. So, the exchange rate will change
randomly over time. Thus, according to the
random walk hypothesis, today’s exchange rate
is the best predictor of tomorrow’s exchange
rate:
St = E[St+1]
While researchers found it difficult to reject the
random walk hypothesis on empirical grounds,
there is no theoretical base of this either.
•
Efficient Markets Approach
• The parity relationships indicate that the current
•
forward exchange rate can be viewed as the
market’s consensus forecast of the future
exchange rate based on the available information
(It) if the foreign exchange markets are efficient,
that is,
Ft = E[St+1| It]
To the extent that interest rates are different
between two countries, the forward exchange
rates will be different from the current spot
exchange rate.
Efficient Markets Approach
• The efficient market hypothesis subscriber may
predict the future exchange rate using either the
current spot exchange rate or the current forward
exchange rate. But which one is better?
– The empirical findings indicate that these two models
registered comparable performances.
• Predicting exchange rates using the efficient
markets approach is affordable and is hard to
beat.
• Advantages of efficient market hypothesis:
– Since both the current spot and forward exchange rates
are public information, generating forecasts using EMH
is costless and freely accessible.
– It is difficult to outperform the market-based forecasts
unless the forecaster has access to private information
that is not yet reflected in the current exchange rate.
Fundamental Approach
• The fundamental approach to exchange
rate forecasting uses various models that
involve econometrics using 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.
Fundamental Approach
• Difficulties of fundamental approach:
 Forecasting a set of independent variables to forecast the
exchange rates
 Forecasting the former will certainly be subject to errors and
may not be necessarily easier than forecasting the latter
 The parameter values (α,β’s) that are estimated using
historical data may change over time because of changes in
government policies and/or the underlying structure of the
economy. Either difficulty can diminish the accuracy of
forecasts even if the model is correct.
 The model itself and thus, the resulting forecasting can be
wrong.
Researchers found that the fundamental models failed to
more accurately forecast exchange rates than either the
forward rate model or the random walk model.
•
Technical Approach
• Technical analysis looks for patterns in the past behavior of
exchange rates and then projects them into the future to
generate forecasts.
• Clearly it is based upon the premise that history repeats
itself.
• Thus it is at odds with the EMH and differs from
fundamental approach in that it does not use the key
economic variables such as money supplies or trade
balances for forecasting exchange rates.
• Example: Moving average crossover rule.
 Moving averages are computed as a way of separating short-
and long-term trends from the vicissitudes of daily exchange
rates and exchange rates may be forecasted based on the
movements of short term moving average(SMA) and long-term
moving average(LMA).
Moving Average Crossover
Rule: A Technical Analysis
D
LMA
A
SMA
tA
Time
tD
Technical Analysis
• While academic studies tend to discredit the
validity of technical analysis, many traders
depend on technical analysis for their trading
strategies. If enough traders use this, the
predictions based on it can become self-fulfilling
to some extent, at least in the short run.
Performance of the
Forecasters
• Instead of using market-determined price such as the forward
exchange rate, some firms and investors subscribe to professional
forecasting services for a fee.
• But can professional forecasters outperform the market?
• Professor Richard Levich of New York University evaluated the
performance of 13 forecasting services that uses different methods of
forecasting (econometrics, technical and judgmental) using the forward
exchange rate as a benchmark–the market’s consensus forecast of
future exchange rate under certain conditions.
• In evaluating the performance of forecasters, Levich computed the
following ratio:
• R = MAE (S)/ MAE (F)
where:
– MAE (S) = mean absolute forecast error of a forecasting service
– MAE (F) = mean absolute forecast error of the forward exchange rate as a
predictor
If MAE (S) < MAE (F), the ratio R will be less than unity for the service
=Professional forecasting provides more accurate forecasts than the forward
exchange rate.
Performance of the
Forecasters
•
•
•
•
Findings:
 24% (25 out of 104) are less than unity, that is, professional
services clearly failed to outperform the forward exchange
rate.
 There are substantial variations in the performance records
across individual services and also across currencies, which
suggests that consumers need to discriminate among
forecasting services depending on what currencies they are
interested in.
Eun and Sabherwal (2002) evaluated the forecasting performance
of 10 major commercial banks around the world using the spot
exchange rate as the benchmark. As a whole, they could not
outperform the random walk model.
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.”
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.
Spot exchange rate
S($/£) = $1.25/£
360-day forward
rate
F360($/ = $1.20/£
£)
U.S. discount rate
i$ = 7.10%
British discount
rate
i£ = 11.56%
IRP and Covered Interest
Arbitrage
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 $1,071.
Interest Rate Parity
& Exchange Rate Determination
According to IRP only one 360-day
forward rate,
F360($/£), can exist. It must be the
case that
F360($/£) = $1.20/£
Why?
If F360($/£)  $1.20/£, an astute trader
could make money with one of the
following strategies:
Arbitrage Strategy I
If F360($/£) > $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 $1,071.
Arbitrage Strategy II
If F360($/£) < $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/£ , $1,071 will be
more than enough to repay your £
obligation of £892.48.
IRP and Hedging Currency
Risk
You are a U.S. importer of British woolens and
have just ordered next year’s inventory. Payment
of £100M is due in one year.
Spot exchange rate
S($/£) = $1.25/£
360-day forward
rate
F360($/ = $1.20/£
£)
U.S. discount rate
i$ = 7.10%
British discount
i£ = 11.56%
IRP implies that
ratethere 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.
IRP and a Forward Market
Hedge
To form a forward market hedge:
Borrow $112.05 million in the U.S. (in one year you will
owe $120 million).
Translate $112.05 million into pounds at the spot rate
S($/£) = $1.25/£ to receive £89.64 million.
Invest £89.64 million in the UK at i£ = 11.56% for one
year.
In one year your investment will have grown to £100
million—exactly enough to pay your supplier.
Forward Market Hedge
Where do the numbers come from? We owe our supplier
£100 million in one year—so we know that we need to have
an investment with a future value of £100 million. Since i£ =
11.56% we need to invest £89.64 million at the start of the
year.
£100
£89.64 
1.1156
How many dollars will it take to acquire £89.64
million at the start of the year if S($/£) = $1.25/£?
$1.00
$112.05  £89.64 
£1.25