topic 3 for students international parity

8/19/2019 Topic 3 for Students International Parity

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INTERNATIONAL PARITY

RELATIONSHIP


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Types of Transactions

A spot trade is an agreement toexchange currency "on the spot“

The exchange rate on a spot trade is

called the spot exchange rateA forward trade is an agreement toexchange currency at some time in thefuture.

The exchange rate that will be used isagreed upon today and is called the forward exchange rate.


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Exap!e "

The spot exchange rate for the Swissfranc is SF1 = !.1##.

The 1#!$day %&$month' forwardexchange rate is SF1 = !.()*.

This means that you can buy a Swissfranc today for !.1##+ or

,ou can agree to ta-e deliery of aSwiss franc in 1#! days and pay!.()* at that time.


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Exap!e "

The Swiss franc is more expensie in theforward mar-et %!.()* ersus !.1##'.

/ecause the Swiss franc is more

expensie in the future than it is today+ itis said to be selling at a premium relatieto the dollar.

For the same reason+ the dollar is said tobe selling at a discount relatie to theSwiss franc.


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Exap!e #

Suppose the spot exchange rate andthe 1#!$day forward rate in terms ofdollars per pound are 1.#!1 = 01

and 1.** = 01+ respectiely.

,ou expect 01million in 1#! days+ andyou agree to a forward trade to

exchange pounds for dollars. Then you will get 01million 2 1.**per pound = 1.** million.


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Exap!e #

• /ecause it is less expensie to buy apound in the forward mar-et than inthe spot mar-et %1.** ersus1.#!1'+ the pound is said to beselling at a discount relatie to thedollar.


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$o%ered InterestAr&itrage

• 3et

S0 = Spot exchange rate

F t = Forward exchange rate forsettlement at time t.

Rus = 4.S. nominal ris-$free interest

rate.Rfc = Foreign country nominal ris-$

free interest rate.


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Suppose we obsere the following informationabout 4.S. and Swiss currencies in the mar-et5

S! = 4S!.)! 6 SF1

F l = 4S!.)7 6 SF 1iUS = 1!8 %home country'

is = )8

where is is the nominal ris-$free rate in

Swit9erland.

The period is one year+ so F1 is the 7&!$day

forward rate.


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• Suppose you hae 1 to inest.• :ne option you hae is to inest the

1 in a ris-less 4.S. inestment suchas a 7&!$day T$bill.

• ;f you do this+ then in one period your1 will be worth5

alue in 1 period = 1 x %1


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Alternatiely+ you can inest in theSwiss ris-$free inestment

onert your 1 to 1 6 S0 = SF (.!!.

At the same time+ enter into a forwardagreement to conert Swiss francsbac- to dollars in one year. /ecause

the forward rate is 4S!.)7 6SF1+ youwill get !.)7 for eery SF1 that youhae in one year.


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7. ;nest your SF(.!! in Swit9erland at is. ;n

one year you will hae5

SF alue in 1 year = SF (.!! 2 %1


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• The return on inestment inSwit9erland is 11.78

• This is higher than the 1!8 returnfrom inestment in the 4S.

• There is an arbitrage opportunity andit is called coered interest arbitrage.


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Interest Rate Parity 'IRP(

There must be some relationshipbetween spot exchange rates+ forwardexchange rates+ and relatie interest

rates as such that coered interestarbitrage opportunities do not exist

;n e>uilibrium+ the forward rate di?ers

from the spot rate by a su@cientamount to o?set the interestdi?erential between two currencies.


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As such5

1 < ih = %1 < if ' 6 S!B x F1

ih = interest rate in home countryif = interest rate in foreign country

Cearranging+ we get interest rateparity %;CD' condition5

F1 = S! %1 < ih' 6 %1 < if 'B


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• To determine forward rate premium5

p = %1 < ih' 6 %1 < if 'B $ 1


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Exap!e )

Suppose the exchange rate for Eapaneseyen+ S!+ is currently 4S!.!!#7 6 ;.

The interest rate in the 4nited States

%home country' is ius = 1! percent

The interest rate in Eapan is i E = )

percent

Ghat must the forward rate be topreent coered interest arbitrageH


17/71

Answer

• F1 = S! %1 < ih' 6 %1 < if 'B

= !.!!#7 %1.1! 6 1.!)'

= !.!!#&


18/71

Answer

Forward premium5

p = %1 < !.1!' 6 %1 < !.!)'B I 1

= !.!*&

ih J if + so it must be forward premium

KS! = !.!!#7

F1 = !.!!#7 x %1 < !.!*&' = !.!!#&


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Exap!e *

Suppose the exchange rate for Lexicanpeso+ S!+ is currently 4S!.1! 6 peso.

The interest rate in the 4nited States

%home country' is ih = ) percent

The interest rate in Lexico is if = &

percent

Ghat must the forward rate be topreent coered interest arbitrageH


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Answer

• F1 = S! %1 < ih' 6 %1 < if 'B• = !.1! %1.!) 6 1.!&'•

= !.!!&


21/71

Answer

Forward premium5

p = %1 < !.!)' 6 %1 < !.!&'B I 1

= $ !.!!

ih M if + so it must be forward discount

KS! = !.1!

F1 = !.1! x %1 I !.!!' = !.!!&


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23/71

Exercise "

The treasurer of a maNor 4.S. Orm has 7! millionto inest for three months.

The annual interest rate in the 4nited States is!.() percent per month.

The interest rate in Preat /ritain is !.1 percentper month.

The spot exchange rate is 0!.)+ and the three$month forward rate is 0!.)7.

;gnoring transaction costs+ in which countrywould the treasurer want to inest the companyQsfundsH GhyH


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Answer

• ;f we inest in the 4.S. for the nextthree months+ we will hae5


25/71

Answer

;f we inest in Preat /ritain+ we mustexchange the dollars today for pounds+and exchange the pounds for dollars in

three months. After ma-ing thesetransactions+ the dollar amount wewould hae in three months would be5


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27/71

Answer


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Exercise )

Ruestion 1* %h. *+ Ladura+ (!1('

The 1$year interest rate in ew ealand is &8.

The 1$year 4.S. interest rate is 1!8.

The spot rate of the ew ealand dollar %' is4S!.)!61.

The forward rate of the ew ealand dollar is4S!.)61.

+,estions-

;s coered interest arbitrage feasible for 4.S.inestorsH

;s it feasible for ew ealand inestorsH


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Answer

• For 4.S. inestors5• ;nestment in ew ealand would

proide return of5• =


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Answer

For ew ealand inestors5

Uirect Ruotation5

Spot rate = 16!.)! = ( 6 4SU1

Forward rate = 16!.) = 1.#) 6 4SU1

;nestment in 4.S. would proide return

of5

=


31/71

Assignent

• hapter *5

R7+ R7!+ R7(+ R&

/lades+ ;nc. ase.


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P,rchasing Power

Parity


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P,rchasing Power ofParity 'PPP(

• Two forms of DDD5

$ Absolute Durchasing Dower Darity

$ Celatie Durchasing Dower Darity


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A&so!,te P,rchasingPower Parity

The basic idea behind absolute purchasing power parity is that a commodity costs thesame regardless of what currency is used topurchase it or where it is selling.

;f a bread costs 0( in 3ondon+ and the exchangerate is 1.&*60 per dollar+ then a bread costs 0(x 1.&* = 7.7 in ew ,or-.

Absolute DDD says that 1 will buy you the samenumber of+ say+ cheeseburgers anywhere in theworld. %This concept is sometimes referred to asthe !aw of one price/. '


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let S0 be the spot exchange rate between

the /ritish pound and the 4.S. dollar today%time !'+ and we are >uoting exchange rates

as the ao,nt of do!!ar per foreignc,rrency

3et Ph and Pf be the current home country

and foreign country prices+ respectiely+ on

a particular commodity+ say+ applesAbsolute DDD simply says that5

Pf = 1/S0 X Ph


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Suppose apples are selling in ew ,or-for per bushel+ whereas in 3ondon theprice is 0(.! per bushel %assume 4.S. is

the home country'. Absolute DDD impliesthat5

Puk = 1/S! X Pus

0(.! = 16S! 2 S0 = 6 0(.!

= 1.&* 6 0


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• ;f DDD did not hold+ arbitrage wouldbe possible %in principle' if appleswere moed from one country to

another.


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Suppose instead that the actual exchangerate is (60. Starting with + a tradercould buy a bushel of apples in ew ,or-+

ship it to 3ondon+ and sell it there for 0(.!. The trader could then conert the 0(.!into dollars at the preailing exchange rate+ (60+ yielding a total of 0(.! x ( = .#!.

The round$trip gain would be #! cents.

! i h i


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Re!ati%e P,rchasingPower Parity

;t tells us what determines the change in theexchange rate oer time.

Suppose the /ritish pound$4.S. dollar exchangerate is currently S0 = (60.

Further suppose that the inVation rate in /ritainis predicted to be 1! percent oer the comingyear+ and %for the moment' the inVation rate inthe 4nited States %home country' is predicted tobe 9ero.

Ghat do you thin- the exchange rate will be in ayearH

! i h i


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S! = urrent %Time !' spot exchange rate

%per foreign c,rrency'.

W%S1' = Wxpected exchange rate in period 1.

Ih = Xome country inVation rate.If = Foreign country inVation rate.

S1 = S0 x %1


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• S1 = S0 x %1


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To compute percentage change in thealue of foreign currency5

ef = %1


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• ef = %1


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• ;n general+ Celatie DDD says that thechange in the exchange rate isdetermined by the di?erence in the

inVation rates of the two countries.

R ! ti P h i


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46/71

Exap!e "

• Xome country inVation rate is )8• Foreign country inVation rate is 78•

According to DDD+ the foreigncurrency will adNust as follow5

ef = %1


47/71

Exercise "

• Assume that 1 can buy you either1!* or 0!.)).

• ;f a TY in 3ondon costs 0)!!+ whatwill that identical TY cost in To-yo ifabsolute purchasing power parityexistsH


48/71

Answer


49/71

Exercise #

;n the spot mar-et+ A1 is currentlye>ual to !.*!(.

The expected inVation rate is 7 percent

in Australia and ( percent in the 4.S.%assume 4.S. is the home country'.

Ghat is the expected exchange rate

one year from now if relatiepurchasing power parity existsH


50/71

Answer


51/71

Exercise )

;n the spot mar-et+ 1 is currentlye>ual to 0!.)).

The expected inVation rate in the 4.[.

is percent and in the 4.S. 7 percent%assume 4.S. is the home country'.

Ghat is the expected exchange rate

two years from now if relatiepurchasing power parity existsH


52/71

Answer


53/71

Exercise *

R4WST;: 1 %h.#+ Ladura+ (!1('

/oston o. will receie 1 million euros in 1 year fromselling exports. ;t did not hedge this future transaction.

/oston beliees that the future alue of the euro will be

determined by purchasing power parity %DDD'. ;t expectsthat inVation in countries using the euro will be 1(percent next year+ while inVation in the 4nited States will

be * percent next year. Today the spot rate of the euro is1.&+ and the 1$year forward rate is 1.)!.

Wstimate the amount of 4.S. dollars that /oston willreceie in 1 year when conerting its euro receiables

into 4.S. dollars.


54/71

Answer


55/71

Assignent

• hapter #5

R7)+ R7(


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Internationa! 1isherE2ect


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1isher E2ect

The relationship between a countryQs nominalinterest rate and inVation.

The Fisher e?ect suggests that the nominalinterest rate contains two components5

%1' expected inVation rate and %(' real rate ofinterest.

The real rate of interest represents the return onthe inestment to saers after accounting forexpected inVation.

Ceal rate of interest = nominal interest rate Iexpected inVation rate

Internationa! 1isher


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The international Fisher %;FW' e?ect inolestwo steps when attempting to predictexchange rate moements between twocountries5

%1' applying the Fisher e?ect to estimatethe expected inVation for each country and

%(' relying on purchasing power parity

theory %DDD' to estimate how the di?erencein expected inVation will a?ect theexchange rate.


59/71

Exap!e "

Assume that the real rate of interest is ( percent inanada and is also ( percent in the 4nited States.

Assume the 1$year nominal interest rate is 17 percentin anada ersus # percent in the 4nited States.

/ased on the Fisher e?ect+ the expected inVation rateoer the next year for anada is 178 $ (8 = 118.

For the 4nited States+ the expected inVation rate is#8 (8 = &8.

Thus+ the di?erential in expected inVation betweenthe two countries is 11 8 $ &8 = )8.


60/71

Exap!e "

%otice that this di?erential in expectedinVation between the two countries ise>ual to the di?erential in nominal interest

rates %178 #8 = )8' between the twocountries.'

Since the expected inVation is ) percenthigher in anada+ the Purchasing Power

Parity suggests that the anadian dollarshould depreciate against the 4.S. dollarby about ) percent.



61/71


• ;FW theory suggests that currencieswith high interest rates will hae highexpected inVation %due to Fisher

e?ect'.• The relatiely high inVation will cause

the currencies to depreciates %due to

DDD e?ect'.


62/71

Exap!e #

The nominal interest rate is # percent in the4nited States and ) percent in Eapan.

Assume the real rate of interest is ( percent

in each country. The 4.S. inVation rate is expected to be &percent+ while the inVation rate in Eapan isexpected to be 7 percent.

According to DDD theory+ the Eapanese yen isexpected to appreciate by the expectedinVation di?erential of 7 percent.


63/71

Exap!e #

;f the exchange rate changes as expected+ Eapanese inestors who attempt to capitali9e on thehigher 4.S. interest rate will earn a return similar towhat they could hae earned in their own country.

Though the 4.S. interest rate is 7 percent higherthan the Eapanese interest rate+ the Eapaneseinestors will repurchase their yen at the end of theinestment period for 7 percent more than the

price at which they initially exchanged yen fordollars. Therefore+ their return from inesting in the4nited States is no better than what they wouldhae earned domestically.



64/71


According to the ;FW+ the e?ectie return on a foreigninestment should+ on aerage+ be e>ual to theinterest rate on a local money mar-et inestment.

To ma-e the inestment in both countries generate

similar returns+ the foreign currency must change by5ef = %1 < ih' 6 %1 < if 'B I 1

when ih J if + ef will be positie and as such foreign

currency will appreciate.

when ih M if + ef will be negatie and as such foreigncurrency will depreciate


65/71

Exercise

• R4WST;: 1 %h.#+ Ladura+ (!1('• Assume that the spot exchange rate

of the Singapore dollar is !.*!.• The 1$year interest rate is 11 percent

in the 4nited States and * percent inSingapore.

• Ghat will the spot rate be in 1 yearaccording to the ;FWH


66/71

Answer

1orward Rates and


67/71

1orward Rates and1,t,re Spot Rates

• Ghat is the connection between theforward rate and the expected futurespot rateH

• the ,n&iased forward rates '31R( condition says that+ on aerage+ theforward exchange rate is e>ual to the

future spot exchange rate.

1orward Rates and


68/71


• The ,n&iased forward rates '31R( condition says that the forward rate. F 1 is e>ual to the expected future

spot rate+ !S1 )5• F 1 = %S1'• Gith t periods+ 4FC would be written

as5• F t = W%St'

1orward Rates and


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Suppose the forward rate for the Eapaneseyen is consistently lower than the futurespot rate by+ say+ 1! yen.

This means that anyone who wanted toconert dollars to yen in the future wouldconsistently get more yen by NOT agreeingto a forward exchange.

Then+ the forward rate would hae to rise toget anyone interested in a forwardexchange.

1orward Rates and


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• Similarly+ if the forward rate wereconsistently higher than the futurespot rate+ then anyone who wanted

to conert yen to dollars would getmore dollars per yen by NOT agreeing to a forward trade.

•

The forward exchange rate wouldhae to fall to attract such traders.


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Assignent

• hapter #5

R7*

/lades+ ;nc. ase

topic 3 for students international parity

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