06 inbu 4200 fall 2010 parity models and the foreign exchange rate (1)

8/9/2019 06 INBU 4200 Fall 2010 Parity Models and the Foreign Exchange Rate (1)

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Parity Models and Foreign Exchange Rates

Assessing the Correctness of the Current

Spot Rate and Estimating Future SpotRates with Parity Models:!" Purchasing Power Parity and#" $nternational Fisher Effect


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What are Parity Models?

Parity is defined as a state of e%uili&rium'Foreign e(change parity models estimatewhat the e%uili&rium spot e(change rateshould &e under the model)s assumptions":

$s today)s spot rate appropriate*+hat might the spot rate &e in the futureforecasting"'

,enerally a long term forecasting hori-on'

Parity models ha.e an economic &asis i'e'/theory" for their spot rate determination'


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Why are Parity Models

Important? 0esting the correctness of a spot rate'Could &e important for a trading strategy'$s the currency o.er.alued or under.alued*

1.er.alued: perhaps a sell short strategy'2nder.alued: perhaps a &uy long strategy'

Esta&lishing a future spot rateCould &e important for:

$nternational capital &udgeting decisionsCon.erting estimated foreign currency cash flows into M3C)s

home currency as part of the capital &udgeting process'$n.estment and Financing decisionsCon.erting estimated in.estment inflows into home currencye%ui.alents and con.erting estimated financing outflows intohome currency e%ui.alents'


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Two Major Spot FX Parity

ModelsPurchasing Power Parity PPP"Model &ased on relati.e rates of inflation&etween two countries as the

determinant of the spot e(change rate'$nternational Fisher Effect $FE"

Model &ased on relati.e rates of interest

&etween two countries as thedeterminant of the spot e(change rate '


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P rchasing Power Parity

Theory 0he Purchasing Power Parity PPP" e(plains and%uantifies the relationship &etween inflation and spote(change rates'0he theory states that the spot e(change rate&etween two currencies should &e e%ual to the ratioof the two countries) price le.els'

$dea was first proposed &y the classical economist/ 4a.idRicardo/ in the !5 th century'

0he concept was fully de.eloped &y the Swedisheconomists/ ,usta. Cassel/ during the years after ++!!5!6 7" when countries in Europe were e(periencinghyperinflation'


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Rationale "ehind the PPP#The $aw o! %ne Price

0he Purchasing Power Parity model is &asedon the 9aw of 1ne Price:

0he 9aw of 1ne Price states that all else e%ual

i'e'/ no transaction costs or other frictions/ li etariffs or cultural differences" a product)s priceshould &e the same in all mar ets '+hy will the product)s price &e the same*

0he principle of competiti.e mar ets assumes thatprices will e%uali-e as consumers shift their purchasesto those mar ets or countries" where prices are thelowest'


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&'sol te PPP and Exchange Rates

0he A&solute PPP states that/ in e%uili&riumafter ad8usting for e(change rates/ the pricesfor similar products should &e the same '

;ased on 9aw of 1ne Price'

E(ample 2sing the 2'S' and


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Example# $aw o! %ne Price

Assume: A ;ig Mac ham&urger costs =#'@@ in the 2nited Statesand0he current yen spot e(change rate 2S4


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The &'sol te PPP Spot Exchange Rate

+e can arrange the 9aw of 1ne Price formula/ which is P= Spot Rate ? P>/ to calculate the A&solute PPP Spot E(changeRate:

A&solute PPP Spot Rate ? P> P=3ote: 0he A&solute PPP is calculated &y the ratio of the two localcurrency prices

0he A&solute PPP spot e(change rate is the e%uili&rium spote(change rate which will result in the prices of similar goods in

one country to &e e%ual to the prices of those goods in anothercountry'


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Example# (alc lating the &'sol te PPP Spot Exchange Rate Assuming a ;ig Mac ham&urger cost =#'@@ in the 2'S' and

D@@ yen in


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&'sol te PPP Spot Exchange Rate# E ropean Terms and &merican Terms,i.en that the a&solute PPP spot rate is simply the ratio

of the two prices of similar goods or a &as et of goods"in two local currencies/ we can sol.e for this e%uili&riume(change rate for either a European terms or an

American terms %uoted currency as follow:For European terms E0":

A&solute PPP E0 ? Foreign price 2'S' priceFor American terms A0":

A&solute PPP A0 ? 2'S' price Foreign price'+e then compare the calculated A&solute PPPe%uili&rium spot rate to the actual spot rate to determineif the currency is o.er.alued or under.alued'


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E ropean Terms Example;ig Mac: 2nited States : =D' ! e(cluding ta(es"

;ig Mac: DD@ e(cluding ta(es"Calculate A&solute PPP European 0erms as follows:

A&solute PPP Spot E(change Rate ? Ben Price 4ollar Price A&solute PPP Spot E(change Rate ? >DD@ =D' !? >66'5

0he A&solute PPP Spot rate is then compared to the actual rate/to determine if the current spot rate is o.er.alued or under.alued'

Rate on 1cto&er !D/ #@!@: 6!'6Guestion: +hat is this model telling us a&out the yen)s current

spot rate i'e'/ is it o.er.alued or under.alued*" A3S+ER:1.er.alued/ &y a&out 5H

66'5 I 6!'6 " 66'5 ? @'@6 H


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&merican Terms Example;ig Mac: 2nited States: =D' ! e(cluding ta(es"

;ig Mac: 2nited Jingdom: K#'D@ e(cluding ta(es"Calculate A&solute PPP American 0erms as follows:

A&solute PPP Spot E(change Rate ? 4ollar Price Pound Price A&solute PPP Spot E(change Rate ? =D' ! K#'D@ ? =!'L!D@

Compare this A&solute PPP Spot rate to the actual rate:Rate on 1cto&er !D/ #@!@: !' 6 LGuestion: +hat is this model telling us a&out the pound)sspot rate i'e'/ is it o.er.alued or under.alued*"

A3S+ER:2nder.alued &y a&out #H"

!' 6 L I !'L!D@" !' 6 L ? @'@! H


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R les !or the &'sol te PPP0he A&solute PPP can &e used to estimate whether

a foreign currency)s spot rate is o.er.alued orunder.alued and &y how much using the following: A&solute PPP European 0erms:

$f PPP Spot Current Spot/ then the currency is under.alued'E'g': PPP ? !@@N Current Spot ? !!@

$f PPP Spot O Current Spot/ then the currency is o.er.alued'E'g': PPP ? !@@N Current Spot ? 5@

A&solute PPP American 0erms:$f PPP Spot O Current Spot/ then the currency is under.alued'

E'g': PPP ? =!'#@N Current Spot ? =!'@@$f PPP Spot Current Spot/ then the currency is o.er.alued'

E'g': PPP ? =!'#@ Current Spot ? =!' @


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)sing the &'sol te PPP $n theory/ the a&solute PPP Spot e(changerate can &e used to assess the correctness of a current spot rate on the &asis of similargoods in different countries'

$t suggests the possi&ility that a currency iso.er.alued or under.alued / and &y how much *

+here can we get data for the A&solute PPPmodel*

0he ;ig Mac inde('http: www'economist'com mar ets ;igmac $nde('cfm
http://www.economist.com/markets/Bigmac/Index.cfmhttp://www.economist.com/markets/Bigmac/Index.cfmhttp://www.economist.com/markets/Bigmac/Index.cfmhttp://www.economist.com/markets/Bigmac/Index.cfm


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"ig Mac Index October 14, 2010

Interpreting the Data$n the 2nited States/ a ;ig Maccosts =D' !'$n China/ a ;ig Mac costs ! 'yuan'

,i.en the current e(change rate2S4 C3B" of L'L ! a ;ig Mac inChina wor s out to =#'!6! ' L'L ! "' 3ote this is the ;igMac price on the chart'

0he A&solute PPP for the yuanis the ratio of the yuan cost tothe dollar cost/ or: ! ' D' ! ?

D'5@6 'Comparing spot L'L ! " to PPPD'5@6 " re.eals that the yuan isunder.alued &y !H

L'L ! 7D'5@6 L'L ! ? ' !H"


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%ne Test o! the "ig*Mac# The Introd ction o! the E ro

0he Euro was introduced on


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What +appened to the E ro? The E ro# ,an ary -. -/// 0 1ecem'er

2-. -///


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&'sol te PPP in Practice$n practice/ use of the a&solute PPP to test thecorrectness of a spot e(change rate depends ona num&er of factors:

,oods that are trada&leN necessary for the assumptionof competiti.e mar ets',oods that are compara&le' Are the goods really similarin %uality and %uantity*

A rigorous test would in.ol.e a mar et &as et of goods/ not 8ustone'Mar et &as et PPP e(change rates are pu&lished &y the 1EC4and the +orld ;an '

http: stats'oecd'org $nde('asp(*datasetcode?S3A 0A;9ESee ne(t slide

Are there go.ernment policies tariffs and %uotas" orcultural differences which render such goods not usefulfor a&solute PPP calculations*
http://stats.oecd.org/Index.aspx?datasetcode=SNA_TABLE4http://stats.oecd.org/Index.aspx?datasetcode=SNA_TABLE4


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%E(1 PPP Exchange Rates 'y 3ear


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( lt ral 1i4erences and5o6ernment Policy Impactson &'sol te PPP Cultural Differences Tariffs and Quotas


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Testing yo r)nderstanding o! the

&'sol te PPP Model,i.en:C-ech Repu&lic Price of a Star&uc )s enti 9atte:!@ CTJ crown"

2'S' Price of a Star&uc )s enti 9atte: =D' A&solute PPP ? !@ D' ? D@' 2S4 CTJ"Current spot rate ? ! ' 2S4 CTJ"

Estimate the correctness of the current spot ratefor the CTJ' $s it o.er.alued or under.alued*+hat trading strategy might you consider in lightof your findings*


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Examining 1iscrepancies !rom &'sol te PPP

+hen a discrepancy from A&solute PPP is identified/it is pro&a&ly useful to e(amine reasons for thediscrepancy to determine if the spot rate will/ or willnot/ mo.e towards the A&solute PPP'$ssues to consider:

E(amine the e(change rate regime and the commitment ofthe go.ernment for that e(change rate regime'

4oes this account for the discrepancy &etween the A&solute PPPand the spot rate*

Chinese yuan is under.alued &y !H ;ig Mac"

Are there economic or financial conditions which couldaccount for the o&ser.ed discrepancy and how long mightthey dominate the spot rate*

Relati.e economic performance/ interest rates/ trade &alances/capital flows/ etc'

;ra-ilian real is o.er.alued &y @H ;ig Mac"


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Relati6e P rchasing Power Parity

0he second PPP model/ the relati.e PurchasingPower Parity model is concerned with the rate ofchange in the e(change rate'

$t is not assessing the correctness of the current spot rate'

0he relati.e PPP model suggests that spote(change rates mo.e in a manner opposite to theinflation differential &etween the two countries'

Specifically/ the Relati.e PPP model suggests that the

percent change in a spot e(change rate should &e e%ual to/&utopposite in direction to / the difference in the rates ofinflation &etween countries'


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Relati6e PPP Example Assume the following:

Annual rate of inflation in 2'S' ? #'@H Annual rate of inflation in 2'J' ? D'@H

According to the Relati.e PPP/ the ;ritish poundshould depreciate !H per year against the 2'S'

dollar'0hus/ if the current spot rate is =!'6@/ then! year from now the spot rate should &e: =!' 6#@

=!'6@ I !'6@ (' @!" ? =!' 6#@

3ote: 0his represents a depreciation of !H o.er the currentspot rate' An amount which is e%ual to the inflation differential'

3ote: See Appendi( ! for specific Relati.e PPP formulas'


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PPP %6er the $ong Term.-/78 * 9888


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The Relati6e PPP in Practice+hile historical data tends to .alidate the

relati.e PPP see last slide"/ the practicalissue for users is estimating future rates ofinflatio'

Uow can we do this*2se recent historical data to estimate the future/ orfor a &enchmar starting point'Com&ine historical data with li ely outcomes whichmight affect inflation e'g'/ go.ernment deficits/economic growth/ monetary policy"2se independent forecasts of inflation date


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+istorical In:ation 1ata

Uistorical and Current 4ata:isit Central ;an +e& sites at:

http: www'&is'org c&an s'htm1r .isit the Economist

http: www'economist'com inde('html9in to Economic and Financial $ndicatorsgo to output/ prices and 8o&s data"'See ne(t slide
http://www.bis.org/cbanks.htmhttp://www.economist.com/index.htmlhttp://www.economist.com/index.htmlhttp://www.bis.org/cbanks.htm


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The Economist, InfationData


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Where can we get In:ation Forecasts?

For Forecasts of $nflation:isit: 0he Economist Maga-ine once amonth/ they pu&lish forecasts forinflation"'

See 3e(t Slide


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The Economist# Monthly Forecasts !or In:ation;%cto'er / th S>
http://www.economagic.com/mgif/M2408019402042223066702626347.gifhttp://www.economagic.com/mgif/M2408019402042223066702626347.gif


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Fisher E4ect# International &ss mptions1n an international le.el/ the Fisher Model assumes

that the real rate re%uirement is similar across ma8orindustrial countries'

Uow realistic is this assumption see ne(t slide"*

0hus any o&ser.ed mar et interest rate differences &etween counties is accounted for on the &asis ofdifferences in inflation e(pectations 'E(ample:

$f the 2nited States ! year mar et interest rate is H andthe 2nited Jingdom ! year mar et interest rate is H/ then:0he e(pected rate of inflation o.er the ne(t !# months must&e #H higher in the 2'J' compared to the 2'S'


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Real Rate Re= irements


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Part 9# International Fisher E4ect0he second part of the Fisher model/ the $nternational

Fisher $FE" effect assumes that:Changes in spot e(change rates are related to differences inmar et interest rates &etween countries'

+hy this assumption*;ecause differences in interest rates capture differences ine(pected inflation'

$FE relationship to E(change RatesCurrencies of high interest rate countries will wea en'

+hy: 0hese countries ha.e high inflationary e(pectations

Currencies of low interest rate countries will strengthen'+hy: 0hese countries ha.e low inflationary e(pectations' 3ote that the $FE is a longer term model and itsconclusions differ from the short term asset choice model'


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IFE Example Assume the following:

$ year ,o.ernment &ond rate in 2'S' ? '@@H! year ,o.ernment &ond rate


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Testing the IFE ModelEmpirical tests of the $FE model ha.e produced

similar results as the tests of the Relati.e PPP'1.er the long run/ the results support an $FE effect/howe.er/ o.er the short run/ the model e(plains little ofthe future spot rate'!55D I #@@@ data correlating %uarterly interest ratedifferentials to %uarterly e(change rate changes AnEmpirical $n.estigation of the $FE/ &y Emil Sund%.ist/#@@#" found the following R7s%uares:

Swedish rona: !!' H


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IFE and the Short Term

+hy does the $FE e(plain little .ariation inshort run mo.es in spot e(change rates*

As with the Relati.e PPP/ short term factors can

mo.e the spot rate away from the e(change ratepredicted &y the $FE'$nterest rate asset choice might dominate in shortrun'

Uigher interest rates are e(pected to produce anappreciating currency'Central &an s certainly operate under this assumption'


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Pro'lematic Iss es Regarding the PPP and IFE

PPP model issues:2ser needs to forecast the future rates of inflation'Uow does one do this for .ery long periods of time*Perhaps it is easier for shorter time periods e'g'/ ! year"'

$FE model issues:2ser relies on mar et interest rate data to pro(y for futureinflation'Uowe.er/ are real rates similar across countries*4o real rates change o.er time*$nflationary e(pectations during the forecasted hori-on aresu&8ect to change'


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Practical )se o! PPP and IFE

3either model appears appropriate for shortterm forecasting';oth models wor &etter for the long term

and in this regard appear to &e goodindicators of the long term trend in thee(change rate:

Relati.ely high inflation currencies will e(hi&it longterm depreciation'Relati.ely high interest rate currencies will e(hi&itlong term depreciation'


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&ppendix -# Form las !or the Relati6e PPP

0he following slides co.er the specific formulasto &e used in calculated the Relati.e PPP spot

rate for some future date' 3ote the formula foran American 0erms %uoted currency and for anEuropean 0erms %uoted currency'


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Relati6e PPP Form la# &merican TermsFor an American 0erm %uoted currency:

PPP Spot Rate ? Current Spot Rate ( ! V inf2S" n ! V infF" n"

+here:PPP Spot Rate is the e(pected spot rate sometime in thefuture'Current spot rate is e(pressed in American terms'$nf2S is the e(pected annual rate of inflation in the 2nitedStates'$nfF is the e(pected annual rate of inflation in the foreigncountry'3 is the num&er of years in the future'


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Relati6e PPP Form la# &merican TermsE(ample:

Current spot rate for ;ritish pounds ? =!'6@E(pected annual rate of inflation in the 2'S' ? #'@HE(pected annual rate of inflation in the 2'J' ? D'@H

0hen/ the spot pound # years from now is e%ual to:PPP Spot Rate ? Current Spot Rate ( ! V inf2S" n ! V infF" n"

Spot rate in # years ? !'6@ !V'@#" # !V'@D"#Spot rate in # years ? !'6@ !'@ @ !'@L@5"Spot rate in # years ? !'6@ '56@ "Spot rate in # years ? =!' L D


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Relati6e PPP Form la# E ropean Terms

E(ample:Current spot rate for


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&ppendix 9# Form las !or the IFE

0he following slides co.er the specific formulasto &e used in calculated the $FE spot rate for

some future date' 3ote the formula for an American 0erms %uoted currency and for anEuropean 0erms %uoted currency'


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IFE Form la# &mericanTermsFor American 0erm %uoted currency:

$FE Spot Rate ? Current Spot Rate ( ! V int2S" n ! V intF" n"3ote the similarity to the Relati.e PPP formula

+here: $FE spot rate is the e(pected spot rate sometime in the future'Current spot rate is e(pressed in American terms'$nt2S is the current annual mar et interest rate in the 2nitedStates'

$ntF is the current annual mar et interest rate in the foreigncountry'3 is the num&er of years in the future'


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IFE Form la# &mericanTermsE(ample:

Current spot rate for ;ritish pounds ? =!'6@ Annual rate of interest in the 2'S' ? '@H Annual rate of interest in the 2'J' ? L'@H

0hen/ the spot pound # years from now is e%ual to:PPP Spot Rate ? Current Spot Rate ( ! V int2S" n ! V intF" n"

Spot rate in # years ? !'6@ !V'@ " # !V'@L"#Spot rate in # years ? !'6@ !'!@# !'!#DL"Spot rate in # years ? !'6@ '56!#"Spot rate in # years ? =!' L 5


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IFE Form la# E ropeanTermsFor European 0erm %uoted currency:

$FE Spot Rate ? Current Spot Rate ( ! V intF" n ! V int2S" n" Again/ note the similarity to the Relati.e PPP formula

+here:

$FE spot rate is the e(pected spot rate sometime in the future'Current spot rate is e(pressed in European terms %uote'$ntF is the current annual mar et interest rate in the foreigncountry'$nt2S is the current annual mar et interest rate in the 2nitedStates'3 is the num&er of years in the future'


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IFE Form la# E ropeanTermsE(ample:

Current spot rate for


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&ppendix 2

0he following two slides will help youtest your understanding of using the $FEto forecast American 0erms andEuropean 0erms spot e(change ratesfor periods greater than one year


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Testing 3o r)nderstanding o! the IFE

Model,o to http: noir'&loom&erg'com,o to mar et data/ rates and &onds'9oo up year ,o.ernment &ond rates for the2nited States and the 2nited Jingdom'2sing the most recent spot e(change rate,;P 2S4"/ calculate the $FE determined spot,;P 2S4 e(change rate fi.e years from now'4oes you forecast call for the pound to wea enor strengthen and why*
http://noir.bloomberg.com/http://noir.bloomberg.com/


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&nother Test o! 3o r)nderstanding o! the IFE

Model,o to http: noir'&loom&erg'com,o to mar et data/ rates and &onds'9oo up year ,o.ernment &ond rates for the

2nited States and the

06 inbu 4200 fall 2010 parity models and the foreign exchange rate (1)

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