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)

1/60

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


2/60

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'


3/60

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'


4/60

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 '


5/60

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'


6/60


7/60

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'


8/60

&'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


9/60

Example# $aw o! %ne Price

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


10/60

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'


11/60

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


12/60

&'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'


13/60

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


14/60

&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


15/60

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 ? =!' @


16/60

)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


17/60

"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"


18/60

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

0he Euro was introduced on


19/60

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

2-. -///


20/60

&'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


21/60

%E(1 PPP Exchange Rates 'y 3ear


22/60

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


23/60

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*


24/60

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"


25/60

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'


26/60

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'


27/60

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


28/60

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


29/60

+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


30/60

The Economist, InfationData


31/60

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


32/60

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


40/60

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'


41/60

Real Rate Re= irements


42/60

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'


43/60

IFE Example Assume the following:

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


44/60

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


45/60

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'


46/60

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'


47/60

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'


48/60

&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'


49/60

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'


50/60

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


51/60


52/60

Relati6e PPP Form la# E ropean Terms

E(ample:Current spot rate for


53/60

&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'


54/60

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'


55/60

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


56/60

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'


57/60

IFE Form la# E ropeanTermsE(ample:

Current spot rate for


58/60

&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


59/60

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/


60/60

&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)

Documents

Transcript of 06 INBU 4200 Fall 2010 Parity Models and the Foreign Exchange Rate (1)