why do risk free rates vary across currencies? january...
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Whydoriskfreeratesvaryacrosscurrencies?January2016Riskfreerates
Aswath Damodaran
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-5.00%
0.00%
5.00%
10.00%
15.00%
20.00%JapaneseYen
CzechKo
runa
SwissFranc
Taiwanese$
BulgarianLev
Euro
Hun
garianForin
t
ThaiBaht
DanishKron
e
SwedishKron
a
HK$
CroatianKu
na
IsraeliShekel
RomanianLeu
Canadian$
NorwegianKron
e
BritishPou
nd
KoreanW
on
PakistaniRup
ee
PhillipinePeso
PolishZloty
VietnameseDon
g
ChineseYuan
US$
Singapore$
MalyasianRinggit
Australian$
NZ$
IcelandKron
a
ChileanPeso
MexicanPeso
IndianRup
ee
PeruvianSol
ColombianPeso
Indo
nesianRup
iah
VenezuelanBolivar
RussianRu
ble
NigerianNaira
TurkishLira
SouthAfricanRand
KenyanShilling
BrazilianReai
RiskfreeRates- January2016
RiskfreeRate DefaultSpreadbasedonrating
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RiskfreeRate:Don’thaveortrustthegovernmentbondrate?1. Buildupapproach:Theriskfreerateinanycurrencycanbe
writtenasthesumoftwovariables:Riskfreerate=ExpectedInflationincurrency+Expectedrealinterestrate
Theexpectedrealinterestratecanbecomputedinoneoftwoways:fromtheUSTIPsrateorsetequaltorealgrowthintheeconomy.Thus,iftheexpectedinflationrateinacountryisexpectedtobe15%andtheTIPsrateis1%,theriskfreerateis16%.
2. US$Rate&DifferentialInflation:Alternatively,youcanscaleuptheUS$riskfreeratebythedifferentialinflationbetweentheUS$andthecurrencyinquestion:
RiskfreerateCurrency=
Thus,iftheUS$riskfreerateis2.00%,theinflationrateintheforeigncurrencyis15%andtheinflationrateinUS$is1.5%,theforeigncurrencyriskfreerateisasfollows:Riskfreerate= 1.02 !.!"
!.!"# − 1=15.57%
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Onemoretestonriskfreerates…
¨ OnJanuary1,2016,the10-yeartreasurybondrateintheUnitedStateswas2.27%,ahistoriclow.AssumethatyouwerevaluingacompanyinUSdollarsthen,butwerewaryabouttheriskfreeratebeingtoolow.Whichofthefollowingshouldyoudo?a. Replacethecurrent10-yearbondratewithamorereasonable
normalizedriskfreerate(theaverage10-yearbondrateoverthelast30yearshasbeenabout5-6%)
b. Usethecurrent10-yearbondrateasyourriskfreeratebutmakesurethatyourotherassumptions(aboutgrowthandinflation)areconsistentwiththeriskfreerate
c. Somethingelse…
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Someperspectiveonriskfreerates
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Interestratefundamentals:T.Bondrates,Realgrowthandinflation
Inflationrate RealGDPgrowth Ten-yearT.Bondrate
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NegativeInterestRates?
¨ In2016,therewereatleastthreecurrencies(SwissFranc,JapaneseYen,Euro)withnegativeinterestrates.Usingthefundamentals(inflationandrealgrowth)approach,howwouldyouexplainnegativeinterestrates?
¨ Hownegativecanratesget?(Isthereabound?)¨ Wouldyouusethesenegativeinterestratesasriskfreerates?¤ Ifno,whynotandwhatwouldyoudoinstead?¤ Ifyes,whatelsewouldyouhavetodoinyourvaluationtobeinternallyconsistent?
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TheEquityRiskPremium
DiscountRates:II44
Aswath Damodaran
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Theubiquitoushistoricalriskpremium
¨ Thehistoricalpremiumisthepremiumthatstockshavehistoricallyearnedoverrisklesssecurities.
¨ Whiletheusersofhistoricalriskpremiumsactasifitisafact(ratherthananestimate),itissensitiveto¤ Howfarbackyougoinhistory…¤ WhetheryouuseT.billratesorT.Bondrates¤ Whetheryouusegeometricorarithmeticaverages.
¨ Forinstance,lookingattheUS:
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Theperilsoftrustingthepast…….
¨ Noisyestimates:Evenwithlongtimeperiodsofhistory,theriskpremiumthatyouderivewillhavesubstantialstandarderror.Forinstance,ifyougobackto1928(about80yearsofhistory)andyouassumeastandarddeviationof20%inannualstockreturns,youarriveatastandarderrorofgreaterthan2%:
StandardErrorinPremium=20%/√80=2.26%¨ SurvivorshipBias:UsinghistoricaldatafromtheU.S.equitymarketsoverthetwentiethcenturydoescreateasamplingbias.Afterall,theUSeconomyandequitymarketswereamongthemostsuccessfuloftheglobaleconomiesthatyoucouldhaveinvestedinearlyinthecentury.
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RiskPremiumforaMatureMarket?Broadeningthesampleto1900-2015
Aswath Damodaran
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Country GeometricERP ArithmeticERP StandardErrorAustralia 5.00% 6.60% 1.70%Austria 2.60% 21.50% 14.30%Belgium 2.40% 4.50% 2.00%Canada 3.30% 4.90% 1.70%Denmark 2.30% 3.80% 1.70%Finland 5.20% 8.80% 2.80%France 3.00% 5.40% 2.10%Germany 5.10% 9.10% 2.70%Ireland 2.80% 4.80% 1.80%Italy 3.10% 6.50% 2.70%Japan 5.10% 9.10% 3.00%Netherlands 3.30% 5.60% 2.10%New Zealand 4.00% 5.50% 1.70%Norway 2.30% 5.20% 2.60%South Africa 5.40% 7.20% 1.80%Spain 1.80% 3.80% 1.90%Sweden 3.10% 5.40% 2.00%Switzerland 2.10% 3.60% 1.60%U.K. 3.60% 5.00% 1.60%U.S. 4.30% 6.40% 1.90%Europe 3.20% 4.50% 1.50%World-ex U.S. 2.80% 3.90% 1.40%World 3.20% 4.40% 1.40%
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Thesimplestwayofestimatinganadditionalcountryriskpremium:Thecountrydefaultspread
¨ Defaultspreadforcountry:Inthisapproach,thecountryequityriskpremiumissetequaltothedefaultspreadforthecountry,estimatedinoneofthreeways:¤ Thedefaultspreadonadollardenominatedbondissuedbythecountry.
(InJanuary2016,thatspreadwas4.83%fortheBrazilian$bond)¤ ThesovereignCDSspreadforthecountry.InJanuary2016,thetenyear
CDSspreadforBrazil,adjustedfortheUSCDS,was5.19%.¤ Thedefaultspreadbasedonthelocalcurrencyratingforthecountry.
Brazil’ssovereignlocalcurrencyratingisBaa3andthedefaultspreadforaBaa3ratedsovereignwasabout2.44%inJanuary2016.
¨ Addthedefaultspreadtoa“mature”marketpremium:ThisdefaultspreadisaddedontothematuremarketpremiumtoarriveatthetotalequityriskpremiumforBrazil,assumingamaturemarketpremiumof6.00%.¤ CountryRiskPremiumforBrazil=2.44%¤ TotalERPforBrazil=6.00%+2.44%=8.44%
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Aswath Damodaran
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AnequityvolatilitybasedapproachtoestimatingthecountrytotalERP
¨ Thisapproachdrawsonthestandarddeviationoftwoequitymarkets,theemergingmarketinquestionandabasemarket(usuallytheUS).Thetotalequityriskpremiumfortheemergingmarketisthenwrittenas:¤ Totalequityriskpremium=RiskPremiumUS*sCountry Equity/sUS Equity
¨ ThecountryequityriskpremiumisbaseduponthevolatilityofthemarketinquestionrelativetoU.Smarket.¤ AssumethattheequityriskpremiumfortheUSis6.00%.¤ AssumethatthestandarddeviationintheBovespa (Brazilianequity)is
30%andthatthestandarddeviationfortheS&P500(USequity)is18%.
¤ TotalEquityRiskPremiumforBrazil=6.00%(30%/18%)=10.0%¤ CountryequityriskpremiumforBrazil=10.00%- 6.00%=4.00%
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Ameldedapproachtoestimatingtheadditionalcountryriskpremium
¨ Countryratingsmeasuredefaultrisk.Whiledefaultriskpremiumsandequityriskpremiumsarehighlycorrelated,onewouldexpectequityspreadstobehigherthandebtspreads.
¨ Anotheristomultiplythebonddefaultspreadbytherelativevolatilityofstockandbondpricesinthatmarket.UsingthisapproachforBrazilinJanuary2016,youwouldget:¤ CountryEquityriskpremium=Defaultspreadoncountrybond*sCountry
Equity /sCountry Bondn StandardDeviationinBovespa (Equity)=30%n StandardDeviationinBrazilgovernmentbond=20%n DefaultspreadforBrazil=2.44%
¤ BrazilCountryRiskPremium=2.44%(30%/20%)=3.66%¤ BrazilTotalERP=MatureMarketPremium+CRP=6.00%+3.66%=9.66%
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ATemplateforCountryRisk
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Black #: Total ERPRed #: Country risk premiumAVG: GDP weighted average
ERP
: Jan
201
6
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FromCountryEquityRiskPremiumstoCorporateEquityRiskpremiums
¨ Approach1:Assumethateverycompanyinthecountryisequallyexposedtocountryrisk.Inthiscase,¤ E(Return)=RiskfreeRate+CRP+Beta(MatureERP)¤ Implicitly,thisiswhatyouareassumingwhenyouusethelocalGovernment’s
dollarborrowingrateasyourriskfreerate.¨ Approach2:Assumethatacompany’sexposuretocountryriskissimilar
toitsexposuretoothermarketrisk.¤ E(Return)=RiskfreeRate+Beta(MatureERP+CRP)
¨ Approach3:Treatcountryriskasaseparateriskfactorandallowfirmstohavedifferentexposurestocountryrisk(perhapsbasedupontheproportionoftheirrevenuescomefromnon-domesticsales)¤ E(Return)=RiskfreeRate+b (MatureERP)+l (CRP)
MatureERP=MaturemarketEquityRiskPremiumCRP=Additionalcountryriskpremium
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Approaches1&2:Estimatingcountryriskpremiumexposure
¨ LocationbasedCRP:Thestandardapproachinvaluationistoattachacountryriskpremiumtoacompanybaseduponitscountryofincorporation.Thus,ifyouareanIndiancompany,youareassumedtobeexposedtotheIndiancountryriskpremium.Adevelopedmarketcompanyisassumedtobeunexposedtoemergingmarketrisk.
¨ Operation-basedCRP:Thereisamorereasonablemodifiedversion.Thecountryriskpremiumforacompanycanbecomputedasaweightedaverageofthecountryriskpremiumsofthecountriesthatitdoesbusinessin,withtheweightsbaseduponrevenuesoroperatingincome.Ifacompanyisexposedtoriskindozensofcountries,youcantakeaweightedaverageoftheriskpremiumsbyregion.
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OperationbasedCRP:SingleversusMultipleEmergingMarkets
¨ Singleemergingmarket:Embraer,in2004,reportedthatitderived3%ofitsrevenuesinBrazilandthebalancefrommaturemarkets.ThematuremarketERPin2004was5%andBrazil’sCRPwas7.89%.
¨ Multipleemergingmarkets:Ambev,theBrazilian-basedbeveragecompany,reportedrevenuesfromthefollowingcountriesduring2011.
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Extendingtoamultinational:RegionalbreakdownCocaCola’srevenuebreakdownandERPin2012
Things to watch out for1. Aggregation across regions. For instance, the Pacific region often includes Australia & NZ with Asia2. Obscure aggregations including Eurasia and Oceania
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