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LocalCurrencyGovernmentBondRates– January2017
Aswath Damodaran
33
Currency Govt BondRate12/31/16 Currency Govt BondRate12/31/16
Australian$ 2.76% Malyasian Ringgit 4.24% BrazilianReai 11.37% MexicanPeso 7.63% BritishPound 1.35% NigerianNaira 15.97% BulgarianLev 2.04% NorwegianKrone 1.61% Canadian$ 1.70% NZ$ 3.25% ChileanPeso 4.12% PakistaniRupee 8.03% ChineseYuan 3.25% PeruvianSol 6.43% ColombianPeso 6.76% PhillipinePeso 4.75% CroatianKuna 3.13% PolishZloty 3.67% CzechKoruna 0.49% RomanianLeu 3.44% DanishKrone 0.42% RussianRuble 8.38% Euro 0.29% Singapore$ 2.45% HK$ 1.69% SouthAfricanRand 8.80% HungarianForint 3.41% SwedishKrona 0.62% IcelandKrona 5.06% SwissFranc -0.19% IndianRupee 6.40% Taiwanese$ 1.17% IndonesianRupiah 7.60% ThaiBaht 2.70% IsraeliShekel 2.06% TurkishLira 11.00% JapaneseYen 0.06% US$ 2.45% KenyanShilling 14.02% VenezuelanBolivar 20.43% KoreanWon 2.08% VietnameseDong 6.10%
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Approach1:DefaultspreadfromGovernmentBonds
The Brazil Default SpreadBrazil 2018 Bond: 4.86%US 2018 T.Bond: 1.22%Spread: 3.64%
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Approach2:CDSSpreads– January2017
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Country CDSSpread CDSSpreadadjforUS Country CDSSpread CDSSpreadadj
forUS Country CDSSpread CDSSpreadadjforUS
AbuDhabi 0.97% 0.59% Hungary 1.67% 1.29% Peru 1.73% 1.35% Argentina 5.14% 4.76% Iceland 1.10% 0.72% Philippines 1.61% 1.23% Australia 0.49% 0.11% India 1.76% 1.38% Poland 1.17% 0.79% Austria 0.52% 0.14% Indonesia 2.25% 1.87% Portugal 3.42% 3.04% Bahrain 3.17% 2.79% Ireland 1.02% 0.64% Qatar 1.17% 0.79% Belgium 0.60% 0.22% Israel 1.12% 0.74% Romania 1.51% 1.13% Brazil 3.59% 3.21% Italy 2.22% 1.84% Russia 2.46% 2.08% Bulgaria 1.87% 1.49% Japan 0.62% 0.24% SaudiArabia 1.45% 1.07% Chile 1.29% 0.91% Kazakhstan 2.13% 1.75% Slovakia 0.85% 0.47% China 1.65% 1.27% Korea 0.67% 0.29% Slovenia 1.52% 1.14% Colombia 2.42% 2.04% Latvia 1.02% 0.64% SouthAfrica 2.87% 2.49% CostaRica 3.40% 3.02% Lebanon 5.57% 5.19% Spain 1.25% 0.87% Croatia 2.60% 2.22% Lithuania 0.94% 0.56% Sweden 0.40% 0.02% Cyprus 2.67% 2.29% Malaysia 1.94% 1.56% Switzerland 0.50% 0.12% CzechRepublic 0.74% 0.36% Mexico 2.20% 1.82% Thailand 1.28% 0.90% Denmark 0.41% 0.03% Morocco 2.11% 1.73% Tunisia 5.00% 4.62% Egypt 4.76% 4.38% Netherlands 0.51% 0.13% Turkey 3.44% 3.06% Estonia 0.81% 0.43% NewZealand 0.50% 0.12% Ukraine 7.64% 7.26% Finland 0.45% 0.07% Nigeria 5.76% 5.38% UnitedKingdom 0.61% 0.23% France 0.70% 0.32% Norway 0.34% 0.00% UnitedStates 0.38% 0.00% Germany 0.44% 0.06% Pakistan 4.18% 3.80% Venezuela 30.82% 30.44% HongKong 0.58% 0.20% Panama 1.94% 1.56% Vietnam 2.61% 2.23%
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Approach3:TypicalDefaultSpreads:January2017
Aswath Damodaran
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S&PSovereignRating Moody'sSovereignRating DefaultSpreadAAA Aaa 0.00% AA+ Aa1 0.46% AA Aa2 0.57% AA- Aa3 0.70% A+ A1 0.81% A A2 0.98% A- A3 1.39% BBB+ Baa1 1.84% BBB Baa2 2.20% BBB- Baa3 2.54% BB+ Ba1 2.89% BB Ba2 3.47% BB Ba3 4.16% B+ B1 5.20% B B2 6.36% B- B3 7.51% CCC+ Caa1 8.66% CCC Caa2 10.40% CCC- Caa3 11.55% CC+ Ca1 13.86% CC Ca2 15.25% CC- Ca3 16.50% C+ C1 18.00% C C2 20.00% C- C3 25.00%
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Gettingtoariskfreerateinacurrency:Example
¨ TheBraziliangovernmentbondrateinnominalreais onJanuary1,2017was11.37%.Togettoariskfree rateinnominalreais,wecanuseoneofthreeapproaches.¨ Approach1:GovernmentBondspread
¤ The2018Brazilbond,denominatedinUSdollars,hasaspreadof3.64%overtheUStreasurybondrate.
¤ Riskfree ratein$R=11.37%- 3.64%=7.73%¨ Approach2:TheCDSSpread
¤ TheCDSspreadforBrazil,adjustedfortheUSCDSspreadwas3.21%.
¤ Riskfree ratein$R=11.37%- 3.21%=8.16%¨ Approach3:TheRatingbasedspread
¤ BrazilhasaBa2localcurrencyratingfromMoody’s.Thedefaultspreadforthatratingis3.47%
¤ Riskfree ratein$R=11.37%- 3.47%=7.90%
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Test4:ARealRiskfreeRate
¨ Insomecases,youmaywantariskfree rateinrealterms(inrealterms)ratherthannominalterms.
¨ Togetarealriskfree rate,youwouldlikeasecuritywithnodefaultriskandaguaranteedrealreturn.Treasuryindexedsecuritiesofferthiscombination.
¨ InJanuary2017,theyieldona10-yearindexedtreasurybondwas0.50%.Whichofthefollowingstatementswouldyousubscribeto?a. This(0.5%)istherealriskfree ratetouse,ifyouarevaluingUS
companiesinrealterms.b. This(0.5%)istherealriskfree ratetouse,anywhereinthe
worldExplain.
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39
Nodefaultfreeentity:Choiceswithriskfreerates….
¨ Estimatearangefortheriskfreerateinlocalterms:¤ Approach1:Subtractdefaultspreadfromlocalgovernmentbondrate:
Governmentbondrateinlocalcurrencyterms- DefaultspreadforGovernmentinlocalcurrency
¤ Approach2:Useforwardratesandtherisklessrateinanindexcurrency(sayEurosordollars)toestimatetherisklessrateinthelocalcurrency.
¨ Dotheanalysisinrealterms(ratherthannominalterms)usingarealriskfreerate,whichcanbeobtainedinoneoftwoways–¤ fromaninflation-indexedgovernmentbond,ifoneexists¤ setequal,approximately,tothelongtermrealgrowthrateoftheeconomy
inwhichthevaluationisbeingdone.¨ Dotheanalysisinacurrencywhereyoucangetariskfreerate,say
USdollarsorEuros.
Aswath Damodaran
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40
RiskfreeRate:Don’thaveortrustthegovernmentbondrate?1. Buildupapproach:Theriskfreerateinanycurrencycanbe
writtenasthesumoftwovariables:Riskfreerate=ExpectedInflationincurrency+Expectedrealinterestrate
Theexpectedrealinterestratecanbecomputedinoneoftwoways:fromtheUSTIPsrateorsetequaltorealgrowthintheeconomy.Thus,iftheexpectedinflationrateinacountryisexpectedtobe15%andtheTIPsrateis1%,theriskfreerateis16%.
2. US$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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Whydoriskfreeratesvaryacrosscurrencies?January2017Riskfreerates
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-5.00%
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
Japane
seYen
CzechKo
runa
Croatia
nKu
naBu
lgarianLev
SwissFranc
Euro
DanishKrone
Taiwanese$
PakistaniRup
eeSw
edish
Krona
HungarianForin
tBritishPou
ndThaiBaht
VietnameseDo
ngRo
manianLeu
IsraeliShekel
HK$
KoreanW
onNo
rwegianKron
eCanadian$
ChineseYuan
PhillipinePeso
US$
Singapore$
PolishZloty
Australian$
Malyasia
nRinggit
NZ$
ChileanPeso
IcelandKron
aIndianRup
eeCo
lombianPeso
PeruvianSol
Indo
nesia
nRu
piah
RussianRu
ble
MexicanPeso
SouthAfricanRand
Vene
zuelanBolivar
BrazilianReai
Turkish
Lira
KenyanShilling
Nigeria
nNa
ira
RiskfreeRates- January2017
RiskfreeRate DefaultSpreadbasedonrating
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Onemoretestonriskfreerates…
¨ OnJanuary1,2017,the10-yeartreasurybondrateintheUnitedStateswas2.45%,lowbyhistoricstandards.AssumethatyouwerevaluingacompanyinUSdollarsthen,butwerewaryabouttheriskfreeratebeingtoolow.Whichofthefollowingshouldyoudo?a. Replacethecurrent10-yearbondratewithamorereasonable
normalizedriskfree rate(theaverage10-yearbondrateoverthelast30yearshasbeenabout5-6%)
b. Usethecurrent10-yearbondrateasyourriskfree ratebutmakesurethatyourotherassumptions(aboutgrowthandinflation)areconsistentwiththeriskfree rate
c. Somethingelse…
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43
Someperspectiveonriskfreerates
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-5%
0%
5%
10%
15%
20%
1954
1956
1958
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
2014
2016
RiskfreeRates:Ten-yearT.BondversusIntrinsicRiskFreeRate
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?
Aswath Damodaran
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TheEquityRiskPremium
DiscountRates:II45
Aswath Damodaran
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Theubiquitoushistoricalriskpremium
¨ Thehistoricalpremiumisthepremiumthatstockshavehistoricallyearnedoverrisklesssecurities.
¨ Whiletheusersofhistoricalriskpremiumsactasifitisafact(ratherthananestimate),itissensitiveto¤ Howfarbackyougoinhistory…¤ WhetheryouuseT.bill ratesorT.Bond rates¤ Whetheryouusegeometricorarithmeticaverages.
¨ Forinstance,lookingattheUS:
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ArithmeticAverage GeometricAverageStocks- T.Bills Stocks- T.Bonds Stocks- T.Bills Stocks- T.Bonds
1928-2016 7.96% 6.24% 6.11% 4.62% StdError 2.13% 2.28% 1967-2016 6.57% 4.37% 5.26% 3.42% StdError 2.42% 2.74% 2007-2016 7.91% 3.62% 6.15% 2.30% Std Error 6.06% 8.66%
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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
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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.
(InJanuary2017,thatspreadwas3.64%fortheBrazilian$bond)¤ ThesovereignCDSspreadforthecountry.InJanuary2017,thetenyear
CDSspreadforBrazil,adjustedfortheUSCDS,was3.21%.¤ Thedefaultspreadbasedonthelocalcurrencyratingforthecountry.
Brazil’ssovereignlocalcurrencyratingisBa2andthedefaultspreadforaBa2ratedsovereignwasabout3.47%inJanuary2017.
¨ Addthedefaultspreadtoa“mature”marketpremium:ThisdefaultspreadisaddedontothematuremarketpremiumtoarriveatthetotalequityriskpremiumforBrazil,assumingamaturemarketpremiumof5.69%.¤ CountryRiskPremiumforBrazil=3.47%¤ TotalERPforBrazil=5.69%+3.47%=9.16%
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AnequityvolatilitybasedapproachtoestimatingthecountrytotalERP
¨ Thisapproachdrawsonthestandarddeviationoftwoequitymarkets,theemergingmarketinquestionandabasemarket(usuallytheUS).Thetotalequityriskpremiumfortheemergingmarketisthenwrittenas:¤ Totalequityriskpremium=RiskPremiumUS*sCountryEquity/sUSEquity
¨ ThecountryequityriskpremiumisbaseduponthevolatilityofthemarketinquestionrelativetoU.Smarket.¤ AssumethattheequityriskpremiumfortheUSis5.69%.¤ AssumethatthestandarddeviationintheBovespa (Brazilianequity)is
30%andthatthestandarddeviationfortheS&P500(USequity)is18%.
¤ TotalEquityRiskPremiumforBrazil=5.69%(30%/18%)=9.48%¤ CountryequityriskpremiumforBrazil=9.48%- 5.69%=3.79%
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Ameldedapproachtoestimatingtheadditionalcountryriskpremium
¨ Countryratingsmeasuredefaultrisk.Whiledefaultriskpremiumsandequityriskpremiumsarehighlycorrelated,onewouldexpectequityspreadstobehigherthandebtspreads.
¨ Anotheristomultiplythebonddefaultspreadbytherelativevolatilityofstockandbondpricesinthatmarket.UsingthisapproachforBrazilinJanuary2016,youwouldget:¤ CountryEquityriskpremium=Defaultspreadoncountrybond*sCountry
Equity /sCountryBondn StandardDeviationinBovespa (Equity)=30%n StandardDeviationinBrazilgovernmentbond=20%n DefaultspreadforBrazil=3.47%
¤ BrazilCountryRiskPremium=3.47%(30%/20%)=5.21%¤ BrazilTotalERP=MatureMarketPremium+CRP=5.69%+5.21%=
11.00%
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ATemplateforEstimatingtheERP
Aswath Damodaran
Black #: Total ERPRed #: Country risk premiumAVG: GDP weighted average
ERP
: Jan
201
7
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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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Twoproblemswiththeseapproaches..
¨ Focusjustonrevenues:Totheextentthatrevenuesaretheonlyvariablethatyouconsider,whenweightingriskexposureacrossmarkets,youmaybemissingotherexposurestocountryrisk.Forinstance,anemergingmarketcompanythatgetsthebulkofitsrevenuesoutsidethecountry(inadevelopedmarket)maystillhaveallofitsproductionfacilitiesintheemergingmarket.
¨ Exposurenotadjustedorbaseduponbeta:Totheextentthatthecountryriskpremiumismultipliedbyabeta,weareassumingthatbetainadditiontomeasuringexposuretoallothermacroeconomicriskalsomeasuresexposuretocountryrisk.
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AProduction-basedERP:RoyalDutchShellin2015
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Country Oil&GasProduction %ofTotal ERPDenmark 17396 3.83% 6.20%Italy 11179 2.46% 9.14%Norway 14337 3.16% 6.20%UK 20762 4.57% 6.81%RestofEurope 874 0.19% 7.40%Brunei 823 0.18% 9.04%Iraq 20009 4.40% 11.37%Malaysia 22980 5.06% 8.05%Oman 78404 17.26% 7.29%Russia 22016 4.85% 10.06%RestofAsia&ME 24480 5.39% 7.74%Oceania 7858 1.73% 6.20%Gabon 12472 2.75% 11.76%Nigeria 67832 14.93% 11.76%RestofAfrica 6159 1.36% 12.17%USA 104263 22.95% 6.20%Canada 8599 1.89% 6.20%Brazil 13307 2.93% 9.60%RestofLatinAmerica 576 0.13% 10.78%RoyalDutchShell 454326 100.00% 8.26%
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Approach3:Estimatealambdaforcountryrisk
¨ Countryriskexposureisaffectedbywhereyougetyourrevenuesandwhereyourproductionhappens,butthereareahostofothervariablesthatalsoaffectthisexposure,including:¤ Useofriskmanagementproducts:Companiescanusebothoptions/futures
marketsandinsurancetohedgesomeorasignificantportionofcountryrisk.¤ Government“national”interests:Therearesectorsthatareviewedasvitalto
thenationalinterests,andgovernmentsoftenplayakeyroleinthesecompanies,eitherofficiallyorunofficially.Thesesectorsaremoreexposedtocountryrisk.
¨ Itisconceivablethatthereisarichermeasureofcountryriskthatincorporatesallofthevariablesthatdrivecountryriskinonemeasure.ThatwaymyrationalewhenIdevised“lambda”asmymeasureofcountryriskexposure.
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