an implied erp - nyupeople.stern.nyu.edu/adamodar/podcasts/cfspr16/session7.pdf · an implied erp...
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AnImpliedERP
Aswath Damodaran
Base year cash flow (last 12 mths)Dividends (TTM): 42.66+ Buybacks (TTM): 63.43
= Cash to investors (TTM): 106.09
Expected growth in next 5 yearsTop down analyst estimate of earnings
growth for S&P 500: 5.55%
Risk free rate = T.Bond rate on 1/1/16= 2.27%
r = Implied Expected Return on Stocks = 8.39%
S&P 500 on 1/1/16= 2043.94
Minus
Implied Equity Risk Premium (1/1/16) = 8.39% - 2.27% = 6.12%
Equals
Earnings and Cash flows grow @2.27% (set equal to risk free rate) a year forever.
Payout ratio assumed to stay stable. 106.09 growing @ 5.55% a year
Last12mths 1 2 3 4 5 TerminalYearDividends+Buybacks 106.09 111.99$ 118.21$ 124.77$ 131.70$ 139.02$ 142.17
2043.94 = 111.99(1 + ,) +118.21(1 + ,)/ +
124.77(1 + ,)1 +
131.70(1 + ,)2 +
139.02(1 + ,)3 +
142.17(, − .0227)(1 + ,)3
You have to solve for the discount rate (r). I
used the solver or Goal seek function in Excel
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ImpliedPremiumsintheUS:1960-2015
Aswath Damodaran
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
19601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982198319841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015
Impl
ied
Prem
ium
Year
Implied Premium for US Equity Market: 1960-2015
Black #: Total ERPRed #: Country risk premiumAVG: GDP weighted average
ERP
: Jan
201
6
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Applica?onTest:Es?ma?ngaMarketRiskPremium
AswathDamodaran
120
¨ Foryourcompany,getthegeographicalbreakdownofrevenuesinthemostrecentyear.Baseduponthisrevenuebreakdownandthemostrecentcountryriskpremiums,es?matetheequityriskpremiumthatyouwoulduseforyourcompany.
¨ Thiscomputa?onwasbaseden?relyonrevenues.Withyourcompany,whatconcernswouldyouhaveaboutyoures?matebeingtoohighortoolow?
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Es?ma?ngBeta
AswathDamodaran
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¨ Thestandardprocedurefores?ma?ngbetasistoregressstockreturns(Rj)againstmarketreturns(Rm):
Rj=a+bRmwhereaistheinterceptandbistheslopeoftheregression.
¨ Theslopeoftheregressioncorrespondstothebetaofthestock,andmeasurestheriskinessofthestock.
¨ TheRsquared(R2)oftheregressionprovidesanes?mateofthepropor?onoftherisk(variance)ofafirmthatcanbeaWributedtomarketrisk.Thebalance(1-R2)canbeaWributedtofirmspecificrisk.
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Es?ma?ngPerformance
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¨ Theinterceptoftheregressionprovidesasimplemeasureofperformanceduringtheperiodoftheregression,rela?vetothecapitalassetpricingmodel.Rj =Rf+b(Rm-Rf)
=Rf(1-b)+bRm ........... CapitalAssetPricingModelRj =a +bRm ........... RegressionEqua?on
¨ If a>Rf(1-b)....StockdidbeWerthanexpectedduringregressionperioda=Rf(1-b)....Stockdidaswellasexpectedduringregressionperioda<Rf(1-b)....Stockdidworsethanexpectedduringregressionperiod
¨ ThedifferencebetweentheinterceptandRf(1-b)isJensen'salpha.Ifitisposi?ve,yourstockdidperformbeWerthanexpectedduringtheperiodoftheregression.
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Se_ngupfortheEs?ma?on
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¨ Decideonanes?ma?onperiod¤ Servicesuseperiodsrangingfrom2to5yearsfortheregression¤ Longeres?ma?onperiodprovidesmoredata,butfirmschange.¤ Shorterperiodscanbeaffectedmoreeasilybysignificantfirm-specific
eventthatoccurredduringtheperiod¤ Decideonareturninterval-daily,weekly,monthly
¤ Shorterintervalsyieldmoreobserva?ons,butsufferfrommorenoise.¤ Noiseiscreatedbystocksnottradingandbiasesallbetastowardsone.
¨ Es?matereturns(includingdividends)onstock¤ Return=(PriceEnd-PriceBeginning+DividendsPeriod)/PriceBeginning¤ Includeddividendsonlyinex-dividendmonth
¨ Chooseamarketindex,andes?matereturns(inclusiveofdividends)ontheindexforeachintervalfortheperiod.
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ChoosingtheParameters:Disney
¨ Periodused:5years¨ ReturnInterval=Monthly¨ MarketIndex:S&P500Index.¨ Forinstance,tocalculatereturnsonDisneyinDecember2009,
¤ PriceforDisneyatendofNovember2009=$30.22¤ PriceforDisneyatendofDecember2009=$32.25¤ Dividendsduringmonth=$0.35(Itwasanex-dividendmonth)¤ Return=($32.25-$30.22+$0.35)/$30.22=7.88%
¨ Toes?matereturnsontheindexinthesamemonth¤ IndexlevelatendofNovember2009=1095.63¤ IndexlevelatendofDecember2009=1115.10¤ DividendsonindexinDecember2009=1.683¤ Return=(1115.1–1095.63+1.683)/1095.63=1.78%
Aswath Damodaran
Disney’sHistoricalBeta
!ReturnonDisney=.0071+1.2517ReturnonMarketR²=0.73386
(0.10)
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AnalyzingDisney’sPerformance
¨ Intercept=0.712%¤ Thisisaninterceptbasedonmonthlyreturns.Thus,ithastobe
comparedtoamonthlyriskfreerate.¤ Between2008and2013
n AverageAnnualizedT.Billrate=0.50%n MonthlyRiskfreeRate=0.5%/12=0.042%n RiskfreeRate(1-Beta)=0.042%(1-1.252)=-.0105%
¨ TheComparisonisthenbetween¤ Intercept versus RiskfreeRate(1-Beta)¤ 0.712% versus 0.0105%¤ Jensen’sAlpha=0.712%-(-0.0105)%=0.723%
¨ Disneydid0.723%beWerthanexpected,permonth,betweenOctober2008andSeptember2013¤ Annualized,Disney’sannualexcessreturn=(1.00723)12-1=9.02%
Aswath Damodaran
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MoreonJensen’sAlpha
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¨ Ifyoudidthisanalysisoneverystocklistedonanexchange,whatwouldtheaverageJensen’salphabeacrossallstocks?a. Dependuponwhetherthemarketwentupordownduringtheperiodb. Shouldbezeroc. Shouldbegreaterthanzero,becausestockstendtogoupmoreopenthandown.
¨ Disneyhasaposi?veJensen’salphaof9.02%ayearbetween2008and2013.Thiscanbeviewedasasignthatmanagementinthefirmdidagoodjob,managingthefirmduringtheperiod.a. Trueb. False
¨ Disneyhashadaposi?veJensen’salphabetween2008and2013.Ifyouwereaninvestorinearly2014,lookingatthestock,youwouldviewthisasasignthatthestockwillbea:a. Goodinvestmentforthefutureb. Badinvestmentforthefuturec. Noinforma?onaboutthefuture
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Es?ma?ngDisney’sBeta
¨ SlopeoftheRegressionof1.25isthebeta¨ Regressionparametersarealwayses?matedwitherror.Theerroriscapturedinthestandarderrorofthebetaes?mate,whichinthecaseofDisneyis0.10.
¨ AssumethatIaskedyouwhatDisney’struebetais,aperthisregression.¤ Whatisyourbestpointes?mate?
¤ Whatrangewouldyougiveme,with67%confidence?
¤ Whatrangewouldyougiveme,with95%confidence?
Aswath Damodaran
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TheDirtySecretof“StandardError”
Distribution of Standard Errors: Beta Estimates for U.S. stocks
0
200
400
600
800
1000
1200
1400
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<.10 .10 - .20 .20 - .30 .30 - .40 .40 -.50 .50 - .75 > .75
Standard Error in Beta Estimate
Num
ber o
f Firm
s
Aswath Damodaran
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BreakingdownDisney’sRisk
¨ RSquared=73%¨ Thisimpliesthat
¤ 73%oftheriskatDisneycomesfrommarketsources¤ 27%,therefore,comesfromfirm-specificsources
¨ Thefirm-specificriskisdiversifiableandwillnotberewarded.
¨ TheR-squaredforcompanies,globally,hasincreasedsignificantlysince2008.Whymightthisbehappening?
¨ Whataretheimplica?onsforinvestors?
Aswath Damodaran
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TheRelevanceofRSquared
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¨ YouareadiversifiedinvestortryingtodecidewhetheryoushouldinvestinDisneyorAmgen.Theybothhavebetasof1.25,butDisneyhasanRSquaredof73%whileAmgen’sRsquaredisonly25%.Whichonewouldyouinvestin?¤ Amgen,becauseithasthelowerRsquared¤ Disney,becauseithasthehigherRsquared¤ Youwouldbeindifferent
¨ Wouldyouranswerbedifferentifyouwereanundiversifiedinvestor?
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BetaEs?ma?on:UsingaService(Bloomberg)
Aswath Damodaran