10 Idiosyncratic Volatility

1IdiosyncraticVolatilityandStockReturns2Debates(1/5)•Traditionalwisdomsuggeststhatidiosyncraticriskdoesnotpredictstockreturns.•Merton(1987)showsthatinthepresenceofmarketfrictionswhereinvestorshavelimitedaccesstoinformation,stockswithhighidiosyncraticvolatilityhavehighexpectedreturnsbecauseinvestorscannotfullydiversifyawayfirm-specificrisk.3Debates(2/5)•Ang,Hodrick,XingandZhang(AHXZ,2006,2009)documentedapuzzlingnegativerelationshipbetweenreturnandidiosyncraticvolatility.•BaliandCakici(2006)havesuggestedthattheAHXZresultisnotrobustandisabsentwhenequally-weightedportfoliosareconsidered.4Debates(3/5)•MalkielandXu(2002);SpiegelandWang(2006);Chua,Goh,andZhang(2008);andFu(2009)findpositiverelationatthefirmorportfoliolevelusingmonthlyreturnstoestimateconditionalidiosyncraticvolatility.•BakerandWurgler(2006)andBoehmeetal.(forthcoming)showthatconditionaloninvestorsentimentorshort-saleconstraints,idiosyncraticriskcanbepositivelyornegativelycorrelatedwithexpectedreturns.5Debates(4/5)•Huangetal.(forthcoming)findthat,aftercontrollingforreturnreversals,thenegativerelationisnolongersignificant.•FollowingFu(2009),moreover,theyestimateconditionalidiosyncraticvolatilitywithanexponentialGARCH(EGARCH)modelusingmonthlyreturnsandconfirmthesignificantlypositiverelationbetweenthisproxyforidiosyncraticriskandexpectedreturns.6Debates(5/5)•However,GeorgeandHuang(2009)showthatonceweexcludethetax-losssellingeffectinJanuaryandexcludepennystocksfromthesample,theAHXZresultisverysignificantinequally-weightedportfoliosandisrobusttoidiosyncraticvolatilitymeasuresofdifferentdatafrequencyandtothereturnsmeasuredindifferentholdingperiods.(Soundslikethemomentumeffect,doesn’tit?)•Lowreturnsofthehighidiosyncraticvolatilitystocksonlyexistinfirmswithlowanalystcoverage.7Ang,A.,Hodrick,R.J.,Xing,Y.,Zhang,X.,2006.Thecross-sectionofvolatilityandexpectedreturns.JournalofFinance51,259–299.AHXZ(2006)8•OnPage283910TableVI.PortfoliosSortedbyVolatility11TableVII.AlphasofPortfoliosSortedonIdiosyncraticVolatilityTherowlabeled“ControllingforSize”averagesacrossthefivesizequintilestoproducequintileportfolioswithdispersioninidiosyncraticvolatility,butwhichcontainallsizesoffirms.First,controlforsizebyfirstformingquintileportfoliosrankedonmarketcapitalization.Then,withineachsizequintile,sortstocksintoquintileportfoliosrankedonidiosyncraticvolatility.12TableVIIIAlphasofPortfoliosSortedonIdiosyncraticVolatilityControllingforPastReturnsFirstsortallstocksonthebasisofpastreturns,overtheappropriateformationperiod,intoquintiles.Then,withineachmomentumquintile,sortstocksintofiveportfoliossortedbyidiosyncraticvolatility,relativetotheFF-3model.Thefiveidiosyncraticvolatilityportfoliosarethenaveragedovereachofthefivecharacteristicportfolios.131415AHXZ(2009)Ang,A.,Hodrick,R.J.,Xing,Y.,Zhang,X.,2009.Highidiosyncraticvolatilityandlowreturns:InternationalandfurtherU.S.evidence.JournalofFinancialEconomics91,1–23.16-0.31%=(-1.224)*(0.460–0.208)1718192021Portfolioformation1.Foreverymonth,withineachcountry,sortfirmsintoquintileportfoliosaccordingtotheW-FFidiosyncraticvolatilitymeasureinEq.(3)usingdailyfirmreturnsoverthepreviousmonth.2.Aggregatethecountryquintileportfoliosintoregionalportfolios,reportedinthetableforgeographicareas(EuropeandAsia),theG7countries(withandwithouttheU.S.),andacrossall23developedmarkets(withandwithouttheU.S.).EachregionalW-FFidiosyncraticvolatilityquintileportfolioisavalue-weightedsumofthecountryquintileportfolios,withtheweightsbeingthemarketcapitalizationofthecorrespondingcountryquintileportfolios.Portfolio1containsfirmswiththelowestvolatilitiesandportfolio5containsfirmswiththehighestvolatilities,while‘‘5–1’’representsastrategythatgoeslongthehighestvolatilityquintileandshortthelowestvolatilityquintile.2223Portfolioformation(1/2)1.Foreverymonth,withineachcountry,firmsaresortedintoquintileportfoliosaccordingtotheW-FFidiosyncraticvolatilitymeasure(seeEq.(3))usingdailyfirmreturnsoverthepreviousmonth.2.Thecountryquintileportfoliosareaggregatedintoregionalquintileportfolios,forgeographicareas(EuropeandAsia),theG7countries(withandwithouttheU.S.),andacrossall23developedmarkets(withandwithouttheU.S.).EachregionalW-FFidiosyncraticvolatilityquintileportfolioisavalue-weightedsumofthecountryquintileportfolios,withtheweightsbeingthemarketcapitalizationofthecorrespondingquintileportfoliosineachcountry.24Portfolioformation(2/2)3.Withineachregion,thereisa‘‘5–1’’strategythatgoeslongthehighestidiosyncraticvolatilityquintileandshortthequintileportfoliowiththehighestidiosyncraticvolatilitystocks.4.FortheU.S.,this5–1strategyisdenotedasVOLUS.Thefollowingtablereportstheestimatesofregressionsfromthefullsamplemonthlyreturnsofthe5–1regionalstrategiesontoaconstant,thethreeW-FFfactors,andtheVOLUSreturns.25Therearelargeandsignificantco-movementsbetweentheidiosyncraticvolatilityportfolioreturnsininternationalmarketsandintheUnitedStates.26Therearelargeandsignificantco-movementsbetweentheidiosyncraticvolatilityportfolioreturnsininternationalmarketsandintheUnitedStates.VOLUSabsorbstheexplanatory