empirical asset pricing realized returns

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1、DoctoralSeminarinEmpiricalFinanceTopic10RealizedReturnsLecturer:LarsA.LochstoerLondonBusinessSchoolFebruary20,20081MainConceptsUpuntilnow,thefocushasbeenon(conditional)expectedreturnsEt1(Rit)Rit=Et1(Rit)+"itNow,shifttorealizedreturns,i.e."it:Twoquestions:1.Howandwhydoesitsconditionalvolat

2、ilityvaryovertime?2.Canwelink"ittofundamentals?Letmeknowofanyerrors,please.ThesenotesdrawontheexcellentPhDcourseinempirical…nanceItookatBerkeley,taughtbyGregoryR.Du¤ee.Contactinfo:LarsLøchstøer,P222,LondonBusinessSchool,SussexPlace,Regent’sPark,NW14SA,London,UnitedKingdom.E-mail:LLochstoer@lon

3、don.edu01.1RealizedAggregateStockReturnVolatilityIfstockreturnsarenotautocorrelated,wecanmeasureex-post(realized)monthlyvolatilitybyXNtexpost2Vart=(ritrit)i=1whererisdailystockreturns,Ntisnumberoftradingdaysinmontht,andritisthesamplemeanreturnformontht.IfdailystockreturnsfollowanMA(1)(which

4、mayareasonableassumptionasdailystockreturnsexhibitmildautocorrelation),wecanestimatetherealizedvolatilitybyXNtNXt1
expost2Vart=(ritrit)+2(ritrit)r(i+1)triti=1i=1Hereweareassumingthattheexpecteddailystockreturnisconstantwithineachmonth.Sincestockreturnsaresovolatile,thespeci…cationofthem

5、onthlymeanre-turnisnotquantitativelyimportant-theestimateisprettymuchthesamewhetherweusethetotalsamplemeanreturn,monthlymeanreturns,orsimplyzero.The…gurebelowshowsrealizedmonthlystandarddeviationsfortheU.S.stockmarketfrom18802004(PanelA).FromPanelA,wecanseeanobviousinstru-mentforcapturingcond

6、itionalvariance-laggedexpostvariance.PanelBshowsconditionalstandarddeviationsfromanAR(12)projectionusingrealizedvariance:P12expostexpostVart=0+iVarti+ti=1P12^2=^+^Varexpostt0itii=11Mainlessonsfromthe…gure:1.Stockreturnstandarddeviationsare2-3timeshigherintheGreatDepressionthanatothertimes2

7、.Substantialshort-lived‡uctuationsinconditionalvolatility3.Nocleartime-trendInparticular,volatilityisnotobviouslylowerpostWW2thanbeforeDepres-sion4.Cannotrejecthypothesisofunitrootinvolatility1.2Schwert(1989)-EconomicDeterminantso