行為金融學(xué)課后答案1至5章anawer

第一章1.Differentiatethefollowingterms/concepts:ProspectandprobabilitydistributionAprospectisalotteryorseriesofwealthoutcomes,eachofwhichisassociatedwithaprobability,whereasaprobabilitydistributiondefinesthelikelihoodofpossibleoutcomes.RiskanduncertaintyRiskismeasurableusingprobability,butuncertaintyisnot.Uncertaintyiswhenprobabilitiescan’tbeassignedorthepossibleoutcomesareunclear.UtilityfunctionandexpectedutilityAutilityfunction,denotedasu(),assignsnumberstopossibleoutcomessothatpreferredchoicesreceivehighernumbers.Utilitycanbethoughtofasthesatisfactionreceivedfromaparticularoutcome.Riskaversion,riskseeking,andriskneutralityRiskaversiondescribessomeonewhopreferstheexpectedvalueofalotterytothelotteryitself.Riskseekingdescribessomeonewhoprefersalotterytotheexpectedvalueofalottery.Andriskneutralitydescribessomeonewhoseutilityoftheexpectedvalueofalotteryisequaltotheexpectedutilityofthelottery.2.Wheneatingout,Roryprefersspaghettioverahamburger.Lastnightshehadachoiceofspaghettiandmacaroniandcheeseanddecidedonthespaghettiagain.Thenightbefore,Roryhadachoicebetweenspaghetti,pizza,andahamburgerandthistimeshehadpizza.Then,todayshechosemacaroniandcheeseoverahamburger.DoesherselectiontodayindicatethatRory’schoicesareconsistentwitheconomicrationality?Whyorwhynot?Rory’spreferencesareconsistentwithrationality.Theyarecompleteandtransitive.Weseethatherpreferenceorderingis:Pizzaspaghettimacaroniandcheesehamburger3.Considerapersonwiththefollowingutilityfunctionoverwealth:u(w)=ew,whereeistheexponentialfunction(approximatelyequalto2.7183)andw=wealthinhundredsofthousandsofdollars.Supposethatthispersonhasa40%chanceofwealthof$50,000anda60%chanceofwealthof$1,000,000assummarizedbyP(0.40,$50,000,$1,000,000).a.Whatistheexpectedvalueofwealth?E(w)=.4*.5+.6*10=6.2U(P)=.4e0.50+.6e10=13,216.54b.Constructagraphofthisutilityfunction.Thefunctionisconvex.c.Isthispersonriskaverse,riskneutral,orariskseeker?Riskseekerbecausegraphisconvex.d.Whatisthisperson’scertaintyequivalentfortheprospect?ew=13,216.54givesw=9.4892244or$948,922.444.Anindividualhasthefollowingutilityfunction:u(w)=w.5wherew=wealth.a.Usingexpectedutility,orderthefollowingprospectsintermsofpreference,fromthemosttotheleastpreferred:P1(.8,1,000,600)P2(.7,1,200,600)P3(.5,2,000,300)Ranking:P2,P3,P1withexpectedutilities31.5972,31.0209,and30.1972forprospects2,3,and1,respectivelyb.WhatisthecertaintyequivalentforprospectP2?998.3830c.Withoutdoinganycalculations,wouldthecertaintyequivalentforprospectP1belargerorsmaller?Why?ThecertaintyequivalentforP1wouldbesmallerbecauseP2isrankedhigherthanP1.5.Considertwoprospects:Problem1:ChoosebetweenProspectA: $2,500withprobability.33,$2,400withprobability.66,Zerowithprobability.01.AndProspectB: $2,400withcertainty.Problem2:ChoosebetweenProspectC: $2,500withprobability.33,Zerowithprobability.67.AndProspectD: $2,400withprobability.34,Zerowithprobability.66.IthasbeenshownbyDanielKahnemanandAmosTversky(1979,“Prospecttheory:Ananalysisofdecisionunderrisk,”Econometrica47(2),263-291)thatmorepeoplechooseBwhenpresentedwithproblem1andwhenpresentedwithproblem2,mostpeoplechooseC.Thesechoicesviolateexpectedutilitytheory.Why?ThisisanexampleoftheAllaisparadox.Thefirstchoicesuggeststhatu(2,400)>.33u(2,500)+.66u(2,400)or.34u(2,400)>.33u(2,500)whilethesecondchoicesuggestsjusttheoppositeinequality.第二章1.Differentiatethefollowingterms/concepts:a.SystematicandnonsystematicriskNondiversifiableorsystematicriskisriskthatiscommontoallriskyassetsinthesystemandcannotbediversified.Diversifiableorunsystematicriskisspecifictotheassetinquestionandcanbediversified.b.BetaandstandarddeviationBetaistheCAPM’smeasureofrisk.Ittakesintoaccountanasset’ssensitivitytothemarketandonlymeasuressystematic,nondiversifiablerisk.Thestandarddeviationisameasureofdispersionthatincludesbothdiversifiableandnondiversifiablerisks.c.DirectandindirectagencycostsAgencycostsarisewhenmanagers’incentivesarenotconsistentwithmaximizingthevalueofthefirm.Directcostsincludeexpendituresthatbenefitthemanagerbutnotthefirm,suchaspurchasingaluxuryjetfortravel.Otherdirectcostsresultfromtheneedtomonitormanagers,includingthecostofhiringoutsideauditors.Indirectcostsaremoredifficulttomeasureandresultfromlostopportunities.d.Weak,semi-strong,andstrongformmarketefficiencyWithweakformmarketefficiencypricesreflectalltheinformationcontainedinhistoricalreturns.Withsemi-strongformmarketefficiencypricesreflectallpubliclyavailableinformation.Withstrongformmarketefficiencypricesreflectinformationthatisnotpubliclyavailable,suchasinsiders’information.2.Astockhasabetaof1.2andthestandarddeviationofitsreturnsis25%.Themarketriskpremiumis5%andtherisk-freerateis4%.a.Whatistheexpectedreturnforthestock?E(R)=.04+1.2(.05)=.10b.Whataretheexpectedreturnandstandarddeviationforaportfoliothatisequallyinvestedinthestockandtherisk-freeasset?E(Rp)=.5(.10)+.5(.04)=.07,σp=(.5)(.25)=.125c.Afinancialanalystforecastsareturnof12%forthestock.Wouldyoubuyit?Whyorwhynot?Ifyoubelievethesourceisverycredible,buyitasitisexpectedtogenerateapositiveabnormal(orexcess)return.3.Whatisthejointhypothesisproblem?Whyisitimportant?Ifwhentestingonehypothesisanothermustbeassumedtohold,ajoint-hypothesisproblemarises.Forus,thisisofparticularinterestwhenwearetestingmarketefficiencybecauseoftheneedtoutilizeaparticularrisk-adjustmentmodeltoproducerequiredreturns,thatis,torisk-adjust.Thiswouldnotbeaproblemifweknewwithcertaintywhatthecorrectriskadjustmentmodelis,butunfortunatelywedonot.IfatestrejectstheEMH,isitbecausetheEMHdoesnothold,orbecausewedidnotproperlymeasureabnormalreturns?Wesimplydonotknowforcertaintheanswertothisquestion.4.WarrenBuffetthasbeenaverysuccessfulinvestor.In2008LuisaKrollreportedthatBuffetttoppedForbesMagazine’slistoftheworld’srichestpeoplewithafortuneestimatedtobeworth$62billion(March5,2008,"\o"/2008/03/05/richest-people-billionaires-billionaires08-cx_lk_0305billie_land.html"Theworld'sbillionaires,"\o"Forbes"Forbes).DoesthisinvalidatetheEMH?WarrenBuffett’sexperiencedoesnotnecessarilyinvalidatetheEMH.Thereisthepossibilitythatheisjustlucky:giventhattherearenumerousmoneymanagers,someareboundtoperformwelljustbyluck.StillmanywouldquestionthisherebecauseBuffett’strackrecordhasbeenconsistentlystrong.5.Youareconsideringwhethertoinvestintwostocks,StockAandStockB.StockAhasabetaof1.15andthestandarddeviationofitsreturnshasbeenestimatedtobe0.28.ForStockB,thebetais0.84andstandarddeviationis0.48.Whichstockisriskier?StockAisriskier,thoughstockBhasgreatertotalrisk.Iftherisk-freerateis4%andthemarketriskpremiumis8%,whatistheexpectedreturnforaportfoliothatiscomposedof60%Aand40%B?Rp=.6(.132)+.4(.1072)=.12208IfthecorrelationbetweenthereturnsofAandBis0.50,whatisthestandarddeviationfortheportfoliothatincludes60%Aand40%B?σp2=(.6)2(.28)2+(.4)2(.48)2+2*.5(.6)(.4)(.28)(.48)=9.7%,σp=31.2%第三章1.Differentiatethefollowingterms/concepts:a.LotteryandinsuranceAlotteryisaprospectwithalowprobabilityofahighpayoff.Manypeoplebuylotterytickets,evenwithnegativeexpectedvalues.Thesesamepeoplebuyinsurancetoprotectthemselvesfromrisk.Normally,insuranceisahedgeagainstalow-probabilitylargeloss.Thesechoicesareinconsistentwithtraditionalexpectedutilityframeworkbutcanbeexplainedbyprospecttheory.b.SegregationandintegrationIntegrationoccurswhenpositionsarelumpedtogether,whilesegregationoccurswhensituationsareviewedoneatatime.c.RiskaversionandlossaversionApersonwhoisriskaversepreferstheexpectedvalueofaprospecttotheprospectitself,whereasforapersonwhoislossaverse,lossesloomlargerthangains.d.WeightingfunctionandeventprobabilityEventprobabilityissimplythesubjectiveviewonhowlikelyaneventis.Theweightingfunctionisassociatedwiththeprobabilityofanoutcome,butisnotstrictlythesameastheprobabilityasinexpectedutilitytheory.2.Accordingtoprospecttheory,whichispreferred?a.ProspectAorB?Decision(i).Choosebetween:A(0.80,$50,$0)andB(0.40,$100,$0)ProspectAispreferredduetoriskaversionforgains.Whilebothhavethesameexpectedchangeinwealth,Ahaslessrisk.b.ProspectCorD?Decision(ii).Choosebetween:C(0.00002,$500,000,$0)andD(0.00001,$1,000,000,$0)ProspectD,withmorerisk,ispreferredduetotheriskseekingthatoccurswhenthereareverylowprobabilitiesofpositivepayoffs.c.Arethesechoicesconsistentwithexpectedutilitytheory?Whyorwhynot?ViolationofEUtheorybecausepreferencesareinconsistent.ThesamesortofAllaisparadoxprooffromchapter1canbeused.Itisalsonecessarytomaketheassumptionofpreferencehomogeneity,whichmeansthatifDispreferredtoC,itwillalsobetruethatD*ispreferredtoC*wheretheseare:C*:(0.00002,$50,$0)andD*:(0.00001,$100,$0)3.Considerapersonwiththefollowingvaluefunctionunderprospecttheory:v(w)=w.5 whenw>0=-2(-w).5 whenw<0a.Isthisindividualloss-averse?Explain.Thispersonislossaverse.Lossesarefelttwiceasmuchasgainsofequalmagnitude.b.Assumethatthisindividualweightsvaluesbyprobabilities,insteadofusingaprospecttheoryweightingfunction.Whichofthefollowingprospectswouldbepreferred?P1(.8,1000,-800)P2(.7,1200,-600)P3(.5,2000,-1000)Wecalculatethevalueofeachprospect:V(P1)=.8(31.62)+.2(-2)(28.27)=13.982V(P2)=.7(34.64)+.3(-2)(24.49)=9.55V(P3)=.5(44.72)+.5(-2)(31.62)=9.265ThereforeprospectP1ispreferred.4.Nowconsiderapersonwiththefollowingvaluefunctionunderprospecttheory:v(z)=z.8 whenz≥0=-3(-z).8 whenz<0Thisindividualhasthefollowingweightingfunction:πππwhereweset=.65.a.Whichofthefollowingprospectswouldhechoose?PA(.001,-5000)PB(-5)Comparethevalueofeachprospect:V(PA)=.983(0)+(-3)(910.28)(.011)=-30.15(noteuseofweights)V(PB)=3*1*-3.62=-10.87ThereforeyouwouldpreferB.b.Repeatthecalculationbutusingprobabilitiesinsteadofweights.Whatdoesthisillustrate?V(PA)=.999*0+3*.001*-910.28=-2.73(noteuseofprobability)V(PB)=3*1*-3.62=-10.87ThereforeyouwouldpreferA.Thereasonfortheswitchisthatriskseekingismaintainedinthedomainoflosses(implyingrejectionoflosses)ifprobabilitiesareusedinsteadofweights.5.Whymightsomepreferaprixfixe(fixedprice)dinnercostingaboutthesameasanalacarteone(whereyoupayindividuallyforeachitem)?(Assumethefoodisidentical.)Paymentdecouplingisencouragedwithprixfixe.Youonlyfacethelossofmoneyonceratherthanmultipletimes(occurringifyouhavetofacethecostofeachitemindividuallyusinganàlacartescheme).第五章1. Differentiatethefollowingterms/concepts:PrimacyandrecencyeffectsAprimacyeffectisthetendencytorelyoninformationthatcomesfirstwhenmakinganassessment,whereasarecencyeffectisthetendencytorelyonthemostrecentinformationwhenmakinganassessment.SalienceandavailabilityThesalienceofaneventreferstohowmuchitstandsoutrelativetootherevents,whereastheavailabilityreferstohoweasilytheeventisrecalledfrommemory.Fast-and-frugalheuristicsandbias-generatingheuristicsFastandfrugalheuristicsrequireaminimumoftime,knowledgeandcomputationinordertomakechoices.Oftentheyleadtoverygoodchoices.Sometimeshoweverheuristicsgoastrayandgeneratebehavioralbias.AutonomicandcognitiveheuristicsAutonomicheuristicsarereflexive,autonomic,non-cognitive,andrequireloweffortlevels.Cognitiveheuristicsrequiremoredeliberation.Autonomicheuristicsareappropriatewhenaveryquickdecisionmustbemadeorwhenthestakesarelow,whereascognitiveheuristicsareappropriatewhenthestakesarehigher.2.WhichdescriptionofMaryhashigherprobability?a.Marylovestoplaytennis.b.Marylovestoplaytennisand,duringthesummer,averagesatleastagameaweek.Explainyouranswer.Definetheconjunctionfallacy.Howdoesitapplyhere?Assumeforthepurposeofillustrationthattheprobabilitythatsomeonelovestoplaytennisis.2;theprobabilitythatsomeoneplaystennisonceormoreaweekduringthesummeris.1;andtheprobabilityofoneortheotherofthesethingsis.22.Pr(lovestennis)=.2Pr(lovestennisANDaverages1+)=Pr(lovestennis)+Pr(averages1+)-Pr(lovestennisORaverages1+)=.2+.1-.22=.08Thesecondprobabilityhastobelessbecauseithasonemorerequirement(notonlydoyouhavetolovetennisbutyoualsohavetoplayregularly,butsometennisloversmightjustbetoobusytodothis).Whenpeoplecommittheconjunctionfallacy(thebeliefthatthejointprobabilityismorelikelythanoneofitscomponents),theywillthinkthesecond(joint)eventismorelikelybecauseitsoundslogicalthatsomeonewholovestenniswillalsoplayregularly.3. Rexisasmartfellow.HegetsanAinacourse80%ofthetime.Stillhelikeshisleisure,onlystudyingforthefinalexaminhalfofthecourseshetakes.Neverthelesswhenhedoesstudy,heisalmostsure(95%likely)togetanA.AssuminghegotanA,howlikelyisithestudied?Ifsomeoneestimatestheabovetobe75%,whaterroraretheycommitting?Explain.P(studied|A)=P(A|studied)*[P(studied)/P(A)]=.95*(.5/.8)=.59375The“sample”isthathegotanA.Withoutkn