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CHAPTER5OUTLINE,5.1DescribingRisk5.2PreferencesTowardRisk5.3ReducingRisk5.4TheDemandforRiskyAssets5.5BehavioralEconomics,UncertaintyandConsumerBehavior,Inordertocomparetheriskinessofalternativechoices,weneedtoquantifyrisk.Wewillexaminepeoplespreferencestowardrisk.Wewillseehowpeoplecansometimesreduceoreliminaterisk.Insomesituations,peoplemustchoosetheamountofrisktheywishtobear.Inthefinalsectionofthischapter,weofferanoverviewoftheflourishingfieldofbehavioraleconomics.,Sometimeswemustchoosehowmuchrisktobear.,DESCRIBINGRISK,Probability,probabilityLikelihoodthatagivenoutcomewilloccur.,Subjectiveprobabilityistheperceptionthatanoutcomewilloccur.,expectedvalueProbability-weightedaverageofthepayoffsassociatedwithallpossibleoutcomes.,ExpectedValue,payoffValueassociatedwithapossibleoutcome.,Theexpectedvaluemeasuresthecentraltendencythepayofforvaluethatwewouldexpectonaverage.,Expectedvalue=Pr(success)($40/share)+Pr(failure)($20/share)=(1/4)($40/share)+(3/4)($20/share)=$25/share,E(X)=Pr1X1+Pr2X2,E(X)=Pr1X1+Pr2X2+.+PrnXn,DESCRIBINGRISK,Variability,variabilityExtenttowhichpossibleoutcomesofanuncertaineventdiffer.,deviationDifferencebetweenexpectedpayoffandactualpayoff.,TABLE5.1IncomefromSalesJobs,DESCRIBINGRISK,Variability,OutcomeProbabilitiesforTwoJobs,ThedistributionofpayoffsassociatedwithJob1hasagreaterspreadandagreaterstandarddeviationthanthedistributionofpayoffsassociatedwithJob2.Bothdistributionsareflatbecausealloutcomesareequallylikely.,Figure5.1,DESCRIBINGRISK,Variability,UnequalProbabilityOutcomes,ThedistributionofpayoffsassociatedwithJob1hasagreaterspreadandagreaterstandarddeviationthanthedistributionofpayoffsassociatedwithJob2.Bothdistributionsarepeakedbecausetheextremepayoffsarelesslikelythanthosenearthemiddleofthedistribution.,Figure5.2,DecisionMaking,Finesmaybebetterthanincarcerationindeterringcertaintypesofcrimes,suchasspeeding,double-parking,taxevasion,andairpolluting.Otherthingsbeingequal,thegreaterthefine,themoreapotentialcriminalwillbediscouragedfromcommittingthecrime.Inpractice,however,itisverycostlytocatchlawbreakers.Therefore,wesaveonadministrativecostsbyimposingrelativelyhighfines.Apolicythatcombinesahighfineandalowprobabilityofapprehensionislikelytoreduceenforcementcosts.,DESCRIBINGRISK,PREFERENCESTOWARDRISK,RiskAverse,RiskLoving,andRiskNeutral,In(a),aconsumersmarginalutilitydiminishesasincomeincreases.Theconsumerisriskaversebecauseshewouldpreferacertainincomeof$20,000(withautilityof16)toagamblewitha.5probabilityof$10,000anda.5probabilityof$30,000(andexpectedutilityof14).,Figure5.3,PREFERENCESTOWARDRISK,RiskAverse,RiskLoving,andRiskNeutral,In(b),theconsumerisriskloving:Shewouldpreferthesamegamble(withexpectedutilityof10.5)tothecertainincome(withautilityof8).Finally,theconsumerin(c)isriskneutral,andindifferentbetweencertainanduncertaineventswiththesameexpectedincome.,Figure5.3,expectedutilitySumoftheutilitiesassociatedwithallpossibleoutcomes,weightedbytheprobabilitythateachoutcomewilloccur.,PREFERENCESTOWARDRISK,riskaverseConditionofpreferringacertainincometoariskyincomewiththesameexpectedvalue.,riskneutralConditionofbeingindifferentbetweenacertainincomeandanuncertainincomewiththesameexpectedvalue.,risklovingConditionofpreferringariskyincometoacertainincomewiththesameexpectedvalue.,DifferentPreferencesTowardRisk,PREFERENCESTOWARDRISK,DifferentPreferencesTowardRisk,RiskPremium,riskpremiumMaximumamountofmoneythatarisk-aversepersonwillpaytoavoidtakingarisk.,RiskPremium,Figure5.4,Theriskpremium,CF,measurestheamountofincomethatanindividualwouldgiveuptoleaveherindifferentbetweenariskychoiceandacertainone.Here,theriskpremiumis$4000becauseacertainincomeof$16,000(atpointC)givesherthesameexpectedutility(14)astheuncertainincome(a.5probabilityofbeingatpointAanda.5probabilityofbeingatpointE)thathasanexpectedvalueof$20,000.,PREFERENCESTOWARDRISK,DifferentPreferencesTowardRisk,RiskAversionandIncome,Theextentofanindividualsriskaversiondependsonthenatureoftheriskandonthepersonsincome.Otherthingsbeingequal,risk-aversepeoplepreferasmallervariabilityofoutcomes.Thegreaterthevariabilityofincome,themorethepersonwouldbewillingtopaytoavoidtheriskysituation.,PREFERENCESTOWARDRISK,DifferentPreferencesTowardRisk,RiskAversionandIndifferenceCurves,Figure5.5,Part(a)appliestoapersonwhoishighlyriskaverse:Anincreaseinthisindividualsstandarddeviationofincomerequiresalargeincreaseinexpectedincomeifheorsheistoremainequallywelloff.Part(b)appliestoapersonwhoisonlyslightlyriskaverse:Anincreaseinthestandarddeviationofincomerequiresonlyasmallincreaseinexpectedincomeifheorsheistoremainequallywelloff.,RiskAversionandIndifferenceCurves,PREFERENCESTOWARDRISK,Arebusinessexecutivesmorerisklovingthanmostpeople?Inonestudy,464executiveswereaskedtorespondtoaquestionnairedescribingriskysituationsthatanindividualmightfaceasvicepresidentofahypotheticalcompany.Thepayoffsandprobabilitieswerechosensothateacheventhadthesameexpectedvalue.Inincreasingorderoftheriskinvolved,thefoureventswere:AlawsuitinvolvingapatentviolationAcustomerthreateningtobuyfromacompetitorAuniondisputeAjointventurewithacompetitorThestudyfoundthatexecutivesvarysubstantiallyintheirpreferencestowardrisk.Moreimportantly,executivestypicallymadeeffortstoreduceoreliminaterisk,usuallybydelayingdecisionsandcollectingmoreinformation.,REDUCINGRISK,Diversification,diversificationPracticeofreducingriskbyallocatingresourcestoavarietyofactivitieswhoseoutcomesarenotcloselyrelated.,negativelycorrelatedvariablesVariableshavingatendencytomoveinoppositedirections.,mutualfundOrganizationthatpoolsfundsofindividualinvestorstobuyalargenumberofdifferentstocksorotherfinancialassets.,positivelycorrelatedvariablesVariableshavingatendencytomoveinthesamedirection.,TheStockMarket,REDUCINGRISK,Insurance,Theabilitytoavoidriskbyoperatingonalargescaleisbasedonthelawoflargenumbers,whichtellsusthatalthoughsingleeventsmayberandomandlargelyunpredictable,theaverageoutcomeofmanysimilareventscanbepredicted.,actuariallyfairCharacterizingasituationinwhichaninsurancepremiumisequaltotheexpectedpayout.,ActuarialFairness,TheLawofLargeNumbers,REDUCINGRISK,Supposeyouarebuyingyourfirsthouse.Toclosethesale,youwillneedadeedthatgivesyouclear“title.”Withoutsuchacleartitle,thereisalwaysachancethatthesellerofthehouseisnotitstrueowner.Insituationssuchasthis,itisclearlyintheinterestofthebuyertobesurethatthereisnoriskofalackoffullownership.Thebuyerdoesthisbypurchasing“titleinsurance.”Becausethetitleinsurancecompanyisaspecialistinsuchinsuranceandcancollecttherelevantinformationrelativelyeasily,thecostoftitleinsuranceisoftenlessthantheexpectedvalueofthelossinvolved.Inaddition,becausemortgagelendersareallconcernedaboutsuchrisks,theyusuallyrequirenewbuyerstohavetitleinsurancebeforeissuingamortgage.,REDUCINGRISK,TheValueofInformation,valueofcompleteinformationDifferencebetweentheexpectedvalueofachoicewhenthereiscompleteinformationandtheexpectedvaluewheninformationisincomplete.,REDUCINGRISK,Per-capitaconsumptionofmilkhasdeclinedovertheyearsasituationthathasstirredproducerstolookfornewstrategiestoencouragemilkconsumption.Onestrategywouldbetoincreaseadvertisingexpendituresandtocontinueadvertisingatauniformratethroughouttheyear.Asecondstrategywouldbetoinvestinmarketresearchinordertoobtainmoreinformationabouttheseasonaldemandformilk.Researchintomilkdemandshowsthatsalesfollowaseasonalpattern,withdemandbeinggreatestduringthespringandlowestduringthesummerandearlyfall.Inthiscase,thecostofobtainingseasonalinformationaboutmilkdemandisrelativelylowandthevalueoftheinformationsubstantial.ApplyingthesecalculationstotheNewYorkmetropolitanarea,wediscoverthatthevalueofinformationthevalueoftheadditionalannualmilksalesisabout$4million.,REDUCINGRISK,Supposeyouwereseriouslyillandrequiredmajorsurgery.Assumingyouwantedtogetthebestcarepossible,howwouldyougoaboutchoosingasurgeonandahospitaltoprovidethatcare?Atrulyinformeddecisionwouldprobablyrequiremoredetailedinformation.Thiskindofinformationislikelytobedifficultorimpossibleformostpatientstoobtain.Moreinformationisoften,butnotalways,better.Whethermoreinformationisbetterdependsonwhicheffectdominatestheabilityofpatientstomakemoreinformedchoicesversustheincentivefordoctorstoavoidverysickpatients.Moreinformationoftenimproveswelfarebecauseitallowspeopletoreduceriskandtotakeactionsthatmightreducetheeffectofbadoutcomes.However,informationcancausepeopletochangetheirbehaviorinundesirableways.,THEDEMANDFORRISKYASSETS,Assets,assetSomethingthatprovidesaflowofmoneyorservicestoitsowner.,riskless(orrisk-free)assetAssetthatprovidesaflowofmoneyorservicesthatisknownwithcertainty.,Anincreaseinthevalueofanassetisacapitalgain;adecreaseisacapitalloss.,RiskyandRisklessAssets,riskyassetAssetthatprovidesanuncertainflowofmoneyorservicestoitsowner.,THEDEMANDFORRISKYASSETS,AssetReturns,returnTotalmonetaryflowofanassetasafractionofitsprice.,realreturnSimple(ornominal)returnonanasset,lesstherateofinflation.,ExpectedversusActualReturns,expectedreturnReturnthatanassetshouldearnonaverage.,actualreturnReturnthatanassetearns.,THEDEMANDFORRISKYASSETS,TheTrade-OffBetweenRiskandReturn,TheInvestmentPortfolio,(5.1),(5.2),TheInvestorsChoiceProblem,(5.3),PriceofriskExtrariskthataninvestormustincurtoenjoyahigherexpectedreturn.,AninvestorisdividingherfundsbetweentwoassetsTreasurybills,whichareriskfree,andstocks.Thebudgetlinedescribesthetrade-offbetweentheexpectedreturnanditsriskiness,asmeasuredbythestandarddeviationofthereturn.Theslopeofthebudgetlineis(RmRf)/m,whichisthepriceofrisk.Threeindifferencecurvesaredrawn,eachshowingcombinationsofriskandreturnthatleaveaninvestorequallysatisfied.Thecurvesareupward-slopingbecausearisk-averseinvestorwillrequireahigherexpectedreturnifsheistobearagreateramountofrisk.Theutility-maximizinginvestmentportfolioisatthepointwhereindifferencecurveU2istangenttothebudgetline.,THEDEMANDFORRISKYASSETS,TheInvestorsChoiceProblem,RiskandIndifferenceCurves,ChoosingBetweenRiskandReturn,Figure5.6,InvestorAishighlyriskaverse.Becausehisportfoliowillconsistmostlyoftherisk-freeasset,hisexpectedreturnRAwillbeonlyslightlygreaterthantherisk-freereturn.HisriskA,however,willbesmall.InvestorBislessriskaverse.Shewillinvestalargefractionofherfundsinstocks.AlthoughtheexpectedreturnonherportfolioRBwillbelarger,itwillalsoberiskier.,THEDEMANDFORRISKYASSETS,TheInvestorsChoiceProblem,RiskandIndifferenceCurves,TheChoicesofTwoDifferentInvestors,Figure5.7,BecauseInvestorAisriskaverse,hisportfoliocontainsamixtureofstocksandrisk-freeTreasurybills.InvestorB,however,hasaverylowdegreeofriskaversion.Herindifferencecurve,UB,istangenttothebudgetlineatapointwheretheexpectedreturnandstandarddeviationforherportfolioexceedthoseforthestockmarketoverall.Thisimpliesthatshewouldliketoinvestmorethan100percentofherwealthinthestockmarket.Shedoessobybuyingstocksonmargini.e.,byborrowingfromabrokeragefirmtohelpfinanceherinvestment.,THEDEMANDFORRISKYASSETS,TheInvestorsChoiceProblem,RiskandIndifferenceCurves,BuyingStocksonMargin,Figure5.8,THEDEMANDFORRISKYASSETS,Whyhavemorepeoplestartedinvestinginthestockmarket?Onereasonistheadventofonlinetrading,whichhasmadeinvestingmucheasier.,ThedividendyieldfortheSconsumersfacebudgetconstraints;andgiventheirpreferences,limitedincomes,andthepricesofdifferentgoods,consumerschoosetobuycombinationsofgoodsthatmaximizetheirsatisfactionorutility.Theseassumptions,however,arenotalwaysrealistic.Perhapsourunderstandingofconsumerdemand(aswellasthedecisionsoffirms)wouldbeimprovedifweincorporatedmorerealisticanddetailedassumptionsregardinghumanbehavior.Thishasbeentheobjectiveofthenewlyflourishingfieldofbehavioraleconomics.,BEHAVIORALECONOMICS,Someexamplesofconsumerbehaviorthatcannotbeeasilyexplainedwiththebasicutility-maximizingassumptions:Therehasjustbeenabigsnowstorm,soyoustopatthehardwarestoretobuyasnowshovel.Youhadexpectedtopay$20fortheshovelthepricethatthestorenormallycharges.However,youfindthatthestorehassuddenlyraisedthepriceto$40.Althoughyouwouldexpectapriceincreasebecauseofthestorm,youfeelthatadoublingofthepriceisunfairandthatthestoreistryingtotakeadvantageofyou.Outofspite,youdonotbuytheshovel.Tiredofbeingsnowedinathomeyoudecidetotakeavacationinthecountry.Ontheway,youstopatahighwayrestaurantforlunch.Eventhoughyouareunlikelytoreturntothatrestaurant,youbelievethatitisfairandappropriatetoleavea15-percenttipinappreciationofthegoodservicethatyoureceived.YoubuythistextbookfromanInternetbooksellerbecausethepriceislowerthanthepriceatyourlocalbookstore.However,youignoretheshippingcostwhencomparingprices.,BEHAVIORALECONOMICS,MoreComplexPreferences,referencepointThepointfromwhichanindividualmakesaconsumptiondecision.,endowmenteffectTendencyofindividualstovalueanitemmorewhentheyownitthanwhentheydonot.,lossaversionTendencyforindividualstopreferavoidinglossesoveracquiringgains.,anchoringTendencytorelyheavilyononeprior(suggested)piecesofinformationwhenmakingadecision.,RulesofThumbandBiasesinDecisionMaking,BEHAVIORALECONOMICS,ProbabilitiesandUncertainty,Animportantpartofdecisionmakingunderuncertaintyisthecalculationofexpectedutility,whichrequirestwopiecesofinformation:autilityvalueforeachoutcome(fromtheutilityfunction)andtheprobabilityofeachoutcome.Peoplearesometimespronetoabiascalledthelawofsmallnumbers:Theytendtooverstatetheprobabilitythatcertaineventswilloccurwhenfacedwithrelativelylittleinformationfromrecentmemory.Formingsubjectiveprobabilitiesisnotalwaysaneasytaskan
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