Chapter5ChoiceUnderUncertainty1Chapter1TopicstobeDiscussedDescribingRiskPreferencesTowardRiskReducingRiskTheDemandforRiskyAssets2Chapter1IntroductionChoicewithcertaintyisreasonablystraightforward.Howdowechoosewhencertainvariablessuchasincomeandpricesareuncertain(i.e.makingchoiceswithrisk)?3Chapter1DescribingRiskTomeasureriskwemustknow: 1) Allofthepossibleoutcomes. 2) Thelikelihoodthateachoutcomewill occur(itsprobability).4Chapter1DescribingRiskInterpretingProbabilityThelikelihoodthatagivenoutcomewilloccur5Chapter1DescribingRiskInterpretingProbabilityObjectiveInterpretationBasedontheobservedfrequencyofpastevents6Chapter1DescribingRiskInterpretingProbabilitySubjectiveBasedonperceptionorexperiencewithorwithoutanobservedfrequencyDifferentinformationordifferentabilitiestoprocessthesameinformationcaninfluencethesubjectiveprobability7Chapter1DescribingRiskExpectedValueTheweightedaverageofthepayoffsorvaluesresultingfromallpossibleoutcomes.TheprobabilitiesofeachoutcomeareusedasweightsExpectedvaluemeasuresthecentraltendency;thepayofforvalueexpectedonaverage8Chapter1DescribingRiskAnExampleInvestmentinoffshoredrillingexploration:TwooutcomesarepossibleSuccess--thestockpriceincreasefrom$30to$40/shareFailure--thestockpricefallsfrom$30to$20/share9Chapter1DescribingRiskAnExampleObjectiveProbability100explorations,25successesand75failuresProbability(Pr)ofsuccess=1/4andtheprobabilityoffailure=3/410Chapter1DescribingRiskAnExample:ExpectedValue(EV)11Chapter1DescribingRiskGiven:TwopossibleoutcomeshavingpayoffsX1

andX2ProbabilitiesofeachoutcomeisgivenbyPr1&Pr212Chapter1DescribingRiskGenerally,expectedvalueiswrittenas:13Chapter1DescribingRiskVariabilityTheextenttowhichpossibleoutcomesofanuncertainevenmaydiffer14Chapter1DescribingRiskAScenarioSupposeyouarechoosingbetweentwopart-timesalesjobsthathavethesameexpectedincome($1,500)Thefirstjobisbasedentirelyoncommission.Thesecondisasalariedposition.Variability15Chapter1DescribingRiskAScenarioTherearetwoequallylikelyoutcomesinthefirstjob--$2,000foragoodsalesjoband$1,000foramodestlysuccessfulone.Thesecondpays$1,510mostofthetime(.99probability),butyouwillearn$510ifthecompanygoesoutofbusiness(.01probability).Variability16Chapter1IncomefromSalesJobsJob1:

Commission .5 2000 .5 1000 1500Job2:Fixedsalary .99 1510 .01 510 1500

Expected Probability Income($) Probability Income($) Income Outcome1 Outcome2DescribingRisk17Chapter1Job1ExpectedIncomeJob2ExpectedIncomeIncomefromSalesJobsDescribingRisk18Chapter1Whiletheexpectedvaluesarethesame,thevariabilityisnot.Greatervariabilityfromexpectedvaluessignalsgreaterrisk.DeviationDifferencebetweenexpectedpayoffandactualpayoffDescribingRisk19Chapter1DeviationsfromExpectedIncome($)Job1 $2,000 $500 $1,000 -$500Job2 1,510 10 510 -900 Outcome1 Deviation Outcome2 DeviationDescribingRisk20Chapter1AdjustingfornegativenumbersThestandarddeviationmeasuresthesquarerootoftheaverageofthesquaresofthedeviationsofthepayoffsassociatedwitheachoutcomefromtheirexpectedvalue.VariabilityDescribingRisk21Chapter1DescribingRiskThestandarddeviationiswritten:Variability22Chapter1CalculatingVariance($)Job1 $2,000 $250,000 $1,000 $250,000 $250,000$500.00Job2 1,510 100 510 980,1009,900 99.50

Deviation Deviation Deviation Standard Outcome1 Squared Outcome2 Squared Squared DeviationDescribingRisk23Chapter1DescribingRiskThestandarddeviationsofthetwojobsare:*GreaterRisk24Chapter1DescribingRiskThestandarddeviationcanbeusedwhentherearemanyoutcomesinsteadofonlytwo.25Chapter1DescribingRiskJob1isajobinwhichtheincomerangesfrom$1000to$2000inincrementsof$100thatareallequallylikely.Example26Chapter1DescribingRiskJob2isajobinwhichtheincomerangesfrom$1300to$1700inincrementsof$100that,also,areallequallylikely.Example27Chapter1OutcomeProbabilitiesforTwoJobsIncome0.1$1000$1500$20000.2Job1Job

2Job1hasgreaterspread:greaterstandarddeviationandgreaterriskthanJob2.Probability28Chapter1DescribingRiskOutcomeProbabilitiesofTwoJobs(unequalprobabilityofoutcomes)Job1:greaterspread&standarddeviationPeakeddistribution:extremepayoffsarelesslikely29Chapter1DescribingRiskDecisionMakingAriskavoiderwouldchooseJob2:sameexpectedincomeasJob1withlessrisk.Supposeweadd$100toeachpayoffinJob1whichmakestheexpectedpayoff=$1600.30Chapter1UnequalProbabilityOutcomesJob1Job2ThedistributionofpayoffsassociatedwithJob1hasagreaterspreadandstandarddeviationthanthosewithJob2.Income0.1$1000$1500$20000.2Probability31Chapter1IncomefromSalesJobs--Modified($)Recall:Thestandarddeviationisthesquarerootofthedeviationsquared.Job1 $2,100 $250,000 $1,100 $250,000 $1,600 $500Job2 1510 100 510 980,100 1,500 99.50

Deviation Deviation Expected Standard Outcome1 Squared Outcome2 Squared Income Deviation32Chapter1DescribingRiskJob1:expectedincome$1,600andastandarddeviationof$500.Job2:expectedincomeof$1,500andastandarddeviationof$99.50Whichjob?Greatervalueorlessrisk?DecisionMaking33Chapter1Supposeacitywantstodeterpeoplefromdoubleparking.Thealternatives…...DescribingRiskExample34Chapter1Assumptions: 1) Double-parkingsavesaperson$5in termsoftimespentsearchingfora parkingspace. 2) Thedriverisriskneutral. 3) Costofapprehensioniszero.ExampleDescribingRisk35Chapter1Afineof$5.01woulddeterthedriverfromdoubleparking.Benefitofdoubleparking($5)islessthanthecost($5.01)equalsanetbenefitthatislessthan0.ExampleDescribingRisk36Chapter1Increasingthefinecanreduceenforcementcost:A$50finewitha.1probabilityofbeingcaughtresultsinanexpectedpenaltyof$5.A$500finewitha.01probabilityofbeingcaughtresultsinanexpectedpenaltyof$5.ExampleDescribingRisk37Chapter1Themoreriskaversedriversare,thelowerthefineneedstobeinordertobeeffective.ExampleDescribingRisk38Chapter1PreferencesTowardRiskChoosingAmongRiskyAlternativesAssumeConsumptionofasinglecommodityTheconsumerknowsallprobabilitiesPayoffsmeasuredintermsofutilityUtilityfunctiongiven39Chapter1PreferencesTowardRiskApersonisearning$15,000andreceiving13unitsofutilityfromthejob.Sheisconsideringanew,butriskyjob.Example40Chapter1PreferencesTowardRiskShehasa.50chanceofincreasingherincometo$30,000anda.50chanceofdecreasingherincometo$10,000.Shewillevaluatethepositionbycalculatingtheexpectedvalue(utility)oftheresultingincome.Example41Chapter1PreferencesTowardRiskTheexpectedutilityofthenewpositionisthesumoftheutilitiesassociatedwithallherpossibleincomesweightedbytheprobabilitythateachincomewilloccur.Example42Chapter1PreferencesTowardRiskTheexpectedutilitycanbewritten:E(u)=(1/2)u($10,000)+(1/2)u($30,000) =0.5(10)+0.5(18) =14E(u)ofnewjobis14whichisgreaterthanthecurrentutilityof13andthereforepreferred.Example43Chapter1PreferencesTowardRiskDifferentPreferencesTowardRiskPeoplecanberiskaverse,riskneutral,orriskloving.44Chapter1PreferencesTowardRiskDifferentPreferencesTowardRiskRiskAverse:Apersonwhoprefersacertaingivenincometoariskyincomewiththesameexpectedvalue.ApersonisconsideredriskaverseiftheyhaveadiminishingmarginalutilityofincomeTheuseofinsurancedemonstratesriskaversivebehavior.45Chapter1PreferencesTowardRiskAScenarioApersoncanhavea$20,000jobwith100%probabilityandreceiveautilitylevelof16.Thepersoncouldhaveajobwitha.5chanceofearning$30,000anda.5chanceofearning$10,000.RiskAverse46Chapter1PreferencesTowardRiskExpectedIncome=(0.5)($30,000)+ (0.5)($10,000)

=$20,000 RiskAverse47Chapter1PreferencesTowardRiskExpectedincomefrombothjobsisthesame--riskaversemaychoosecurrentjobRiskAverse48Chapter1PreferencesTowardRiskTheexpectedutilityfromthenewjobisfound:E(u)=(1/2)u($10,000)+(1/2)u($30,000)E(u)=(0.5)(10)+(0.5)(18)=14E(u)ofJob1is16whichisgreaterthantheE(u)ofJob2whichis14.RiskAverse49Chapter1PreferencesTowardRiskThisindividualwouldkeeptheirpresentjobsinceitprovidesthemwithmoreutilitythantheriskyjob.Theyaresaidtoberiskaverse.RiskAverse50Chapter1Income

($1,000)UtilityTheconsumerisriskaversebecauseshewouldpreferacertainincomeof$20,000toagamblewitha.5probabilityof$10,000anda.5probabilityof$30,000.E101015201314161801630ABCDRiskAversePreferencesTowardRisk51Chapter1PreferencesTowardRiskApersonissaidtoberiskneutraliftheyshownopreferencebetweenacertainincome,andanuncertainonewiththesameexpectedvalue.RiskNeutral52Chapter1Income

($1,000)1020Utility0306AEC1218Theconsumerisriskneutralandisindifferentbetweencertaineventsanduncertaineventswiththesameexpectedincome.PreferencesTowardRiskRiskNeutral53Chapter1PreferencesTowardRiskApersonissaidtoberisklovingiftheyshowapreferencetowardanuncertainincomeoveracertainincomewiththesameexpectedvalue.Examples:Gambling,somecriminalactivityRiskLoving54Chapter1Income

($1,000)Utility03102030AEC818Theconsumerisrisklovingbecauseshewouldpreferthegambletoacertainincome.PreferencesTowardRiskRiskLoving55Chapter1PreferencesTowardRiskTheriskpremiumistheamountofmoneythatarisk-aversepersonwouldpaytoavoidtakingarisk.RiskPremium56Chapter1PreferencesTowardRiskAScenarioThepersonhasa.5probabilityofearning$30,000anda.5probabilityofearning$10,000(expectedincome=$20,000).Theexpectedutilityofthesetwooutcomescanbefound:E(u)=.5(18)+.5(10)=14RiskPremium57Chapter1PreferencesTowardRiskQuestionHowmuchwouldthepersonpaytoavoidrisk?RiskPremium58Chapter1Income

($1,000)Utility01016Here,theriskpremiumis$4,000becauseacertainincomeof$16,000givesthepersonthesameexpectedutilityastheuncertainincomethathasanexpectedvalueof$20,000.101830402014ACEG20FRiskPremiumPreferencesTowardRiskRiskPremium59Chapter1PreferencesTowardRiskVariabilityinpotentialpayoffsincreasetheriskpremium.Example:Ajobhasa.5probabilityofpaying$40,000(utilityof20)anda.5chanceofpaying0(utilityof0).RiskAversionandIncome60Chapter1PreferencesTowardRiskExample:Theexpectedincomeisstill$20,000,buttheexpectedutilityfallsto10.Expectedutility=.5u($)+.5u($40,000) =0+.5(20)=10RiskAversionandIncome61Chapter1PreferencesTowardRiskExample:Thecertainincomeof$20,000hasautilityof16.Ifthepersonisrequiredtotakethenewposition,theirutilitywillfallby6.RiskAversionandIncome62Chapter1PreferencesTowardRiskExample:Theriskpremiumis$10,000(i.e.theywouldbewillingtogiveup$10,000ofthe$20,000andhavethesameE(u)astheriskyjob.RiskAversionandIncome63Chapter1PreferencesTowardRiskTherefore,itcanbesaidthatthegreaterthevariability,thegreatertheriskpremium.RiskAversionandIncome64Chapter1PreferencesTowardRiskCombinationsofexpectedincome&standarddeviationofincomethatyieldthesameutilityIndifferenceCurve65Chapter1RiskAversionand

IndifferenceCurvesStandardDeviationofIncome

ExpectedIncomeHighlyRiskAverse:Anincreaseinstandarddeviationrequiresalargeincreaseinincometomaintainsatisfaction.U1U2U366Chapter1RiskAversionand

IndifferenceCurvesStandardDeviationofIncome

ExpectedIncomeSlightlyRiskAverse:Alargeincreaseinstandarddeviationrequiresonlyasmallincreaseinincometomaintainsatisfaction.U1U2U367Chapter1BusinessExecutives

andtheChoiceofRiskStudyof464executivesfoundthat:20%wereriskneutral40%wererisktakers20%wereriskadverse20%didnotrespondExample68Chapter1Thosewholikedriskysituationsdidsowhenlosseswereinvolved.Whenrisksinvolvedgainsthesame,executivesoptedforlessriskysituations.ExampleBusinessExecutives

andtheChoiceofRisk69Chapter1Theexecutivesmadesubstantialeffortstoreduceoreliminateriskbydelayingdecisionsandcollectingmoreinformation.ExampleBusinessExecutives

andtheChoiceofRisk70Chapter1ReducingRiskThreewaysconsumersattempttoreduceriskare: 1)Diversification 2)Insurance 3)Obtainingmoreinformation71Chapter1ReducingRiskDiversificationSupposeafirmhasachoiceofsellingairconditioners,heaters,orboth.Theprobabilityofitbeinghotorcoldis0.5.Thefirmwouldprobablybebetteroffbydiversification.72Chapter1IncomefromSalesofAppliancesAirconditionersales $30,000 $12,000Heatersales 12,000 30,000*0.5probabilityofhotorcoldweather HotWeather ColdWeather73Chapter1ReducingRiskIfthefirmssellsonlyheatersorairconditionerstheirincomewillbeeither$12,000or$30,000.Theirexpectedincomewouldbe:1/2($12,000)+1/2($30,000)=$21,000Diversification74Chapter1ReducingRiskIfthefirmdividestheirtimeevenlybetweenappliancestheirairconditioningandheatingsaleswouldbehalftheiroriginalvalues.Diversification75Chapter1ReducingRiskIfitwerehot,theirexpectedincomewouldbe$15,000fromairconditionersand$6,000fromheaters,or$21,000.Ifitwerecold,theirexpectedincomewouldbe$6,000fromairconditionersand$15,000fromheaters,or$21,000.Diversification76Chapter1ReducingRiskWithdiversification,expectedincomeis$21,000withnorisk.Diversification77Chapter1ReducingRiskFirmscanreduceriskbydiversifyingamongavarietyofactivitiesthatarenotcloselyrelated.Diversification78Chapter1ReducingRiskDiscussionQuestionsHowcandiversificationreducetheriskofinvestinginthestockmarket?Candiversificationeliminatetheriskofinvestinginthestockmarket?TheStockMarket79Chapter1ReducingRiskRiskaversearewillingtopaytoavoidrisk.Ifthecostofinsuranceequalstheexpectedloss,riskaversepeoplewillbuyenoughinsurancetorecoverfullyfromapotentialfinancialloss.Insurance80Chapter1TheDecisiontoInsureNo $40,000 $50,000 $49,000 $9,055Yes 49,000 49,000 49,000 0Insurance Burglary NoBurglary Expected Standard (Pr=.1) (Pr=.9) Wealth Deviation81Chapter1ReducingRiskWhiletheexpectedwealthisthesame,theexpectedutilitywithinsuranceisgreaterbecausethemarginalutilityintheeventofthelossisgreaterthanifnolossoccurs.Purchasesofinsurancetransferswealthandincreasesexpectedutility.Insurance82Chapter1ReducingRiskAlthoughsingleeventsarerandomandlargelyunpredictable,theaverageoutcomeofmanysimilareventscanbepredicted.TheLawofLargeNumbers83Chapter1ReducingRiskExamplesAsinglecointossvs.largenumberofcoinsWhomwillhaveacarwreckvs.thenumberofwrecksforalargegroupofdriversTheLawofLargeNumbers84Chapter1ReducingRiskAssume:10%chanceofa$10,000lossfromahomeburglaryExpectedloss=.10x$10,000=$1,000withahighrisk(10%chanceofa$10,000loss)100peoplefacethesameriskActuarialFairness85Chapter1ReducingRiskThen:$1,000premiumgeneratesa$100,000fundtocoverlossesActualFairnessWhentheinsurancepremium=expectedpayoutActuarialFairness86Chapter1TheValueofTitleInsurance

WhenBuyingaHouseAScenario:Priceofahouseis$200,0005%chancethatthesellerdoesnotownthehouseExample87Chapter1TheValueofTitleInsurance

WhenBuyingaHouseRiskneutralbuyerwouldpay:Example88Chapter1TheValueofTitleInsurance

WhenBuyingaHouseRiskaversebuyerwouldpaymuchlessByreducingrisk,titleinsuranceincreasesthevalueofthehousebyanamountfargreaterthanthepremium.Example89Chapter1ReducingRiskValueofCompleteInformationThedifferencebetweentheexpectedvalueofachoicewithcompleteinformationandtheexpectedvaluewheninformationisincomplete.TheValueofInformation90Chapter1ReducingRiskSupposeastoremanagermustdeterminehowmanyfallsuitstoorder:100suitscost$180/suit50suitscost$200/suitThepriceofthesuitsis$300TheValueofInformation91Chapter1ReducingRiskSupposeastoremanagermustdeterminehowmanyfallsuitstoorder:Unsoldsuitscanbereturnedforhalfcost.Theprobabilityofsellingeachquantityis.50.TheValueofInformation92Chapter1TheDecisiontoInsure1.Buy50suits $5,000 $5,000 $5,0002.Buy100suits 1,500 12,000 6,750

Expected Saleof50 Saleof100 Profit93Chapter1ReducingRiskWithincompleteinformation:RiskNeutral:Buy100suitsRiskAverse:Buy50suits94Chapter1ReducingRiskTheexpectedvaluewithcompleteinformationis$8,500.8,500=.5(5,000)+.5(12,000)Theexpectedvaluewithuncertainty(buy100suits)is$6,750.TheValueofInformation95Chapter1ReducingRiskThevalueofcompleteinformationis$1,750,orthedifferencebetweenthetwo(theamountthestoreownerwouldbewillingtopayforamarketingstudy).TheValueofInformation96Chapter1PercapitamilkconsumptionhasfallenovertheyearsThemilkproducersengagedinmarketresearchtodevelopnewsalesstrategiestoencouragetheconsumptionofmilk.ReducingRiskTheValueofInformation:Example97Chapter1FindingsMilkdemandisseasonalwiththegreatestdemandinthespringEpisnegativeandsmallEIispositiveandlargeReducingRiskTheValueofInformation:Example98Chapter1Milkadvertisingincreasessalesmostinthespring.AllocatingadvertisingbasedonthisinformationinNewYorkincreasedsalesby$4,046,557andprofitsby9%.Thecostoftheinformationwasrelativelylow,whilethevaluewassubstantial.ReducingRiskTheValueofInformation:Example99Chapter1AssetsSomethingthatprovidesaflowofmoneyorservicestoitsowner.Theflowofmoneyorservicescanbeexplicit(dividends)orimplicit(capitalgain).TheDemandforRiskyAssets100Chapter1CapitalGain

Anincreaseinthevalueofanasset,whileadecreaseisacapitalloss.TheDemandforRiskyAssets101Chapter1TheDemandforRiskyAssetsRiskyAssetProvidesanuncertainflowofmoneyorservicestoitsowner.Examplesapartmentrent,capitalgains,corporatebonds,stockpricesRisky&RisklessAssets102Chapter1TheDemandforRiskyAssetsRisklessAssetProvidesaflowofmoneyorservicesthatisknownwithcertainty.Examplesshort-termgovernmentbonds,short-termcertificatesofdepositRisky&RisklessAssets103Chapter1TheDemandforRiskyAssetsAssetReturnsReturnonanAssetThetotalmonetaryflowofanassetasafractionofitsprice.RealReturnofanAssetThesimple(ornominal)returnlesstherateofinflation.104Chapter1TheDemandforRiskyAssetsAssetReturns105Chapter1TheDemandforRiskyAssetsExpectedReturnReturnthatanassetshouldearnonaverageExpectedvs.ActualReturns106Chapter1TheDemandforRiskyAssetsActualReturnReturnthatanassetearnsExpectedvs.ActualReturns107Chapter1Investments--Risk

andReturn(1926-1999)Commonstocks(S&P500) 9.5 20.2Long-termcorporatebonds 2.7 8.3U.S.Treasurybills 0.6 3.2 Risk RealRateof (standard Return(%) deviation,%)108Chapter1TheDemandforRiskyAssetsHigherreturnsareassociatedwithgreaterrisk.Therisk-averseinvestormustbalanceriskrelativetoreturnExpectedvs.ActualReturns109Chapter1TheDemandforRiskyAssetsAninvestorischoosingbetweenT-Billsandstocks:T-bills(riskless)versusStocks(risky)Rf=thereturnonriskfreeT-billsExpectedreturnequalsactualreturnwhenthereisnoriskTheTrade-OffBetweenRiskandReturn110Chapter1TheDemandforRiskyAssetsAninvestorischoosingbetweenT-Billsandstocks:Rm=theexpectedreturnonstocksrm=theactualreturnsonstockTheTrade-OffBetweenRiskandReturn111Chapter1TheDemandforRiskyAssetsAtthetimeoftheinvestmentdecision,weknowthesetofpossibleoutcomesandthelikelihoodofeach,butwedonotknowwhatparticularoutcomewilloccur.TheTrade-OffBetweenRiskandReturn112Chapter1TheDemandforRiskyAssetsTheriskyassetwillhaveahigherexpectedreturnthantheriskfreeasset(Rm>Rf).Otherwise,risk-averseinvestorswouldbuyonlyT-bills.TheTrade-OffBetweenRiskandReturn113Chapter1TheDemandforRiskyAssetsHowtoallocatesavings:

b=fractionofsavingsinthestock market 1-b=fractioninT-billsTheInvestmentPortfolio114Chapter1TheDemandforRiskyAssetsExpectedReturn:

Rp:weightedaverageoftheexpectedreturnonthetwoassets

Rp=bRm+(1-b)Rf

TheInvestmentPortfolio115Chapter1TheDemandforRiskyAssetsExpectedReturn: IfRm=12%,Rf=4%,andb=1/2 Rp=1/2(.12)+1/2(.04)=8%TheInvestmentPortfolio116Chapter1TheDemandforRiskyAssetsQuestionHowriskyistheirportfolio?TheInvestmentPortfolio117Chapter1TheDemandforRiskyAssetsRisk(standarddeviation)oftheportfolioisthefractionoftheportfolioinvestedintheriskyassettimesthestandarddeviationofthatasset:TheInvestmentPortfolio118Chapter1TheDemandforRiskyAssetsDeterminingb:TheInvestor’sChoiceProblem119Chapter1TheDemandforRiskyAssetsDeterminingb:TheInvestor’sChoiceProblem120Chapter1TheDemandforRiskyAssetsObservations 1) Thefinalequation isabudgetlinedescribingthetrade- offbetweenriskandexpected return.RiskandtheBudgetLine121Chapter1TheDemandforRiskyAssetsObservations: 2) Isanequationforastraightline: 3)RiskandtheBudgetLine122Chapter1TheDemandforRiskyAssetsObservations 3) Expectedreturn,RP,increasesas riskincreases. 4) Theslopeisthepriceofriskorthe risk-returntrade-off.RiskandtheBudgetLine123Chapter1ChoosingBetween

RiskandReturn0ExpectedReturn,RpU2

istheoptimalchoiceofthoseobtainable,sinceitgivesthehighestreturnforagivenriskandistangenttothebudgetline.RfBudgetLineRmR*U2U1U3124Chapter1RfBudgetlineTheChoicesof

TwoDifferentInvestors0ExpectedReturn,RpGiventhesamebudgetline,investorAchooseslowreturn-lowrisk,whileinvestorB

chooseshighreturn-highrisk.UARAUBRBRm125Chapter1RfBudgetlineBuyingStocksonMargin0ExpectedReturn,RpUARAUA:Highriskaversion--Stock&T-billportfolioUBRBRmUA:Lowriskaversion--Theinvestorwouldinvestmorethan100%oftheirwealthbyborrowingorbuyingonthemargin.126Chapter1InvestingintheStockMarketObservationsPercentofAmericanfamilieswhohaddirectlyorindirectlyinvestedinthestockmarket1989=32%1995=41%127Chapter1InvestingintheStockMarketObservationsShareofwealthinthestockmarket1989=26%1995=40%128Chapter1InvestingintheStockMarketObservationsParticipationinthestockmarketbyageLessthan351989=23%1995=29%Morethan35Smallincrease129Chapter1InvestingintheStockMarketWhatDoYouThink?Whyaremorepeopleinvestinginthestockmarket?130Chapter1SummaryConsumersandmanagersfrequentlymakedecisionsinwhichthereisuncertaintyaboutt