财务管理英文课件

chapter1&3Scopeandenvironmentoffinancialmanagementchapter1&31一二请在这里输入您的主要叙述内容整体概述三请在这里输入您的主要叙述内容请在这里输入您的主要叙述内容一二请在这里输入您的主要叙述内容整体概述三请在这里输入您的主2DevelopmentofFinancialManagementEarly20thcentury:Concentratedonreportingtooutsiders.Early21stcentury:Insidersmanagingandcontrollingthefirm’sfinancialoperations.DevelopmentofFinancialManag3Attheturnofthetwentiethcenturyfinancialtopicsfocusedontheformationofnewcompaniesandtheirlegalregulationandtheprocessofraisingfundsinthecapitalmarkets.Thecompany’ssecretarywasinchargeofraisingfundsandproducingtheannualreports,aswellastheaccountingfunction.Attheturnofthetwentiethc4BusinessfailuresduringtheGreatDepressionofthe1930shelpedchangethefocusoffinance.Increasedemphasiswasplacedonbankruptcy,liquiditymanagementandavoidanceoffinancialproblems.BusinessfailuresduringtheG5AfterWorldWarⅡtheemphasisofcorporatefinanceswitchedfromfinancialaccountingandexternalreportingtocostaccountingandreportingandfinancialanalysisonbehalfofthefirm’smanagers.Thatis,theperspectiveoffinancechangedfromreportingonlytooutsiderstothatofaninsiderchargedwiththemanagementandcontrolofthefirm’sfinancialoperations.AfterWorldWarⅡtheemphasis6Capitalbudgetingbecameamajortopicinfinance.Thisledtoanincreasedinterestinrelatedtopics,mostnotablyfirmvaluation.Interestinthesetopicsgrewandinturnspurredinterestinsecurityanalysis,portfoliotheoryandcapitalstructuretheory.Capitalbudgetingbecameamaj7ChiefAccountantCorporateTreasurerTypicalFinanceStructureChiefFinancialOfficerChiefAccountantCorporateTrea8Chiefaccountantisalsocalledfinancialcontroller,whoseresponsibilitiesincludefinancialreportingtooutsidersaswellascostandmanagerialaccountingandfinancialanalysisonbehalfofthefirm’smanagers.Corporatetreasurerisinchargeofraisingfunds,managingliquidityandbankingrelationshipsandcontrollingrisks.Chiefaccountantisalsocalle9FinancialGoaloftheFirmProfitmaximisation?Inmicroeconomicscoursesprofitmaximisationisfrequentlygivenasthefinancialgoalofthefirm.Profitmaximisationfunctionslargelyasatheoreticalgoal.

FinancialGoaloftheFirmProf10Problems:UNCERTAINTYofreturnsTIMINGofreturns

Problems:11Shareholderwealthmaximisation?

Sameas:MaximisingfirmvalueMaximisingsharevaluesShareholderwealthSameas:12Ittakesintoaccountuncertaintyorrisk,time,andotherfactorsthatareimportanttotheowners.Butmanythingsaffectshareprices.Difficulty:TheagencyproblemIttakesintoaccountuncertai13AgencyproblemTheagencyproblemreferstothefactthatafirm’smanagerswillnotworktomaximisebenefitstothefirm’sownersunlessitisinthemanagers’interesttodoso.Thisproblemistheresultofaseparationofthemanagementandownershipofthefirm.AgencyproblemTheagencyprobl14AgencyCostsThecosts,suchasreducedshareprice,associatedwithpotentialconflictbetweenmanagersandinvestorswhenthesetwogroupsarenotthesame.AgencyCostsThecosts,suchas15Inordertolessentheagencyproblem,somecompanieshaveadoptedpracticessuchasissuingstockoptions(shareoptions)totheirexecutives.Inordertolessentheagency16FinancialDecisionsandRisk-returnRelationshipsAlmostallfinancialdecisionsinvolvesomesortofrisk-returntrade-off.Themoreriskthefirmiswillingtoassume,thehighertheexpectedreturnfromagivencourseofaction.FinancialDecisionsandRisk-r17RiskandReturnsRiskExpectedReturnsRiskandReturnsRiskExpectedR18WhyPricesReflectValueEfficientMarketsMarketsinwhichthevaluesofallassetsandsecuritiesatanyinstantintimefullyreflectallavailableinformation.AssumptionWhyPricesReflectValueEffici19OrganisationalFormsSoleproprietorshipsPartnershipsCompaniesOrganisationalFormsSolepropr20NatureoftheorganisationalformsSoleproprietorshipOwnedbyasingleindividualAbsenceofanyformallegalbusinessstructureTheownermaintainstitletotheassetsandispersonallyresponsible,generallywithoutlimitation,fortheliabilitiesincurred.Theproprietorisentitledtotheprofitsfromthebusinessbutalsoabsorbanylosses.Natureoftheorganisationalf21PartnershipTheprimarydifferencebetweenapartnershipandasoleproprietorshipisthatthepartnershiphasmorethanoneowner.Eachpartnerisjointlyandseverallyresponsiblefortheliabilitiesincurredbythepartnership.Partnership22CompanyAcompanymayoperateabusinessinitsownright.Thatis,thisentityfunctionsseparatelyandapartfromitsowners.Theownerselectaboardofdirectors,whosemembersinturnselectindividualstoserveascorporateofficers,includingthemanagerandthecompanysecretary.Theshareholder’sliabilityisgenerallylimitedtotheamountofhisorherinvestmentinthecompany.Company23Limitedcompany(Ltd)andproprietarylimitedcompany(PtyLtd)Ltdcompaniesaregenerallypubliccompanieswhosesharesmaybelistedonastockexchange,ownershipinsuchsharesbeingtransferablebypublicsalethroughtheexchange.PtyLtdcompaniesarebasicallyprivateentities,asthesharescanonlybetransferredprivately.Limitedcompany(Ltd)andprop24ComparisonofOrganisationalformsOrganisationrequirementsandcostsLiabilityofownersContinuityofbusinessTransferabilityofownershipManagementcontrolEaseofcapitalraisingIncometaxesComparisonofOrganisationalf25TheflowoffundsSavingsdeficitunitsSavingssurplusunitsFinancialmarketsfacilitatetransfersoffundsfromsurplustodeficitunitsDirectflowsoffindsIndirectflowsoffundsTheflowoffundsSavingsdefic26DirecttransferoffundsCashSecuritiessaversfirmsDirecttransferoffundsCashSe27TypesofsecuritiesTreasuryBillsandTreasuryBondsCorporateBondsPreferredSharesOrdinarySharesRisk?HighReturns?Relationship?TypesofsecuritiesTreasuryBi28Broking&

investmentbankingHowdobrokers

/investmentbankershelpfirmsissuesecurities?AdvisingthefirmUnderwritingtheissueDistributingtheissueEnhancingCredibilityBroking&

investmentbankingHo29IndirecttransferoffundsIntermediarySecuritiesFirmSecuritiesfinancialintermediaryfirmssaversFundsFundsIndirecttransferoffundsInte30ComponentsoffinancialmarketsPrimaryandsecondarymarketsCapitalandmoneymarketsForeign-exchangemarketsDerivativesmarketsStockexchangemarketsComponentsoffinancialmarket31Primaryand

secondarymarketsPrimarymarketsSellingofnewsecuritiesFundsraisedbygovernmentsandbusinessesSecondarymarketsResellingofexistingsecuritiesAddsmarketabilityandliquiditytoprimarymarketsReducesriskonprimaryissuesFundsraisedbyexistingsecurityholdersPrimaryand

secondarymarketsP32Capital&moneymarketsCapitalmarketsMarketsinlong-termfinancialinstrumentsByconvention:termsgreaterthanoneyearLong-termdebtandequitymarketsBonds,shares,leases,convertiblesMoneymarketsMarketsinshort-termfinancialinstrumentsByconvention:termslessthanoneyearTreasurynotes,certificatesofdeposit,commercialbills,promissorynotesCapital&moneymarketsCapital33ReviewsIntroducethehistoryoffinancialmanagementUnderstandthefinancialgoalofdecision-makingUnderstandthelimitationsofagoalofprofitmaximisationIntroducerisk-returntrade-offofdecisionsIntroducemarketefficiencyDistinguishbetweentheformsofbusinessorganisationsUnderstandthefinancialmarketReviewsIntroducethehistory34EndofChapter1EndofChapter135Chapter4:MathematicsofFinance

Chapter4:MathematicsofFina36TheTimeValueofMoneyCompoundingandDiscounting:SinglesumsTodayFutureTheTimeValueofMoneyCompoun37Weknowthatreceiving$1todayisworthmorethan$1inthefuture.ThisisduetoOPPORTUNITYCOSTS.Theopportunitycostofreceiving$1inthefutureistheinterestwecouldhaveearnedifwehadreceivedthe$1sooner.TodayFutureWeknowthatreceiving$1toda38wecanMEASUREthisopportunitycostby:Translate$1todayintoitsequivalentinthefuture(COMPOUNDING).Translate$1inthefutureintoitsequivalenttoday(DISCOUNTING).??TodayFutureTodayFuturewecanMEASUREthisopportunit39Note:It’seasiesttouseyourfinancialfunctionsonyourcalculatortosolvetimevalueproblems.However,youwillneedalotofpracticetoeliminatemistakes.Note:It’seasiesttouseyour40FutureValueFutureValue41FutureValue-singlesums

Ifyoudeposit$100inanaccountearning6%,howmuchwouldyouhaveintheaccountafter1year?MathematicalSolution:FV1=PV(1+i)1=100(1.06)1

=$106

0 1PV=-100 FV=?FutureValue-singlesums

If42FutureValue-singlesums

Ifyoudeposit$100inanaccountearning6%,howmuchwouldyouhaveintheaccountafter2year?MathematicalSolution:FV2=FV1(1+i)1=PV(1+i)2=100(1.06)2

=$112.4

0 2PV=-100 FV=?FutureValue-singlesums

If43FutureValue-singlesums

Ifyoudeposit$100inanaccountearning6%,howmuchwouldyouhaveintheaccountafter3year?MathematicalSolution:FV3=FV2(1+i)1=PV(1+i)3=100(1.06)3

=$119.1

0 3PV=-100 FV=?FutureValue-singlesums

If44FutureValue-singlesums

Ifyoudeposit$100inanaccountearning6%,howmuchwouldyouhaveintheaccountafter4year?MathematicalSolution:FV4=FV3(1+i)1=PV(1+i)4=100(1.06)4

=$126.2

0 4PV=-100 FV=?FutureValue-singlesums

If45FutureValue-singlesums

Ifyoudeposit$100inanaccountearning6%,howmuchwouldyouhaveintheaccountafter5years?MathematicalSolution:FV5=FV4(1+i)1=PV(1+i)5=100(1.06)5

=$133.82

0 5PV=-100 FV=?FutureValue-singlesums

If46FutureValue-singlesums

Ifyoudeposit$100inanaccountearningi,howmuchwouldyouhaveintheaccountafternyears?MathematicalSolution:FVn=PV(1+i)n=PV(FVIFi,n

)

0 nPV=-100 FV=?FutureValue-singlesums

If47Example4.1Example4.2Example4.3Example4.4Example4.148Untilnowithasassumedthatthecompoundingperiodisalwaysannual.Butinterestcanbecompoundedonaquarterly,monthlyordailybasis,andevencontinuously.Example4.5Untilnowithasassumedthat49FutureValue-singlesums

Ifyoudeposit$100inanaccountearning6%withquarterlycompounding,howmuchwouldyouhaveintheaccountafter5years?MathematicalSolution:FV=PV(FVIFi,n

)FV=100(FVIF.015,20

)(can’tuseFVIFtable)FV=PV(1+I/m)mxNFV=100(1.015)20=$134.68

0 20PV=-100 FV=?FutureValue-singlesums

If50PresentValuePresentValue51Incompoundingwetalkedaboutthecompoundinterestrateandinitialinvestment;Indeterminingthepresentvaluewewilltalkaboutthediscountrateandpresentvalue.Thediscountrateissimplytheinterestratethatconvertsafuturevaluetothepresentvalue.Incompoundingwetalkedabout52Example4.7Example4.8Example4.753PresentValue-singlesums

Ifyouwillreceive$1005yearsfromnow,whatisthePVofthat$100ifyouropportunitycostis6%?MathematicalSolution:PV=FV/(1+i)n=100/(1.06)5=$74.73PV=FV(PVIFi,n

)=100(PVIF.06,5

)(usePVIFtable)=$74.73

0 5PV=? FV=100PresentValue-singlesums

If54

0 5PV=5,000 FV=11,933PresentValue-singlesums

Ifyousoldlandfor$11,933thatyoubought5yearsagofor$5,000,whatisyourannualrateofreturn?0 55MathematicalSolution:PV=FV(PVIFi,n)5,000=11,933(PVIF?,5)PV=FV/(1+i)n5,000=11,933/(1+i)5

.419=((1/(1+i)5)2.3866=(1+i)5(2.3866)1/5=(1+i)i=0.19MathematicalSolution:56Example4.9Example4.957TheTimeValueofMoneyCompoundingandDiscountingCashFlowStreams01234TheTimeValueofMoneyCompoun58AnnuitiesAnnuity:asequenceofequalcashflows,occurringattheendofeachperiod.01234AnnuitiesAnnuity:asequence59ExamplesofAnnuities:Ifyoubuyabond,youwillreceiveequalcouponinterestpaymentsoverthelifeofthebond.Ifyouborrowmoneytobuyahouseoracar,youwillpayastreamofequalpayments.ExamplesofAnnuities:Ifyoub60FutureValue-annuity

Ifyouinvest$1,000attheendofthenext3years,at8%,howmuchwouldyouhaveafter3years?

0 1 2 3

1000 1000 1000FutureValue-annuity

Ifyou61MathematicalSolution:FV=PMT(FVIFAi,n

)FV=1,000(FVIFA.08,3

)(useFVIFAtable,or)FV=PMT(1+i)n-1 iFV=1,000(1.08)3-1=$3246.40 0.08MathematicalSolution:62Example4.11Example4.1163PresentValue-annuity

WhatisthePVof$1,000attheendofeachofthenext3years,iftheopportunitycostis8%?

0 1 2 3

1000 1000 1000PresentValue-annuity

Whati64MathematicalSolution:PV=PMT(PVIFAi,n

)PV=1,000(PVIFA.08,3

)(usePVIFAtable,or) 1PV=PMT1-(1+i)n

i 1PV=10001-(1.08)3 =$2,577.10 .08MathematicalSolution:65Example4.12Example4.1266Interpolationwithinfinancialtables:findingmissingtablevaluesExample1:PV=1000(PVIFA2.5%,6)Example2:1000=100(PVIFA?%,12months)Interpolationwithinfinancial67PerpetuitiesSupposeyouwillreceiveafixedpaymenteveryperiod(month,year,etc.)forever.Thisisanexampleofaperpetuity.Youcanthinkofaperpetuityasanannuitythatgoesonforever.PerpetuitiesSupposeyouwillr68PresentValueofaPerpetuityWhenwefindthePVofanannuity,wethinkofthefollowingrelationship:

PV=PMT(PVIFAi,n)PresentValueofaPerpetuityW69Mathematically,(PVIFAi,n)=Wesaidthataperpetuityisanannuitywheren=infinity.Whathappenstothisformulawhenngetsvery,verylarge?Mathematically,701-1(1+i)niWhenngetsverylarge,

1we’releftwithPVIFA= i1-1(1+i)niWhenngetsver71PMTiPV=So,thePVofaperpetuityisverysimpletofind:PV=PMT/iPresentValueofaPerpetuityPMTiPV=So,thePVofaperp72Whatshouldyoubewillingtopayinordertoreceive$10,000annuallyforever,ifyourequire8%peryearontheinvestment?PMTiPV==$10,000

0.08=

$125,000Whatshouldyoubewillingto73Example4.13Example4.1374OtherCashFlowPatterns0123OtherCashFlowPatterns012375$1000$1000$100045678OrdinaryAnnuityversusDueAnnuity$1000$1000$1000476Earlier,weexaminedthis“ordinary”annuity:Usinganinterestrateof8%,wefindthat:TheFutureValue(at3)is$3,246.40.ThePresentValue(at0)is$2,577.10.

0 1 2 3 1000 1000 1000Earlier,weexaminedthis“ord77Whataboutthisannuity?Same3-yeartimeline,Same3$1000cashflows,butThecashflowsoccuratthebeginningofeachyear,ratherthanattheendofeachyear.Thisisan“annuitydue.”

0 1 2 3

1000 1000 1000Whataboutthisannuity?Same378

0 1 2 3

-1000 -1000 -1000FutureValue-annuitydue

Ifyouinvest$1,000atthebeginningofeachofthenext3yearsat8%,howmuchwouldyouhaveattheendofyear3?

0 1 2 379MathematicalSolution:

SimplycompoundtheFVoftheordinaryannuityonemoreperiod:FV=PMT(FVIFAi,n

)(1+i)FV=1,000(FVIFA.08,3

)(1.08) (useFVIFAtable,or)FV=PMT(1+i)n–1(1+i) iFV=1,000(1.08)3-1(1.08)=$3,506.11 0.08MathematicalSolution:80

0 1 2 3

10001000 1000PresentValue-annuitydue

WhatisthePVof$1,000atthebeginningofeachofthenext3years,ifyouropportunitycostis8%?

0 1 2 381MathematicalSolution:

SimplycompoundtheFVoftheordinaryannuityonemoreperiod:PV=PMT(PVIFAi,n

)(1+i)PV=1,000(PVIFA.08,3

)(1.08) (usePVIFAtable,or) 1PV=PMT1-(1+i)n(1+i) i 1PV=10001-(1.08)3(1.08) =2,783.26 0.08

MathematicalSolution:Simply82Isthisanannuity?HowdowefindthePVofacashflowstreamwhenallofthecashflowsaredifferent?(Usea10%discountrate).UnevenCashFlows01234-10,0002,0004,0006,0007,000Isthisanannuity?UnevenCash83UnevenCashFlowsSorry!There’snoquickieforthisone.Wehavetodiscounteachcashflowbackseparately.01234-10,0002,0004,0006,0007,000UnevenCashFlowsSorry!There84

period

CF

PV(CF)0 -10,000 -10,000.001 2,000 1,818.182 4,000 3,305.793 6,000 4,507.894 7,000 4,781.09PVofCashFlowStream:$4,412.9501234-10,0002,0004,0006,0007,000period CF PV(CF85RetirementExampleAftergraduation,youplantoinvest$400permonthinthestockmarket.Ifyouearn12%peryearonyourstocks,howmuchwillyouhaveaccumulatedwhenyouretirein30years?0123...360400400400400RetirementExampleAftergradua86MathematicalSolution:FV=PMT(FVIFAi,n

)FV=400(FVIFA.01,360

)(can’tuseFVIFAtable)FV=PMT(1+i)n-1 i

FV=400(1.01)360-1=$1,397,985.65 .01MathematicalSolution:87HousePaymentExampleIfyouborrow$100,000at7%fixedinterestfor30yearsinordertobuyahouse,whatwillbeyourmonthlyhousepayment?HousePaymentExampleIfyoubo88MathematicalSolution:PV=PMT(PVIFAi,n

)100,000=PMT(PVIFA.005833,360

)(can’tusePVIFAtable) 1PV=PMT1-(1+i)n

i

1100,000=PMT1-(1.005833)360 PMT=$665.30 0.005833 MathematicalSolution:89CalculatingPresentandFutureValuesforsinglecashflowsforanunevenstreamofcashflowsforannuitiesandperpetuitiesForeachproblemidentify:

i,n,PMT,PVandFVSummaryCalculatingPresentandFuture90chapter9Riskandratesofreturnchapter991Infinancialmarkets,firmsseekfinancingfortheirinvestmentsandshareholdersofacompanyachievemuchoftheirwealththroughsharepricemovements.Involvementwithfinancialmarketsisrisky.Thedegreeofriskvariesfromonefinancialsecuritytoanother.Infinancialmarkets,firmsse92ImportantprincipleReturnRiskAlmostalwaystrue:Thegreatertheexpectedreturn,thegreatertheriskImportantprincipleReturnRiskA931926-1999：theannualratesofreturninAmericanfinancialmarket1926-1999：theannualratesof94RatesofreturnHistoricalreturn ThereturnthatanassethasalreadyproducedoveraspecifiedperiodoftimeExpectedreturn ThereturnthatanassetisexpectedtoproduceoversomefutureperiodoftimeRequiredreturn Thereturnthataninvestorrequiresanassettoproduceifhe/sheistobeafutureinvestorinthatassetRatesofreturnHistoricalretu95RatesofreturnNominal TheactualrateofreturnpaidorearnedwithoutmakinganyallowanceforinflationReal ThenominalrateofreturnadjustedfortheeffectofinflationEffective Thenominalrateofreturnadjustedformorefrequentcalculation(orcompounding)thanonceperannumRatesofreturnNominal96Whenaninterestrateisquotedinfinancialmarketsitisgenerallyexpressedasanominalrate.Forexample,ifabankadvertisesthatitwillpayinterestof5%perannumondeposits,thisinterestrateismostlikelytobethenominalrate.Wheninflationisdeductedfromthisnominalrate,therealrateofinterestisobtained.(Butthisisnotexactlycorrect!)Tobemoreprecise,……Whenaninterestrateisquote97InterestratedeterminantsInterestRatesInterestratedeterminantsInte98AdjustingforinflationConceptually:Nominalinterestratei=RealinterestrateR+AnticipatedinflationraterMathematically:(1+i)=(1+R)(1+r)Þ

i=R+r+rRUsuallysmallandignoredAdjustingforinflationConcept99CalculatingexpectedreturnsStateofeconomyRecessionNormalBoomProbabilityP0.200.500.30ReturnAB4%10%14%-10%14%30%ExpectedreturnisjustaweightedaverageR*=P(R1)xR1+P(R2)xR2+…+P(Rn)xRnCalculatingexpectedreturnsSt100CasestudyStateofeconomyRecessionNormalBoomProbabilityP0.200.500.30ReturnAB4%10%14%-10%14%30%CompanyAR*=P(R1)xR1+P(R2)xR2+…+P(Rn)xRnRA*=0.2x4%+0.5x10%+0.3x14%=10%CasestudyStateofRecessionPro101CasestudyStateofeconomyRecessionNormalBoomProbabilityP0.200.500.30ReturnAB4%10%14%-10%14%30%CompanyBR*=P(R1)xR1+P(R2)xR2+…+P(Rn)xRnRB*=0.2x-10%+0.5x14%+0.3x30%=14%CasestudyStateofRecessionPro102Basedonlyonyourexpectedreturncalculations,whichcompanysharewouldyouprefer?Basedonlyonyourexpectedre103Theaboveexampleillustratesthat,

Althoughitisextremelydifficulttopredictwithaccuracywhatthereturnwillbeonaninvestment,whatwecandoismakepredictionsabouttherangeofreturns,theprobabilitywithwhichacertainreturnwilleventuateandhencethereturnthatwecouldexpecttoget.So,theexpectedrateofreturnmaybedefinedastheweightedaverageofallpossibleoutcomes!Theaboveexampleillustrates104HaveyouconsideredRISK?HaveyouconsideredRISK?105RiskWhatisrisk TheuncertaintyorvariabilityordispersionaroundthemeanvalueHowtomeasurerisk Variance,standarddeviation,betaHowtoreducerisk DiversificationHowtopricerisk Securitymarketline,CAPM,APTRiskWhatisrisk106ForaTreasurysecurity,whatistherequiredrateofreturn?Requiredrateofreturn=Risk-freerateofreturnReason:TreasurysecuritiesarefreeofdefaultriskForaTreasurysecurity,what107Foracompanysecurity,whatistherequiredrateofreturn?Requiredrateofreturn=Risk-freerateofreturnHowlargeariskpremiumshouldwerequiretobuyacorporatesecurity?+RiskpremiumForacompanysecurity,whati108Foracompanystock,whatistherequiredrateofreturn?Requiredrateofreturn=Risk-freerateofreturnHowlargeariskpremiumshouldwerequiretobuyastock?+RiskpremiumForacompanystock,whatist109ReturnRiskAlmostalwaystrue:Thegreatertheexpectedreturn,thegreatertheriskReturnRiskAlmostalwaystrue:1101926-1999：theannualratesofreturninAmericanfinancialmarket1926-1999：theannualratesof111Whatisrisk?ThepossibilitythatanactualreturnwilldifferfromourexpectedreturnUncertaintyinthedistributionofpossibleoutcomesWhatisrisk?Thepossibilityt112Uncertaintyinthedistributionofpossibleoutcomesreturn(%)Company2Company1return(%)Uncertaintyinthedistributio113Howdowemeasurerisk?Generalidea:Share’spricerangeoverthepastyearMorescientificapproach:Share’sstandarddeviationofreturnsStandarddeviationisameasureofthedispersionofpossibleoutcomesThegreaterthestandarddeviation,thegreatertheuncertainty,andtherefore,thegreatertheriskHowdowemeasurerisk?General114Standarddeviation–probabilitydata=(

Ri-

R*

)2P(

Ri

)sS

ni=1Standarddeviation–probabili115CalculatingStandarddeviationStateofeconomyRecessionNormalBoomProbabilityP0.200.500.30ReturnAB4%10%14%-10%14%30%RA=10%RB=14%CalculatingStandarddeviation116Casestudy=(

Ri-

R*

)2P(

Ri

)sS

ni=1CompanyA(4%-10%)2(0.2) =7.2(10%-10%)2(0.5) =0.0(14%-10%)2(0.3) =4.8 Variance=s2 =12.0Standarddeviation =Ö12.0=3.46%Casestudy=(Ri-R117Casestudy=(

Ri-

R*

)2P(

Ri

)sS

ni=1CompanyB(-10%-14%)2(0.2) =115.2(14%-14%)2(0.5) =0.0