1.1.1.1.TheTimeValueofMoneyInterestrate:requiredrateofreturn,discountedrate,opportunitycostNominalinterestrate=realrisk-freeinterestrate+inflationpremium

+defaultriskpremium

+liquiditypremium

+Maturitypremium3.EAR=(1+rs/m)^m-1rs=Ln.(1+HYR),EAR=e^rs-1whencontinuouscompoundingNominalriskfreeinterestrateFV=PV(1+R)^nBeginmodeandEndmodePV=D/RandPV=D/(r-g)(presentvalueofperpetuity),risdiscountedrate,ggrowthrateNPVandIRRMoney-weightreturn(MWR)similarIRR:CF0+CF1/(1+MWR)+…+CFn/(1+MWR)^N=0Timeweightedreturn(TWR):=【(endvalue1/beginvalue1)(endvalue2/beginvalue2)..(endvaluen/beginvaluen}】^1/n-1HPR=P1-P0+D1/P0Holdingperiodyield(HPY)=(endingvalue/beginvalue)-1Bankdiscountyield(BDY)=(discount/facevalue)x(360/daystomaturity)simpleinterestMoneymarketyield(MMY)=(discount/price)x(360/daystomaturity)simpleinterestBondequivalentyield(BEY)=(discount/price)x(365/daystomaturity)simpleinterestEffectiveannualyield(EAY)=(1+HPY)^365/days-1compoundinterest2.TheTimeValueofMoneyNominalTheTimeValueofMoneyNominal

Chebyshev’sinequity:1-1/k^2,kstandarddeviation調(diào)和平均：固定金額的投資購買股份的平均成本3.

Chebyshev’sinequity:1-1

Chebyshev’sinequity:1-1Mutuallyexclusiveevents,exhaustiveevents,independentevents,dependenteventOddfor/oddagainstempiricalprobabilityprioriprobability/subjectiveprobability,Unconditionalprob.conditionalprob.(prob.ofanevent(A)conditionedonanotherevent(B),denotedP(A|B)

4.Mutuallyexclusiveevents,exMutuallyexclusiveevents,ex

5.

5.

5.

5.

6.

6.

6.

6.7.7.7.7.1.Overthepast240months,aninvestor’sportfoliohadameanmonthlyreturnof0.79%,withastandarddeviationofmonthlyreturnsof1.16%.AccordingtoChebyshev’sinequality,theminimumnumberofthe240monthlyreturnsthatfallintotherangeof?0.95%to2.53%is

closest

to:A.80.B.107.C.133.2.Youhavedevelopedasetofcriteriaforevaluatingdistressedcredits.Companiesthatdonotreceiveapassingscoreareclassedaslikelytogobankruptwithin12months.Yougatheredthefollowinginformationwhenvalidatingthecriteria:Fortypercentofthecompaniestowhichthetestisadministeredwillgobankruptwithin12months:P(nonsurvivor)=0.40.Fifty-fivepercentofthecompaniestowhichthetestisadministeredpassit:

P(passtest)=0.55.Theprobabilitythatacompanywillpassthetestgiventhatitwillsubsequentlysurvive12months,is0.85:P(passtest

|

survivor)=0.85.A.WhatisP(passtest|nonsurvivor)?B.UsingBayes’formula,calculatetheprobabilitythatacompanyisasurvivor,giventhatitC.passesthetest;thatis,calculate

P(survivor|passtest).D.Whatistheprobabilitythatacompanyisa

nonsurvivor,giventhatitfailsthetest?Isthetesteffective?8.1.Overthepast240months,a1.Overthepast240months,a3.Aportfoliomanagerannuallyoutperformsherbenchmark60%ofthetime.Assumingindependentannualtrials,whatistheprobabilitythatshewilloutperformherbenchmarkfourormoretimesoverthenextfiveyears?A.0.26B.0.34C.0.484.Astockispricedat$100.00andfollowsaone-periodbinomialprocesswithanupmovethatequals1.05andadownmovethatequals0.97.If1millionBernoullitrialsareconducted,andtheaverageterminalstockpriceis$102.00,theprobabilityofanupmove(p)is

closest

to:A.0.375.B.0.500.C.0.625.5.Acalloptiononastockindexisvaluedusingathree-stepbinomialtreewithanupmovethatequals1.05andadownmovethatequals0.95.Thecurrentleveloftheindexis$190,andtheoptionexercisepriceis$200.Iftheoptionvalueispositivewhenthestockpriceexceedstheexercisepriceatexpirationand$0otherwise,thenumberofterminalnodeswithapositivepayoffis:Aone.B.two.C.three.9.3.Aportfoliomanagerannuall3.Aportfoliomanagerannuall

AllocationAAllocationBAllocationCExpectedannualreturn6.5%7.5%8.5%Standarddeviationofreturns8.35%10.21%14.34%6.Aclientholdinga￡2,000,000portfoliowantstowithdraw￡90,000inoneyearwithoutinvadingtheprincipal.AccordingtoRoy’ssafety-firstcriterion,whichofthefollowingportfolioallocationsisoptimal?A.AllocationAB.AllocationBC.AllocationC7.Whichsamplingbiasis

mostlikely

investigatedwithanout-of-sampletest?A.Look-aheadbiasB.Data-miningbiasC.Sampleselectionbias8.Aninvestorwantstomaximizethepossibilityofearningatleast5%onherinvestmentseachyear.UsingRoy’ssafety-firstcriterion,whichofthefollowingportfoliosisthemostappropriatechoice?

ExpectedStandardRoy’sSafety-FirstPortfolioreturndeviationvalue1

0.352

0.64322%40%

10.

AllocationAAllocationBAlloc

AllocationAAllocationBAlloc9.Aninvestorpurchasesoneshareofstockfor$85.Exactlyoneyearlater,thecompanypaysadividendof$2.00pershare.Thisisfollowedbytwomoreannualdividendsof$2.25and$2.75insuccessiveyears.Uponreceivingthethirddividend,theinvestorsellsthesharefor$100.Themoney-weightedrateofreturnonthisinvestmentisclosestto:

A.7.97%.B.8.15%.C.8.63%.10.Aninvestordeposits￡2,000intoanaccountthatpayscontinuouslycompoundedinterestof6%(nominalannualrate).Thevalueoftheaccountattheendoffouryearsisclosestto:12am11.Thefollowingendofmonthpaymentsof$400,$700,and$300,(respectively)aredue.Givenastatedannualinterestrateof3.60percent,theminimumamountofmoneyneededinanaccounttodaytosatisfythesefuturepaymentsisclosestto:9pm

A.$1,308.B.$1,387.C.$1,391.12.Thejointprobabilityofreturns,forsecuritiesAandB,areasfollows:

ReturnonsecurityB=30%ReturnonsecurityB=20%

Returnonsecurity0.600A=25%

Returnonsecurity00.40A=20%

ThecovarianceofthereturnsbetweensecuritiesAandBisclosestto:10pm11.9.Aninvestorpurchasesones9.Aninvestorpurchasesones12.12.12.12.13.13.13.13.14.14.14.14.15.15.15.15.16.1.16.1.TheTimeValueofMoneyInterestrate:requiredrateofreturn,discountedrate,opportunitycostNominalinterestrate=realrisk-freeinterestrate+inflationpremium

+defaultriskpremium

+liquiditypremium

+Maturitypremium3.EAR=(1+rs/m)^m-1rs=Ln.(1+HYR),EAR=e^rs-1whencontinuouscompoundingNominalriskfreeinterestrateFV=PV(1+R)^nBeginmodeandEndmodePV=D/RandPV=D/(r-g)(presentvalueofperpetuity),risdiscountedrate,ggrowthrateNPVandIRRMoney-weightreturn(MWR)similarIRR:CF0+CF1/(1+MWR)+…+CFn/(1+MWR)^N=0Timeweightedreturn(TWR):=【(endvalue1/beginvalue1)(endvalue2/beginvalue2)..(endvaluen/beginvaluen}】^1/n-1HPR=P1-P0+D1/P0Holdingperiodyield(HPY)=(endingvalue/beginvalue)-1Bankdiscountyield(BDY)=(discount/facevalue)x(360/daystomaturity)simpleinterestMoneymarketyield(MMY)=(discount/price)x(360/daystomaturity)simpleinterestBondequivalentyield(BEY)=(discount/price)x(365/daystomaturity)simpleinterestEffectiveannualyield(EAY)=(1+HPY)^365/days-1compoundinterest17.TheTimeValueofMoneyNominalTheTimeValueofMoneyNominal

Chebyshev’sinequity:1-1/k^2,kstandarddeviation調(diào)和平均：固定金額的投資購買股份的平均成本18.

Chebyshev’sinequity:1-1

Chebyshev’sinequity:1-1Mutuallyexclusiveevents,exhaustiveevents,independentevents,dependenteventOddfor/oddagainstempiricalprobabilityprioriprobability/subjectiveprobability,Unconditionalprob.conditionalprob.(prob.ofanevent(A)conditionedonanotherevent(B),denotedP(A|B)

19.Mutuallyexclusiveevents,exMutuallyexclusiveevents,ex

20.

5.

20.

5.

21.

6.

21.

6.22.7.22.7.1.Overthepast240months,aninvestor’sportfoliohadameanmonthlyreturnof0.79%,withastandarddeviationofmonthlyreturnsof1.16%.AccordingtoChebyshev’sinequality,theminimumnumberofthe240monthlyreturnsthatfallintotherangeof?0.95%to2.53%is

closest

to:A.80.B.107.C.133.2.Youhavedevelopedasetofcriteriaforevaluatingdistressedcredits.Companiesthatdonotreceiveapassingscoreareclassedaslikelytogobankruptwithin12months.Yougatheredthefollowinginformationwhenvalidatingthecriteria:Fortypercentofthecompaniestowhichthetestisadministeredwillgobankruptwithin12months:P(nonsurvivor)=0.40.Fifty-fivepercentofthecompaniestowhichthetestisadministeredpassit:

P(passtest)=0.55.Theprobabilitythatacompanywillpassthetestgiventhatitwillsubsequentlysurvive12months,is0.85:P(passtest

|

survivor)=0.85.A.WhatisP(passtest|nonsurvivor)?B.UsingBayes’formula,calculatetheprobabilitythatacompanyisasurvivor,giventhatitC.passesthetest;thatis,calculate

P(survivor|passtest).D.Whatistheprobabilitythatacompanyisa

nonsurvivor,giventhatitfailsthetest?Isthetesteffective?23.1.Overthepast240months,a1.Overthepast240months,a3.Aportfoliomanagerannuallyoutperformsherbenchmark60%ofthetime.Assumingindependentannualtrials,whatistheprobabilitythatshewilloutperformherbenchmarkfourormoretimesoverthenextfiveyears?A.0.26B.0.34C.0.484.Astockispricedat$100.00andfollowsaone-periodbinomialprocesswithanupmovethatequals1.05andadownmovethatequals0.97.If1millionBernoullitrialsareconducted,andtheaverageterminalstockpriceis$102.00,theprobabilityofanupmove(p)is

closest

to:A.0.375.B.0.500.C.0.625.5.Acalloptiononastockindexisvaluedusingathree-stepbinomialtreewithanupmovethatequals1.05andadownmovethatequals0.95.Thecurrentleveloftheindexis$190,andtheoptionexercisepriceis$200.Iftheoptionvalueispositivewhenthestockpriceexceedstheexercisepriceatexpirationand$0otherwise,thenumberofterminalnodeswithapositivepayoffis:Aone.B.two.C.three.24.3.Aportfoliomanagerannuall3.Aportfoliomanagerannuall

AllocationAAllocationBAllocationCExpectedannualreturn6.5%7.5%8.5%Standarddeviationofreturns8.35%10.21%14.34%6.Aclientholdinga￡2,000,000portfoliowantstowithdraw￡90,000inoneyearwithoutinvadingtheprincipal.AccordingtoRoy’ssafety-firstcriterion,whichofthefollowingportfolioallocationsisoptimal?A.AllocationAB.AllocationBC.AllocationC7.Whichsamplingbiasis

mostlikely

investigatedwithanout-of-sampletest?A.Look-aheadbiasB.Data-miningbiasC.Sampleselectionbias8.Aninvestorwantstomaximizethepossibilityofearningatleast5%onherinvestmentseachyear.UsingRoy’ssafety-firstcriterion,whichofthefollowingportfoliosisthemostappropriatechoice?

ExpectedStandardRoy’sSafety-FirstPortfolioreturndeviationvalue1

0.352

0.64322%40%

25.

AllocationAAllocationBAlloc

AllocationAAllocationBAlloc