CFA-LEVEL-I-数量总结PPT课件

1,.,TheTimeValueofMoneyInterestrate:requiredrateofreturn,discountedrate,opportunitycostNominalinterestrate=realrisk-freeinterestrate+inflationpremium+defaultriskpremium+liquiditypremium+Maturitypremium3.EAR=(1+rs/m)m-1rs=Ln.(1+HYR),EAR=ers-1whencontinuouscompounding,Nominalriskfreeinterestrate,FV=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/P0,Holdingperiodyield(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-1compoundinterest,2,.,Chebyshevsinequity:1-1/k2,kstandarddeviation,调和平均：固定金额的投资购买股份的平均成本,3,.,Mutuallyexclusiveevents,exhaustiveevents,independentevents,dependenteventOddfor/oddagainstempiricalprobabilityprioriprobability/subjectiveprobability,Unconditionalprob.conditionalprob.(prob.ofanevent(A)conditionedonanotherevent(B),denotedP(A|B),4,.,5,.,6,.,7,.,1.Overthepast240months,aninvestorsportfoliohadameanmonthlyreturnof0.79%,withastandarddeviationofmonthlyreturnsof1.16%.AccordingtoChebyshevsinequality,theminimumnumberofthe240monthlyreturnsthatfallintotherangeof0.95%to2.53%isclosestto: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.UsingBayesformula,calculatetheprobabilitythatacompanyisasurvivor,giventhatitC.passesthetest;thatis,calculateP(survivor|passtest).D.Whatistheprobabilitythatacompanyisanonsurvivor,giventhatitfailsthetest?Isthetesteffective?,8,.,3.Aportfoliomanagerannuallyoutperformsherbenchmark60%ofthetime.Assumingindependentannualtrials,whatistheprobabilitythatshewilloutperformherbenchmarkfourormoretimesoverthenextfiveyears?A.0.26B.0.34C.0.48,4.Astockispricedat$100.00andfollowsaone-periodbinomialprocesswithanupmovethatequals1.05andadownmovethatequals0.97.If1millionBernoullitrialsareconducted,andtheaverageterminalstockpriceis$102.00,theprobabilityofanupmove(p)isclosestto: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,.,6.Aclientholdinga2,000,000portfoliowantstowithdraw90,000inoneyearwithoutinvadingtheprincipal.AccordingtoRoyssafety-firstcriterion,whichofthefollowingportfolioallocationsisoptimal?,A.AllocationAB.AllocationBC.AllocationC,7.Whichsamplingbiasismostlikelyinvestigatedwithanout-of-sampletest?A.Look-aheadbiasB.Data-miningbiasC.Sampleselectionbias,8.Aninvestorwantstomaximizethepossibilityofearningatleast5%onherinvestmentseachyear.UsingRoyssafety-firstcriterion,whichofthefollowingportfoliosisthemostappropriatechoice?,10,.,9.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.Aninvestordeposits2,000intoanaccountthatpayscontinuouslycompoundedinterestof6%(nominalannualrate).Thevalueoftheaccountattheendoffouryearsisclosestto:12am,11.Thefollowingendofmonthpaymentsof$400,$700,and$300,(respectively)aredue.Givenastatedannualinterestrateof3.60percent,theminimumamountofmoneyneededinanaccounttodayto