2017年CFA一级公式表

金程教育=Nominalrisk-freerate+Defaultriskpremium+Liquidityriskpremium+MaturityriskpremiumNominalrisk-freerate=Realrisk-freerate+expectedinflationrateRequiredRateofReturn()(1r)(1)(1)1frealfERIPRPrIPRPSAR=Statedannualrate=rp×mrp=periodrate;m=numberofcompoundingperiodsperpearEAR=Effectiveannualrate11()mprThefuturevalueofcashflowFutureValue(FV):amounttowhichinvestmentgrowsafteroneormorecompoundingperiods.(1)nFVPVr1/nFVPVIY（）Annuities:seriesofequalcashflowsthatoccuratevenlyspacedintervalsovertime.Ordinaryannuity:cashfolwatend-of-timeperiod.Annuitydue:cashflowatbeginning-of-timeperiod.Perpetuities:annuitieswithinfinitelives.FVAo=Futurevalueofanannuity=[(1)1]nPMTrrPVAo=Presentvalueofanannuity=11(1)nPMTrrFVAD=Futurevalueofannuitydue=FVAo×(1+r)PVAD=Presentvalueofannuitydue=PVAo×(1+r)PresentValueofPerpetuity=PMT/rFutureValueofUnevenCashFlows=1(1)TTtttFVCrPresentValueofUnevenCashFlows=1(1)TtttCPVrDiscountedCashFlowApplicationsNPV=Netpresentvalue0(1)TtttCFrTheIRRrule:00(1)NtttCFNPVIRRIfIRR≥costofcapital,acceptit;IfIRRcostofcapital,rejectit.HoldingPeriodReturn=holdingperiodyield=HPYt=1111ttttttttPPDPDHPRPPMoneyWeightedReturnisanIRRcalculation.TimeWeightedReturnmeasurescompoundgrowthandpast-periodreturnfornperiodsTWR=123(1)(1)(1)...(1)1nnrrrrThenannualizethetime-weightedreturn.BDY=BankDiscountYield=0()360BDFVPrFVtEAY=Effectiveannualyield=(1+HRY)365/t-1Moneymarketyield=HPY×(360/t)Moneymarketyield=BDY/(1-BDY×t/360)StatisticalConceptsandMarketReturnsPositionoftheobservationatagivenpercentile,y;(1)100yyLnArithmeticmean:sumofallobservationvaluesinsample/population,dividedbynumberofobservations.Geometricmean:usedwhencalculatinginvestmentreturnsovermultipleperiodsortomeasurecompoundgrowthrates.金程教育Samplemean:1niiXXnWeightedmean:1()niiiXwXwhereiwareweightsthatsumto1.Geometricmean:1/1231...()NNNNiiGXXXXXGeometricmeanreturn:12(1)(1)(1)1NGnRRRR…Harmonicmean:1(1/)HNiiNXXYthpercentile=(1)100YyLnMAD=Meanabsolutedeviation=1NiiXNVarianceandStandardDeviationVariance:averageofsquareddeviationsfrommean.Standarddeviation:squarerootofvariance.Populationvariance=221()NiiXNPopulationstandarddeviation=221()NiiXNσMADthatholdsingeneralSamplevariance=221()1niiXXsnSamplestandarddeviation=21()1niiXXsnChebyshev’sinequality:21()1PxkkCoefficientofVariation(CV):expresshowmuchdispersionexistsrelativetomeanofadistribution.CV=Coefficientofvariance=sXSharpratioPfPRRSK=Sampleskewness313()1NiiXnPositiveskewness:ModeMedianMeanNegativeskewness:ModeMedianMeanSamplekurtosis=414()1niiPXXKnExcesskurtosis=samplekurtosis–3ProbabilityConceptsJointprobability=()()()PABPBPABAdditionruleofprobability=()()()()PABPAPBPABUITotalProbabilityRule=P(R)=P(R│S1)P(S1)+…+P(R│SN)P(SN)S1,S2,…,SNaremutuallyexclusiveandexhaustiveExpectedvalue=1()()niiiEXXPX金程教育222211222()()()()()()()()()iinnXPXxEXPXxEXPXxEXPXxEXLCovariance:(,)[()][()]CovXYEXEXYEYCorrelationcoefficient:,(,)XYXYCovXYPortfolioexpectedvalue:11221()()()()...()nPiinniERwERwERwERwERPortfoliovariance:11()(,)nnijjPiijVarRwwCovRRBayes’Formula:Updatedprobability=Probabilityofnewinformationforagivenevent/Unconditionalprobabilityofnewinformation×Priorprobabilityofevent=P(A1|B)=[P(B|A1|)/P(B)]*P(A1)Multinominallabelling:1212!!!...!...kknnnnnnnnCombination(binominallabelling):!!()!nrnCrnrPermutation:!()!nrnPnrCommonProbabilityDistributionsBinomialProbability:()(1)xxnxnpxCppE(X)=npσ2=np(1-p)ContinuousUniformDistribution:0,()(),1,xaxaFxPXxaxbbaxbNormalDistribution:1.Completelydescribedbymeanandvariance(μ,σ2)2.Itissymmetricwithskewnessmeasureof0,i.e.,mean=mode=median3.Kurtosis=34.Linearcombinationsofnormalrandomvariablesarenormallydistributed.Z-score:xz68%ofobservationsfallwithin190%fallwithin1.6595%fallwithin1.9699%fallwithin2.58ConfidenceIntervalforSampleMean:czStandardizedNormalVariate:XzSafetyFirstRatio:()PLPERRSFRIfNormaldistr.,SFRmaxP(RpRL)minLognormalDistributionforassetprice:Ln(X)~N(μ,σ2)EAR=ercontinuous×1–1Sampling&EstimationSamplingDistribution:Probabilitydistributionofallpossiblesamplestatisticscomputedfromasetofequal-sizesamplesrandomlydrawnfromthesamepopulation.Thesamplingdistributionofthemeanisthedistributionofthemean.CentralLimitTheorem:Whenselectingsimplerandomsamplesofsizenfromapopulationwithameanμandafinitevarianceσ2,thesamplingdistributionofthesamplemeanapproachesanormalprobabilitydistributionwithmeanμanda金程教育(n≥30).2~N(,)nXStandardErrorofSampleMean:Xn(knownpopulationvariance)Xssn(unknownpopulationvariance)Confidenceinterval:Pointestima