FRM一级公示表（培训资料）

金程教育FRMPartIEasySheetOFRISKMANAGEMENTManagementTheoryPortfolioReturn:MeasuresRSharpeRatioERωωσPortfolioVariance:RTreynor22222βσωσωσ2ρωωσσPAABBABABσσσ2ωωBMARSortino1T∑RMARCapitalMarketLine(CML):R其中RMARERRσσInformationRRR(Method1)(Method2)(Nisthenumberofperiodsmeasured)CAPM(SML)RR，其中Alpha:,βffPMαβRPricingTheoryRβRβR⋯βRRβR⋯βRff1专业来自101%的投入金程教育FRMPartIEasySheet2专业来自101%的投入金程教育FRMPartIEasySheetMETHODSContinuousUniformDistribution:0forxaxaforaxbba1forxbBasicExpectedValue...BinomialdistributionCpVarianceσnppPoissonDistributionCovarianceYλkenpk!λλCorrelationCovX,YNormalDistribution:Completelydescribedbymeanandvariance(μ,σ)ρσσItissymmetricwithskewnessmeasureof0,i.e.,mean=mode=medianSumsRandomVariablesKurtosis=3IfXandYareanyrandomvariables:YLinearcombinationsofnormalrandomvariablesarenormallydistributed.IfXandYareindependent:YStandardizedNormalDistributionXμZ∼IfXandYarenotindependent:YYσConfidenceInterval68%ofobservationsfallwithin1σ90%ofobservationsfallwithin1.65σ95%ofobservationsfallwithin1.96σ99%ofobservationsfallwithin2.58σSkewness&kurtosisμSkewnessσPositiveskewness:Mode<Median<MeanNegativeskewness:Mode>Median>MeanStudent’s‐distribution:Student’s‐distribution:issymmetric;fattertails;Degreesoffreedom=(n‐1).μKurtosisμExcesskurtosis=samplekurtosis–3LimitTheorem:Whenselectingsimplerandomsamplesofsizenfromapopulationwithameanμandafinitevarianceσ2,CommonProbabilityDistributions3专业来自101%的投入金程教育FRMPartIEasySheetthesamplingdistributionofthesamplemeanapproachesanormalprobabilitydistributionwithmeanμandavarianceσ2/nequaltoasthesamplesizebecomeslarge(n≥30).Knownpopulationvariance:σσ√nUnknownpopulationvariance:sσs√nnEstimationMeasureoftendencyPointestimation:unbiasness,efficiency,mean:consistency∑XConfidenceintervalestimation:Confidenceinterval:givesrangeofvaluesthemeanvaluebebetween,withagivenprobability(say90%or95%).Withknownvariance,formulaforaconfidenceintervalis:Pointestimate+/‐(reliabilityfactor*standarderror)μNSamplemean:∑XXnofdispersionPopulationvariance:Withknownvariance:σXz⁄σ√nNPopulationstandarddeviation:Withunknownvariance:sXt⁄√nσNHypothesisSamplevariance:∑n2NullandAlternativeHypothesesNullhypothesis(H0):XXii12sHypothesistheresearcherwantstoreject;thehypothesisthatisactuallytested;theforselectionoftheteststatistics.n1Samplestandarddeviation:Alternativehypothesis(H):sn1Concludedifthereissufficientevidencetorejectthenullhypothesis.Sampling&EstimationTestMean:SamplingDistribution:μS⁄√ntProbabilitydistributionofallpossiblesamplestatisticscomputedfromasetofequal‐sizesamplesrandomlydrawnfromthesamepopulation.Thesamplingdistributionofthemeanisthedistributionofestimatesthemean.z⁄√TestTwoMeans:TSSYStandardErrorSampleMean:nStandarderrorofthesamplemeanisthestandarddeviationofdistributionofthesamplemean.DifferenceBetweenOne‐andTwo‐TailedTests:One‐tailedtest:testswhethervalueisgreaterthanor4专业来自101%的投入金程教育FRMPartIEasySheetlessthanagivennumber.ε=errortermH:μ0;H0MultipleLinearRegressionTwo‐tailedtest:testswhethervalueisequaltoagivenYαβXβX⋯βXεnumber.TotalSumSquaresH:μ0;H0sumofsquares=explainedsumofsquares+theresidualsumofsquaresTypesIandTypeIIErrors:∧∧YYYIrejectionofnullwhenitisactuallytrue.TSS=ESS+RSSIInullwhenitisactuallyMeasuresFitnessFitnessIfDecisionHistrueHisESSR2R1ICorrectTSSTSSSignificantαistheprobabilityoftypeIRejectHofdefinedas1βr2(correlationrR→rRCorrectIIβ)rejectHk11R2S⁄n1TypesHypothesisTests:MeanHypothesisNormallyANOVATableXμdistribution,knownvarianceNormallyzN(0,1)t(n-1)σ⁄√nDfKSSXμS⁄√ndistribution,unknowntN‐K‐1N‐1‐K‐1)varianceHypothesis‐Normally1sχ(n–1)σdistributionindependentnormallyF‐testinrestrictedandunrestrictedmodelF(n–1,n12Fs⁄sFFnK1–1)/nK1distributionRRK1RegressionSimpleLinearRegressiondistanceYαβXε∑YYY=dependentorexplainedvariableX=independentorexplanatoryvariable=interceptcoefficientDKSβ=slopecoefficient5专业来自101%的投入金程教育FRMPartIEasySheetStationaryTimeSeriesautocovarianceNon‐StationaryTimeSeriesLinearTrendγYδδtεWold’srepresentationYεψεψε⋯ψεNonlinearTrendYδδtδt⋯δtεLog‐lineartrendlnYδδtεrunmeanAR(1)δμMeasuringandCorrelationJarque‐BeraTest1ϕrunmeanAR(P)JB1δ624Eμ1ϕϕ⋯ϕSpearmancorrelationBox‐PierceStatisticandLjung‐BoxStatistic6dρ11Kendall’sƬnnT2Ti;QTQTτ16专业来自101%的投入金程教育FRMPartIEasySheet7专业来自101%的投入金程教育FRMPartIEasySheetFINANCIALMARKETSPRODUCTSCompoundingRmAeRmAeValuationFKofLongRiskMetricsDuration∆BDB∆yKofLongSMacaulayDuration1y⁄mKModifiedDurationofLongSIofLongConvexitySK1∆BDB∆y2ConvexityModifiedConvexityFuturesPriceFBondsF1RBill360nQCFS1QFSeandthirty‐secondsofadollarwithaof$100andthirty‐secondsofadollarBondwithaof$100InterestRateParityRRFSCountConventionsTreasuryBonds:actual/actualTreasuryBills:actual/360FuturesProductsS&P500CorporateandMunicipalBonds:30/360Index×$250(multiplierof250)FuturesCleanPrice&DirtyPriceDirtyprice=CleanPrice+AccruedInterestSincetheLastCouponDateFacevalue:$100,000TreasuryBondCheapest‐toDeliverBond:FuturesCostQ–SfMBSFacevalue:$1millionMaturity:Three‐monthConvexityAdjustment:CPR1EurodollarFuturesPayoff8专业来自101%的投入金程教育FRMPartIEasySheetVAVFForwardRateFuturesrate0.5σ0.25∗NhHedgingEquityPositionN∗βNormalandInvertedMarket(Normal)S<FOptionUpperandLowerBoundsOptionMinValue–0–0MaxValueS>FEuropeanCallAmericanCallEuropeanPutAmericanPutSS–S,0–S,0HedgingKHedgeRatioσσh∗ρPut‐CallParitypScTailingtheHedgepSc9专业来自101%的投入金程教育FRMPartIEasySheet10专业来自101%的投入金程教育FRMPartIEasySheetANDRISKMODELSBondInterestRates∆ue√de√∆e∆dpedSpotRates:orpududf∆f12eBSMModelRates:cSKep2ppppdSd⋯222⁄Kσdσ√T100⁄KσForwardRates:d