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1、FundationsofriskmanagementPortfolioManagementTheoryPortfolioReturn:ERERERPortfolioVariance:Op3汩攵2pwAwBCTACTB2covA,BCapitalMarketLine(CML):CAPM(SML)ERPRfERmRf.其中MeasuresofPerformanceERRSharpeRatioSRERRTreynorRatioTRPERMARSortinoRatioIyRMART其中RMARERERInformationRatioIRRRTrackingErrorRR(Method1)(Method
2、2)(Nisthenumberofreturnperiodsmeasured)JensensAlpha:ERRERRArbitragePricingTheoryERRGRRBRRERRfERRfQUANTITATIVEMETHODSBayes,FormulaPBlAPAIBPA1PBBasicStatisticsExpectedValueEXPxxPXX,s,PXXContinuousUniformDistribution:OforxaXaFx；foraxbba1forXbVariance EX CovarianceCov X,Y EX EX Y EYCorrelationCov X,YP S
3、ums of Random Variables IfX and Y are any random variables:EX Y E X E Y IfX and Y are independent:Var X YVar XVar Y IfX and Y are not independent:Var X YVar XVar Y 2Cov X,Ycfa frm cpa cma video,weixin : 804283381SkeWness& kurtosis E X Skewness Positive skewness: Mode Median Median MeanE X Kurtosis C
4、 ” E X Excess kurtosis = sample kurtosis - 3Common Probability DistributionsBinomialdistributionpxCplpEXnpDXnp1pPoissonDistribution入pkPXke入npEX入DXNormalDistribution:.(Idmameif!tscwiibbdkw*eaBrabyHr由Iirfe(XU,t?)mean=mode=medianKurtosis=3Linearcombinationsofnormalrandomvariablesarenormallydistributed.
5、StandardizedNormalDistributionZ-_-N0,1ConfidenceInterval68%ofobservationsfallwithinl90%ofobservationsfallwithin1.6595%ofobservationsfallwithin1.9699%ofobservationsfallwithin2.58Studentst-distribution:Studentst-distribution:issymmetric;fattertails;Degreesoffreedom=(n-l).CentralLimitTheorem:Whenselect
6、ingsimplerandomsamplesofsizenfromapopulationwithameanandafinitevariance2,thesamplingdistributionofthesamplemeanapproachesanormalprobabilitydistributionwithmeanandavariance2nequaltoasthesamplesizebecomeslarge(n30).MeasureofCentraltendencyPopulationmean:XSamplemean:XMeasurementofdispersionPopulationva
7、riance:XPopulationstandarddeviation:Knownpopulationvariance:Unknownpopulationvariance:SS/EstimationPointestimation:unbiasness,efficiency,consistencyConfidenceintervalestimation:Confidenceinterval:givesrangeofvaluesthemeanvaluewillbebetween,withagivenprobability(say90%or95%).Withknownvariance,formula
8、foraconfidenceintervalis:Pointestimate+/-(reliabilityfactor*standarderror)/Withknownvariance:XZ而/thunknownvariance:s*Samplevariance:2ilXXzSamplestandarddeviation:Sampling&EstimationSamplingDistribution:Probabilitydistributionofallpossiblesamplestatisticscomputedfromasetofequal-sizesamplesrandomlydra
9、wnfromthesamepopulation.Thesamplingdistributionofthemeanisthedistributionofestimatesthemean.StandardErrorofSampleMean:StandarderrorofthesamplemeanisthestandarddeviationOfdistributionofthesamplemean.HypothesisTestingNullandAlternativeHypothesesNullhypothesis(H0):Hypothesistheresearcherwantstoreject;t
10、hehypothesisthatisactuallytested;thebasisforselectionoftheteststatistics.Alternativehypothesis(Ha):Concludedifthereissufficientevidencetorejectthenullhypothesis.TestofMean:XUttfzkTestofTwoMeans:禺PSS2C0VX,Y-n-DifferenceBetweenOne-andTwo-TailedTests:One-tailedtest:testswhethervalueisgreaterthanorlesst
11、hanagivennumber.H：uO;HOTwo-tailedtest:testswhethervalueisequaltoagivennumber.H：u0;H0TypesIandTypeIlErrors:TypeIerror:rejectionofnullhypothesiswhenitisactuallytrue.TypeIlerror:failuretorejectnullhypothesiswhenitisactuallyfalse.DecisionIfHistrueHisfalseRejectHTypeIerrorSignificantlevelistheprobability
12、oftypeIerrorCorrectPoweroftestisdefinedasl-FailtorejectHCorrectTypeIlerror()cfafrmcpacmavideofweixin:804283381TypesofHypothesisTests:MeanHypothesisTestingNonnallydistribution,knownvarianceXPnN(0,l)Normallydistribution,unknownvariancetXS/Vnt11-l)VarianceHypothesisTestingNormallydistributionn1sX(n-1)T
13、woindependentnormallydistributionFs/sF(11-1,&-1)RegressionSimpleLinearRegressionYXY=dependentorexplainedvariableX=independentorexplanatoryvariable=interceptcoefficient=slopecoefficient=errortermMultipleLinearRegressionYXX-XTotalSumofSquaresTotalsumofsquarcs=explaincdsumofsquarcsthcresidualsumofsquar
14、esYYYYYYTSS=ESSRSSMeasuresofFitnessMeasuresofFitnessRiESSRSSR1TSSTSSr2(correlationcoefficient)rRrFAdjustedR2RSS/nk11TSS/n1ANOVATableANOVATableDfSSMSSRegressionKESSESS/KResidualN-K-IRSSRSS(n-K-l)TotalN-ITSS-F-testinrestrictedandunrestrictedmodelCook*sdistanceStationaryTimeSeriesNon-StationaryTimeSeri
15、esautocovarianceLinearTrendjEYEYYEYYtWold,srepresentationNonIinearTrendYtttYLog-lineartrendInYtLongrunmeanofAR(I)MeasuringReturns,VolatilityandCorrelation1Jarque-BeraTestLongrunmeanofAR(P)sK3il1624EYU1SpearmancorrelationBox-PierceStatisticandLjung-BoxStatistic6dQTP；QlT2PTiPnn1KendalsTnnnn1/2FINANCIA
16、LMARKETSANDPRODUCTSPayoff = ST-KCompoundingInterestRFatureValueA1mFatureValueAeAeA1mRiskMetricsDurationBDByMacaulayDurationModifiedDuration1y/mConvexityBDByLCByValuationFKValueofLongForwardContract-KValueofLongForwardContractSKValueofLongForwardContractSIValueofLongForwardContractSK1Q-1Modified Conv
17、exity 万Treasury BondsFuturesFuturesPriceFSlRFSllRTreasuryBiIl360Q100CnTreasuryNotesDollarsandthirty-secondsofadollarwithafacevalueof$100TreasuryBondDollarsandthirty-secondsofadollarwithafacevalueof$100FSeInterestRateParityDayCountConventionsTreasuryBonds:actual/actualTreasuryBills:actual/360Corporat
18、eandMunicipalBonds:30/360cfafrmcacmavideo,weiin：804283381CleanPrice&DirtyPriceDirtyprice=CleanPrice+AccruedInterestSincetheLastCouponDateMBSCPR11SMMForwardPayoffFuturesProductsS&P500FuturesIndexX$250(multiplierof250)TreasuryBondFuturesFacevalue:$100,000Cheapest-to-DeliverBond:CostQ-SfEurodollarFutur
19、esFacevalue:$1millionMaturity:Three-monthConvexityAdjustment:ForwardRateFuturesrate0.5TT0.25Contango(Normal)SFSpotPriceFuturesPricenaBackwardationHedgingHedgeRatio1h*p_-TailingtheHedgeN*NHedgingEquityPositionN*HVOptionUpperandLowerBoundsOptionMinValueMaxValueEuropeanCallmaxS-PVK,0SAmericanCallmaxS-P
20、VK,0SEuropeanPutmaxPVK-S1OPVKAmericanPutmaxK-S,0KPut-CallParitypScPVKpScPVDivsPVKVALUATIONANDRISKMODELSBondValuationValuationYieldtoMaturityPc/2c/2c/2171y/21y/2100c/2Iy/2-C11002r71y/2Annuitiesc1P一1yiyPerpetuitypSyeJAeAdPorpudfepf1BSMModelCSNdKeNdpKeNdSNdInS/Kr/2TfInS/Kr/2T_dLdTTcSeNdKeNdpKeNdSeNdInS
21、/Krq/2TTInS/Krq/2T_dJdTTMeasuresofFinalhcialRiskExpectedShortfalle/ExpectedShortfall1X2MeasuringandMontoringVolatilityOptionValuationBinomialTreesOne-StepCalculationEWMACOV1rcov1xyGARCHVrYV1MeasuringCreditRiskGaussianCopulaModelOne-FactorCorrelationModelVasicekModelNPDaFDefaultRateasafunctionofFN八vlOperationalRiskPowerLawPvxKX
