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1、汩 G I QuantitativeAnalysisandtheUseofCalculatorJFRMPartIProgramThe Introduction of FinancialCalculatorAnnuityProbabilityStatisticLinear Regression菖W，MfFrameworkQuantitativeAnalysisTheIntroductionofFinancialCalculatorMW腼tl)GRILRGZUXYLUXZNKKGSBAIIPlus/Professional:/Bi 二 r 二上4 : -&-: W.二二二B一口19)GRILRGZ
2、UXYLUX次KKGSHP12CPreparations设置选项枝键显示默认设置自口匚nu-(U小数位数函FORMATDEC0-9（按9设？为评点小数）2角度即位QDEG()RAD(MK)DEGIIViUS(mm-dd-yyyy)Eur(dd-mm-yyyy)US分隔符QUS(1,000.00)Eur(1000,00)US计力Ift式GJChn（6tA）AOS（代数运。系统）ChnResetthecalculator按下（三）他SH）屯迎）1.bWSfTjB.RST?fwENTERffW1W注拿：7；爱以沟丽WIt作.拉F画MEtt.J*f.0.002.技卜&7匿，!认rmv*f.RSTHi0
3、.0015WJfttI注，小置时HHH/息出JL讷先按EEE*请泣所的出Ht仿息.硬重置好也1以通ii计0器背向。RESET处的小孔小Nil-JK.用欠物11-11+EAR=(1+)m=er,Tsemi,m=2;r,Cquarterly1m=4e0jWE:EAR二annualinterestrate1M,*+ftgreatempoundingfrequency,thegreatertheEARwillbeincomparisontothestatedratethegreaterthedifferencebetweenEARandthestatedrateMfWflAnnuityAnnuitie
4、s:isafinitesetoflevelsequentialcashflows.equalintervalsequalamountofcashflowssamedirectionConcept:N=numberofperiodsI/Y=interestrateperperiodPV=presentvalue=currentvalueofsomefuturecashflowsPMT=amountofeachperiodicpaymentFV=futurevalue=amounttowhichinvestmentgrowsafteroneormorecompoundingperiods16-91
5、)GRiCrgajtm6gtj,四KKfftjLMlMJ4OllIl；清?演溜演4漆溜潢63:液溜溃6流濡潢)6:漆消，,oKrffifiO61791SUVQMt)GRIRG3OTM6GTJ,pv-r专攻QIMm)GRIRGZOTM4.stl巾匚匚3MIO。匚SLOoMu8%jbLLjJELL50S?8/12=0.6667演I/Y沸溜。1演PMT藻渭一10演PV沸濡50演FV沸溜沼CPT液消N藻ON=143.80渡jOJbO143.8.1211.9812匚克OSd渡19-9163:,TT0Z_CompositionofannuityInterestpaymentandprincipalpaym
6、entUsetheAMORTfunctioninacalculatorClassificationofannuityOrdinaryannuities，i:Thefirstcashflowoccursattheendoffirstperiod.Example-mortgageloans,investments,etc.Annuitydueiil:ThefirstcashflowoccursimmediatelyExample-rentalfees,tuitionfees,livingexpenses,etc.Usecalculator,putthecalculatorintheBGNmodea
7、ndinputrelevantdata.20-91UV.Ml.tl.CalculatingPMTm匚sJNhk*ew0j,Bj(2NB,llfS2NDQUIT)yTVMN=20,IY=4,PMT=100,000FV=OCPTPV=-ll413,393.94”世MRM.HCalculating PMT.H11rioJ11seTBGNjL(2NDBGN,2NDS,2NDQU11)H与匚WM专2HjNN=4fIY=4,PMT=50,000,FV=OCRTPV=-188,754.55uewnaExample1.Acompanyplanstoborrow$50,000forfiveyears.Theco
8、mpanysbankwilllendthemoneyatarateof9%andrequiresthattheloanbepaidoffinfiveequalend-of-yearpayments.Calculatetheamountofthepaymentthatthecompanymustmakeinordertofullyamortizethisloaninfiveyears.Answer:N=5,IY=9,RV=50,000,FV=0;CPT:PMT=-12,854.62ExampleO2.Usingtheloandescribedintheprecedingexample,deter
9、minethepaymentamountifthebankrequiresthecompanytomakequarterlypayments.Answer:N=54=20zI=94=2.25,PV=50,000,FV=O;CPT:PMT=-3f132.1025-91氐蚀MR!Example3.SmithIncsbondwithremaining5yearsissoldat$1,030,parvalueis$1,000andcouponrate10%andthecouponispaidsemiannually.CalculatethecostofdebtofSmithInc?Answer:N=I
10、OPV=-1030FV=100OPMT=SOfCPTIY=4.6186SorthecostofdebtofSmithIncis9.24%.26-91y0JointprobabilityP(AB)isthejointprobability,whichmeanstheprobabilitythattwoeventsoccursimultaneously.ProbabilityJointprobability:P(AB)Multiplicationrule:ThejointprobabilityofAandBcanbeexpressed:P(AB)=P(AB)hP(B)IfAandBaremutua
11、llyexclusiveevents,then:P(AB)=P(AIB)=P(BIA)=OProbabilitythatatleastoneoftwoeventswilloccur:Additionrule:GiveneventsAandB1theprobabilitythatAorBoccurs,orbothoccur,isequaltotheprobabilitythatAoccurs,plustheprobabilitythatBoccurs,minustheprobabilitythatbothAandBoccur.P(AorB)=P（八）+P(B)-P(AB)IfAandBaremu
12、tuallyexclusiveevents,then:P(AorB)=P（八）P(B)36-91meProbabilityIndependentevents:DefinitionofIndependentEvents:TwoeventsAandBareindependentifandonlyifP(AB)=P（八）or,equivalently,P(BA)=P(B).MultiplicationRuleforIndependentEvents.Whentwoeventsareindependent,thejointprobabilityofAandBequalstheproductofthei
13、ndividualprobabilitiesofAandB:P(AB)=P（八）hP(B)IndependenceandMutuallyExclusivearequitedifferentIfexclusive,mustnotindependence;37-91CauseexclusivemeansifAoccur,Bcannotoccur,AinfluentsB.侬.em.is.ProbabilityConditionalindependence1.ikeprobabilityfindependenceCanberedefinedtoholdconditionalonanotherevent
14、(C),twoeventsAandBareconditionallyindependentif:P(ABQ=P(AQP(BQNotethattwotypesofindependenceunconditionalandconditionaldonotimplyeachother.Eventscanbebothunconditionallydependentandconditionallyindependent.38-91Eventscanbeindependentyetconditionalonanothereventtheymaybedependent.侬MR”DefinitionofPopu
15、lationApopulationisdefinedasallmembersofaspecifiedgroup.Anydescriptivemeasureofapopulationcharacteristiciscalledaparameter.DefinitionofSample:Asampleisasubsetofapopulation.40-91Asamplestatistic(orstatistic)isaquantitycomputedfromorusedtodescribeasample.M皿MR“StatisticalConceptsDescriptivestatisticsDe
16、scriptivestatisticsisthestudyofhowdatacanbesummarizedeffectivelytodescribetheimportantaspectsoflargedatasets.Byconsolidatingamassofnumericaldetails,descriptivestatisticsturnsdataintoinformation.Inferentialstatistics41-91Makesestimationsaboutalargesetofdata(apopulationwithsmallergroupofdata.WTMR!*.De
17、scriptivestatisticsRelativefrequencyTherelativefrequencyofobservationsinanintervalisthenumberofobservations(theabsolutefrequency)intheintervaldividedbythetotalnumberofobservations.FrequencydistributionAfrequencydistributionisatabulardisplayofdatasummarizedintoarelativelysmallnumberofintervals.Freque
18、ncydistributionspermitanalysttoevaluatehowdataaredistributed.Cumulativefrequency/cumulativerelativefrequencyThecumulativerelativefrequencycumulates(addsup)therelativefrequenciesaswemovefromthefirstintervaltothelast.DescriptivestatisticsConstructingafrequencydistributionReal(Inflation-Adjusted)Equity
19、Returns:NineteenMajorEquityMarkets,1900=2010CountryArithmeticMean(%)CountryArithmeticMean(%)Australia9.1Netherlands7.1Belgium5.1NewZealand7.6Canada73NorWay7.2Denmark6.9SouthAfrica95Finland93Spain5.8France5.7Sweden8.7Germany8.1Switzerland6.1Ireland6.4UnitedKingdom7.2Italy6.1UnitedStates83JaPan&5.Desc
20、riptivestatisticsConstructingafrequencydistributionFrequencyDistributionofAverageRealEquityReturnsReturnInterval(%)AbsoluteFrequencyRelativeFrequency(%)CumulativeAbsoluteFrequencyCumulativeRelativeFrequency(%)5.0to6031579315,796.0to7.0421.05736.847.0to8.0S26.321263168.0to9.042L051684.219.0to10315.79
21、19100.00gem.t.DescriptivestatisticsDatavisualizationVisualizationreferstohowthedatawillbeformatted,displayed,andsummarizedingraphicalform.Tagcloud.InferentialstatisticsWhatisStatisticalInference?Concernedwithdrawingconclusionsaboutthenatureorsomepopulation(eg,thenormal)onthebasisofarandomsamplethats
22、upposedlybeendrawnfromthatpopulation.1.ooselyspeaking,isthestudyoftherelationshipbetweenapopulationandasampledrawnfromthatpopulation.SamplingandEstimation-Xfr11、Ipopulation一populationparameterI一,!samplingestimationrrIIsample；samplestatistic；l.InferentialstatisticsThechoicesamplingMethods:Reducecogni
23、tivebiasSimplerandomsampling47-91Stratifiedrandomsampling.Inferentialstatistics1936SzJdRooojetlsejM1137O,161景J113EJI11JJb澧JLD口唯*1948jfr49-91uk*wn.InferentialstatisticsOutliersOutliersaresmallnumbersofobservationsateitherextreme(smallorlarge)ofasample.Ifoutlierscontaininformation,theyshouldbeincluded
24、inthesample.Ifoutlierscontainnoinformation,theyshouldbeexcluded.50-91y.OM.!.HInferentialstatisticsTheaveragesalaryofnineriskmanagers:$258,000H52-91H12345678910, KXCMK Yim:XTIGZKJ GKXGMK YIUXKTheaveragesalaryoftenriskmanagers,includingthesalaryofJackMa:$1,000,000,000M.InferentialstatisticsCasestudy:T
25、hefinalscoreofanshootingcompetition雪世WE.InferentialstatisticsIndependenceofsampleThesampledatashouldbeindependentofeachother.Thedegreeoffreedomisusedtodescribethedependenceofsample.渡卜口-uLKlLk趾 AMlqEq,h M:hw3熙i Zl 且 fi拒绝人云亦云55-91K . MR . IB.Inferential statistics.Case StudyMeasures of central tendenc
26、y: mode, median, meanThe arithmetic mean:X=Theweightedmean:几=Wi=v(/+W/+h心X)I=IThegeometricmean;Theharmonicmean:Xh=w.CaseStudyAbsolutedispersion:istheamountofvariabilitypresentwithoutcomparisontoanyreferencepointorbenchmark.Range=maximumvalue-minimumvalueMAD58-91MWMrt!.CaseStudyHOCjMJSL0%5%10%co:按键解释
27、显示(2nd)DATA)进入DATA功能01=0.002ndCEC清除DATA功能中的存储记忆X01=OOO(X)0ENTER第一个收益率01=000U)U5ENTER第二个收益率02=5.00i)il10(ENTER第三个收益率X03=10.00U11l15ENTER第四个收益率X04=15.00UlUl20ENTER第五个收益率X05=20.000059-91三wrQiwti.CaseStudySTATJ按健显示解释(2nd)8(STALINLlN衣示输入的数据之间是线性关系Wn=5.0000GDATA功能中，共输入了5个数据ri瑜入的5个数据的均值是10US1=7.9057如果输入的为个
28、样本，样本标准总是7.9057UJ5=7.0711如果瑜入的为总体.总体标准基是7.071160-91与Wrflartti.CovarianceCovarianceCvXrY)=E(X-E(X)Y-EY)=E(XY)-E(X)E(Y)Covariancemeasureshowonerandomvariablemoveswithanotherrandomvariable.61-91Covariancerangesfromnegativeinfinitytopositiveinfinity.uk*wnCorrelationCoefficientCorrelationcoefficientCol(X
29、方PropertiesofCorrelationcoefficientCorrelationhasnounits,rangesfrom-1to+1.Correlationmeasuresthelinearrelationshipbetweentworandomvariables.Iftwovariablesareindependent,theircovarianceiszero,therefore,thecorrelationcoefficientwillbezero.Theconverse,however,isnottrue.Forexample,Y=X2.Variancesofcorrel
30、atedvariables:y . OM . !2(XrY-2=X2(Y)r2pgX=62-91CorrelationCoefficientCorrelationcoefficientInterpretationr=+1perfectpositivecorrelationOr+1positivelinearcorrelationr=Onolinearcorrelation-1rOnegativelinearcorrelationr=-1perfectnegativecorrelationperfectpositiveperfectpositiveperfectpositiveperfectnegativeperfectnegativecorrelationr=+1correlationr=0.8correlationr=Ocorrelationr=-0.7correlationr=-1CommonProbabilityDistributionsCommonProbabilityDistributionsPropertiesofdiscretedistributionandcontinuousdistributionDiscreteuniformdi
