FRM一级前导班：定量分析+计算器的使用-讲义打印版.docx

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)GRILRGZUXYLUX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）1.¼b®WSfTjB.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.RSTHi0.0015WJ<fttI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<妊拆的InlIff计或类似的物M）松经地Wi入深小乱就也跳了硬不K.7-9111EU侬.MR.”Modifications如果影4愉入rVi识的教值后井没有技bitn»（例MLs或回）.您以门接修收读喻入HIftJ不必清守计舒M.拉卜日.粽按FK03篇除签个字.注意：0核F运口tJt技Wat公帖柬正。进打的运口.例制：您想计力3X1234.56的结也似皱入了123486.操作按示开始输入A达K.3回3.00M人故价.1234.861.234.86清除整入Wl误.SB1.234.被入正一的数伤.561,234.56计算结果.3,703.68侬MR”*GZKIUTZOTM.卫液治三i3i沛号生+8沸溜济诺灌潢ELM承9礴滦演6滦?33*j?*J30¾33UrMRttBasicfunctionswith"="运算技tt星示的结果E法达口646回4回10.00城泣运N6-46日4回2.00*ri½ff646,4厄24.00除法运作646Q4H1.50求J义可stb33EJ1.25H3.95使用觊括弓，7*(3+5)70CD30S11)56.00求门分比:$453的4%453田4SH18.1210-91M皿l三“Basicfunctionswith运算按健显示的结果求百分率：14是25的百分之几14回25回回56.00求百分比加成价格：$498+7%昔业税498国7隘E)34.86532.86求百分比折扣价格：$69.99-10%折扣69.9910®07.0062.99求组合数：n=52,r=5522nd11Cr5回2,598,960.00求排列数：n=8,r=38l¾dl,3回336.0011-91UV*MR*meBasicfunctionswithout"="掾作按健显示2r*&36.3039.69求年方b15.5而3.94未例数：1/3.23.2的0.31求阶袋：5!5砌120.00求自然对BbIn203.45203.45画5.32求反白然对数:e.69315®”2.00求2-3的tft.按设定的小数位妆四舍K入25)3S®ROUND0.6712-91曲awtraRounding11111111tHfCIu0UL3昌TmT=*2,0000323=2ndround0.6667IiiLJIO.6667j各一3-»=2,000113-91M业，国麻n9Annuity14-91与城，国三TimeValueofMoneyEARcalculation:EAR三(1+periodrate>11-1>1+EAR=(1+)m=er,Tsemi,m=2;r,Cquarterly1m=4e0jWE":EAR二annualinterestrate1'M,*+"ftgreatempoundingfrequency,thegreatertheEARwillbeincomparisontothestatedratethegreaterthedifferencebetweenEARandthestatedrate'MfWflAnnuityAnnuities:isafinitesetoflevelsequentialcashflows.equalintervalsequalamountofcashflowssamedirectionConcept:N=numberofperiodsI/Y=interestrateperperiodPV=presentvalue=currentvalueofsomefuturecashflowsPMT=amountofeachperiodicpaymentFV=futurevalue=amounttowhichinvestmentgrowsafteroneormorecompoundingperiods16-91)GRiCrgajtm6<gtj,<四KKfftjLMlMJ4OllIl；清?演溜演4漆溜潢63:液溜溃6流濡潢)6:漆消，<演#>,oKrffifi¾<sLLL口；渝?液溜清4藻溜沼63:滩浦沼，流溜清)6:藻消6藻-#>O617"91SUVQMt»)GRIRG3OTM6<GTJ,<AboutperpetuityDefinition:Aperpetuityisasetoflevelnever-endingsequentialcashflows,withthefirstcashflowoccurringoneperiodfromnow.CalculationPV=-+j4T+r口#r)t+rfAAA(+rpv=A+*歹1+r(l+r(l+r)3rXpv=A>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_CompositionofannuityInterestpaymentandprincipalpaymentUsetheAMORTfunctioninacalculatorClassificationofannuityOrdinaryannuities，i:Thefirstcashflowoccursattheendoffirstperiod.Example-mortgageloans,investments,etc.Annuitydueiil:ThefirstcashflowoccursimmediatelyExample-rentalfees,tuitionfees,livingexpenses,etc.Usecalculator,putthecalculatorintheBGNmodeandinputrelevantdata.20-91UV.Ml.tl.CalculatingPMTm匚s<y口口匚JarjNhcjW'CMiH日光沙口N=20*12=240,IY=6.212,PV=700f000,FV=OCPTPMT=-5096.12*'jf?卜J二?3jCWAMORT%RNDPVPl=IP2=l弘L=698,520.5485PRN=-lf479.4515NT=-3,616666721'91M”.®m.m.HCalculatingPMT；e7L澳R610>JNhk*ew0j,Bj(2NB,llfS2NDQUIT)yTVM¾N=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.Thecompany'sbankwilllendthemoneyatarateof9%andrequiresthattheloanbepaidoffinfiveequalend-of-yearpayments.Calculatetheamountofthepaymentthatthecompanymustmakeinordertofullyamortizethisloaninfiveyears.Answer:N=5,IY=9,RV=50,000,FV=0;CPT:PMT=-12,854.62ExampleO2.Usingtheloandescribedintheprecedingexample,determinethepaymentamountifthebankrequiresthecompanytomakequarterlypayments.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=IOPV=-1030FV=100OPMT=SOfCPTIY=4.6186SorthecostofdebtofSmithIncis9.24%.26-91y<am*taExample4.Aninvestmentof$500,000todaythatgrowsto$800,000aftersixyearshasastatedannualinterestrateisclosestto(semiannuallycompounded):AnswerN=12PV=-SOOfOOOFV=800,000PMT=0,CPTIY=3.99Sotthestatedannualinterestrateis3.99%×2=7.98%Probability28-91SW(MlEProbability三函瓦瓦施五N费*nXwq中二FIProbabilityHHHHH731-91aiau则弊喙啷彝pb三V'.*SHGE%敏LK外a出肾至"*=噌鼻吃或业©Ml!ProbabilityRandomexperimentAnobservationormeasurementprocesswithmultiplebutuncertainoutcomes.SampleSpaceAsetcontainingallpossibleoutcomesofanexperiment.E.g.,thesamplespaceofarollingasinglesix-sideddieis,2,6EventsSubsetsofsamplespace,i.e.,asetofoutcomesandmaycontainoneormoreofthevaluesinthesamplespace,oritmayevencontainnoelements.EventSpaceTheeventspaceconsistsofallcombinationsofoutcomes.BUrettR.taProbabilityVennDiagramsComplementUnionintersectionMutuallyexclusiveeventsEventsthatcannotbothhappenatthesametime.AB=0ProbabilityAxiomsofProbabilityAnyeventAintheeventspacehasPAR(OrOPr（八）0),Theprobabilityofalleventsinsamplespaceis1.IfeventsA1andAZaremutuallyexclusive,P1UA2)=PRi*P&).ExtensionsTheprobabilityofaneventoritscomplementmustbe1P(AUAc)=P(出+P(Ac)=134-91Theprobabilityoftheunionofanytwosetscanbedecomposedinto:P(AUB)=P（八）+P(B)-P(An出M皿MR“ProbabilityUnconditionalProbability(MarginalProbability)Theprobabilityofaneventwithoutanyrestrictions(orlackinganypriorinformation),commonlyknownasP（八）.ConditionalProbabilityTheprobabilityonconditionthatanothereventoccursfirst.TheconditionalprobabilityofEventB,conditionalonEventArisgivenbyP(AB)P(BlA)=P（八）；PO>0JointprobabilityP(AB)isthejointprobability,whichmeanstheprobabilitythattwoeventsoccursimultaneously.ProbabilityJointprobability:P(AB)Multiplicationrule:ThejointprobabilityofAandBcanbeexpressed:P(AB)=P(AB)hP(B)IfAandBaremutuallyexclusiveevents,then:P(AB)=P(AIB)=P(BIA)=OProbabilitythatatleastoneoftwoeventswilloccur:Additionrule:GiveneventsAandB1theprobabilitythatAorBoccurs,orbothoccur,isequaltotheprobabilitythatAoccurs,plustheprobabilitythatBoccurs,minustheprobabilitythatbothAandBoccur.P(AorB)=P（八）+P(B)-P(AB)IfAandBaremutuallyexclusiveevents,then:P(AorB)=P（八）÷P(B)36-91meProbabilityIndependentevents:DefinitionofIndependentEvents:TwoeventsAandBareindependentifandonlyifP(AB)=P（八）or,equivalently,P(BA)=P(B).MultiplicationRuleforIndependentEvents.Whentwoeventsareindependent,thejointprobabilityofAandBequalstheproductoftheindividualprobabilitiesofAandB:P(AB)=P（八）hP(B)IndependenceandMutuallyExclusivearequitedifferentIfexclusive,mustnotindependence;37-91CauseexclusivemeansifAoccur,Bcannotoccur,AinfluentsB.侬.em.is.ProbabilityConditionalindependence1.ikeprobabilityfindependenceCanberedefinedtoholdconditionalonanotherevent(C),twoeventsAandBareconditionallyindependentif:P(ABQ=P(AQ×P(BQNotethattwotypesofindependenceunconditionalandconditionaldonotimplyeachother.Eventscanbebothunconditionallydependentandconditionallyindependent.38-91Eventscanbeindependentyetconditionalonanothereventtheymaybedependent.侬MR”DefinitionofPopulationApopulationisdefinedasallmembersofaspecifiedgroup.Anydescriptivemeasureofapopulationcharacteristiciscalledaparameter.DefinitionofSample:Asampleisasubsetofapopulation.40-91Asamplestatistic(orstatistic)isaquantitycomputedfromorusedtodescribeasample.M皿MR“StatisticalConceptsDescriptivestatisticsDescriptivestatisticsisthestudyofhowdatacanbesummarizedeffectivelytodescribetheimportantaspectsoflargedatasets.Byconsolidatingamassofnumericaldetails,descriptivestatisticsturnsdataintoinformation.Inferentialstatistics41-91Makesestimationsaboutalargesetofdata(apopulationwithsmallergroupofdata.WTMR!*.DescriptivestatisticsRelativefrequencyTherelativefrequencyofobservationsinanintervalisthenumberofobservations(theabsolutefrequency)intheintervaldividedbythetotalnumberofobservations.FrequencydistributionAfrequencydistributionisatabulardisplayofdatasummarizedintoarelativelysmallnumberofintervals.Frequencydistributionspermitanalysttoevaluatehowdataaredistributed.Cumulativefrequency/cumulativerelativefrequencyThecumulativerelativefrequencycumulates(addsup)therelativefrequenciesaswemovefromthefirstintervaltothelast.DescriptivestatisticsConstructingafrequencydistributionReal(Inflation-Adjusted)EquityReturns:NineteenMajorEquityMarkets,1900=2010CountryArithmeticMean(%)CountryArithmeticMean(%)Australia9.1Netherlands7.1Belgium5.1NewZealand7.6Canada73NorWay7.2Denmark6.9SouthAfrica95Finland93Spain5.8France5.7Sweden8.7Germany8.1Switzerland6.1Ireland6.4UnitedKingdom7.2Italy6.1UnitedStates83JaPan&5.DescriptivestatisticsConstructingafrequencydistributionFrequencyDistributionofAverageRealEquityReturnsReturnInterval(%)AbsoluteFrequencyRelativeFrequency(%)CumulativeAbsoluteFrequencyCumulativeRelativeFrequency(%)5.0to6031579315,796.0to7.0421.05736.847.0to8.0S26.321263168.0to9.042L051684.219.0to10315.7919100.00gem.t.DescriptivestatisticsDatavisualizationVisualizationreferstohowthedatawillbeformatted,displayed,andsummarizedingraphicalform.Tagcloud.InferentialstatisticsWhatisStatisticalInference?Concernedwithdrawingconclusionsaboutthenatureorsomepopulation(eg,thenormal)onthebasisofarandomsamplethatsupposedlybeendrawnfromthatpopulation.1.ooselyspeaking,isthestudyoftherelationshipbetweenapopulationandasampledrawnfromthatpopulation.SamplingandEstimation-Xfr11、Ipopulation一populationparameterI一,!samplingestimationrrIIsample；samplestatistic；l.InferentialstatisticsThechoicesamplingMethods:ReducecognitivebiasSimplerandomsampling47-91Stratifiedrandomsampling.Inferentialstatistics1936SzJdRoooj>etlsejM1137O,161景J113EJI>11JJb澧JLD口唯*1948jf>r49-91uk*wn«.InferentialstatisticsOutliersOutliersaresmallnumbersofobservationsateitherextreme(smallorlarge)ofasample.Ifoutlierscontaininformation,theyshouldbeincludedinthesample.Ifoutlierscontainnoinformation,theyshouldbeexcluded.50-91y.OM.!.HInferentialstatisticsTheaveragesalaryofnineriskmanagers:$258,000H52-91H12345678910, KXCMK Yim:XTIGZKJ GKXGMK YIUXKTheaveragesalaryoftenriskmanagers,includingthesalaryofJackMa:$1,000,000,000'M'.InferentialstatisticsCasestudy:Thefinalscoreofanshootingcompetition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 tendency: mode, median, meanThe arithmetic mean:X=Theweightedmean:几=Wi¥=v½(/+W/+h心X)I=IThegeometricmean;Theharmonicmean:Xh=w.CaseStudyAbsolutedispersion:istheamountofvariabilitypresentwithoutcomparisontoanyreferencepointorbenchmark.Range=maximumvalue-minimumvalueMAD58-91MWMrt!.CaseStudyHOCjMJSL0%5%10%c¾o¾:按键解释显示(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.CaseStudySTAT¾J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*wn«CorrelationCoefficientCorrelationcoefficientCol(X方PropertiesofCorrelationcoefficientCorrelationhasnounits,rangesfrom-1to+1.Correlationmeasuresthelinearrelationshipbetweentworandomvariables.Iftwovariablesareindependent,theircovarianceiszero,therefore,thecorrelationcoefficientwillbezero.Theconverse,however,isnottrue.Forexample,Y=X2.Variancesofcorrelatedvariables:y . OM . !2(XrY-2=X2(Y)r2pgX=62-91CorrelationCoefficientCorrelationcoefficientInterpretationr=+1perfectpositivecorrelationO<r<+1positivelinearcorrelationr=Onolinearcorrelation-1<r<Onegativelinearcorrelationr=-1perfectnegativecorrelationperfectpositiveperfectpositiveperfectpositiveperfectnegativeperfectnegativecorrelationr=+1correlationr=0.8correlationr=Ocorrelationr=-0.7correlationr=-1CommonProbabilityDistributionsCommonProbabilityDistributionsPropertiesofdiscretedistributionandcontinuousdistributionDiscreteuniformdi