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1、QuantitativeAnalysisandtheUseofCalculatorFRMPartIProgramiGI吵8巾油捡MM山PYof0m(5 FrameworkQuantitative AnalysisTheIntroductionofFinancialCalculatorAnnuityProbabilityStatistic1.inearRegression行业创新憎值Il -O2m-eu-epueuzJoUO-IUnPO=UI Hl lllO0!三eojCQQOQQO0IIlAnMmHS-SYXWlKyKh.HEEIYNV 3s3OsWAOVA与手7世幻:遍S以啡ZtZI-何而吁
2、JoVjXJ2+八困5-BU.2ss4!Jo.ld、sn-dII 0MxNZX5AXnZ9工IN。( - -I6lUZIdH-中翁 M3力 37B3NB乂 Preparations设置选项按键显示默认设置*小数位数函1FORMATDEC0-9（按9设置为浮2月点小数）WT口角度单位EDEG(度)DEGRAD(弧度)日期IHUS(mm-dd-yyyy)USEur(dd-mm-yyyy)分隔符US(1,000.00)USEur(1.000,00)计算模式E）Chn（链式）ChnAoSTM（代数运算系统）Il三三导)I6rtDIU3UBoHS三Hu三tg3总釜包金fr。非注三wMsg!3SWH总运后
3、之奖泳_2为阁空后书。项e三王后5ls*三l定烹注WJ王项e拒王.s瞥次“艇lOO.OHe第；苫Is宴1.CM。000长力晚冷xsl.se恭玄沼三H三次5-三ttlfettn.L-OIe3*3q二sMoenfiCationS如果您在输入了错误的数值后并没有按卜运算健（例如，国或区）,您可以直接修改该输入项而不必清空计算器。按卜.日他，删除最后一位数字。按卜.画键，清除整个数字。注意：在按卜运算健后，按底图键会结束正在进行的运算。例如:您想计算31234.56的结果，但键入了1234.86.操作按键显示开始输入表达式。303.00输入数值。1234.861,234.86清除输入错误。日S1,23
4、4.健入正确的数值。561,234.56计算结果。03,703.68*GZKIUTZOTMJJ潢TJ:雍潢沸口EWl漆潢流潢淡沼+4:+8淡治6流罪山?三添潢漆治+4:+8漆潢6流演）6:：雍J3崂33*?*33?运算按键显示的结果加法运算6+4604010.00减法运算6-460402.00乘法运算64604024.00除法运算646日4回1.50求广义基运算：3L25301.2503.95使用圆括号:7(3+5)7回11335Q356.00求百分比:$453的4%453回4M日18.12运算按键显示的结果求百分率：14是25的百分之几14日25园回56.00求百分比加成价格：$498+7%
5、营业税498回7函S34.86532.86求百分比折扣价格：$69.99-10%折扣69.99010(%S7.0062.99求组合数：n=52,r=55212ndCr5H2,598,960.00求排列数：n=8,r=38矗Pr3H336.00操作按键显示2平方6.36.3园39.69求平方根：15.515.5血3.94求倒数：1/3.23.2画0.31求阶乘：5!5id1!l120.00求自然对数：In203.45203.45O5.32求反自然对数：e69315.693152ndle-v12.00求23的值，按设定的小数位数四舍五入2(3302ndROUND0.67RoundingILtjii
6、!LILIL:5昌3=2.000032,3=2ndrouncl0.6667EiLi0.6667s3=2.0001Il三三I6&I3三UU4TimeValueofMoneyEAR = (1 + period rate)m 1 1 + EAR =(EARcalculation:1+m=em/匚，semi,m=2;匚叫quarterly,m=411O4DMt:EAR=annualinterestrate1o+,8%.jEAR:匚匚yThegreaterthecompoundingfrequency,thegreatertheEARwillbeincomparisontothestatedrateth
7、egreaterthedifferencebetweenEARandthestatedrateAnnuityAnnuities:isafinitesetoflevelsequentialcashflows.equalintervalsequalamountofcashflowssamedirectionConcept:N=numberofperiodsI/Y=interestrateperperiodPV=presentvalue=currentvalueofsomefuturecashflowsPMT=amountofeachperiodicpaymentFV=futurevalue=amo
8、unttowhichinvestmentgrowsafteroneormorecompoundingperiods)GRIRGZOTM6GTJ,W4ig消63:涌甯遣6行雍溜潢）6:涟潢,行雍。，#K匚口匚K口匚3gQgg治/?潍浦治4,雍溜潢63:，雍浦潢，G雍浦沼）6:流潢6行雍o6d-HAdXUZQ+1)I+I+HAHL+)E(J+cZ(J+E)+-BAUnbesBu-Pububabu-JoISB-AEnlBdJBdHy.TVM,-O渡N=20*12=240,I=6.212,PV=700,000,FV=OCPTPMT=-5096.12，3匚r匚-K口Jj匚心隐2yAMORT2NDPVPl
9、=IP2=lSL=698,520.5485PRN=-L479.4515INT=-3,616.6667)J11*3e匚，僚1ZeK)Henj11111111111111M11BGN.ul(2NDBGN,2NDSET,2NDQUIT)yTVM书N=20,IY=4,PMT=100zOOOFV=OCPTPV=-1,413,393.94s 3，Iro3s EHSNJuL(21NbBGN,2NDSET,2NDQUIT)yTVMN=4,IY=4,PMT=50z000zFV=OCPTPV=-188,754.551.Acompanyplanstoborrow$50,000forfiveyears.Thecomp
10、any,sbankwilllendthemoneyatarateof9%andrequiresthattheloanbepaidoffinfiveequalend-of-yearpayments.Calculatetheamountofthepaymentthatthecompanymustmakeinordertofullyamortizethisloaninfiveyears.Answer:N=5fIY=9fPV=50,000,FV=0;CPT:PMT=-12f854.622.Usingtheloandescribedintheprecedingexample,determinethepa
11、ymentamountifthebankrequiresthecompanytomakequarterlypayments.Answer:N=54=20fIY=94=2.25,PV=5OfOOO,FV=O;CPT:PMT=-3f132.103.SmithIc,sbondwithremaining5yearsissoldat$1,030,parvalueis$1,000andcouponrate10%andthecouponispaidsemiannually.CalculatethecostofdebtofSmithInc.?Answer:N=IOPV=-1030FV=1000PMT=50fC
12、PTIY=4.6186SofthecostofdebtofSmithIncis9.24%.114.Aninvestmentof$500,000todaythatgrowsto$800,000aftersixyearsihasastatedannualinterestrateisclosestto(semiannuallycompounded):Answer:N=12PV=-500f000R=800f000PMT=OfCPTIY=399So,thestatedannualinterestrateis3.99%x2=7.98%Il三三I6zZaf三HAH口知-nvk30-5hiJ 7Ho 7H U
13、LiV aL*ka常B 里 I 血巢q M 口口您鬻仇 J 致 Ig e匚错 优Iau算Il弊嘴嘴更P蠢出鬻仇燃痫HG韭d(11)BHka(Siifwdwlrqv通,UUJiaD)嘲uIIdXIghi%7.,f,+4X,，+，,、I-密8J+2+y+5+6口系l0y=3.5专业创新憎值RandomexperimentAnobservationormeasurementprocesswithmultiplebutuncertainoutcomes.SampleSpaceAsetcontainingallpossibleoutcomesofanexperiment.E.g.,thesamplesp
14、aceofarollingasinglesix-sideddieis工,2,6.EventsSubsetsofsamplespace,i.e.,asetofoutcomesandmaycontainoneormoreofthevaluesinthesamplespace,oritmayevencontainnoelements.EventSpaceTheeventspaceconsistsofallcombinationsofoutcomes.MutuallyexclusiveeventsEventsthatcannotbothhappenatthesametime.AB=0AxiomsofP
15、robabilityAnyeventAintheeventspacehasPa0“(Pr&才0).Theprobabilityofalleventsinsamplespaceis1.IfeventsA1andA2aremutuallyexclusive,PafJA2#PAJPR2)ExtensionsTheprobabilityofaneventoritscomplementmustbe1P(AUAC)=P&)+PGC)=ITheprobabilityoftheunionofanytwosetscanbedecomposedinto:P(AUB)=Pe)+P)-PenB)Uncondition
16、alProbability(MarginalProbability)Theprobabilityofaneventwithoutanyrestrictions(orlackinganypriorinformation),commonlyknownasP（八）.ConditionalProbabilityTheprobabilityonconditionthatanothereventoccursfirst.TheconditionalprobabilityofEventB,conditionalonEventA,isgivenbyP(AB)P(BlA)=xa；P（八）。Jointprobabi
17、lityP(AB)isthejointprobability,whichmeanstheprobabilitythattwoeventsoccursimultaneously.Jointprobability:P(AB)Multiplicationrule:ThejointprobabilityofAandBcanbeexpressed:P(AB)=P(AB)hP(B)IfAandBareFnUtUallyexclusiveevents,then:P(AB)=P(AIB)=P(BIA)=OProbabilitythatatleastoneoftwoeventswilloccur:Additio
18、nrule:GiveneventsAandB,theprobabilitythatAorBoccurs,orbothoccur,isequaltotheprobabilitythatAoccurs,plustheprobabilitythatBoccurs,minustheprobabilitythatbothAandBoccur.P(AorB)=P（八）+P(B)-P(AB)IfAandBaremutuallyexclusiveevents,then:P(AorB)=P（八）+P(B)Independentevents:DefinitionofIndependentEvents:Twoeve
19、ntsAandBareindependentifandonlyifP(AB)=P（八）or,equivalently,P(BA)=P(B).MultiplicationRuleforIndependentEvents.Whentwoeventsareindependent,thejointprobabilityofAandBequalstheproductoftheindividualprobabilitiesofAandB:P(AB)=P（八）hP(B)IndependenceandMutuallyExclusivearequitedifferentIfexclusive,mustnotin
20、dependence;CauseexclusivemeansifAoccur,Bcannotoccur,AinfluentsB.Conditionalindependence1.ikeprobability,independencecanberedefinedtoholdconditionalonanotherevent(C),twoeventsAandBareconditionallyindependentif:P(ACBC)=PeC)XP)Notethattwotypesofindependenceunconditionalandconditionaldonotimplyeachother
21、.Eventscanbebothunconditionallydependentandconditionallyindependent.Eventscanbeindependent,yetconditionalonanothereventtheymaybedependent.Il三丽而三lll16mroU4S4SSStatisticalConceptsDefinitionofPopulation:Apopulationisdefinedasallmembersofaspecifiedgroup.Anydescriptivemeasureofapopulationcharacteristicis
22、calledaparameter.DefinitionofSample:Asampleisasubsetofapopulation.Asamplestatistic(orstatistic)isaquantitycomputedfromorusedtodescribeasample.StatisticalConceptsDescriptivestatisticsDescriptivestatisticsisthestudyofhowdatacanbeSUmmariZede仟ectivelytodescribetheimportantasPeCtSOfIargedatasets.Byconsol
23、idatingamassofnumericaldetails,descriptivestatisticsturnsdataintoinformation.InferentialstatisticsMakesestimationsaboutaIargeSetOfdata(aPoPU止tionWithSmallergroupOfdata.RelativefrequencyTherelativefrequencyofobservationsinanintervalisthenumberofobservatios(theabsolutefrequency)intheintervaldividedbyt
24、hetotalnumberofobservations.FrequencydistributionAfrequencydistributionisatabulardisplayofdatasummarizedintoarelativelysmallnumberofintervals.Frequencydistributionspermitanalysttoevaluatehowdataaredistributed.Cumulativefrequency/cumulativerelativefrequencyThecumulativerelativefrequencycumulates(adds
25、up)therelativefrequenciesaswemovefromthefirstintervaltothelast.ConstructingafrequencydistributionReal(Inflation-Adjusted)EquityReturns:NineteenMajorEquityMarkets,1900-2010CountryArithmeticMean(%)CountryArithmeticMean(%)Australia9,1Netherlands7.1Belgium5.1NewZealand7.6Canada7.3Norway7.2Denmark6.9Sout
26、hAfrica9.5Finland9.3Spain5.8France5.7Sweden8.7Germany8.1Switzerland6.1Ireland6.4UnitedKingdom7.2Italy6.1UnitedStates8.3Japan8.5ConstructingafrequencydistributionFrequencyDistributionofAverageRealEquityReturnsReturnInterval(%)AbsoluteFrequencyRelativeFrequency(%)CumulativeAbsoluteFrequencyCumulativeR
27、elativeFrequency(%)5.0to6.0315.79315796.0to7.042105736.847.0to8.0526321263.168.0to9.0421.051684.219.0to10315.7919100.00DatavisualizationVisualizationreferstohowthedatawillbeformatted,displayed,andsummarizedingraphicalform.Tag cloud加快学匀技术娱WhatisStatisticalInference?Concernedwithdrawingconclusionsabou
28、tthenatureorsomepopulation(e.g.,thenormal)onthebasisofarandomsamplethatsupposedlybeendrawnfromthatpopulation.1.ooselyspeaking,isthestudyoftherelationshipbetweenapopulationandasampledrawnfromthatpopulation.SamplingandEstimationipopulationsamplingI*populationparameter;IIestimation三samplesamplestatisti
29、cThechoicesamplingMethods:ReducecognitivebiasSimplerandomsamplingStratifiedrandomsamplingn三丽司三lll16tz3门今口4000rt-J11dnMSUnSnGS-BnUalaJUIn三丽司三lll166寸=-q-Mpo-.-xmI1!isiihi-0，：ac39C*3Bl-二；二fz二3wWW工7,M7jMj/(-。5w三lS53B。匚MllEOi三59w1.三O3嘛c一口口4口4*口一口r口一口口出口口8寸613+三SAGS-BnUalaJUIOutliersOutliersaresmallnumber
30、sofobservationsateitherextreme(smallorlarge)ofasample.Ifoutlierscontaininformation,theyshouldbeincludedinthesample.Ifoutlierscontainnoinformation,theyshouldbeexcluded.Theaveragesalaryofnineriskmanagers:$258,000HSalary(三)Theaveragesalaryoftenriskmanagers,includingthesalaryofJackMa:$1,000,000,0001E+10
31、9E+098E+097E+096E+095E+094E+093E+092E+091E+O912345678910 Salary($)0Casestudy:ThefinalscoreofanshootingcompetitionKXGMKYIUXK:XTIGZKJGKXGMKYIUXKn三丽司三lll164S-duesJoBUUBPUBdBP一gq_bsP0PSn-Ulopoo.!*JoJ6P-cl.一ot-uo-u-eqP-FloilSBp-ELll-dulesOvcccSUnSnGS-BAUalaJUIEnUIMUII3sUmEBEH6ue&BLULPUqOIUodUU右；UB0一UoSPB
32、dUJOUInOw-MSaId三n-roroos0E一-ZUO.SJds.ploosqvAPmSseu盟OjmJ0%5%X)%15%20MDATA巾按键解释显示2ndDATA进入DATA功能X01=0.00002ndC曰C清除DATA功能中的存储记忆X01=0.00000ENTER第一个收益率X01=0.0000WW5ENTER第二个收益率X02=5.0000WU10ENTER第三个收益率X03=10.0000WW15ENTER第四个收益率X04=15.0000WW20ENTER第五个收益率X05=20.0000.CaseStudyHSTAR按键显示解释2nd8STATLINLlN表示输入的数
33、据之间是线性关系Wn=5.0000在DATA功能中，共输入了5个数据W输入的5个数据的均值是10WSx=7.9057如果输入的为一个样本，样本标准差是7.9057Jx=7.0711如果输入的为总体，总体标准差是7.0711n三丽司三lll1619.1M=U-三SodOlA-UJ-4B6UEO-JJS6UB：JUB30D-qeBLUOPUXJLouBW-M0Ez-v-roIUoPU巴0MoLll-DraEurol-ou（八）UJLUUJ()xLIJ00ucQsouuueceouCorrelationcoefficientcv式，y)P-XYbbxyPropertiesofCorrelationc
34、oefficientCorrelationhasnounits,rangesfrom-1to+1.Correlationmeasuresthelinearrelationshipbetweentworandomvariables.Iftwovariablesareindependent,theircovarianceiszero,therefore,thecorrelationcoefficientwillbezero.Theconverse,however,isnotVariaSPEiifi8S0faafces:02(XrY=2=X2(Y)r2p=X=Y=62-91CorrelationcoefficientInterpretationr=+1perfectpositivecorrelation0r+1positivelinearcorr
