綜合b前導課程全

MeasuresofCalculateandinterpretMeasuresofCalculateandinterpretrange,meanabsolutedeviation,varianceandstandarddeviation;MastertheapplicationofChebyshev’sCalculateandinterpretcoefficientofvariationandtheSharperatio.MeasuresofVariabilityaroundtheMeasuresofVariabilityaroundthecentraltendency,usuallyusedtoaddresstherisk.Range=MaximumValue–MinimumEasyforcomputation,butonlyusetwonumbersandtellnothingaboutthedistributionofthedataset.MeasuresofMeanAbsoluteDeviationnXi-MeasuresofMeanAbsoluteDeviationnXi-MAD nWhere:Xisthesamplemean,nisthenumberofMeasuresofVariance:equaltoaverageofthesumofsquareddeviationsaroundthemean.N2X-μi MeasuresofVariance:equaltoaverageofthesumofsquareddeviationsaroundthemean.N2X-μi NPopulation=Where:μisthepopulationmean,Nisthesizeofn2X-iSample=n-Where:Xisthesamplemean,nisthesampleMeasuresofStandarddeviation:positivesquaredrootofN2i NPopulationStandardσMeasuresofStandarddeviation:positivesquaredrootofN2i NPopulationStandardσWhere:μisthepopulationmean,Nisthesizeofn)2X-i n-SampleStandardsWhere:Xisthesamplemean,nisthesampleMeasuresofChebyshev’sForanyMeasuresofChebyshev’sForanydistributionwithfinitevariance,theminimumpercentageofobservationsthatliewithinkstandarddeviationsofthemeanwouldbe1-1/k2,givenk>1.AccordingtoChebyshev’sinequality,whatistheminimumpercentageofobservationsliewithin2standarddeviationsofthemean?Answer:1-MeasuresofTheMeasuresofTheratioofthestandarddeviationofasetofobservationstotheirmeanvalue.CV=XCVhasnounitsofmeasurement,sopermitscomparisonsofdispersionsacrossdifferentdataAmeasureofriskperunitofmeanreturn,thusthelowerisbetter.MeasuresofSharpeTheratiooftheMeasuresofSharpeTheratioofthemeanexcessreturnonportfolioPtothestandarddeviationofthereturnsofportfolioP.Nounitsofmeasurement,sopermitsdirectcomparisonsofdispersionsacrossdifferentdatasets.Ameasureofexcessreturnperunitofrisk,thushigherisbetter(onlyvalidforpositiveSharpeApplicationofProbabilityinCalculateandinterpretexpectedvalue,variance,standarddeviation,andApplicationofProbabilityinCalculateandinterpretexpectedvalue,variance,standarddeviation,andcovarianceandcorrelationofreturnsonaportfolio;IdentifythemostappropriatemethodtosolveparticularcountingTheprobability-weightedaverageoftheTheprobability-weightedaverageofthepossibleoutcomesoftherandomvariable(X).EX= +P(x2+...+Totalprobabilityrulesforexpected=E(X|S1)P(S1)+E(X|S2)P(S2)+…+Wherein:S1,S2,……SnaremutuallyexclusiveAnexampleofexpectedvalueaboutanReturnAnexampleofexpectedvalueaboutanReturnE(X)=InvestmentProb.ofdeclininginterestrates=0.60P=P=Prob.ofinterestrate=PInvestmentProb.ofdeclininginterestrates=0.60P=P=Prob.ofinterestrate=P=E(EPS)=2.6x0.15+2.45x0.45+2.2x0.24+2.0x=P=σ2(X)=P(x)[x-E(X)]2+P(x)[x-E(X)]2+......+P(x)[x-112σ2(X)=P(x)[x-E(X)]2+P(x)[x-E(X)]2+......+P(x)[x-1122nnStandarddeviation:positivesquaredrootofP(xi)[xiE(X)= AmeasureofhowtwovariablesAmeasureofhowtwovariablesmoveCov(Ri,Rj)=P(Ri,Rj)-ERiRj-ERjn?Positivecovariance:thetwovariablestendtobeorbelowtheirexpectedvaluesatthesametime;Negativecovariance:onevariabletendtobeaboveitsexpectedvaluewhentheotherisbelowitsexpected?CovarianceExampleofcovariancegivenajointprobabilityCovAB=0.15(0.20–0.13)(0.40–0.18)+CovarianceExampleofcovariancegivenajointprobabilityCovAB=0.15(0.20–0.13)(0.40–0.18)+0.6(0.15–0.13)(0.20–0.18)0.25(0.04–0.13)(0–=RB=RB=RB=E(RB)=RA=RA=RA=E(RA)=CovarianceValuesCovarianceValuesrangefromminusinfinitytopositiveUnitsofcovariancedifficulttoAstandardizedmeasureoflinearrelationshipbetweenCov(RiAstandardizedmeasureoflinearrelationshipbetweenCov(RiCov(Riρi,jσiσj?Valuesrangefrom+1(perfectpositivecorrelation)to-Acorrelationof0(uncorrelatedvariables)indicatesanabsenceofanylinear(straight-line)relationship;Thebiggertheabsolutevalue,thestrongerthe??Labeling,Combination,andThenumberofwaysLabeling,Combination,andThenumberofwaysthatnobjectscanbelabeledwithkdifferentlabels,withn1ofthefirsttype,n2ofthesecondtype,andsoon,withn1+n2+...+nk=n.Numberofways= n1!n2!...Labeling,Combination,andOutof10stocks,5willbeLabeling,Combination,andOutof10stocks,5willberatedbuy,3willberatedand2willberatedHowmanywaysarethereto5!·3!·Labeling,Combination,andThenumberofwaysthatweLabeling,Combination,andThenumberofwaysthatwecanchooserobjectsfromatotalofnobjects,whentheorderinwhichtherobjectsarelisteddoesnot= (n-nLabeling,Combination,andOutof10stocks,5willLabeling,Combination,andOutof10stocks,5willberatedbuy,theorderofpurchasedoesmatter.Howmanywaysaretheretodo(10-Labeling,Combination,andThenumberofwaysthatweLabeling,Combination,andThenumberofwaysthatwecanchooserobjectsfromatotalofnobjects,whentheorderinwhichtherobjectsarelisteddoes= (n-nLabeling,Combination,andOutof10stocks,5willLabeling,Combination,andOutof10stocks,5willberatedbuy,theorderofpurchasedoesmatter.Howmanywaysaretheretodo(10-Importance:?Probabilityweightedmean,varianceandImportance:?Probabilityweightedmean,varianceandCovarianceandLabeling,combination,and??Exam常考點：covarianceandcorrelationBasicsofProbabilityDefineBasicsofProbabilityDefineprobabilityDefinediscreteuniformrandomvariable,Bernoullirandomvariable,andbinomialrandomvariable.ProbabilitySpecifiestheprobabilitiesProbabilitySpecifiestheprobabilitiesofallpossibleoutcomesforarandomvariable.Discretedistribution:thedistributionofthediscreterandomvariable.Discreterandomvariable:takesonafinitecountablenumberofpossibleProbabilitySpecifiestheProbabilitySpecifiestheprobabilitiesofallpossibleoutcomesforarandomvariable.Continuousdistribution:thedistributionofthecontinuousrandomvariable.Continuousrandomvariable:takesonaninfiniteuncountablenumberofpossibleProbabilitySpecifiestheprobabilityProbabilitySpecifiestheprobabilitythatthediscreterandomtakesonaspecificP(X=x)istheprobabilitythatarandomvariableXtakesonthevaluex.Specifiestheprobabilitythatthecontinuousrandomvariabletakesonavaluewithinarange.TheprobabilityoftakingonanspecificvalueisProbabilityGivesProbabilityGivestheprobabilitythatarandomvariableXislessthanorequaltoaparticularvaluex,P(X≤x).ForbothdiscreteandcontinuousrandomF(x)=P(X≤P(x1<X≤x2)=F(x2)-HasafiniteHasafinitenumberofpossibleoutcomes,allofwhichareequallylikely.P(x)=0.2,forX={1,2,3,4,5};???P(2)=F(3)=P(2≤X≤4)=P(2)+P(3)+P(4)=Randomvariableswithonlytwooutcomes,onerepresentssuccess(denotedas1),theotherrepresentsfailure(denotedasThenumberThenumberofsuccessesinnBernoullitrials,assumingTheprobabilityofsuccess(p)isconstantforallThetrailsareallExpectedvalueforbinomialrandomvariable=Varianceforbinomialrandomvariable=np(1-TheprobabilityofbinomialrandomP(x)=Cxpx(1-p)n-xTheprobabilityofbinomialrandomP(x)=Cxpx(1-p)n-x= px(1-p)n-xn(n-Whatistheprobabilityofdrawingexactlytwowhitemarblesfromabowlofwhiteandblackmarblesinsixtriesiftheprobabilityofselectingwhiteis0.4eachP(2)= (0.4)2(1-0.4)6-2=0.31(6-Binomialtreeforstockpricet=tt=t=Upfactor(u)>1;downfactor(d)=Binomialtreeforstockpricet=tt=t=Upfactor(u)>1;downfactor(d)=Probabilityofmove-up=p,probabilityofmove-downE.g.,P(uudS)= (1-(3-Importance:???DiscreteandcontinuousImportance:???DiscreteandcontinuousProbabilityfunctionandprobabilitydensityfunction;Discreteuniformdistributionandbinomialdistribution.Exam?？键c：binomialdistributionCentrallimitExplaincentrallimitCentrallimitExplaincentrallimitCalculateandinterpretconfidenceintervalforapopulationmean,givenanormaldistributionwithknownandunknownpopulationvariance,andunknownvarianceandalargesampleGivenapopulationdescribedbyanyprobabilitydistributionhavingmeanμandGivenapopulationdescribedbyanyprobabilitydistributionhavingmeanμandfinitevarianceσ2,thesamplingdistributionofthesample,fromsamplesofsizenfromthispopulation,willapproximatelynormalwithmeanμ(thepopulationandvarianceσ2/n(thepopulationvariancedividedbyn)whenthesamplesizenislarge.Thestandarddeviationofthedistributionofsamplestatistic(samplingdistribution).Standarderrorofsamplemean:thestandardThestandarddeviationofthedistributionofsamplestatistic(samplingdistribution).Standarderrorofsamplemean:thestandarddeviationthedistributionofsampleWhenthepopulationstandarddeviation(σ)isσXnWhenthepopulationstandarddeviation(σ)is= sXnThemeanP/Eforasampleof41firmsis19.0,andthestandarddeviationofthepopulationis6.6.WhatisthestandarderrorofthesampleThemeanP/Eforasampleof41firmsis19.0,andthestandarddeviationofthepopulationis6.6.Whatisthestandarderrorofthesampleσ==XInterpretation:forsamplesofsizen=41,theofthesamplemeanswouldhaveameanof19.0andstandarddeviationofConfidenceintervalConfidenceintervalforpopulationArangethatcontainthepopulationmeanwithagivenconfidencelevel(1-α).Thecentrallimittheoremcanbeusedtoconstructconfidenceintervalsforpopulationmeans:Confidenceintervalofpopulation=Pointestimateofpopulation±ReliabilityfactorxStandarderrorofsampleThemeanP/E(pointestimate)forasampleof41firmsis19.0,samplestandarddeviationis6.6.Thepopulationisnormallydistributed.Whatisthe95%confidenceintervalforthepopulationmean?S=S=ThemeanP/E(pointestimate)forasampleof41firmsis19.0,samplestandarddeviationis6.6.Thepopulationisnormallydistributed.Whatisthe95%confidenceintervalforthepopulationmean?S=S=6.6ThestandardXSo,the95%confidenceintervalforthepopulation=19+/-1.96x1.03;or17.0toIfσstandardizedusingLargeIfσstandardizedusingLargeIfσ*z-statisticistheoreticallyacceptablehere,butuseofthestatistic*z-statisticistheoreticallyacceptablehere,butuseofthestatisticismoreWhensamplingfromReliabilityNotNotConfidenceintervalofpopulationmeanwithsX–a2nConfidenceintervalConfidenceintervalofpopulationmeanwithsX–a2nConfidenceintervalofpopulationmeanwithsX–a2nDegreesoffreedom(df)=n-ThemeanP/E(pointestimate)forasampleof41firmsis19.0,samplestandarddeviationis6.6.Whatisthe90%confidenceintervalforthepopulationmean?SThemeanP/E(pointestimate)forasampleof41firmsis19.0,samplestandarddeviationis6.6.Whatisthe90%confidenceintervalforthepopulationmean?S=S=6.6ThestandardXThet-distributionreliabilityfactor=1.684(df=40,So,the90%confidenceintervalforthepopulation=19+/-1.684x1.03;or17.27toFactorsonwidthofconfidenceWidthofFactorsonwidthofconfidenceWidthofconfidenceLargerconfidencelevel(1-LargersignificancelevelLargersamplesize(n,LargersamplestandardImportance:??CentrallimittheoremandImportance:??CentrallimittheoremandstandardConfidenceintervalforpopulationmeanandExam?？键c1：考概念題，centrallimittheorem的條件、結論常考點2：考計算題，standarderror的計算，構建總體均置信區(qū)間HypothesisTestingDescribeandinterpretHypothesisTestingDescribeandinterpretthechoiceofthenullandalternativehypotheses;Distinguishbetweenone-tailedandtwo-tailedExplainteststatistic,significancelevel,p-value,TypeIandTypeIIerrors.Addressesthequestionssuchas“whatisthisparameter’sHypothesisHypothesis:astatementaboutoneormoreAddressesthequestionssuchas“isthevalueoftheparameterequaltoaspecificvalue”.HypothesisStepHypothesisStep1:statingthehypotheses:relationtobeStep2:identifyingtheappropriateteststatisticanditsprobabilitydistribution;Step3:specifyingthesignificanceStep4:statingthedecisionStep5:collectingthedataandcalculatingthetestStep6:makingthestatisticalStep7:makingtheeconomicorinvestmentHypothesisHypothesisNullhypothesisHypothesistobeE.g.,averagemonthlyreturnforstockAisequaltoThe“=“signwillbeonlyshowedinnullHypothesisHypothesisAlternativehypothesisTheoppositesideofnullE.g.,averagemonthlyreturnforstockAisnotequaltoHypothesisthatanalystwantstoapproveorAcceptedwhenthenullhypothesisisHypothesisAquantitycalculatedbasedonHypothesisAquantitycalculatedbasedonaTest=Samplestatistic-ValueofthepopulationparameterunderStandarderrorofthesampleAvaluewithwhichthecomputedteststatisticiscomparedtodecidewhethertorejectornotrejectthenullHypothesisSignificancelevelThelevelHypothesisSignificancelevelThelevelofsignificancereflectshowmuchsampleevidencewerequiretorejectthenull.p-Thesmallestlevelofsignificanceatwhichthenullhypothesiscanberejected.HypothesisHypothesisUsedtotestifapopulationparameterisdifferentfromaspecifiedvalue.H0:θ=θ0vs.Ha:θ≠One-tailedUsedtotestifaparameterisaboveorbelowaspecifiedH0:θ≤θ0vs.Ha:θ>H0:θ≥θ0vs.Ha:θ<HypothesisExample:HypothesisExample:two-tailedtestofpopulation0H0:μ=0versusHa:μHypothesisExample:HypothesisExample:one-tailedtestofpopulationH0:μ0versusHa:μ>HypothesisIfteststatisticHypothesisIfteststatisticisoutsidetherangeofcriticalvalue(teststatistic≥uppercriticalvalue,orteststatistic≤lowercriticalvalue),rejectthenullhypothesis;Ifthep-valueislessorequaltothelevelofsignificancerejectthenullHypothesisAnexampleHypothesisAnexampleofdecisionTwo-tailedhypothesistestwithp-value=HypothesisTypeIerror&HypothesisTypeIerror&TypeIITypeIerror:rejectingnullhypothesiswhenitisP(TypeIError)=SignificancelevelTypeIIerror:failingtorejectthenullhypothesiswhenitisP(TypeIIError)=Poweroftest:rejectingthenullhypothesiswhenitisPoweroftest=1-P(TypeIIError)=1-HypothesisTypeIerror&TypeIIerrorHypothesisTypeIerror&TypeIIerrorH0H0DonotrejectCorrectTypeIIerror(Probability=β)RejectH0(acceptTypeIerror(Probability=α)Correctdecision(Poweroftest:1-β)HypothesisStatisticalHypothesisStatisticalsignificancedoesnotnecessarilyimplyeconomicsignificance,dueto:???Importance:??Nullhypothesisvs.alternativeImportance:??Nullhypothesisvs.alternativeTeststatistic&criticalvalue,significancelevel&p-two-tailedtest&one-tailedtest,typeIerrorandtypeIIExam常考點1：nullhypothesis和alternativehypothesis的設定?？键c2：two-tailedtest和one-tailedtest的選擇?？键c3：是否拒絕原假設的decisionrulesHypothesisTestingIdentifytheappropriateHypothesisTestingIdentifytheappropriateteststatisticandinterpretresultsforahypothesistestconcerningthepopulationmeanandvariance.HypothesisTeststatisticforHypothesisTeststatisticforhypothesistestsofpopulationmeanKnownz=X-σn????z=z-=sampleμ0=hypothesizedvalueofthepopulationσ=populationstandardHypothesisHypothesistestconcerningasingleTeststatisticforhypothesistestsofpopulationmeanHypothesisHypothesistestconcerningasingleTeststatisticforhypothesistestsofpopulationmeanunknown =X-tn-Sn?=t-statisticwithn-1degreesoffreedom(nissample=sampleμ0=hypothesizedvalueofthepopulations=samplestandard???HypothesisTeststatisticforHypothesisTeststatisticforhypothesistestsofpopulationmeanunknownvarianceandlargesamplez=X-sn????z=z-=sampleμ0=hypothesizedvalueofthepopulations=samplestandardHypothesisTestthehypothesisthatHypothesisTestthehypothesisthatafund’smeanreturnisequalto1%permonthat5%significancelevel,thepopulationisnormaldistributed.Thedataprovided???Samplemean:Samplesize:Standarddeviationofpopulation:HypothesisStep1:HHypothesisStep1:H0:μ=0.01andHa:μ≠Step2:withknownpopulationvariance(standarddeviation),usetwo-tailedz-test;Step3:Thecriticalz-valuesfor5%significancelevel(95%confidenceinterval)are+/-1.96;Step4:decisionrule:ifthez-statisticisoutsidetherangecriticalvalues(-1.96to+1.96),rejectHypothesisStep5:calculatetheteststatistic;z-statistic=0.015-0.01=2.396StepHypothesisStep5:calculatetheteststatistic;z-statistic=0.015-0.01=2.396Step6:rejectH0(meanreturn=1%),becausethez-(2.396)isoutsidetherangeofcriticalvalues(-1.96RejectH0–0HypothesisResearcherbelievesafund’smeanreturns(μFund)exceedHypothesisResearcherbelievesafund’smeanreturns(μFund)exceed1%permonth.Samplesizeis36,samplemeanis1.5%,andsamplestandarddeviationis1.8%.Thepopulationisnormaldistributed.Testthenullhypothesisat5%significanceHypothesisStep1:H0:μ≤HypothesisStep1:H0:μ≤0.01andHa:μ>Step2:withunknownpopulationvarianceandlargesamplesize(36),useone-tailedz-test(righttail);Step3:Thecriticalz-valuefor5%significancelevelisStep4:decisionrule:ifthez-statisticisabovethecriticalvalues(1.65),rejectH0;z=0.015-0.01Step5:calculatethetestStep6:rejectthenullHypothesisNullhypothesesHypothesisNullhypothesesandalternative???H0:H0:H0:=≥≤andHa:andHa:andHa:≠<>HypothesisTeststatisticforhypothesistestsofthedifferenceoftwoindependentpopulationmeanswithvarianceunknownbutassumed(n1-1)s2+(n2HypothesisTeststatisticforhypothesistestsofthedifferenceoftwoindependentpopulationmeanswithvarianceunknownbutassumed(n1-1)s2+(n2-(x1-x2)-(μ1-μ212twhere:sp=1n+n-2s12p+pdf=+-n1122HypothesisTeststatisticforhypothesistestsofthedifferenceoftwoindependentpopulationmeanswithvarianceunknownbutassumedunequal. 1+2(x1-x2HypothesisTeststatisticforhypothesistestsofthedifferenceoftwoindependentpopulationmeanswithvarianceunknownbutassumedunequal. 1+2(x1-x2)-(μ1-μ2twhere:df12122snsn12 + 2+nn12HypothesisAlsoreferredHypothesisAlsoreferredtoaspairedcomparisonNullhypothesesandalternative???H0:H0:H0:=μ0andHa:≥μ0andHa:≤μ0andHa:≠<>HypothesisTeststatisticforhypothesistestsoftheHypothesisTeststatisticforhypothesistestsofthemeandifferencesbetweentwodependentpopulationswithunknowntdwhere:n=thenumberofpairedd=samplemeansd=thestandarderrorofd;df=n-1.HypothesisHypothesisNullhypothesesandalternative???H0:σ=σ0andHa:σ≠H0:σ≥σ0andHa:σ<H0:σ≤σ0andHa:σ>HypothesisTeststatisticforhypothesistestsofHypothesisTeststatisticforhypothesistestsofavalueofapopulation(n-=(Chi-n-0where:n=sample=sample=thehypothesized0df=n-HypothesisNullhypothesesandalternativeHypothesisNullhypothesesandalternativeH0:σ1=σ2andHa:σ1≠TeststatisticforhypothesistestsofequalityofFwithdfof(n-1,n-122where:=thenumberoflargesample=thenumberofsmallsample=thelargesamplevariance=thesmallsamplevariancein12HypothesisHypothesisBasedonassumptionsaboutpopulationdistributionsandpopulationparameters.E.g.,t-test,z-test,F-HypothesisHypothesisNonparametricTestthingsotherthanparameterAppliedDatadonotmeetdistributionalDataaregiveninThehypothesisweareaddressingdoesnotconcernaImportance:?TeststatisticforpopulationImportance:?Teststatisticforpopulationmeanwithknownvarianceandunknownvariance(t),differenceofmeans(t),meandifferences(t),andpopulationvariance(χ2),equalityoftwovarianceExamExplainprinciplesoftechnicalanalysis,Explainprinciplesoftechnicalanalysis,itsapplications,anditsunderlyingassumptions;DescribecommonchartpatternsDescribetheusageofcycles,Elliottwavetheory,FibonacciAnalyzedusingpriceandPricesaredeterminedbysupplyandMarketreflectsthecollectiveknowledgeandsentimentofmanyvariedparticipantsandtheamountofbuyingandsellingactivityinaparticularThetradesdeterminevolumeandMarketpricereflectsbothrationalandirrationalbehaviorofmarketparticipants;TheEfficientMarketHypothesis(EMH)doesnotThesecuritiesarefreelytradedintheThetrendsandpatternstendtorepeatthemselveswhichmakesthepricepredictable.ItisbasedonactualtradeItcanbeusedforassetswithnocashflowstobediscountedforvaluation(e.g.,commodities,currencies).MaynotworkiniIIiquidMaynotworkinmarketssubjecttoMaynotworkforvaluingbankruptStockprice→0,butshortcoveringmaycreatepositivetechnicalpatterns.Studyingthepri