CFA考试二级最详细笔记.docx
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CFA考试二级最详细笔记.docx
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CFA考试二级最详细笔记
统计学
Reading11相关和回归Reading12多元线性回归
1.相关分析:
1)协方差和相关系数的计算;
2)相关系数的检验(ρ=0):
t=r((n-2)/(1–r2))1/2,df=n–2.
2.线性回归:
1)模型及假设,dependentvariable(Y)andindependentvariable(X).
2)参数估计(minSSE):
bi=Cov(Xi,Y)/Var(Xi),b0=E(Y)–Σbi*E(Xi).
3)回归系数的置信区间和统计检验:
t=(bi–βi)/sbi,df=n–k–1.
注:
k为independentvariable的数目,不要求计算标准误sbi.
3.线性模型的显著性检验:
1)Totalsumofsquares(SST)=Σ(Y–E(Y))2,Y–观测值;
Regressionsumofsquare(RSS)=Σ(y–E(Y))2,y–拟合值;
Sumofsquarederror(SSE)=Σ(Y-y)2;
SST=RSS+SSE.
2)方差分析表(ANOVA):
Sourceofvariation
Sumofsquares
Degreeoffreedom
Meansumofsquare
Regression
RSS
k(#independentvariable)
MSR=RSS/k
Error
SSE
n–k–1
MSE=SSE/(n–k-1)
Total
SST
n–1
Var(Y)=SST/(n-1)
StandarderrorofestimateSEE=(MSE)1/2.
3)DeterminationcoefficientR2=RSS/SST,
AdjustedR2=1–(n-1)/(n–k-1)*(1–R2):
adjusttheimpactofadditionalvariables.
4)F-检验:
F=MSR/MSE,df=(k,n–k-1).
4.模型前提假设的检验:
1)Heteroskedasticity:
A)Effect:
Unconditional:
heteroskedasticityisunrelatedtothelevelofX,nomajorproblem;
Conditional:
coefficientestimatesarenotaffected,buts.e.andF-testareunreliable.
B)Detecting:
a)Residualplot:
residual=actual–predicted.
b)Breusch-pagantest(H0:
noheteroskedasticity):
n*Rresid2~χ2(k),其中Rresid2是residual对X回归的决定系数.
C)Correcting:
usingrobustorcorrecteds.e.
2)Serialcorrelation:
residualtermsarecorrelatedwitheachother:
A)Effect:
Positiveserialcorrelation:
underestimatings.e.,unreliableF-test;
Negativeserialcorrelation:
overestimatings.e.,unreliableF-test.
B)Detecting:
a)Residualplot.
b)Durbin-Watsontest(H0:
noserialcorrelation):
DW≈2(1-r),其中r是残差的自相关系数,0≤DW≤4.
C)Correcting:
correcteds.e.forbothserialcorrelationandheteroskedasticity.
3)Multicollinearity:
independentvariablesarehighlycorrelatedwitheachother:
A)Effect:
individualvariablesarenotsignificant(larges.e.)buttheircombinationis.
B)Detecting:
a)Noneofindividualcoefficientissignificant,butF-testis.
b)Correlationsbetweenvariables(>0.7).
注:
两变量间的相关系数并未考虑变量线性组合的相关性,因此低相关系数并不一定意味着不存在multicollinearity.
C)Correcting:
omitcorrelatedvariablesortakestepwiseregression.
4)Modelmisspecification:
不合适地选取解释变量(实际意义不对或不满足线性模型的前提假设)或不恰当的变量转换等.
5.Dummyvariable(0–1variable):
1)Independentdummyvariable:
linearregressionisappropriate.
注:
nclasses→(n-1)dummyvariable.
2)Qualitativedependentvariable(Y取0,1):
ordinaryregressionmaynotbeappropriate,uselogitregressionmodelordiscriminatemodel.
Reading13时间序列分析
1.Trendmodel:
1)Linear:
xt=b0+b1t+εt;
2)Log-linear:
ln(xt)=b0+b1t+εt,常用于为增长率建模.
2.Autoregressivemodel(AR):
1)AR(p):
xt=b0+b1xt-1+…+bpxt-p+εp,lag:
1,…,p.
2)Covariancestationarity:
a)ConstantandfiniteE(Xt):
mean-revertinglevelforAR
(1)E(Xt)=b0/(1–b1).
Randomwalks(unitrootprocess):
xt=b0+xt-1+εt不是平稳过程.
b)ConstantandfiniteVar(Xt);
c)ConstantandfiniteCov(Xt,Xt-k):
对AR平稳序列,自相关系数Cor(Xt,Xt-k)=ρk→0.
3)Forecasting:
a)In-sample(withintherangeofdata)andout-sampleforecasts.
b)Shorttimeseries:
morestable(nodramaticchange);
Long-timeseries:
morereliable.
c)Predictingpower:
rootmeansquarederror(RMSE)ontheout-sampledata.
3.AR模型的检验与修正:
1)Nonstationarity:
a)Detecting:
Dickey-Fuller(DF)testorunitroottest:
ForAR
(1):
xt–xt-1=b0+(b1-1)xt-1+εt,H0:
b1=1,t-testwithmodifieds.e.
b)Correcting-differencing:
Forrandomwalks:
令yt=xt–xt-1,有yt=b0+εt.
2)Serialcorrelation(residualtermsshouldnotexhibitserialcorrelation):
a)Detecting:
H0:
Cor(εt,εt-k)=0foranylagk;t=Cor(εt,εt-k)/(1/T)1/2,df=T–p-1.
注:
T–numberofeffectiveobservations,T=n–p.
一般线性回归中的DW检验不适用于AR模型。
b)Correcting:
increasetheorderpuntilallserialcorrelationsareremoved.
3)Seasonality:
a)Detecting:
seasonallagk:
Cor(εt,εt-(k-1))=0,butCor(εt,εt-k)≠0(同上述t检验).
b)Correcting:
includeaseasonallagterm:
xt=AR(p)+bkxt-k.
4)Conditionalheteroskedasticity:
a)Autoregressiveconditionalheteroskedasticitymodel(ARCH):
εt2=a0+a1*εt-12+ηt
b)Detecting:
H0:
a1=0.
4.Multivariatetimeseriesmodel(Yt~Xt):
1)Premiseforregressionmodel:
a)YtandXtarebothstationary;
b)YtandXtarebothnon-stationarybutcointegrated.
2)Cointegrationtest:
yt=b0+b1xt+εt,εtistestedforaunitrootusingDFtest.
经济学
Reading14经济增长Reading20经济衡量
1.Measuringeconomicactivity:
1)Measuresofeconomicactivity:
GNI(国民总收入)=GDP+netpropertyincomefromabroad;
NNI(国民净收入)=GNI–depreciation.
2)GDPatcurrentprice=GDPatconstantprice*(1+GDPdeflator).
注:
GDP平减指数既包含物价变动,也包含GDP组分的变动
2.Measuringeconomicgrowth:
1)GrowthrateinrealGDP;
2)Ruleof70:
ApproximateyearsforrealGDPtodouble=70/growthrate(percentage).
3.Sourcesofeconomicgrowth:
1)Preconditions:
incentivesystem–markets,propertyrightsandmonetaryexchange.
2)Keyfactorsdrivingeconomicgrowth:
a)Labor:
investmentinhumancapital;
b)Capital:
savingandinvestmentinnewcapital;
c)Entrepreneurialability:
discoveryofnewtechnologies.
3)Productivitycurve:
laborproductivity(realGDPperlaborhour)~capitalperlaborhour
a)Growthincapitalperlaborhour–movementalongcurve,lawofdiminishingreturns;
b)Growthintechnology–curveshiftupwards.
c)One-thirdrule:
Laborproductivitygrowthresultsfromcapitalgrowth=1/3*growthincapitalperlaborhour;
Laborproductivitygrowthresultsfromtechnologygrowth=laborproductivitygrowth-laborproductivitygrowthresultsfromcapitalgrowth.
4.Growththeory:
1)Classicalgrowththeory(constantsubsistencelevel):
laborproductivityrisesabovethesubsistencelevel→subsistencerealwagesriseabovetheminimumrequired→populationexplosion→laborproductivityisdrivenbacktothesubsistencelevel.
2)Neoclassicalgrowththeory(constanttargetrealrateofreturn=ΔrealGDPperlaborhour/Δcapitalperlaborhour):
laborproductivityrisesduetoluckytechnologychanges→increaseinrealrateofreturn→moreinvestmentandsavings,butlawofdiminishingreturnholds→realrateofreturnisdrivenbacktothetargetrate.
注:
Populationgrowthisindependentofeconomicgrowthintheneoclassicalmodel.Thetechnology(andproductivity)maystopgrowingwhentherealinterestrateisequaltothetargetrateofreturn.
3)Newgrowththeory(continuouseconomicgrowth):
innovation→higherreturn→competition→lowerreturn→incentiveforinnovation.
注:
Knowledgecapitalispublicgoodsanditisnotsubjecttothelawofdiminishingreturnduetotheincentiveforinnovation.
Reading15产业政策
1.Industryregulation:
1)Socialregulation:
forallindustries,suchasproductqualityandsafety.
2)Economicregulation:
pricingpolicyforthefirmswithinaindustry:
a)Cost-of-serviceregulation:
setthemaximumprice;
b)Rate-of-returnregulation:
setthemaximumrateofreturn.
2.Effectsofregulation:
1)Negativeeffects:
highercostsofproductresponsetoregulation;
Deregulationhasnegativeeffectsintheshortrun,butthelong-runbenefitsincludelowercostandbetterproducts.
2)Regulators’behavior:
a)Capturehypothesis:
regulatorswillbecapturedbytheindustrythatisregulated.
b)Share-the-gains,share-the-painstheory:
regulatorswillstrivetoallthreeinterestedpartiesincludinglegislators,customersandregulatedindustries.
Reading16世界贸易
1.Comparativeadvantage:
1)Concept:
thelowestopportunitycostofaproduct.FortwogoodsAandB,ifonecountryhascomparativeadvantageinA,theothermusthavecomparativeadvantageinB.
2)Lawofcomparativeadvantage:
totalproductionandconsumptionwillincreaseiftradepartnersexportgoodswithcomparativeadvantageandimportgoodswithoutadvantage.
2.Traderestrictions:
1)Reasonsfortraderestrictions:
a)Desirebygovernmentfortariffrevenue.
b)Domesticindustriestogainprotection(infantindustryargument,anti-dumpingargument).
c)Otherargumentsnotsupportedbyeconomictheoryinthelongrun:
protectjobsandhighwagelevels.
2)Tradebarriers:
a)Tariffs(关税):
benefitprotectedindustryandgovernment.
b)Quotas:
benefitprotectedindustryandimportlicenseholders.
c)Voluntaryexportrestraints(exportingcountriesvoluntarilylimitthequalityofgoodsforexporting):
benefitprotectedindustriesandexportlicenseholders.
3.Balance-of-payments(BOP)accounts(国际收支账户)(Reading17):
1)Accountingequation:
currentaccount+capitalaccount+officialreserveaccount=0.
2)Currentaccount=export–import:
exchangeofgoodsandservices.
3)Capitalaccount=investmentin–investmentout,includingequityanddebt;
Borrowing(capitalaccount>0)tofinanceacurrentaccountdeficit.
4)Officialreserveaccount:
Ifcurrentaccount+capitalaccount>0(收支盈余),officialreserveaccount<0(而外汇储备增加).
Reading18汇率
1.Exchangerate:
1)Quotation,currencyappreciationanddepreciation:
a)Directquotes:
DC/FC,orFC:
DC(注意后者不表示相比);
b)Indirectquotes:
FC/DC,orDC:
FC.
注:
一般汇率S均指直接标价,S↑外币升值(本币贬值)。
2)Bid-askspread:
a)Direct:
e.g.FC:
DC=0.6000/0.6015:
0.6000–bidprice(dealerbuy),0.6015–askprice(dealersell);
Percentspread=(ask–bid)/ask.
b)Indirect:
DC:
FC=(1/0.6015)/(1/0.6000),bidprice 3)Crossrates: crossratebetweenXandY: a
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