9300 ASSIGNMENT 1 MONASH UNIVERSITY.docx
- 文档编号:5775953
- 上传时间:2023-01-01
- 格式:DOCX
- 页数:9
- 大小:119.42KB
9300 ASSIGNMENT 1 MONASH UNIVERSITY.docx
《9300 ASSIGNMENT 1 MONASH UNIVERSITY.docx》由会员分享,可在线阅读,更多相关《9300 ASSIGNMENT 1 MONASH UNIVERSITY.docx(9页珍藏版)》请在冰豆网上搜索。
9300ASSIGNMENT1MONASHUNIVERSITY
LinearRegressionAnalysisAssignment
1.Introduction
1.1.DataSetting
Accordingtotherawsourceofthisassignment,theoriginaldatahavecollectedthedailydigitsofASX200index,twoindustry-portfolios(bankingandtelecom)andtheannualreturnrateof90-daysgovernmentbond(1yearconsistsof365days)from17October2001to31January2012.
Beforestartingthisanalysis,weassumethatthereturnrateofASX200indexand90-daysgovernmentbondcanrepresentforthereturnrateofmarketportfolio(Rmt)andriskfreeasset(Rft).Basedonthesetimeserialdata,weemploythecontinuouslycompoundedlogreturntocalculatethereturnrateofASX200indexandtwoindustry-portfolios.Forexample,thereturnrateofASX200indexis:
WhereRmtisthedailyreturnrateofASX200index,ASX200isthevalueofASX200indexatdayt,ASX200(-1)isthedigitASX200indexatdayt-1.WecangetthedailyreturnrateoftelecomportfolioandbankingportfoliobyrunningthesameprocessinEviews,respectivelyareR1tandR2t.
Becausetheriskfreereturnisannualreturnrateof90-daysgovernmentbond,toemployallfactorsofCAPMequationatsametimefrequency,wedividetheannualreturnrateof90-daysgovernmentbondby365days.
1.2.AnalysingEquationofCAPM
Afterthedatareprocession,weestablishtheequationofsimplelinearregressionanalysisfollowingtheCAPMtheory:
Rjtrepresentsthereturnrateofportfoliojatdayt(telecomj=1,bankingj=2),Rftistheriskfreerateatdayt,Rmtisthereturnofmarketportfolioatdayt,μjtistheerrortermofportfoliojatdayt,αjandβjarethecoefficientswhichwillbeestimated.
2.RegressionEquation
2.1.RegressionEquationofTelecomPortfolio
TheeconometricmodelofCAPMfortelecomportfolioispresentedasbelow:
EmpolyR1t-RftandRmt-Rftasthetwovariables(y1andx)toestimatetheequationinEviews,theresultisexpressedas:
Table1ResultofLinearRegressionofTelecomPortfolio
Ifweusea1andb1torepresenttheestimatedvalueofα1andβ1,thefittedregressionequationoftelecomportfoliois:
Itshouldbenoticedthatr-squareofthisequationis18.37%,whichmeans18.37%datacanbeexplainedbytheregressionanalysis.Since0 2.2.RegressionEquationofBankingPortfolio TheequationofCAPMforbankingportfoliois: ConsiderR2t-RftandRmt-Rftasthetwovariables(y2andx)intheequation,theresultoflinearregressionanalysisis: Table2ResultofLinearRegressionofBankingPortfolio Theresultpresentsthatifa2andb2aretheestimatedvaluesofα2andβ2,thefittedregressionlineofbankingportfoliowillbe: Comparedwiththefittedequationoftelecomportfolio,r-squareofbankingportfolioregressionis67.62%,whichmeansthisfittedequationcanexplainthedatamoreaccurately.Becauseb1>1,thebankingportfolioisanaggressiveportfoliowhichhasgreatervolatilitythanthemarketportfolio.Sincea2=0.00016,thebankingportfoliohasextrareturnbesidetheriskfreeasset,butitisalmost0. 3.HypothesisTestofFittedRegressionEquation 3.1.HypothesisTestofα1 Ifweassumethehypothesisaboutα1as: H0: α1=0Therearenoextrareturnsoverthereturnofriskfreeassetwhichcanbemadefromtelecomportfolio H1: α1≠0Thereareextrareturnsoverthereturnofriskfreeassetwhichcanbemadefromtelecomportfolio Then,setupthesignificantlevelat5%.Therearetwowaytoprocessthehypothesistest.Thetestingprocedureisasbelow: (1)P-valueTest P-valueisthepossibilitythatwegetthecurrentestimatewhenthenullhypothesisistrue,α1=0.AccordingtoTable1,thep-valueofα1is17.85%,whichisgreaterthansignificantlevel.Wefailtorejectthenullhypothesisunderthesignificantlevelis5%. (2)Two-tailedT-statisticTest Applythesamehypothesis,wecalculatethet-statisticvalueofα1employingtheformulaasbelow,whichalsocanbegainedfromTable1: BasedonthehypothesisH0: α1=0andH1: α1≠0,two-tailedtestwillbemoresuitableforthistestratherthenone-tailedtest.Then,thet-criticalvalueoftwo-tailedtest,|tcritical|=1.960878,whichcanbegainedunderthecondition: 5%significantlevel,2.5%oneachrejectionregion,2600observations,2degreeoffreedomand2variables.Itisobviousthat|tα1|<|tcritical|,wefailtorejectthenullhypothesiswith5%significantlevel. (3)Discussion Followingthetest,weconcludethatwhenp-value>significantlevelor|tstatistic|<|tcritical|,thenullhypothesiswillbefailedtoreject,H0canbeaccpeted(α1=0).Itindicatesthatthereturnoftelecomportfoliotendstoberelatedtotheriskpremiumofmarketportfoliosignificantly,α1haslesscontributiononinfluencingthedependentvariabley1.Inanotherword,peoplehavelesschancetoearninvestingreturnmorethanthereturnofriskfreeassetwhentheriskpremiumofmarketportfolioisequalto0. 3.2.HypothesisTestofα2 Thehypothesisaboutα2is: H0: α2=0Therearenoextrareturnsoverthereturnofriskfreeassetwhichcanbemadefrombankingportfolio H1: α2≠0Thereareextrareturnsoverthereturnofriskfreeassetwhichcanbemadefrombankingportfolio Then,thesignificantlevelremainsat5%. (1)P-valueTest Thep-valueofα2is99.19%(SeeTable2),whichisdistinctlygreaterthansignificantlevel.Itshouldacceptthenullhypothesiswhenthesignificantlevelis5%. (2)Two-tailedT-statisticTest Applythesamehypothesis,wecalculatethet-statisticvalueofα2employingtheformulaasbelow,whichisalsoexpressedinTable2: Comparedwitht-criticalvalueoftwo-tailedtestunderthesamecondition,|tcritical|=1.960878.Because|tα2|<|tcritical|,wefailtorejectthenullhypothesis. (3)DiscussionandSummary Accordingtothetestabove,itissameasthehypothesistestofα1,thenullhypothesisofα2isfailedtoreject.Thereturnofbankingportfoliorelativelydependsontheriskpremiumofmarketportfolioratherthantheextrareturnoverthereturnofriskfreeasset.Therearenoextrareturnovertheriskfreeassetcanbemadefromthebankingportfolio. Insummary,whenthep-valueofαj(telecomj=1,bankingj=2)isgreaterthanthesignificantlevelorthet-statisticvalueofαjislessthanthet-criticalvalueundertheconditionabove,thehypothesesofαjisfailedtoreject.Butitshouldbeawarethatα1=-0.0294,andα2=0.00016whicharecloseto0,especiallyforα1.Itimpliesthatthecorrespondingportfolioshaveextremelytinyextrareturnovertheriskfreeasset,whichcansupporttherejectionsofnullhypothesesinanotherway. 3.3.HypothesisTestofβ1,β1≠1 Thehypothesisaboutβ1is: H0: β1=1Thetelecomportfolioisatrackingportfoliowhichtracksthemarketportfolioexactly H1: β1≠1Thetelecomportfolioisnotatrackingportfoliowhichtracksthemarketportfolioexactly (1)Two-tailedT-statisticTest Thet-statisticvalueofβ1isexhibitedasbelowwhenthenullhypothesisisβ1=1: Undertheconditionthat5%significantlevel,2.5%oneachrejectionregion,2600observationsand2degreeoffreedomand2variables,|tcritical|isequalto1.960878,|tβ1|>|tcritical|,werejectthenullhypothesis. (2)Discussion When|tstatistic|>|tcritical|,thenullhypothesiswillberejected.Inthistwo-tailedtest,thenullhypothesisisβ1=1.Ifwerejectthat,itmeansthatthetelecomportfolioisnottrackingportfoliowhichtracksthemarketportfolioexactly. 3.4.HypothesisTestofβ2,β2≠1 (1)Two-tailedT-statisticTest Thehypothesisaboutβ2is: H0: β2=1Thebankingportfolioisatrackingportfoliowhichtracksthemarketportfolioexactly H1: β2≠1Thebankingportfolioisnotatrackingportfoliowhichtracksthemarketportfolioexactly Thet-statisticvalueofβ2isasbelow: Becasuetcriticalisequalto1.960878,|tβ2|>|tcritical|,werejectthenullhypothesisunderthespecificcondition. (2)Discussion Wefailtorejectthenullhypothesis,thebankingportfolioisnottrackingportfoliowhichtracksthemarketportfolioexactly.Butthereisanotherissueweshouldmention,thesetwo-tailedtestsaboutβ1andβ2onlyconcludethatβ1≠1andβ2≠1underaspecificconditionaswehaveexpressedbefore,whiletheotherhypothesesaboutβ1andβ2havenotbeentested,suchasβ1>1,0<β1<1,β1=0,-1<β1<0orβ1=-1. 3.5.HypothesisTestofβ2,β2>1 Thehypothesisaboutβ2is: H0: β2=1Thetelecomportfolioisatrackingportfoliowhichtracksthemarketportfolioexactly H1: β2>1Thetelecomportfolioisanaggressiveportfoliowhichhasgreatervolatilitythanthemarketportfolio (1)One-tailedT-statisticTest Accordingtothehypothesis,thetestingmethodpreferstotheone-tailedtestratherthanthetwo-tailedtest.Recalltheconditionoft-statistictest,thesignificantlevelis5%,insteadof2.5%oneachrejectionregionoftwo-tailedtest,one-tailedtestsets5%ononerejectionregion. Aswehavecalculatedthatthet-statisticvalueofβ2is4.515676.Whilethet-criticalvalueofone-tailedtesthaschangedto1.64544.Itissignificantthat|tβ2|>|tcritical|,whichmeansthatwecanrejectofthenullhypothesisaboutβ2. (2)DiscussionandSummary Sincewehaverejectedthenullhypothesisofβ2,β2>1isacceptable.InthecontextofCAPM,thebankingportfolioismorelikeanaggressiv
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 9300 ASSIGNMENT MONASH UNIVERSITY
![提示](https://static.bdocx.com/images/bang_tan.gif)