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
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