投资学10版习题答案13Word文档格式.docx
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投资学10版习题答案13Word文档格式.docx
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Observations
12
Alpha
9.00
-0.63
-0.64
-5.05
0.73
-4.53
5.94
-2.41
5.92
Beta
-0.47
0.42
1.38
0.90
1.78
0.66
1.91
2.08
t-Alpha
-0.04
-0.06
-0.41
0.05
-0.45
0.33
-0.27
0.64
t-Beta
-0.81
0.78
2.42
1.42
3.83
4.51
4.81
4.Thehypothesesforthesecond-passregressionfortheSMLare:
∙Theinterceptiszero.
∙Theslopeisequaltotheaveragereturnontheindexportfolio.
5.Thesecond-passdatafromfirst-pass(SCL)estimatesare:
AverageExcessReturn
5.18
4.19
2.75
6.15
8.05
9.90
11.32
13.11
22.83
M
8.12
S
Thesecond-passregressionyields:
RegressionStatistics
MultipleR
0.7074
0.5004
AdjustedR-square
0.4291
Standarderror
4.6234
9
Coefficients
StandardError
tStatisticforβ=0
tStatisticforβ=8.12
Intercept
3.92
2.54
1.54
Slope
5.21
1.97
2.65
-1.48
6.Aswesawinthechapter,theinterceptistoohigh(3.92%peryearinsteadof0)andtheslopeistooflat(5.21%insteadofapredictedvalueequaltothesample-averageriskpremium:
rMrf=8.12%).Theinterceptisnotsignificantlygreaterthanzero(thet-statisticislessthan2)andtheslopeisnotsignificantlydifferentfromitstheoreticalvalue(thet-statisticforthishypothesisis1.48).Thislackofstatisticalsignificanceisprobablyduetothesmallsizeofthesample.
7.ArrangingthesecuritiesinthreeportfoliosbasedonbetasfromtheSCLestimates,thefirstpassinputdataare:
Year
ABC
DEG
FHI
1
15.05
25.86
56.69
2
-16.76
-29.74
-50.85
3
19.67
-5.68
8.98
4
-15.83
-2.58
35.41
5
47.18
37.70
-3.25
6
-2.26
53.86
75.44
7
-18.67
15.32
12.50
8
-6.35
36.33
32.12
7.85
14.08
50.42
10
21.41
12.66
52.14
11
-2.53
-50.71
-66.12
-0.30
-4.99
-20.10
Average
4.04
8.51
15.28
Std.Dev.
19.30
29.47
43.96
Thefirst-pass(SCL)estimatesare:
0.04
0.48
0.82
Alpha
2.58
0.54
-0.34
0.18
0.98
1.92
0.08
0.62
3.02
6.83
GroupingintoportfolioshasimprovedtheSCLestimatesasisevidentfromthehigherR-squareforPortfolioDEGandPortfolioFHI.Thismeansthatthebeta(slope)ismeasuredwithgreaterprecision,reducingtheerror-in-measurementproblemattheexpenseofleavingfewerobservationsforthesecondpass.
Theinputsforthesecondpassregressionare:
DEH
FGI
Thesecond-passestimatesare:
0.9975
0.9949
0.9899
0.5693
tStatisticforβ=0
tStatisticforβ=8.12
2.62
0.58
4.55
6.47
0.46
14.03
-3.58
Despitethedecreaseintheinterceptandtheincreaseinslope,theinterceptisnowsignificantlypositive,andtheslopeissignificantlylessthanthehypothesizedvaluebymorethanthreetimesthestandarderror.
8.Roll’scritiquesuggeststhattheproblembeginswiththemarketindex,whichisnotthetheoreticalportfolioagainstwhichthesecondpassregressionshouldhold.RememberthatRollsuggeststhetruemarketportfoliocontainseveryassetavailabletoinvestors,includingrealestate,commodities,artifacts,andcollectibleitemssuchasHollywoodmemorabilia,whichthisindexobviouslydoesnothave.Hence,eveniftherelationshipisvalidwithrespecttothetrue(unknown)index,wemaynotfindit.Asaresult,thesecondpassrelationshipmaybemeaningless.
9.
ExceptforStockI,whichrealizedanextremelypositivesurprise,theCMLshowsthattheindexdominatesallothersecurities,andthethreeportfoliosdominateallindividualstocks.Thepowerofdiversificationisevidentdespitetheverysmallsamplesize.
10.Thefirst-pass(SCL)regressionresultsaresummarizedbelow:
0.07
0.36
0.11
0.44
0.24
0.84
0.12
0.68
0.71
9.19
-1.89
-1.00
-4.48
-3.47
5.32
-2.64
5.66
BetaM
0.41
1.39
0.89
1.79
0.65
BetaF
-0.35
2.33
-1.05
1.03
-1.95
1.15
0.43
t-intercept
-0.13
-0.08
-0.37
0.01
-0.52
0.29
-0.28
t-BetaM
-0.77
0.87
0.75
2.46
1.40
5.80
4.35
4.65
t-BetaF
2.06
-1.08
0.94
-3.69
0.77
0.57
0.63
11.Thehypothesesforthesecond-passregressionforthetwo-factorSMLare:
∙Themarket-indexslopecoefficientequalsthemarket-indexaveragereturn.
∙Thefactorslopecoefficientequalstheaveragereturnonthefactor.
(Notethatthefirsttwohypothesesarethesameasthoseforthesinglefactormodel.)
12.Theinputsforthesecondpassregressionare:
ExcessReturn
0.60
0.7234
0.5233
0.3644
4.8786
tStatisticforβ=0.6
3.35
2.88
1.16
5.53
2.16
2.56
-1.20
0.80
0.56
0.14
Theseresultsareslightlybetterthanthoseforthesinglefactortest;
thatis,theinterceptissmallerandtheslopeofMisslightlygreater.Wecannotexpectagreatimprovementsincethefactorweaddeddoesnotappeartocarryalargeriskpremium(averageexcessreturnislessthan1%),anditseffectonmeanreturnsisthereforesmall.Thedatadonotrejectthesecondfactorbecausetheslopeisclosetotheaverageexcessreturnandthedifferenceislessthanonestandarderror.However,withthissamplesize,thepowerofthistestisextremelylow.
13.Whenweusetheactualfactor,weimplicitlyassumethatinvestorscanperfectlyreplicateit,thatis,theycaninvestinaportfoliothatisperfectlycorrelatedwiththefactor.Whenthisisnotpossible,onecannotexpecttheCAPMequation(thesecondpassregression)tohold.Investorscanuseareplicatingportfolio(aproxyforthefactor)thatmaximizesthecorrelationwiththefactor.TheCAPMequationisthenexpectedtoholdwithrespecttotheproxy
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