投资学第10版习题答案06Word文档下载推荐.docx
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投资学第10版习题答案06Word文档下载推荐.docx
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d.Foragivenexpectedcashflow,portfoliosthatcommandgreaterriskpremiumsmustsellatlowerprices.Theextradiscountfromexpectedvalueisapenaltyforrisk.
5.WhenwespecifyutilitybyU=E(r)–0.5Aσ2,theutilitylevelforT-billsis:
0.07
Theutilitylevelfortheriskyportfoliois:
U=0.12–0.5×
A×
(0.18)2=0.12–0.0162×
A
Inorderfortheriskyportfoliotobepreferredtobills,thefollowingmusthold:
0.12–0.0162A>
0.07⇒A<
0.05/0.0162=3.09
Amustbelessthan3.09fortheriskyportfoliotobepreferredtobills.
6.PointsonthecurvearederivedbysolvingforE(r)inthefollowingequation:
U=0.05=E(r)–0.5Aσ2=E(r)–1.5σ2
ThevaluesofE(r),giventhevaluesofσ2,aretherefore:
σ
σ2
E(r)
0.00
0.0000
0.05000
0.05
0.0025
0.05375
0.10
0.0100
0.06500
0.15
0.0225
0.08375
0.20
0.0400
0.11000
0.25
0.0625
0.14375
Theboldlineinthegraphonthenextpage(labeledQ6,forQuestion6)depictstheindifferencecurve.
7.RepeatingtheanalysisinProblem6,utilityisnow:
U=E(r)–0.5Aσ2=E(r)–2.0σ2=0.05
Theequal-utilitycombinationsofexpectedreturnandstandarddeviationarepresentedinthetablebelow.Theindifferencecurveistheupwardslopinglineinthegraphonthenextpage,labeledQ7(forQuestion7).
0.0500
0.0550
0.0700
0.0950
0.1300
0.1750
TheindifferencecurveinProblem7differsfromthatinProblem6inslope.WhenAincreasesfrom3to4,theincreasedriskaversionresultsinagreaterslopefortheindifferencecurvesincemoreexpectedreturnisneededinordertocompensateforadditionalσ.
8.Thecoefficientofriskaversionforariskneutralinvestoriszero.Therefore,thecorrespondingutilityisequaltotheportfolio’sexpectedreturn.Thecorrespondingindifferencecurveintheexpectedreturn-standarddeviationplaneisahorizontalline,labeledQ8inthegraphabove(seeProblem6).
9.Arisklover,ratherthanpenalizingportfolioutilitytoaccountforrisk,derivesgreaterutilityasvarianceincreases.Thisamountstoanegativecoefficientofriskaversion.Thecorrespondingindifferencecurveisdownwardslopinginthegraphabove(seeProblem6),andislabeledQ9.
10.Theportfolioexpectedreturnandvariancearecomputedasfollows:
(1)
WBills
(2)
rBills
(3)
WIndex
(4)
rIndex
rPortfolio
(1)×
(2)+(3)×
σPortfolio
(3)×
20%
σ2Portfolio
0.0
5%
1.0
13.0%
13.0%=0.130
20%=0.20
0.2
5
0.8
13.0
11.4%=0.114
16%=0.16
0.0256
0.4
0.6
9.8%=0.098
12%=0.12
0.0144
8.2%=0.082
8%=0.08
0.0064
6.6%=0.066
4%=0.04
0.0016
5.0%=0.050
0%=0.00
11.ComputingutilityfromU=E(r)–0.5×
Aσ2=E(r)–σ2,wearriveatthevaluesinthecolumnlabeledU(A=2)inthefollowingtable:
σ2Portfolio
U(A=2)
U(A=3)
0.130
0.0900
.0700
0.114
0.16
0.0884
.0756
0.098
0.12
0.0836
.0764
0.082
0.08
0.0756
.0724
0.066
0.04
0.0644
.0636
0.050
.0500
ThecolumnlabeledU(A=2)impliesthatinvestorswithA=2preferaportfoliothatisinvested100%inthemarketindextoanyoftheotherportfoliosinthetable.
12.ThecolumnlabeledU(A=3)inthetableaboveiscomputedfrom:
U=E(r)–0.5Aσ2=E(r)–1.5σ2
Themoreriskaverseinvestorsprefertheportfoliothatisinvested40%inthemarket,ratherthanthe100%marketweightpreferredbyinvestorswithA=2.
13.Expectedreturn=(0.7×
18%)+(0.3×
8%)=15%
Standarddeviation=0.7×
28%=19.6%
14.
Investmentproportions:
30.0%inT-bills
0.7×
25%=
17.5%inStockA
32%=
22.4%inStockB
43%=
30.1%inStockC
15.Yourreward-to-volatilityratio:
Client'
sreward-to-volatilityratio:
16.
17.a.E(rC)=rf+y×
[E(rP)–rf]=8+y×
(18-8)
Iftheexpectedreturnfortheportfoliois16%,then:
16%=8%+10%×
y⇒
Therefore,inordertohaveaportfoliowithexpectedrateofreturnequalto16%,theclientmustinvest80%oftotalfundsintheriskyportfolioand20%inT-bills.
b.
Client’sinvestmentproportions:
20.0%inT-bills
0.8×
20.0%inStockA
25.6%inStockB
34.4%inStockC
c.σC=0.8×
σP=0.8×
28%=22.4%
18.a.σC=y×
28%
Ifyourclientprefersastandarddeviationofatmost18%,then:
y=18/28=0.6429=64.29%investedintheriskyportfolio.
b.
19.a.y*
Therefore,theclient’soptimalproportionsare:
36.44%investedintheriskyportfolioand63.56%investedinT-bills.
b.E(rC)=0.08+0.10×
y*=0.08+(0.3644×
0.1)=0.1164or11.644%
σC=0.3644×
28=10.203%
20.a.Iftheperiod1926–2012isassumedtoberepresentativeoffutureexpectedperformance,thenweusethefollowingdatatocomputethefractionallocatedtoequity:
A=4,E(rM)−rf=8.10%,σM=20.48%(weusethestandarddeviationoftheriskpremiumfromTable6.7).Theny*isgivenby:
Thatis,48.28%oftheportfolioshouldbeallocatedtoequityand51.72%shouldbeallocatedtoT-bills.
b.Iftheperiod1968–1988isassumedtoberepresentativeoffutureexpectedperformance,thenweusethefollowingdatatocomputethefractionallocatedtoequity:
A=4,E(rM)−rf=3.44%,σM=16.71%andy*isgivenby:
Therefore,30.80%ofthecompleteportfolioshouldbeallocatedtoequityand69.20%shouldbeallocatedtoT-bills.
c.Inpart(b),themarketriskpremiumisexpectedtobelowerthaninpart(a)andmarketriskishigher.Therefore,thereward-to-volatilityratioisexpectedtobelowerinpart(b),whichexplainsthegreaterproportioninvestedinT-bills.
21.a.E(rC)=8%=5%+y×
(11%–5%)⇒
b.σC=y×
σP=0.50×
15%=7.5%
c.Thefirstclientismoreriskaverse,preferringinvestmentsthathavelessriskasevidencedbythelowerstandarddeviation.
22.Johnsonrequeststheportfoliostandarddeviationtoequalonehalfthemarketportfoliostandarddeviation.Themarketportfolio
whichimplies
.TheinterceptoftheCMLequals
andtheslopeoftheCMLequalstheSharperatioforthemarketportfolio(35%).ThereforeusingtheCML:
23.Data:
rf=5%,E(rM)=13%,σM=25%,and
=9%
TheCMLandindifferencecurvesareasfollows:
24.Forytobelessthan1.0(thattheinvestorisalender),riskaversion(A)mustbelargeenoughsuchthat:
⇒
Forytobegreaterthan1(theinvestorisaborrower),Amustbesmallenough:
Forvaluesofriskaversionwithinthisrange,theclientwillneitherborrownorlendbutwillholdaportfoliocomposedonlyoftheoptimalriskyportfolio:
y=1for0.64≤A≤1.28
25.a.ThegraphforProblem23hastoberedrawnhere,with:
E(rP)=11%andσP=15%
b.Foralendingposition:
Foraborrowingposition:
Therefore,y=1for0.89≤A≤2.67
26.Themaximumfeasiblefee,denotedf,dependsonthereward-to-variabilityratio.
Fory<
1,thelendingrate,5%,isviewedastherelevantrisk-freerate,andwesolveforfasfollows:
Fory>
1,theborrowingrate,9%,istherelevantrisk-freerate.Thenwenoticethat,evenwithoutafee,theactivefundisinferiortothepassivefundbecause:
.11–.09–f
=0.13<
.13–.09
=0.16→f=–.004
.15
.25
Morerisktolerantinvestors(whoaremoreinclinedtoborrow)willnotbeclientsofthefund.Wefindthatfisnegative:
thatis,youwoul
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