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Midterm

FNCE30001 Midterm: 7Exam


Department
Finance
Course Code
FNCE30001
Professor
Brown
Study Guide
Midterm

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MIDSEMESTEREXAMINATIONSEMESTER1,2011
SUBJECTNUMBER:  FNCE30001
SUBJECTNAME:  INVESTMENTS
InQuestions1and2,you’veestimatedthefollowingoutcomes:
ProbabilityReturnonStockABD ReturnonMarketIndex
State150%6% 4%
State250%14% 10%
Theriskfreerateiscurrently5%.
1. Whatisbeta?
a) 3/4
b) 4/3
c) 5/3
d) 7/3
e) Noneoftheabove
(b)
Solveforcov(ABD,M)=.0012.Solveforvar(M)=.0009
Beta=12/9=4/3
**Wecouldhavesolvedforthisbytakingtheslopeofthecharacteristicline,asina
regression.Thetwopointswewouldplotwouldbe(1,1)and(5,9),implyingtheslopewould
be(91)/(5(1))=8/6=4/3
*Notethatwearenotinequilibrium,soitisnotthecasethat105=Beta(7‐5)
2. Isthereanarbitrageopportunity?
a) No:Arbitrageisonlypossiblewithwelldiversifiedportfolios.
b) No:JustbecausetheexpectedreturnofABDisgreaterthantheexpectedreturnon
themarketindex,thatdoesn’tmeanthere’sanarbitrage.
c) Maybe:Dependsonwhattheriskfreerateis.
d) Maybe:Dependsontheinvestor’sriskaversion.
e) Yes.
(e)Thereisanopportunity.ThereturnonABDishigherthanthemarketreturninbothstates,
meaningifyouwentlonginABDandshortinthemarket,you’dalwaysgenerateapositive
return.

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FNCE30001InvestmentsMidtermExaminationSemester1,2011
2
3. WhichofthefollowingisNOTanassumptionoftheAPT?
a) Thereareasufficientnumberofsecuritiestoformwelldiversifiedportfolios.
b) Allinvestorsarerationalmeanvarianceoptimizers.
c) Therearenopersistentarbitrageopportunities.
d) Returnscanbedescribedbyafactorstructure.
e) AlloftheaboveareassumptionsoftheAPT.
(b)isanassumptionoftheCAPM,notAPT.
4. Giventhefollowinginformation:
ExpectedReturn StandardDeviation
DDD10% 30%
EEE6% 20%
RiskFree3% ‐‐
ThecorrelationbetweenDDDandEEEis0.4,andtheinvestor’sriskaversionparameter
Ais4.Roundingtothenearestwholenumber,whatistheapproximateweightonEEEin
heroptimalriskyportfolio?
a) 19%
b) 33%
c) 37%
d) 81%
e) Noneoftheabove
(b)
Numerator:(.10.03)*(.20)^2(.06.03)*(.4*.3*.2)=0.00208
Denominator:(0.1‐0.03)*(0.2)^2+(0.060.03)*0.3^2‐(0.060.03+0.10.03)*(0.4*0.3*0.2)=
0.0031
WeightonDDD=.67→WeightonEEE=1.67=.33
5. ConsiderthesinglefactorAPT.PortfolioAhasabetaof1.2andanexpectedreturnof
10%.PortfolioBhasabetaof0.8andanexpectedreturnof8%.Theriskfreerateof
returnis4%.
Whatisthearbitragestrategy?
a) Borrowattheriskfreerate,shortB,andtakealongpositioninA
b) Lendattheriskfreerate,shortB,andtakealongpositioninA
c) Borrowattheriskfreerate,shortA,andtakealongpositioninB
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