DONOTTURNOVERTHEPAGEUNTILINSTRUCTED UNIVERSITYOFCAPETOWN
SCHOOLOFMANAGEMENTSTUDIES
FINANCE2CLASSTEST
BUS3026W
APRIL2007
TotalMarks:120
Time:2hours
INSTRUCTIONS:
TODOSO
ANSWERALLQUESTIONS
ANSWEREACHSECTIONINADIFFERENTBOOK
NO QUESTIONS WILL BE ANSWERED DURING THE
EXAM. CLEARLY STATE ANY ASSUMPTIONS MADE
INANSWERINGEACHQUESTION.
Examiners:F.Toerien
R.Kruger
SECTIONA:MCQ
Marking:
[30MARKS]
3marksforacorrectanswer
markforanincorrectanswer
0marksfornoanswer
1) Whichofthefollowingstatementsrelatingtosecuritiestradingis/arecorrect?
i) Anadvantageofalimitorderisthatitisnotaffectedbytransactionscosts.
ii) Inshareissues,theunderwritersarecompensatedthoughunderwriterspreadsand
underwriterfees(theexplicitcoststotheissuingcompany).
iii) Inafirmcommitmentscenario,abusinessexistingshareholdersarethemain
loserswhenanewshareissueinthebusinessisoverpriced.
a)
b)
c)
d)
e)
i.
ii.
iii
iandii
iiandiii
2) Thestandarddeviationofaportfoliois
i) thesquarerootoftheweightedsumofcovariances,witheachweighttheproduct
oftheproportionsofthepairofassetsinthecovarianceterm.
ii) aweightedaverageoftherisksoftheconstituentsecurities,iftheyareperfectly
negativelycorrelated.
iii) always less than a simple weighted average of the risks of the constituent
securities.
iv) ameasureofthetotalriskoftheportfolio.
a)
b)
c)
d)
e)
iandiionly
iiandiiionly
i,iiandivonly
iandivonly
ii,iiiandivonly
3) Whichofthefollowingstatementsis/areincorrect?
i) ThePICmanagespublicsectorpensionfunds.
ii) Itisillegaltotradeinequitiesbasedonanyformofnonpublicinformation.
iii) During a closed period, the management of a company may not speak to
investmentanalysts.
a)
b)
c)
d)
e)
i.
ii
iii
iiandiii
All3statementsarecorrect
4) Aninvestmentwithapositiveriskpremiumwouldbeacceptablefor
a)
b)
c)
d)
e)
ariskaverseinvestorandarisklover.
ariskaverseinvestorandariskneutralinvestor.
ariskaverseinvestoronly.
ariskaverseinvestor,riskneutralinvestorandrisklover.
ariskneutralinvestorandarisklover.
5) Whichofthefollowingarenotclassifiedastightlyheldshares?
a)
b)
c)
d)
e)
Familyholdings.
Strategicholdings
Shareincentiveschemes.
PICholdings.
Parastatalholdings.
6) Theoptimalriskyportfoliois
i) thesameforanyinvestor,regardlessofriskaversion.
ii) theportfolioontheefficientportfolioopportunitysetthathasthehighestreward
tovariabilityratio.
iii) atangentpointtotheefficientportfolioopportunityset.
iv) determinedbyacapitalallocationdecision.
a)
b)
c)
d)
i,iiandiiionly
i,iiiandivonly
ii,iii,andivonly
iiandiiionly
e) i,ii,iiiandivonly
7) Whichofthefollowingstatementsis/arecorrect?
i) InTopDownanalysis,theEconomicAnalysishelpsthemanagerofabalanced
funddecideontheweightings ofthedifferentindustrysectors(financials,
industrialsetc.)inhis/herequityportfolio.
ii) Rand appreciation against the US$ is good for a South African retailer that
importsTaiwanesemadecomputerequipmentpricedinUS$.
iii) Itisnearlyimpossibletofindgoodequityinvestmentsindecliningindustries.
a)
b)
c)
d)
e)
i.
ii.
iii
iandii
iiandiii
8) WhichofthefollowingassumptionsaretruefortheCAPMmodel?
i)
ii)
iii)
iv)
Therearemanyinvestors,eachwithasmallinitialendowment.
Investorsmayborrowandlendatdifferentrates.
Investorsonlytradeinpubliclytradedassets
Investorspaytaxesbutincurnotransactioncosts
a)
b)
c)
d)
e)
iandiionly
i,iiandiiionly
ii,iiiandivonly
iandiiionly
alloftheabove
9) ThefollowinginformationappliestoAlphadex:
The total dividend payment for 2007 (one year from now) is expected to be
R725,000,andthetotaldividendfor2008willprobablybeR760,000.
Thereafterdividendswillgrowat5%peryear.
Therequiredrateofreturnonequityis12%.
ThetotalmarketvalueofthedebtofAlphadexisR4,900,000.
Whichofthefollowingnumbersisclosesttothevalueofthebusiness(allnumbersarein
000s)?
a)
b)
c)
d)
e)
9,370
10,340
12,650
14,270
15,240
10) Whichofthefollowingstatementsarefalse?(Thisquestionwasscrapped)
i) Stockswithabetaofzeroofferanexpectedrateofreturnofzero.
ii) TheCAPMimpliesthatinvestorsrequireahigherreturntoholdhighlyvolatile
securities.
iii) Youcanconstructaportfoliowithbetaof0.75byinvesting75%ofthe
investmentbudgetinTBillsandtheremainderinthemarketportfolio.
iv) Theriskpremiumonanindividualsecurityisafunctionofitscovariancewiththe
market.
a)
b)
c)
d)
e)
ionly
iandiionly
iiandiiionly
iiandivonly
alloftheabove
11) GiventhefollowingforBennyandCo(allnumbers,exceptshareprice,inmillions):
Tax:
Depreciationandamortisation:
Interestpaid:
Netearningsaftertax:
Marketvalueofthecompanysdebt:
Assets
Liabilities
Goodwill
Debtors
Numberofsharesinissue:
Currentshareprice:
R45
R70
R80
R120
R1,200
R1,580
R675
R75
R60
265
880cps
Which ofthefollowingis closesttothe(i)Enterprise Value:EBITDA multiple
(EV:EBITDA),and(ii)Price:tangiblenetassetvalue(P:TNAV)ofthecompany?
a)
b)
c)
d)
e)
(i)
(i)
(i)
(i)
(i)
9.8
10.2
10.6
11.2
12.2
(ii)3.0
(ii)2.8
(ii)3.0
(ii)2.8
(ii)3.0
12) WithinthecontextoftheCAPM,assume:
Expectedreturnonthemarket=15%
ExpectedrateofreturnonXYZ=17%
Riskfreerate=8%
BetaofXYZ=1.25
Whichoneofthefollowingiscorrect?
a)
b)
c)
d)
e)
XYZisoverpriced
XYZisfairlypriced
XYZsalphais0.25%
XYZsalphais0.25%
Noneoftheabove
13) Whichofthefollowingstatementsis/arecorrect?
i) Discountmodelsarepopularwithequityanalystsasanequityvaluationtool.
ii) AlowP/Eratiosindicatesthatacompanysshareischeapanditshoulddefinitely
bebought.
iii) AdisadvantageofthePrice:SalesRatioisthatsalesdonotnecessarilyimplythat
acompanyismakingprofits.
a)
b)
c)
d)
e)
i.
ii.
iii
iandii
iiandiii
14) Allofthefollowingarewaysinwhichmanagementcanincreasecurrentearnings,
except:
a) Capitalisingoperatingcosts.
b) Increasing the discount rate used to value future defined benefit pension
liabilities.
c) Aggressiverecognitionofuncertainrevenues.
d) Increasingprovisions.
e) Depreciating a large new asset using straight line depreciation instead of an
accelerateddepreciationmethod(e.g.,sumoftheyeardigits).
15) AccordingtoCAPM,theexpectedrateofreturnonaportfoliowithabetaof1.0and
alphaof0is:
a)
b)
c)
d)
e)
BetweenrMandrf
Theriskfreerate,rf
B(rMrf)
Theexpectedreturnonthemarket,rM
Noneoftheabove
16) Whichofthefollowingstatementsis/arecorrect?
i) Underinflationaryconditions,theearningsunderaLIFOsystemwillbehigher
thanunderFIFO.
ii) A company with regular (guaranteed) income, will have a higher quality of
earningsthananequivalentcompanythatdoesnot.
iii) TheReturnonEquitythataninvestorrequiresconsistsoftheinvestorsriskfree
rateplusariskpremium.
a)
b)
c)
d)
e)
i,iiandiii.
ionly.
iandii.
iiandiii.
iionly.
17) Allofthefollowingstatementsarecorrectintechnicalanalysis,except:
a) Bullsforcesharepriceshigher.
b) Ahighliquidityinaspecificsharemakesiteasiertogetoutofapositioninthat
share.
c) Supportlevelsareformedwherebearsconsistentlycomeintothemarket.
d) A trend is considered to be more reliable if it is supported by high trading
volumes.
e) Arisingtrendconsistsofaseriesofrisingresistancelevels.
18) Thefollowingtableshowsriskandreturnmeasuresfortwoportfolios:
Portfolio
R
AllShareIndex
ForecastReturn
11%
14%
StandardDeviation
10%
12%
Beta
0.5
1.0
WhenplottingportfolioRrelativetotheSML,itlies:
a)
b)
c)
d)
OntheSML
BelowtheSML
AbovetheSML
Insufficientdatagiven
19) Whichofthefollowingstatementsis/arecorrect?
i) Technicalanalystsconsideradoublebottomsharepricepatterntobeavery
bearishindicator.
ii) Technical analysts generally ignore companyspecific information when
analysingashareandpredictingitsfutureperformance.
iii) Contrarianssellwhenpricemomentumisdownwards.
a)
b)
c)
d)
e)
ionly.
iandii.
iionly.
iiandiii.
iiionly.
20) ThefollowinginformationappliestoGeminiCorp.:
Percentagedebt(@marketvalue):
Interestrateondebt:
PercentageEquity(@marketvalue):
Requiredreturnonequity:
Freecashflowgrowthrate(toinfinity):
Taxrate:
30%
10%
70%
15%
5%
30%
BasedontheinformationaboveandtheSinglePeriodFCFEModel,whatwillbethe
denominatorintheformularequiredtocalculateGeminisFreeCashFlowtoEquity:
a)
b)
c)
d)
e)
8%.
9%.
10%.
14%.
15%.
SECTIONB:CALCULATIONQUESTIONS
[30MARKS]
Question21
Given the following information for Jupiter Traders, calculate the Present Value of
GrowthOpportunities(PVGO)persharethatthemarketiscurrentlyassigningtothis
firm.Showallcalculations.
Currentshareprice:
Expectedearningsnextyear:
BetaforGemini:
Marketreturn:
Riskfreerate:
775cps
65cps
0.75
15%
8%
[4marks]
Question22
ABCLtdiscurrentlytradingatapriceofR28pershare.Youforecastthatthesharewill
tradeatapriceofR30byyearendandthatadividendofR2willbepaidduringthat
period.
Youranalysisofthemarketindicatesthatthemarketriskpremiumis8%andtherisk
freerateis5%.ABCsbetarelativetothemarketis1.3.
Assuming you already manage a welldiversified portfolio of shares, would you add
ABCtoyourportfolio?Whyorwhynot?Drawagraphandplottheforecastsharereturn
relativetotheSMLtoillustrateyouranswer.
[8marks]
Question23
ThefinancialstatementsofCrookes&Swindleshowthefollowing:
Reportednet(aftertax)earnings:R42million
R 20 million of research expenses was capitalised to intangible assets at the
beginningofthefinancialyear.
Thecompanystaxrateis30%
Intangibleassetsareamortisedover5years.
Sharesinissue:25million
What is the value per share if an appropriate historical P/E multiple is 8x and you
considerthecapitalisationoftheresearchexpensestohavebeenunjustified.
[4marks]
Question24:
Supposethattheriskpremiumonthemarketportfolioisestimatedat8%withastandard
deviationof22%.Whatistheriskpremiumonaportfolioinvested25%inGMand75%
inFord,iftheyhavebetasof1.10and1.25respectively.
[3
marks]
Question25
ThefinancialstatementsofHentuHoldingsshowthefollowing:
st
Interimfor1 half2006
Finalfor2006
Interimfor1sthalf2007
Earnings
188cps
422cps
238cps
Dividend
49cps
215cps
144cps
Thecurrentsharepriceforthecompanyis2400cps.
a) Determinethecurrentdividendyieldforthecompany
[2]
b) DeterminetheP/Eratiotheshareiscurrentlytradingon
Question26
[1]
Giventhefollowinginformation:
EquityFund
BondFund
ExpectedReturn
21%
15%
StandardDeviation
28%
18%
Thecorrelationbetweenthefundreturnsis0.2.Youplantoinvest20%intheriskfree
assetand80%intheoptimalriskyportfoliocomprisingtheabovefunds.Theriskfree
rateis5%.
Whataretheinvestmentproportionsintheoptimalriskyportfolio?Whatproportionof
yourtotalcapitalallocationshouldbeinvestedintheequityfundandthebondfund?
[4marks]
Question27
Thefollowinginformationrelatestoaspecificinstitutionalsharetransaction:
Time
09:15
09:20
10:00
SharePrice
(cps)
Portfoliomanageraskstradingdesktobuy200,000PTT
shares.
Tradingdeskgivesinstructiontoabrokertobuytheshares.
Thebrokeronlymanagestobuy120,000PTTshares.
180
184
190*
*Averagepriceatwhichbought.
Thebrokercommissionisatarateof1%oftransactionvalue.
OneweekaftertheshareswereboughtthePTTsharepriceis227cps
TwoweeksaftertheshareswereboughtthePTTsharepriceis218cps
Forthishypotheticaltrade,calculatethefollowing(inRands):
a) Commission
b) PriceImpactCosts
c) TraderTimingCost
d) Opportunitycost(basedonatwoweekperiod)
[1]
[1]
[1]
[1]
SECTIONC:WRITTENQUESTIONS
[30MARKS]
Question28
a) ExplaintheroleoftheFinancialServicesBoardintheSouthAfricanfinancialsector.
(maximum150words)
[3marks]
b) In no more than 3 sentences each, define Fundamental Analysis, Quantitative
AnalysisandTechnicalAnalysis.
[3
marks]
c) Explainhowtechnicalanalystswouldusethenperiodmovingaverageofashare
pricetodeterminewhethertheshareshouldbeboughtorsold. (maximum 150
words)
[3marks]
Question29
a) Compareandcontrasttheconceptsofariskaverseinvestor,riskneutralinvestorand
risk lover with specific reference to risk premiums and the appetite for risk.
(maximum150words)
[3marks]
b) Explainhowthepricesonbothanunderpricedandoverpricedstockwouldadjust
suchthatthesecuritieswouldagainbefairlypricedinthemarket.(maximum150
words)
[4marks]
c) The CAPM proposes that all investors in the market will derive the same risky
portfolio,themarketportfolio.Explainwhythisissowithspecificreferencetothe
assumptionsunderlyingtheCAPM.(maximum150words)
[5marks]
d) Thederivationoftheoptimalriskyportfolioisfrequentlycalledatechnicaldecision
asitfailstotakeintoaccountthepersonalriskaversionofindividualinvestors.When
does thepersonalriskaversionofaninvestor becomeimportant andhowdowe
incorporateitintoourcapitalallocationdecision?(maximum150words)
[4marks]
e) Assumewehavealreadyderivedourefficientportfolioopportunitysetandoptimal
riskyportfolio.Iftherewasnoriskfreerateinthemarkethowwouldwereconcile
theindividualriskaversionofaninvestorwiththeoptimalriskyportfolio?Illustrate
youranswerbymeansofaroughdiagram.
[5
marks]
END
FormulaSheet
w MIN (D) =
WD =
wD =
2
2
E Cov(rD , rE )
2
E + D 2Cov(rD , rE )
2
E(rD ) E(rE ) + 0.01A( E D E DE )
2
0.01A(2 D + E 2D E DE )
2
[E(rD ) rf ]E [E(rE ) rf ]Cov(rD , rE )
2
2
[E(rD ) rf ]E + [E(rE ) rf ]D [E(rD ) rf + E(rE ) rf ]Cov(rD , rE )
BUS3026WCLASSTEST
MEMO
APRIL2007
SectionA
1. b
2. d
3. b
4. bordwereaccepted
5. d
6. a
7. b
8. d
9. e
10. thisquestionwasscrappedasiandiiiwouldhavebeenthecorrectanswerbutthat
optionwasnotprovided
11. d
12. d(ealsoacceptedduetoerrorinnamingofstockinquestion)
13. c
14. d
15. d
16. d
17. c
18. d
19. c
20. c
SectionB
Question21
r=rf+(rmrf)
=8%+0.75(15%8%)
=13.25%
[2marks1answer,1formula]
PVGO=P0E1/r
=775cps(65cps/13.25%)
=775cps491cps
=284cps
[2marks1answer,1formula]
Question22
Forecastreturnontheshareis:
=[(3028)+2]/28=14.3%
[2marks]
TheexpectedreturnbasedontheCAPMis:
=5+1.3(8)=15.4%
[2marks]
Theshareisthereforeoverpricedasithasanegativealpha(1.1%).Wewouldtherefore
notaddittoourportfoliobutweshouldshortselltheshareandinvesttheproceedsinour
portfoliototakeadvantageofitsmispricing. [2marks]
E(r)
SML
15.4%
14.3%
rf
1.3
[2marks]
Question23
Requiredearningsadjustment:
Capitalisedcosts:
Lessamortization(20/5)
amortisation]
Taxfactor
R20mn
R4mn
[1markforcorrecttreatmentof
R16.0mn
x0.7
R11.2mn
[1markforadjustmentvalue]
Magnitudeofadjustment:R11.2mn
Correctearnings:R42mnR11.2mn=R30.8mn
[1mark]
Value=(CorrectearningsxP/E)/#shares
=(30.8x8)/25
=R9.86
[1mark]
Note:thesequenceofcalculationsmaydiffer.
Question24
p
=wFordFord+wGMGM
=(0.75x1.25)+(0.25x1.10)=1.2125
[1mark]
Asthemarketriskpremium,E(rMrf)is8%,theportfolioriskpremiumwillbe:
E(rp)rf
Question25
=p[E(rM)rf]
=1.2125x9=9.7%
[2marks]
Effectivelast12months=(Full20061H2006)+1H2007
Dividends:(21549)+144=310cps
Earnings:(422188)+238=472cps
[1Mark]
Dividendyield=dividends/shareprice
=310/2400=12.9%
[1Mark]
P/E=shareprice/earnings
=2400/472=5.08
[1Mark]
Question26
Iforgottheriskfreerateinsettingthisquestion.Anannouncementwasmadeineach
venuethatstudentsshoulduseariskfreerateof5%inansweringthequestion.Anumber
ofthemhadalreadyattemptedthequestionandmadeassumptions,however.
Pleaseworkwiththeanswersofanystudentswhomadeanassumptionabouttherisk
freerateorasuitableriskaversionrate(andusedthesecondequationintheformula
sheet).
wD =
2
[E(rD ) rf ]E [E(rE ) rf ]Cov(rD , rE )
2
2
[E(rD ) rf ]E + [E(rE ) rf ]D [E(rD ) rf + E(rE ) rf ]Cov(rD , rE )
=
[0.150.05]x0.28x0.28[0.210.05]x0.2x0.28x0.18
[0.150.05]x0.28x0.28+[0.210.05]x0.18x0.18[0.150.05+0.210.05]x0.2x0.28x
0.18
=
0.007840.0016128
0.00784+0.0051840.0026208
=0.0062272
0.0104032
=60%
Thesplitistherefore60%indebtand40%equity.
[3marks]
Fromacapitalallocationperspectiveweareinvesting0.8x60%indebt(48%)and0.8x
40%inequity(32%).
[1mark]
Question27
a)
Commission=120,000xR1.90x0.01
=R2,280
b)
[1mark]
PriceImpactCost=120,000x(R1.90R1.84)
=R7,200
TraderTimingCost=120,000x(R1.84R1.80)
=R4,800
[1mark]
c)
d)
[1mark]
Theoreticalpriceincreasepershare(2weeks):
=R2.18R1.80(calculatedfromorderinitiation)
=R0.38
Sharesnotbought:80,000
Totalopportunitycost=80,000xR0.38
=R30,400
SectionC
Question28
a)
[1mark]
EstablishedbystatuteandfundedbytheSAfinancialindustry.
Oversees the regulation of financial markets (including the JSE) and institutions,
includinginsurers,fundmanagersandbrokingoperations
Responsibilitiesexcludesbanks,whichfallundertheSouthAfricanReserveBank.
b)
FundamentalAnalysis: Usingeconomicandcompanyspecificinformationtotryto
predictfutureearningsetc.andvaluingthefirm/equitybasedonthese.
QuantitativeAnalysis: Usingstatisticalandmathematicaltechniquestoextrapolate
historicalrelationships,values,sharepricesetc.togettoavaluefortheequity.
TechnicalAnalysis: Interpretingtrendsandrelationshipsinsharepricesgraphically
andpredictingthefuturesharepricesbasedonthese.
c)
Comparethecurrentsharepricewiththenperiodmovingaverage.
ConsiderbuyingiftheshareistradingaboveitMAthismeansthemarketispositive
ontheshareanditisonitswayup(themarketismorepositivethanitwasonaverage
overtheMAperiod).
Considersellingtheshareisitistradingbelowitsmovingaveragethemarketis
negativeonthesharerelativetoitspreviousviewsandtheshareistradingdown.
Question29
a) Riskaverse:Riskaverseinvestorswillrejectafairgameorworseonlyaccepting
investmentswithpositiveriskpremia.He/shepenalizestheE(r)toaccountforthe
riskinvolved.
Note:Thequestionspecificallyrequestedthatyoudiscussthesethreeconceptswith
referencetoriskpremiums.Thisisparticularlyimportantforariskaverseinvestor
whodoesntsimplyrequireariskpremium,butrequiresapositiveriskpremium.
Riskneutral:JudgeriskyprospectssolelybyE(r)asthelevelofriskisirrelevant.
Theinvestmentscertaintyequivalentisthereforetheexpectedreturn.
Risklover:Willingtoengageinfairgamesandgambles.AdjuststheE(r)upbythe
thrilloftakingonmorerisk.Riskpremiumisirrelevant.
[1markeach]
b) Underpricedstockswouldbepurchasedbypeoplewhoveidentifiedthemispricing.
Theincreaseddemandwouldincreasethepriceofthesharestherebyerodingthe
potentialforprofitontheinvestment.Thiswouldslowlydecreasetheforecastreturn
ontheshareanderodeitspositivealphauntilitplotsbackontheSML.[2marks]
Overpricedstockswouldbesoldinthemarketbythosewhoveidentifiedthemas
mispriced. The increased supply would decrease the price of the shares thereby
increasingthepotentialforprofitontheinvestment.Thiswouldslowlyincreasethe
forecastreturnontheshareanderodeitsnegativealphauntilitplotsbackonthe
SML.
[2marks]
c) Thereareanumberofassumptionswhichcontributetotheexistenceofthemarket
portfolio.Forexample,thefactthatborrowingandlendingratesarethesamegives
risetoasituationwherewehaveequalamountsinborrowingandlendingwhichnet
eachotheroffandthuswehaveinvestmentonlyinthemarketportfolio.Students
were awarded marks as long as they were able to explain how the assumptions
influencedtheexistenceofthemarketportfolio.Simplylistingalltheassumptions
wasnotsufficienttogainthemaximumof5marksonoffer.
Themostimportantfactoristhatinvestorshavehomogenousexpectationsandare
meanvarianceoptimizers.
Asaresulttheyanalysesecuritiesinthesameway
Havethesameeconomicviewoftheworld
Haveidenticalprobabilitydistributionsforreturns
UsethesameinputlistfortheMarkowitzmodel.
Theresultisthatallinvestorsgeneratethesameefficientfrontierandoptimalrisky
portfolio,whichisthemarketportfolio.[
[5marks]
d) Theriskaversionoftheinvestorisrelevantonlywhendeterminingtheallocation
betweentheriskyportfolioandriskfreeasset.Thisisdonebydrawingatangent
fromtheriskfreeratetotheoptimalriskyportfolioontheefficientriskyfrontier.
Thislinerepresentsallpossibleoptimalcombinationsoftheriskyassetandriskfree
assetandisknownastheCapitalAllocationLine.OncewehavetheCAL,weplot
theinvestorsutilitycurvesonthegraphandfindthepointatwhichautilitycurveis
atangenttotheCAL.Thisrepresentstheoptimalrisky/riskfreesplitfortheinvestor.
Theoptimalriskyproportioniscalculatedasfollows:
y* =
E(rp ) rf
0.01A p
2
e) IntheabsenceofariskfreeassetthereisnoCAL.Instead,theonlydecisioninvolves
reconcilingtheinvestorsriskaversionwiththerangeofefficientriskyportfolios.
Thisisdonebyplottingtheinvestorsutilitycurvesonthegraphandfindingthe
pointatwhichtheutilitycurveisatangenttotheefficientriskyopportunityset.
Thisrepresentstheoptimalriskyportfoliogiventheinvestorslevelofrisk.
Pleasedonotdrawtheinefficientportionofthefrontierandlabeltheentireline
efficient.Also,thereshouldbenoCALonthegraphwhatsoever.TheCALimplies
theexistenceofariskfreerateregardlessofwhetheritgoesthroughtheorigin.In
thatcaseweresimplysayingtheriskfreereturnis0%.Intheabsenceofariskfree
assetthereisnoCALatall.
Also,itwasnotsufficientsimplytodrawthegraphanddiscusswhatutilitycurves
differentlevelsofriskwouldyieldontheefficientfrontier.Youneededtoexplainthat
therewouldnotbeaCALandwhy,andwhyonewouldthensimplymaptheutility
curvesinstead.
Investors
Utility Curve
E(r)
Efficient
frontier of
risky assets
P
Optimal Risky
Investment
St. Dev