CFA课后习题：投资组合

©CFAInstitute.Forcandidateuseonly.Notfordistribution.

Reading51■PortfolioManagement:AnOverview

112

PRACTICEPROBLEMS

1

2

Investorsshoulduseaportfolioapproachto:

A

B

C

reducerisk.

monitorrisk.

eliminaterisk.

Whichofthefollowingisthebestreasonforaninvestortobeconcernedwith

thecompositionofaportfolio?

A

B

C

Riskreduction.

Downsideriskprotection.

Avoidanceofinvestmentdisasters.

3

4

5

6

7

8

9

Withrespecttotheformationofportfolios,whichofthefollowingstatementsis

mostaccurate?

A

B

C

Portfoliosaffectrisklessthanreturns.

Portfoliosaffectriskmorethanreturns.

Portfoliosaffectriskandreturnsequally.

Whichofthefollowinginstitutionswillonaveragehavethegreatestneedfor

liquidity?

A

B

C

Banks.

Investmentcompanies.

Non-lifeinsurancecompanies.

Whichofthefollowinginstitutionalinvestorswillmostlikelyhavethelongest

timehorizon?

A

B

C

Definedbenefitplan.

Universityendowment.

Lifeinsurancecompany.

Adefinedbenefitplanwithalargenumberofretireesislikelytohaveahigh

needfor

A

B

C

income.

liquidity.

insurance.

Whichofthefollowinginstitutionalinvestorsismostlikelytomanageinvest-

mentsinmutualfunds?

A

B

C

Insurancecompanies.

Investmentcompanies.

Universityendowments.

Withrespecttotheportfoliomanagementprocess,theassetallocationisdeter-

minedinthe:

A

B

C

planningstep.

feedbackstep.

executionstep.

eplanningstepoftheportfoliomanagementprocessisleastlikelytoinclude

anassessmentoftheclient’s

©2011CFAInstitute.Allrightsreserved.

©CFAInstitute.Forcandidateuseonly.Notfordistribution.

PracticeProblems

113

A

B

C

securities.

constraints.

risktolerance.

10Withrespecttotheportfoliomanagementprocess,therebalancingofaportfo-

lio’scompositionismostlikelytooccurinthe:

A

B

C

planningstep.

feedbackstep.

executionstep.

11Ananalystgathersthefollowinginformationfortheassetallocationsofthree

portfolios:

Portfolio

FixedIncome(%)

Equity(%)

AlternativeAssets(%)

1

2

3

25

60

15

60

25

60

15

15

25

Whichoftheportfoliosismostlikelyappropriateforaclientwhohasahigh

degreeofrisktolerance?

A

B

C

Portfolio1.

Portfolio2.

Portfolio3.

12Whichofthefollowinginvestmentproductsismostlikelytotradeattheirnet

assetvaluepershare?

A

B

C

Exchangetradedfunds.

Open-endmutualfunds.

Closed-endmutualfunds.

13Whichofthefollowingfinancialproductsisleastlikelytohaveacapitalgain

distribution?

A

B

C

Exchangetradedfunds.

Open-endmutualfunds.

Closed-endmutualfunds.

14Whichofthefollowingformsofpooledinvestmentsissubjecttotheleast

amountofregulation?

A

B

C

Hedgefunds.

Exchangetradedfunds.

Closed-endmutualfunds.

15Whichofthefollowingpooledinvestmentsismostlikelycharacterizedbyafew

largeinvestments?

A

B

C

Hedgefunds.

Buyoutfunds.

Venturecapitalfunds.

©CFAInstitute.Forcandidateuseonly.Notfordistribution.

Reading51■PortfolioManagement:AnOverview

114

SOLUTIONS

1

2

Aiscorrect.Combiningassetsintoaportfolioshouldreducetheportfolio’svol-

atility.Specifically,“individualsandinstitutionsshouldholdportfoliostoreduce

risk.”Asillustratedinthereading,however,riskreductionmaynotbeasgreat

duringaperiodofdramaticeconomicchange.

Aiscorrect.Combiningassetsintoaportfolioshouldreducetheportfolio’svol-

atility.eportfolioapproachdoesnotnecessarilyprovidedownsideprotection

orguaranteethattheportfolioalwayswillavoidlosses.

3

4

Biscorrect.Asillustratedinthereading,portfoliosreduceriskmorethanthey

increasereturns.

Aiscorrect.eexcessreservesinvestedbybanksneedtoberelativelyliquid.

Althoughinvestmentcompaniesandnon-lifeinsurancecompanieshavehigh

liquidityneeds,theliquidityneedforbanksisonaveragethegreatest.

5

6

Biscorrect.Mostfoundationsandendowmentsareestablishedwiththeintent

ofhavingperpetuallives.Althoughdefinedbenefitplansandlifeinsurance

companieshaveportfolioswithalongtimehorizon,theyarenotperpetual.

Aiscorrect.Incomeisnecessarytomeetthecashflowobligationtoretirees.

Althoughdefinedbenefitplanshaveaneedforincome,theneedforliquidity

typicallyisquitelow.Aretireemayneedlifeinsurance;however,adefinedben-

efitplandoesnotneedinsurance.

7

8

9

Biscorrect.Investmentcompaniesmanageinvestmentsinmutualfunds.

Althoughendowmentsandinsurancecompaniesmayownmutualfunds,they

donotissueorredeemsharesofmutualfunds.

Ciscorrect.eclient’sobjectivesandconstraintsareestablishedintheinvest-

mentpolicystatementandareusedtodeterminetheclient’stargetassetalloca-

tion,whichoccursintheexecutionstepoftheportfoliomanagementprocess.

Aiscorrect.Securitiesareanalyzedintheexecutionstep.Intheplanningstep,

aclient’sobjectivesandconstraintsareusedtodeveloptheinvestmentpolicy

statement.

10Biscorrect.Portfoliomonitoringandrebalancingoccursinthefeedbackstep

oftheportfoliomanagementprocess.

11Ciscorrect.Portfolio3hasthesameequityexposureasPortfolio1andhasa

higherexposuretoalternativeassets,whichhavegreatervolatility(asdiscussed

inthesectionofthereadingcomparingtheendowmentsfromYaleUniversity

andtheUniversityofVirginia).

12Biscorrect.Open-endfundstradeattheirnetassetvaluepershare,whereas

closed-endfundsandexchangetradedfundscantradeatapremiumora

discount.

13Aiscorrect.Exchangetradedfundsdonothavecapitalgaindistributions.Ifan

investorsellssharesofanETF(oropen-endmutualfundorclosed-endmutual

fund),theinvestormayhaveacapitalgainorlossonthesharessold;however,

thegain(orloss)fromthesaleisnotadistribution.

14Aiscorrect.Hedgefundsarecurrentlyexemptfromthereportingrequire-

mentsofatypicalpublicinvestmentcompany.

15Biscorrect.Buyoutfundsorprivateequityfirmsmakeonlyafewlargeinvest-

mentsinprivatecompanieswiththeintentofsellingtherestructuredcompa-

niesinthreetofiveyears.Venturecapitalfundsalsohaveashorttimehorizon;

however,thesefundsconsistofmanysmallinvestmentsincompanieswiththe

expectationthatonlyafewwillhavealargepayoff(andthatmostwillfail).

©CFAInstitute.Forcandidateuseonly.Notfordistribution.

PracticeProblems

177

PRACTICEPROBLEMS

1

2

Aninvestorpurchased100sharesofastockfor$34.50pershareatthebegin-

ningofthequarter.Iftheinvestorsoldallofthesharesfor$30.50pershare

afterreceivinga$51.55dividendpaymentattheendofthequarter,theholding

periodreturnisclosestto:

A

B

C

−13.0%.

−11.6%.

−10.1%.

Ananalystobtainsthefollowingannualratesofreturnforamutualfund:

Year

Return(%)

2008

2009

2010

14

−10

−2

efund’sholdingperiodreturnoverthethree-yearperiodisclosestto:

A

B

C

0.18%.

0.55%.

0.67%.

3

Ananalystobservesthefollowingannualratesofreturnforahedgefund:

Year

Return(%)

2008

2009

2010

22

−25

11

ehedgefund’sannualgeometricmeanreturnisclosestto:

A

B

C

0.52%.

1.02%.

2.67%.

4

5

Whichofthefollowingreturncalculatingmethodsisbestforevaluatingthe

annualizedreturnsofabuy-and-holdstrategyofaninvestorwhohasmade

annualdepositstoanaccountforeachofthelastfiveyears?

A

B

C

Geometricmeanreturn.

Arithmeticmeanreturn.

Money-weightedreturn.

Aninvestorperformsthefollowingtransactionsonthesharesofafirm.

Att=0,shepurchasesasharefor$1,000.

●■

Att=1,shereceivesadividendof$25andthenpurchasesthreeadditional

sharesfor$1,055each.

●■

Att=2,shereceivesatotaldividendof$100andthensellsthefourshares

for$1,100each.

●■

emoney-weightedrateofreturnisclosestto:

A

4.5%.

©2019CFAInstitute.Allrightsreserved.

178

Reading52■PortfolioRiskandReturn:PartI

B

C

6.9%.

7.3%.

6

Afundreceivesinvestmentsatthebeginningofeachyearandgeneratesreturns

asshowninthetable.

AssetsUnder

Managementatthe

beginningofeachyear

ReturnduringYearof

Investment

YearofInvestment

1

2

3

$1,000

$4,000

$45,000

15%

14%

–4%

Whichreturnmeasureoverthethree-yearperiodisnegative?

A

B

C

Geometricmeanreturn

Time-weightedrateofreturn

Money-weightedrateofreturn

7

8

AtthebeginningofYear1,afundhas$10millionundermanagement;itearns

areturnof14%fortheyear.efundattractsanother$100millionatthestart

ofYear2andearnsareturnof8%forthatyear.emoney-weightedrateof

returnismostlikely:

A

B

C

lessthanthetime-weightedrateofreturn.

thesameasthetime-weightedrateofreturn.

greaterthanthetime-weightedrateofreturn.

Aninvestorevaluatingthereturnsofthreerecentlyformedexchange-traded

fundsgathersthefollowinginformation:

ETF

TimeSinceInception

ReturnSinceInception(%)

1

2

3

146days

5weeks

15months

4.61

1.10

14.35

eETFwiththehighestannualizedrateofreturnis:

A

B

C

ETF1.

ETF2.

ETF3.

9

Withrespecttocapitalmarkettheory,whichofthefollowingassetcharac-

teristicsisleastlikelytoimpactthevarianceofaninvestor’sequallyweighted

portfolio?

A

B

C

Returnontheasset.

Standarddeviationoftheasset.

Covariancesoftheassetwiththeotherassetsintheportfolio.

10Aportfoliomanagercreatesthefollowingportfolio:

Expected

StandardDeviation

(%)

Security

SecurityWeight(%)

1

2

30

70

20

12

PracticeProblems

179

Ifthecorrelationofreturnsbetweenthetwosecuritiesis0.40,theexpected

standarddeviationoftheportfolioisclosestto:

A

B

C

10.7%.

11.3%.

12.1%.

11Aportfoliomanagercreatesthefollowingportfolio:

Expected

StandardDeviation

(%)

Security

SecurityWeight(%)

1

2

30

70

20

12

Ifthecovarianceofreturnsbetweenthetwosecuritiesis−0.0240,theexpected

standarddeviationoftheportfolioisclosestto:

A

B

C

2.4%.

7.5%.

9.2%.

ThefollowinginformationrelatestoQuestions

12–13

Aportfoliomanagercreatesthefollowingportfolio:

Expected

Security

SecurityWeight(%)

StandardDeviation(%)

1

2

30

70

20

12

12Ifthestandarddeviationoftheportfoliois14.40%,thecorrelationbetweenthe

twosecuritiesisequalto:

A

B

C

−1.0.

0.0.

1.0.

13Ifthestandarddeviationoftheportfoliois14.40%,thecovariancebetweenthe

twosecuritiesisequalto:

A

B

C

0.0006.

0.0240.

1.0000.

ThefollowinginformationrelatestoQuestions

14–17

Ananalystobservesthefollowinghistoricgeometricreturns:

180

Reading52■PortfolioRiskandReturn:PartI

AssetClass

GeometricReturn(%)

Equities

8.0

6.5

2.5

2.1

CorporateBonds

Treasurybills

Inflation

14erealrateofreturnforequitiesisclosestto:

A

B

C

5.4%.

5.8%.

5.9%.

15erealrateofreturnforcorporatebondsisclosestto:

A

B

C

4.3%.

4.4%.

4.5%.

16eriskpremiumforequitiesisclosestto:

A

B

C

5.4%.

5.5%.

5.6%.

17eriskpremiumforcorporatebondsisclosestto:

A

B

C

3.5%.

3.9%.

4.0%.

18Withrespecttotradingcosts,liquidityisleastlikelytoimpactthe:

A

B

C

stockprice.

bid–askspreads.

brokeragecommissions.

19Evidenceofriskaversionisbestillustratedbyarisk–returnrelationshipthatis:

A

B

C

negative.

neutral.

positive.

20Withrespecttorisk-averseinvestors,arisk-freeassetwillgenerateanumerical

utilitythatis:

A

B

C

thesameforallindividuals.

positiveforrisk-averseinvestors.

equaltozeroforriskseekinginvestors.

21Withrespecttoutilitytheory,themostrisk-averseinvestorwillhaveanindif-

ferencecurvewiththe:

A

B

C

mostconvexity.

smallestinterceptvalue.

greatestslopecoefficient.

PracticeProblems

181

1

2

22Withrespecttoaninvestor’sutilityfunctionexpressedas:U=E(r)−Aσ,

2

whichofthefollowingvaluesforthemeasureforriskaversionhastheleast

amountofriskaversion?

A

B

C

−4.

0.

4.

ThefollowinginformationrelatestoQuestions

23–26

Afinancialplannerhascreatedthefollowingdatatoillustratetheapplicationofutility

theorytoportfolioselection:

Expected

Expected

Investment

Return(%)

StandardDeviation(%)

1

2

3

4

18

19

20

18

2

8

15

30

23Arisk-neutralinvestorismostlikelytochoose:

A

B

C

Investment1.

Investment2.

Investment3.

1

2

24Ifaninvestor’sutilityfunctionisexpressedasU=E(r)−Aσ2andthe

measureforriskaversionhasavalueof−2,therisk-seekinginvestorismost

likelytochoose:

A

B

C

Investment2.

Investment3.

Investment4.

1

2

25Ifaninvestor’sutilityfunctionisexpressedasU=E(r)−Aσandthe

2

measureforriskaversionhasavalueof2,therisk-averseinvestorismostlikely

tochoose:

A

B

C

Investment1.

Investment2.

Investment3.

1

2

26Ifaninvestor’sutilityfunctionisexpressedasU=E(r)−Aσ2andthe

measureforriskaversionhasavalueof4,therisk-averseinvestorismostlikely

tochoose:

A

Investment1.

182

Reading52■PortfolioRiskandReturn:PartI

B

C

Investment2.

Investment3.

27Withrespecttothemean–varianceportfoliotheory,thecapitalallocationline,

CAL,isthecombinationoftherisk-freeassetandaportfolioofall:

A

B

C

riskyassets.

equitysecurities.

feasibleinvestments.

28Twoindividualinvestorswithdifferentlevelsofriskaversionwillhaveoptimal

portfoliosthatare:

A

B

C

belowthecapitalallocationline.

onthecapitalallocationline.

abovethecapitalallocationline.

ThefollowinginformationrelatestoQuestions

29–31

Aportfoliomanagercreatesthefollowingportfolio:

Security

ExpectedAnnualReturn(%)ExpectedStandardDeviation(%)

1

2

16

12

20

20

29Iftheportfolioofthetwosecuritieshasanexpectedreturnof15%,thepropor-

tioninvestedinSecurity1is:

A

B

C

25%.

50%.

75%.

30Ifthecorrelationofreturnsbetweenthetwosecuritiesis−0.15,theexpected

standarddeviationofanequal-weightedportfolioisclosestto:

A

B

C

13.04%.

13.60%.

13.87%.

31Ifthetwosecuritiesareuncorrelated,theexpectedstandarddeviationofan

equal-weightedportfolioisclosestto:

A

B

C

14.00%.

14.14%.

20.00%.

32Asthenumberofassetsinanequally-weightedportfolioincreases,thecontri-

butionofeachindividualasset’svariancetothevolatilityoftheportfolio:

A

increases.

decreases.

B

PracticeProblems

183

C

remainsthesame.

33Withrespecttoanequally-weightedportfoliomadeupofalargenumber

ofassets,whichofthefollowingcontributesthemosttothevolatilityofthe

portfolio?

A

B

C

Averagevarianceoftheindividualassets.

Standarddeviationoftheindividualassets.

Averagecovariancebetweenallpairsofassets.

34ecorrelationbetweenassetsinatwo-assetportfolioincreasesduringa

marketdecline.Ifthereisnochangeintheproportionofeachassetheldinthe

portfolioortheexpectedstandarddeviationoftheindividualassets,thevolatil-

ityoftheportfolioismostlikelyto:

A

B

C

increase.

decrease.

remainthesame.

ThefollowinginformationrelatestoQuestions

35–37

Ananalysthasmadethefollowingreturnprojectionsforeachofthreepossibleout-

comeswithanequallikelihoodofoccurrence:

Outcome1

(%)

Outcome2

(%)

Outcome3

(%)

ExpectedReturn

(%)

Asset

1

2

3

12

12

0

0

6

6

6

0

12

6

6

6

35Whichpairofassetsisperfectlynegativelycorrelated?

A

B

C

Asset1andAsset2.

Asset1andAsset3.

Asset2andAsset3.

36Iftheanalystconstructstwo-assetportfoliosthatareequally-weighted,which

pairofassetshasthelowestexpectedstandarddeviation?

A

B

C

Asset1andAsset2.

Asset1andAsset3.

Asset2andAsset3.

37Iftheanalystconstructstwo-assetportfoliosthatareequallyweighted,which

pairofassetsprovidestheleastamountofriskreduction?

A

B

C

Asset1andAsset2.

Asset1andAsset3.

Asset2andAsset3.

38Whichofthefollowingstatementsisleastaccurate?eefficientfrontieristhe

setofallattainableriskyassetswiththe:

A

highestexpectedreturnforagivenlevelofrisk.

184

Reading52■PortfolioRiskandReturn:PartI

B

C

lowestamountofriskforagivenlevelofreturn.

highestexpectedreturnrelativetotherisk-freerate.

39eportfolioontheminimum-variancefrontierwiththeloweststandarddevi-

ationis:

A

B

C

unattainable.

theoptimalriskyportfolio.

theglobalminimum-varianceportfolio.

40esetofportfoliosontheminimum-variancefrontierthatdominatesallsets

ofportfoliosbelowtheglobalminimum-varianceportfolioisthe:

A

B

C

capitalallocationline.

Markowitzefficientfrontier.

setofoptimalriskyportfolios.

41edominantcapitalallocationlineisthecombinationoftherisk-freeasset

andthe:

A

B

C

optimalriskyportfolio.

leveredportfolioofriskyassets.

globalminimum-varianceportfolio.

42Comparedtotheefficientfrontierofriskyassets,thedominantcapitalalloca-

tionlinehashigherratesofreturnforlevelsofriskgreaterthantheoptimal

riskyportfoliobecauseoftheinvestor’sabilityto:

A

B

C

lendattherisk-freerate.

borrowattherisk-freerate.

purchasetherisk-freeasset.

43Withrespecttothemean–variancetheory,theoptimalportfolioisdetermined

byeachindividualinvestor’s:

A

B

C

risk-freerate.

borrowingrate.

riskpreference.

Solutions

185

SOLUTIONS

1

Ciscorrect.−10.1%istheholdingperiodreturn,whichiscalculatedas:(3,050

−3,450+51.55)/3,450,whichiscomprisedofadividendyieldof1.49%=51.55/

(3,450)andacapitallossyieldof−11.59%=–400/(3,450).

2

3

Biscorrect.[(1+0.14)(1−0.10)(1−0.02)]–1=0.0055=0.55%.

Aiscorrect.[(1+0.22)(1−0.25)(1+0.11)](1/3)−1=1.0157(1/3)−1=0.0052=

0.52%

4

5

Aiscorrect.egeometricmeanreturncompoundsthereturnsinsteadofthe

amountinvested.

Biscorrect.Computationofthemoney-weightedreturn,r,requiresfindingthe

discountratethatsumsthepresentvalueofcashflowstozero.

efirststepistogroupnetcashflowsbytime.Forthisexample,wehave

−$1,000forthet=0netcashflow,−$3,140=−$3,165+$25forthet=1net

cashflow,and$4,500=$4,400+$100forthet=2netcashflow

Solvingforr,

CF=−1,000

0

CF=−3,140

1

CF=+4,500

2

CF

CF

CF2

(1+IRR)2

0

1

+

+

0

1

(1+IRR)

(1+IRR)

−1,000

−3,140

(1+IRR)1

4,500

(1+IRR)2

=

+

+

=0

1

resultsinavalueofr=6.91%

6

Ciscorrect.emoney-weightedrateofreturnconsidersboththetimingand

amountsofinvestmentsintothefund.Tocalculatethemoney-weightedrateof

return,tabulatetheannualreturnsandinvestmentamountstodeterminethe

cashflows

Year

1

2

3

Balancefrompreviousyear

Newinvestment

Netbalanceatthebeginningofyear

Investmentreturnfortheyear

Investmentgain(loss)

0

$1,150

$2,850

$4,000

14%

$560

$4,560

$40,440

$45,000

–4%

–$1,800

$43,200

$1,000

$1,000

15%

$150

Balanceattheendofyear

$1,150

$4,560

CF=–$1,000,CF=–$2,850,CF=–$40,440,CF=+$43,200

0

1

2

3

Eachcashinfloworoutflowoccursattheendofeachyear.us,CFrefersto

0

thecashflowattheendofYear0orbeginningofYear1,andCFreferstothe

3

cashflowatendofYear3orbeginningofYear4.Becausecashflowsarebeing

discountedtothepresent—thatis,endofYear0orbeginningofYear1—the

periodofdiscountingCFiszerowhereastheperiodofdiscountingforCFis3

0

3

years.

186

Reading52■PortfolioRiskandReturn:PartI

Solvingforr,

CF=−1,000

0

CF=−2,850

1

CF=−40,440

2

CF=+43,200

3

CF

CF

CF2

CF

0

1

3

+

+

+

0

1

(1+IRR)2(1+IRR)

3

(1+IRR)

(1+IRR)

−1,000

−2,850

(1+IRR)1

−40,440

(1+IRR)2

43,200

(1+IRR)3

=

+

+

+

=0

1

resultsinavalueofr=–2.22%

NotethatBisincorrectbecausethetime-weightedrateofreturn(TWR)ofthe

fundisthesameasthegeometricmeanreturnofthefundandisthuspositive:

TWR=3(1.15)(1.14)(0.96)−1=7.97%

7

Aiscorrect.Computationofthemoney-weightedreturn,r,requiresfindingthe

discountratethatsumsthepresentvalueofcashflowstozero.Becausemost

oftheinvestmentcameduringYear2,themeasurewillbebiasedtowardthe

performanceofYear2.ecashflowsareasfollows:

CF=−10

0

CF=−100

1

CF=+120.31

2

eterminalvalueisdeterminedbysummingtheinvestmentreturnsforeach

period[(10×1.14×1.08)+(100×1.08)]

CF

CF

CF2

(1+IRR)2

0

1

+

+

0

1

(1+IRR)

(1+IRR)

−10

1

−100

(1+IRR)1

120.31

(1+IRR)2

=

+

+

resultsinavalueofr=8.53%

etime-weightedreturnofthefundis=2(1.14)(1.08)−1=10.96%.

8

9

Biscorrect.eannualizedrateofreturnforETF2is12.05%=(1.011052/5)−

1,whichisgreaterthantheannualizedrateofETF1,11.93%=(1.0461365/146)

−1,andETF3,11.32%=(1.143512/15)−1.Despitehavingthelowestvaluefor

theperiodicrate,ETF2hasthehighestannualizedrateofreturnbecauseofthe

reinvestmentrateassumptionandthecompoundingoftheperiodicrate.

Aiscorrect.easset’sreturnsarenotusedtocalculatetheportfolio’svariance

[onlytheassets’weights,standarddeviations(orvariances),andcovariances(or

correlations)areused].

10Ciscorrect.

2

2

22

σ

=

wσ+wσ+2wwρσσ

1122121,212

port

2

2

2

2

=(0.3)(20%)+(0.7)(12%)+2(0.3)(0.7)(0.40)(20%)(12%)

=(0.3600%+0.7056%+0.4032%)0.5=(1.4688%)0.5=12.11%

Solutions

187

11Aiscorrect.

2

2

22

σ

=

wσ+wσ+2wwCov(RR)

port

1

1

2

2

12

2

12

2

2

2

=(0.3)(20%)+(0.7)(12%)+2(0.3)(0.7)(−0.0240)

=(0.3600%+0.7056%−1.008%)0.5=(0.0576%)0.5=2.40%

12Ciscorrect.Aportfoliostandarddeviationof14.40%istheweightedaverage,

whichispossibleonlyifthecorrelationbetweenthesecuritiesisequalto1.0.

13Biscorrect.Aportfoliostandarddeviationof14.40%istheweightedaverage,

whichispossibleonlyifthecorrelationbetweenthesecuritiesisequalto1.0.

Ifthecorrelationcoefficientisequalto1.0,thenthecovariancemustequal

0.0240,calculatedas:Cov(R,R)=ρσσ=(1.0)(20%)(12%)=2.40%=0.0240.

1

2

1212

14Biscorrect.(1+0.080)/(1+0.0210)–1=5.8%

15Aiscorrect.(1+0.065)/(1+0.0210)–1=4.3%

16Aiscorrect.(1+0.080)/(1+0.0250)–1=5.4%

17Biscorrect.(1+0.0650)/(1+0.0250)–1=3.9%

18Ciscorrect.Brokeragecommissionsarenegotiatedwiththebrokeragefirm.

Asecurity’sliquidityimpactstheoperationalefficiencyoftradingcosts.

Specifically,liquidityimpactsthebid–askspreadandcanimpactthestockprice

(iftheabilitytosellthestockisimpairedbytheuncertaintyassociatedwith

beingabletosellthestock).

19Ciscorrect.Historicaldataoverlongperiodsoftimeindicatethatthereexists

apositiverisk–returnrelationship,whichisareflectionofaninvestor’srisk

aversion.

20Aiscorrect.Arisk-freeassethasavarianceofzeroandisnotdependenton

whethertheinvestorisriskneutral,riskseekingorriskaverse.atis,given

1

2

thattheutilityfunctionofaninvestmentisexpressedasU=E(r)−Aσ,

2

whereAisthemeasureofriskaversion,thenthesignofAisirrelevantifthe

varianceiszero(likethatofarisk-freeasset).

21Ciscorrect.emostrisk-averseinvestorhastheindifferencecurvewiththe

greatestslope.

22Aiscorrect.Anegativevalueinthegivenutilityfunctionindicatesthatthe

investorisariskseeker.

23Ciscorrect.Investment3hasthehighestrateofreturn.Riskisirrelevantto

arisk-neutralinvestor,whowouldhaveameasureofriskaversionequalto0.

Giventheutilityfunction,therisk-neutralinvestorwouldobtainthegreatest

amountofutilityfromInvestment3.

Expected

Expected

Utility

Investment

Return(%)

StandardDeviation(%)

A=0

1

2

3

4

18

19

20

18

2

8

15

30

0.1800

0.1900

0.2000

0.1800

24Ciscorrect.Investment4providesthehighestutilityvalue(0.2700)forarisk-

seekinginvestor,whohasameasureofriskaversionequalto−2.

188

Reading52■PortfolioRiskandReturn:PartI

Expected

Expected

Return(%)

StandardDeviation

(%)

Utility

A=–2

Investment

1

2

3

4

18

19

20

18

2

8

15

30

0.1804

0.1964

0.2225

0.2700

25Biscorrect.Investment2providesthehighestutilityvalue(0.1836)forarisk-

averseinvestorwhohasameasureofriskaversionequalto2.

Expected

Expected

Utility

Investment

Return(%)

StandardDeviation(%)

A=2

1

2

3

4

18

19

20

18

2

8

15

30

0.1796

0.1836

0.1775

0.0900

26Aiscorrect.Investment1providesthehighestutilityvalue(0.1792)forarisk-

averseinvestorwhohasameasureofriskaversionequalto4.

Expected

Expected

Utility

Investment

Return(%)

StandardDeviation(%)

A=4

1

2

3

4

18

19

20

18

2

8

15

30

0.1792

0.1772

0.1550

0.0000

27Aiscorrect.eCAListhecombinationoftherisk-freeassetwithzerorisk

andtheportfolioofallriskyassetsthatprovidesforthesetoffeasibleinvest-

ments.Allowingforborrowingattherisk-freerateandinvestingintheportfo-

lioofallriskyassetsprovidesforattainableportfoliosthatdominateriskyassets

belowtheCAL.

28Biscorrect.eCALrepresentsthesetofallfeasibleinvestments.Eachinves-

tor’sindifferencecurvedeterminestheoptimalcombinationoftherisk-free

assetandtheportfolioofallriskyassets,whichmustlieontheCAL.

29Ciscorrect.

R=w×R+(1−w)×R

2

p

1

1

1

R=w×16%+(1−w)×12%

p

1

1

15%=0.75(16%)+0.25(12%)

30Aiscorrect.

2

2

22

σ

=

wσ+wσ+2wwρσσ

1122121,212

port

2

2

2

2

=(0.5)(20%)+(0.5)(20%)+2(0.5)(0.5)(−0.15)(20%)(20%)

=(1.0000%+1.0000%−0.3000%)0.5=(1.7000%)0.5=13.04%

Solutions

189

31Biscorrect.

2

2

22

σ

=

wσ+wσ+2wwρσσ

1122121,212

port

2

2

2

(

2

)

=(0.5)(20%)+(0.5)20%+2(0.5)(0.5)(0.00)(20%)(20%)

=(1.0000%+1.0000%+0.0000%)0.5=(2.0000%)0.5=14.14%

32Biscorrect.econtributionofeachindividualasset’svariance(orstandard

deviation)totheportfolio’svolatilitydecreasesasthenumberofassetsinthe

equallyweightedportfolioincreases.econtributionoftheco-movement

measuresbetweentheassetsincreases(i.e.,covarianceandcorrelation)asthe

numberofassetsintheequallyweightedportfolioincreases.efollowing

equationforthevarianceofanequallyweightedportfolioillustratesthese

2

2

σ

N−1

N

σ

N−1

N

points:σ2

=

+

COV=

+

ρσ.

2

p

N

N

33Ciscorrect.eco-movementmeasuresbetweentheassetsincreases(i.e.,

covarianceandcorrelation)asthenumberofassetsintheequallyweighted

portfolioincreases.econtributionofeachindividualasset’svariance(or

standarddeviation)totheportfolio’svolatilitydecreasesasthenumberofassets

intheequallyweightedportfolioincreases.efollowingequationforthevari-

anceofanequallyweightedportfolioillustratesthesepoints:

σ2N−1

σ2N−1

2

ρσ2

σ

=

+

COV=

+

p

N

N

N

N

34Aiscorrect.Highercorrelationswillproducelessdiversificationbenefits

providedthattheothercomponentsoftheportfoliostandarddeviationdonot

change(i.e.,theweightsandstandarddeviationsoftheindividualassets).

35Ciscorrect.Asset2an