電子版所有期末考試2013答案

UniversityofBathSchoolofManagement

MN50322–UnitTitle

Dateandtime–willbecompletedoncescheduled

AnswerALLquestionsTherearethreesectionsinthepaper.

SectionA(20%ofmarks)consistsof15multiplechoicequestions;

SectionB(30%ofmarks)consistsofthreeshortquestions;and

SectionC(50%ofmarks)consistsoftwolongerquestions.

UsemultiplechoiceanswersheetsforSectionA‘OnlyUniversitydcalculatorsmaybeused’

SECTIONA(20%oftotalmarks)

1.

Abondwithacouponof10.00%andaparvalueof1,000andamaturitydatein10yearsiscurrentlysellingfor960.Itscurrentyieldis:

10.00%

11.46%

9.38%

10.42%

D

CurrentYield=AnnualCashCoupon/BondPrice=100/960=

10.42%

R&BChapt.19

Bonds

2.

Whichoneofthefollowingwillinvalidatetheuseofthedividenddiscountmodel?

Thestockpaysdividends

Therequiredreturnonequitymustbegreaterthanthedividendgrowthrate

Thedividendgrowthratebeinggreaterthantherequiredreturnonequity

Dividendsgrow onstantrate.

C

DDMRequiredRateofReturnhastobegreaterthanGrowth,otherwiseyougetanegativevalue.

R&BChapt.11

Valuation

3.

Ifyouwantedtoeliminateallsystematicriskfromaportfolio,thenyouwould:

Investinthemarketportfolio

Diversifyasmuchaspossibleonaglobalbasis

Diversifyasmuchaspossibleandrebalanceregularly

Investinariskasset.

D

R&BChapt.6

PortfolioMgt

4.

Atwhatstageintheindustriallifecycleisthereaninfluxofcompetition?

Earlypioneeringdevelopment

Rapidacceleratinggrowth

Maturegrowth

Stabilizationandmarketmaturity

C

R&BChapt.14

AssetAll

5.

Whatistheimpliedgrowthrate,ifthestockissellingat￡20.00pershareandthe

annualdividendis￡2.00andipectedtogrow onstantrate.Therequiredrateofreturnis15%,thereforetheimpliedgrowthrateis:

C

(DDMUsingtheDDM:P0=D0x

(1+g)/(k-g)Rearrangingwegetg=(P0xk-D0)/

DDM

4.00%

3.33%

4.55%

3.41%

(P0+D0)=(20x

.15–2)/(20+2)=

4.55%R&BChapter

11)

6.

Whichoneofthefollowingistrueforapriceweightedindex?

Theuseofthegeometricmeancreatesadownwardbiasinthereturnoftheindex

Stockswithalargecapitalizationhaveagreaterimpactontheindex

Withoutanadjustment,companiessplittingtheirstockwillloseweightintheindex

Theuseofthearithmeticmeancreatesadownwardbiasintheweightedreturnoftheindex.

C

R&BChap.5

StockMkt

7.

Inwhatphaseofthelifecycleisahouseholdwithacoupleintheir40’swhosechildrenwillbegoingtouniversityinthenextfiveyears?

Spendingphase

Consolidationphase

Accumulationphase

Giftingphase.

C

R&BChapt.2

AssetAll

8.

WhichoneofthefollowingisNOTacharacteristicofanefficientmarket?

Largenumberofbuyerandsellers.

Profitabletradingrulescanbeimplemented.

Informationcomestothemarketinarandomfashion

Securitypricesreactquicklytonewinformation

B

EMH

9.

Themaindifferenc weenaclosed-endfundandanopen-endfundis

Thewaytheyaretradedaftertheinitialpublicoffering

Thereisnoimportantdifference

A

R&BChapt.25

Alternative

C.Theminimuminitialinvestment

D.Thetypeofallowableinvestmentsinwhichtheymayallocatefunds.

10.

Youareprovidedwiththefollowinginformation:nominalreturnontherisk-asset=4.5%;expectedreturnforasseti=12.75%;expectedreturnonthemarketportfolio=9.25%.Calculatetheriskpremiumforasseti

4.5%

8.25%

4.75%

3.5%

B

R&BChapt.25

Returns

11.

Animportantreasonforconstructinganinvestor’sstatementisthatit:

helpsinvestorsdecideonrealisticinvestmentgoals

createsastandardtojudgetheperformanceofthemarket

developsaninstrumenttojudgerisk

allowsinvestorstoinvestinriskyassets.

A

R&BChapt.2

PortfolioMgt

12.

RiskAverseinvestorsarebestcharacterisedbytheirdesireto:

isethetotalreturnontheirportfolio

Minimisethesystematicriskoftheirportfolio

Diversifytoneutralisethenon-systematicriskoftheirportfolio

Diversifytoneutralisethetotalriskoftheirportfolio.

C

AssetAll

13.

Overthelast40yearsUKpensionfundshavesignificantlyshiftedtheirassetallocationstowards

reasedallocationtooverseasequities

reasedallocationtodomesticequities

Decreasedallocationtoindexlinkedbonds

Decreasedallocationtoalternative

A

PortfolioMgt

investments.

14.

A hasjustpaidanannualdividend

B

DDM

of￡1,andexpectsdividendstogrowat10%

nextyearandat5%thereafter.Iftherequiredrateofreturnis8%,thenusingthedividenddiscountmodelthevalueofthestocktodayis:

GetthePVofthenextyearsofdividends:Nextyearsofdividends(growingat10%)is1.1.

Discountthisat8%to

getaPVof1.02.

34.97

36.67

35.64

37.20

GetthePVoftheConstantgrowthDividendsP1=D2/(k-g)

=1.1x1.05/(0.08-

.05)=38.5PV(P1)=

35.65.

PVofallDividends=

1.02+35.65=36.67

15.

Aportfolioperformancemeasurementtechniquethat posesthereturnofamanager’sholdingstoapredeterminedbenark’sreturnsandseparatesthedifferenceintolocationandselectioniscalled

B R&Bp.1130

PortfolioPerformance

Immunizationysis

Attributionysis

Strategicassetallocation

Hedging

SECTIONB(30%oftotalmarks)

QUESTION16

ThetablebelowliststhreestocksquotedonaUKstockexchange,andtheirstockprices:

Stock

#shares

Priceat31Dec

Priceat31

2011(￡)

Dec2012(￡)

AB

5,000,000

4.30

3.10

CD

1,000,000

5.50

6.40

EF

2,000,000

2.20

3.50

a)Construct

i. aprice-weightedindexforthesethreestocks

. acapitalization-weightedindexforthesethreestocks

i. computethepercentagechangeintherespectiveindicesoverthetwelvemonthperiod,

iv. commentonanydifferencesintheabovetwomeasures

[6marks]

b)Identifythemainusesofstockmarketindices

[4marks]

ANSWER

21,500,000

5,500,000

4,400,000

31,400,000

10,466,667

a)

Stock

#shares

Priceat31Dec

2003

(￡)

Priceat31Dec

2004(￡)

MarketValueat31Dec2003

(￡)

MarketValueat31Dec2004(￡)

AB

5,000,000

4.3

3.1

15,500,000

CD

1,000,000

5.5

6.4

6,400,000

EF

2,000,000

2.2

3.5

7,000,000

sum

12

13

28,900,000

average

4

4.33

9,633,333

%change

8.33%

-7.96%

Astockmarketindexisusedtoreflectthemovementsofagroupofsecurities.Securitymarketindicesareused:

Asben arkstoevaluatetheperformanceiffundmanagers

Tocreateanindexfund(ortrackerfund)

Tomeasureaggregatestockpricemovements

Topredictfuturemarketmovementsbytechnicaltraders

Asa forthemarketportfolio,whencalculatinghesystematicriskofanasset

QUESTION17

Youaregiventhefollowinginformationaboutthree ernmentbonds:

Price

Coupon

FaceVale

Time toMaturity

Yield toMaturity

Bond1

101.04

5%

100

1

?

Bond2

108.50

12%

100

2

?

Bond3

96.00

8%

100

3

9.597

Fromtheinformationinthetable

Estimatethetermstructureofinterestrates

[3marks]

Estimatetheyieldcurve

[3marks]

Exinthedifferencweentheyieldcurveandthetermstructure,andcommentontheapplicabilityofeachfunction.

[4marks]

ANSWER

And

b)

R1=105/101.04-1=0.0392,soIRR1=0.0392

108.5=12/1.0392+112/(1+R2)2R2=0.0748,andIRR2=0.0728.

96=8/1.0392+8/1.07482+108/(1+R3)3

R3=0.0989.

Whatisthedifferenc weentheyieldcurveandthetermstructure?Slightdifferenc weenyieldandspotrates

Yieldisacomplicatedweightedaverageofspotrates

Atasinglepointintime,therewillbejustoneuniquespotrate,buttherewillbemanyyields-to-maturity:oneforeverybondthatmaturesatthatpointintimeButtheyieldswillbeveryclosetooneanother

Usingthespotratesimplicitinthetermstructuretopricebondisthearbitrage-

methodofvaluingbonds

Usingtheyieldonasimilarbond,willbeapproxima ycorrect,butnotquitecorrect.

Therewouldbearbitrageopportunitiesifbondswerepricedaccordingtotheyieldcurve

QUESTION18

AninvestorcomestoyouforconsultationonhisgloballydiversifiedportfolioconsistingofstocksfromtheUSandtheUKmarkets.Therisk-returncharacteristicsofhisholdingsinthesetwomarketscanbeapproximatedbytheequitymarketindicesobtainedfromthesetwomarkets.Yourassistantprovidesyouwiththefollowingtableofinformation:

INDEX

S&P500

FTSE100

Proportion

40%

60%

ExpectedReturn

12.6%

8.3%

Standarddeviation

19.8%

12.8%

Covariance (S&P500,

FTSE100)estimatedovertheperiod2003-2008

0.0172

Whatistheexpectedreturnandstandarddeviationofthe’sportfolio?

[2marks]

Whatisthecorrelationbetweenthe’sholdingsintheUSandUKmarkets?

[2marks]

NowassumethatthecorrelationbetweentheUSandtheUKequitymarketshasreasedsubstantiallyduringtherecentfinancialcrisistoalmostperfectlypositive.Howdoesthischange orrelationbetweentheindicesimpactonthe

investor’sportfolio?

[3marks]

Ifthereisanalternativeinvestmentopportunitywiththefollowingrisk-returncharacteristics,andtheiswillingtoreceoneofhisnationalholdingsbythisnewinvestment,whichnationalholding(i.e.theUSortheUK)willyou

mendtheinvestortorecetoimprovethediversificationeffect?

AlternativeInvestment

ExpectedReturn

5.0%

Standarddeviation

6.2%

Correlationvs.S&P500

0.56

Correlationvs.FTSE100

0.42

[3marks]

Answer:

Index

S&P500

FTSE100

Propotion

40%

60%

ExpectedReturn

12.6%

8.3%

StandardDeviation

19.80%

12.8%

Covariance

1.72%

AlternativeInvestment

ExpectedReturn

5.0%

StandardDeviation

6.2%

Correlationvs.S&P500

0.56

Correlationvs.FTSE100

0.42

Ans

Qa.

Var-CovMatrix

3.92%

1.72%

1.72%

1.64%

PortfolioReturn

10.02%

PortfolioStdev.

14.30%

Qb.

Correlation

Qc.

68.00%

Var-CovMatrix

3.92%

2.53%

2.53%

1.64%

NewPortfolioStdev.

15.60%

Diff.PortfolioStdev.

1.30%

Qd.

Var-CovifReceSP500

0.38%

0.33%

0.33%

1.64%

NewPortfolioStdev.

9.01%

Var-CovifReceFTSE100

3.92%

0.52%

0.52%

0.38%

NewPortfolioStdev.

10.07%

Final mendation:FTSE100ShouldbeRe

ced

SECTIONC(50%oftotalmarks)

QUESTION19

Thetablecomparestheperformanceofaninvestmentfund,consistingoflargeEuropeanstocks,withtheperformanceoftheEuro-500ShareIndex(avalueweightedstockmarketindexofthelargest500Europeanstocks)overthepreviousfiveyears.

EuropeanLargeCap

Euro-500Index

Risk

Mean

Fund

12%

16%

5%

Standarddeviation

10%

14%

Beta

0.55

1

Usingthisdata,calculatetheTreynorandSharpeperformancemeasuresfortheEuropeanLarge-CapFundandfortheEuro-500Index

[4marks]

CommentontherelativeperformanceoftheFundandtheEuro-500Index,andsuggestpossiblereasonsforanyingresultsbetweentheseperformancemeasures.

[3marks]

OutlineanyproblemsintheuseoftheJensenmeasureofinvestmentfundperformance,andexinhowtheseproblemscanberesolved.

[9marks]

ExintheBerkandGreen(2004)argumentthatfundflowswillpreventanyperformancepersistenceinmutualfundreturns.

[9marks]

ANSWER

a).

Investment

Sharpe

Treynor

Fund

0.70

0.13

Market 0.79 0.11 0.00

TheTreynormeasure(T)relatestherateofreturnearnedabovetherisk- ratetotheportfoliobetaduringtheperiodunderconsideration.Therefore,theTreynormeasureshowstheriskpremium(excessreturn)earnedperunitofsystematicrisk:

TreynorMeasure PerformanceRelativetotheMarket

T=13% Outperformed

MarketTM=11.0%

TheSharpemeasure(S)relatestherateofreturnearnedabovetherisk ratetothetotalriskofaportfolioby ludingthestandarddeviationofreturns.Therefore,theSharpemeasureindicatestheriskpremium(excessreturn)perunitoftotalrisk:

SharpeMeasure PerformanceRelativetotheMarket

S=70% Underperformed

MarketSM=79%

Forafundnotcompleydiversified,Treynor’s“T”valuewillunderstateriskandoverstateperformance.Sharpe(1966)dividedafund’sexcessreturnbyitsstandarddeviation.Sharpe’s“S”valuewillproduceevaluationsverysimilartoTreynor’sforfundsthatarewelldiversified.

Forperfectlydiversifiedportfolios(thatis,thosewithoutanyunsystematicorspecificrisk),theTreynorandSharpemeasureswouldgiveconsistentresultsrelativetothemarketindexbecausethetotalvarianceoftheportfoliowouldbethesameasitssystematicvariance(beta).ApoorlydiversifiedportfoliocouldshowbetterperformancerelativetothemarketiftheTreynormeasureisusedbutlowerperformancerelativetothemarketiftheSharpemeasureisused.Anydifferencweenthetwomeasuresrelativetothemarketswouldcomedirectlyfromadifferenceindiversification.

EuroLargeCapoutperformedthemarketifmeasuredbytheTreynormeasurebutdidnotperformaswellasthemarketusingtheSharpemeasure.ThereasonisthatEuroLargeCapFundmusthavealargeamountofunsystematicrisk.SuchriskisnotafactorindeterminingthevalueoftheTreynormeasurefortheportfolio,becausetheTreynormeasureconsidersonlysystematicrisk.TheSharpemeasure,however,considerstotalrisk(thatis,bothsystematicandunsystematicrisk).EuroLargeCapFund,whichhasalowamountofsystematicrisk,couldhaveahighamountoftotalrisk,becauseofitslackofdiversification.Hence,EuroLargeCapFundwouldhaveahighTreynormeasure(becauseoflowsystematicrisk)andalowSharpemeasure(becauseofhightotalrisk).

Jensen(1968)measureusesSecurityMarketLineasthebasisforacomparisonofperformance(whichallowsfortheriskinessofafund).Standardresultisthataverageabnormalreturnacrossfundoffeesisnegative,butifexpensesaddedbackinto

thegrossreturn,averageabnormalreturnapprox.zero.Hencemarketprofessionalsdonotappeartobeabletobeatthemarket.Jensen’stechniqueeasilyextendedtoadditionalfactors

ProblemswithJensen-alpha lude:

appropriatemarketindexa)Ben arkusedforcomparisonmaybeinappropriate;

b)Wrongassetpricingmodel(Fama-French,92);c)Fundmanagermayhaveexplicit

differentben ark ontract;andd)RollCritique

MarketTiming;Markettimingiswhenfundmanagerstakeanaggressivepositioninabullmarket,butadefensivepositioninabearmarket.Whenportfoliomanagersexpectthemarketportfoliotoriseinvalue,theymayswitchfrombondsintoequitiesand/ortheymayinvestinmorehighbetastocks.Whentheyexpectthemarkettofalltheywillundertakethereversestrategy:sellhighbetastocksandmoveinto“defensive”stocks.Ifmanagerssuccessfullyengageinmarkettimingthen,returnstothefundwillbehighwhenthemarketishigh,andalsorelativelyhighwhenthemarketislow.Testformarkettiming ludeTreynor-MazuyTest&Merton-Henrikssontest.

Conditionalperformanceevaluation:onlywanttoassessmanager’sperformancethatcouldnotbereplicatedbypublicinformation(stockmarketanomalies)

Needforbootstraptechniques,sepropensityfortimeseriesreturnsofindividualfundstoexhibitnon-normaldistribution:a)Fundmanagersmayholdheavypositionsinfewstocksorsectors;b)Marketbenarksmaybenon-normal/autocorrelated;c)Fundsmayundertakedynamicstrategiesinresponsetorealisedreturns;ord)Returnseriesoneachfundmaynotbe t(Fundfamiliesand/orHerding).Thesereasonsmayleadtocomplexcross-sectioninctions

Bootstrapmethods:Kosowski,etal(2006)vsFamaandFrench(2010)

AfterbootstrapKosowskietal(2006)assesshowmanyfundsfromalargegrouponewouldexpecttoobservehavinglargealphasbyluck,andhowmanyareactuallyobserved.Theyshowthatbyluckalone9fundswouldbeexpecttoachievephaof10%overatleasta5-yearperiod.Infact,29fundsachievethisbarrier.Theyfindimportantdifferencesinthecrosssectionoffundsthatbelongtodifferentinvestmentobjectivecategories.Strongevidenceofsuperiorperformanceamonggrowth-orientedfunds

HoweverFama&French(2010)suggestcalculatingαforeachfund,andthencomputingpseudoreturnsbydeductingαfromactualreturn–toobtainbenarkadjusted(zero-α)returns.Theyreportthatthedistributionoftheactualt(α)-valuesaremuchlowerthanthesimulatedt(α)-values:particularlyforthenegativealphas,butalsoformostofthepositivealphas.Theyconcludethatthereislittleevidenceofmutualfundmanagerskills

D)BerkandGreen

Berk&Green(2004)offerex nationastowhyfundflowsfollo

stperformanceif

thereisnoperformancepersistence?.Theydistinguishbetweengrossreturns(Rt)andnetreturnsandassumethattheunitcostfromactivefundmanagementandismadeupoffixedandvariablecostsproportionofassetsundermanagementsothecostfunctionisconvexinassets-under-management(AUM).Thisreflectsideathatitismoredifficult

toactivelymanagealargefund.Theyallowfordifferentialmanagerialability,andinvestorsupdatetheexpectationsofmanagerabilityonpastperformance–highreturnlikelytobefrombettermanagers.Fundsflowintothosemutualfundswhodemonstratehighreturns,andoutofthosefundswithpoorperformance.ThiswillcontinuetoflowuntilE(rt+1)=0:betterperformingfundsgrowbigger,butbecauseofcostfunctionconvexity:performancewillworsen.Underperformingfundswillshrinkinsize,makingiteasierforfundstoimproveperformance

SefundmanagerfeesaretypicallyapercentageofAUM,thebettermanagerswillmanagelargerfunds,andwillreceivehigherfees(andsalaries)commensuratewiththeirhigherskills.Hencehigh-abilitymanagersearnthe“economicrents”fromtheirscarceskills,butoutsideinvestorscanonlyexpecttoearnnormalratesofreturnontheirinvestmentfunds

Chen,Hong,HarrisonandKubick(2004,AER)findthatsizeisdetrimentaltofundperformance.PolletandWilson(2008,JF)findthatinflowsintofundsareusedto“scaleup”existingstrategieswhichislikelytourscalediseconomies.ButFama&

French(2010)challengethefindingsofBerk&Greenandarguethereisnoevidenceofmanagerialskill

QUESTION20

YouareafundmanagerdecidingwhethertoallocatepartofyourportfoliotothePangeaeneconomy.Pangaeaisalargedevelopedeconomy,anditsmainstockmarketindexisthePAN100(beingavalue-weightedindexofthe100largestlistedcompanies).Thefollowinghistoricaldataareavailable:

31st

Dec2008

31stDec2009

31stDec2010

31stDec2011

ShorttermPangaeanernmentbonds

n/a

2.5%

3.0%

3.5%

LongtermPangaeanernmentbonds

n/a

5.0%

5.5%

6.0%

IndexValueofPAN100

120

130

155

162

DividendyieldonPAN100

n/a

2.8%

3.0%

2.5%

EarningsonPAN100companies

n/a

6.5

8.7

7.3

ReturnonEquity(ROE)

n/a

12.0%

16.0%

14.0%

n/adenotesdatanotavailable

Computetheaveragerealizedreturn(holdingperiodyield)toequitiesinPangaea,andcompareittotheaveragereturnonequity.

[5marks]

WhathasbeenthehistoricalriskpremiumonthePAN100,andhencetherequiredrateofreturnonthePAN100?

[5marks]

ComputetwomeasuresofthegrowthrateofdividendsonthePAN100index

[5marks]

Usetheaggregatedividenddiscountmodel(DDM)forthePangaeaneconomy,toassesswhetherat31stDecember2011thePAN100isoverorundervalued,andwhetherasafundmanageryoushouldinvestinthiscountry’seconomy.

[5marks]

CampbellandShiller(2001)usehistoricalpatternsindividendyieldsandPEratiostopredicttheaggregaevelofacountry’sstockmarket.ExinthedifferencweenthisapproachandtheuseofaggregateDDMinpartd)

[5marks]

ANSWER

Firstcomputereturnsonindex=capitalapprec.+dividendyield

Pangaea

Solution

31stDec2008

31stDec2009

31stDec2010

31stDec2011

ArithmetricAverage

3.00%

5.50%

2.77%

14.00%

10.69%

Shortterm

2.5%

3.0%

3.5%

ernment

bonds

Longterm

5.0%

5.5%

6.0%

ernment

bonds

IndexValueof

120

130

155

162

PAN100

Dividendyield

2.8%

3.0%

2.5%

onPAN100

Earnings

6.5

8.7

7.3

Returnon

12.0%

16.0%

14.0%

Equity

Cap

8.3%

19.2%

4.5%

appeciation

Totalreturn 11.13% 22.23%

7.02%

13.46%

Dividendspaidonindex 3.64 4.65

4.05

5.48%

D0

4.05

Riskpremium 8.63% 19.23%

3.52%

10.46%

Retentionratio 44.00% 46.55%

44.52%

45.02%

growthratefromdivgrowth

5.48%

growthratefromGordonGrowthmodel

6.30%

Arith

Expectedreturnonequity(shorttermrf)

13.46%

Expectedreturnonequity(long-termrf)

15.96%

Arithmeticmeanis AM

t1

AM=13.46%

Averagereturnonequityis14.0%

HistoricalriskpremiumonthePAN100

Theequityriskpremiumistheexcessreturnthatanindividualstockortheoverallstockmarketprovidesoverarisk- rate.Thi cessreturncompensatesinvestorsfortakingontherelativelyhigherriskoftheequitymarket.Thesizeofthepremiumwillvaryastheriskinaparticularstock,orinthestockmarketasawhole,changes;high-riskinvestmentsarecompensatedwithahigherpremium.

Definingriskpremiumasdifferenc weenreturnonequityindexandshort-terminterestrate(T-Bills)then

Arithmeticmean=10.46%

Issuesinestimatingtheequityriskpremium

Equitypremiumisdifferenc weenreturnonriskyassetsandreturnonsafebonds.Shouldyouusehistoricalaverage?EvidencefromUSisthattheriskpremiumchangesovertime.Theremaybesurvivorshipbiasesinindexreturnsonlythesuccessfulcompaniessurvive.Isthefuturedifferentfromthepast?

Shouldyouusearithmeticaverageratherthangeometric:notevolatilitywillresulti agebeingmuchhigherthangeometric?Mayneedtomake:Inflationadjustments,Technologyadjustments;Demographicadjustments

RequiredrateofreturnonthePAN100isrf+r