券和组合课后习题答案：sm05

CHAPTER5

SECURITY-MARKETINDICATORSERIES

Answerst。Ouestions

1.Thepurposeofmarketindicatorseriesistoprovideageneralindicationoftheaggregate

marketchangesormarketmovements.Morespecifically,theindicatorseriesareusedto

derivemarketreturnsforaperiodofinterestandthenusedasabenchmarkforevaluating

theperformanceofalternativeportfolios.Aseconduseisinexaminingthefactorsthat

influenceaggregatestockpricemovementsbyformingrelationshipsbetweenmarket

(series)movementsandchangesintherelevantvariablesinordertoillustratehowthese

variablesinfluencemarketmovements.Afurtheruseisbytechnicianswhousepast

aggregatemarketmovementstopredictfuturepricepatterns.Finally,averyimportant

useisinportfoliotheory,wherethesystematicriskofanindividualsecurityis

determinedbytherelationshipoftheratesofreturnfortheindividualsecuritytoratesof

returnforamarketportfolioofriskyassets.Here,arepresentativemarketindicatorseries

isusedasaproxyfbrthemarketportfolioofriskyassets.

2.Acharacteristicthatdifferentiatesalternativemarketindicatorseriesisthesample-the

sizeofthesample(howrepresentativeofthetotalmarketitis)andthesource(whether

securitiesareofaparticulartypeoragivensegmentofthepopulation(NYSE,TSE).

Theweightgiventoeachmemberplaysadiscriminatoryrole-withdiversemembersina

sample,itwouldmakeadifferencewhethertheseriesisprice-weighted,value-weighted,

orunweighted.Finally,thecomputationalprocedureusedforcalculatingreturn-i.e.,

whetherarithmeticmean,geometricmean,etc.

3.Aprice-weightedseriesisanunweightedarithmeticaverageofcurrentpricesofthe

securitiesincludedinthesample-i.e.,closingpricesofallsecuritiesaresummedand

dividedbythenumberofsecuritiesinthesample.

A$10()securitywillhaveagreaterinfluenceontheseriesthana$25securitybecausea

10percentincreaseintheformerincreasesthenumeratorby$10whileittakesa40

percentincreaseinthepriceofthelattertohavethesameeffect.

4.Avalue-weightedindexbeginsbyderivingtheinitialtotalmarketvalueofallstocksused

intheseries(marketvalueequalsnumberofsharesoutstandingtimescurrentmarket

price).Theinitialvalueistypicallyestablishedasthebasevalueandassignedanindex

valueof100.Subsequently,anewmarketvalueiscomputedfbrallsecuritiesinthe

sampleandthisnewvalueiscomparedtotheinitialvaluetoderivethepercentchange

whichisthenappliedtothebeginningindexvalueof100.

5.Givenafoursecurityseriesanda2-for-1splitforsecurityAanda3-fbr-lsplitfor

securityB,thedivisorwouldchangefrom4to2.8fbraprice-weightedseries.

StockBeforeSplitPriceAfterSplitPrices

A$20$10

B3010

c2020

D3030

Total100/4=2570/x=25

x=2.8

Theprice-weightedseriesadjustsforastocksplitbyderivinganewdivisorthatwill

ensurethatthenewvaluefortheseriesisthesameasitwouldhavebeenwithoutthesplit.

Theadjustmentforavalue-weightedseriesduetoastocksplitisautomatic.Thedecrease

instockpriceisoffsetbyanincreaseinthenumberofsharesoutstanding.

BeforeSplit

StockPrice/Share#ofSharesMarketValue

A$201,000,000$20,()0(),()0()

B3()500,00()15,00(),()0()

c202,00(),()0()40,()()(),()()()

D3()3,500,00()1()5.()()(),()()()

Total$180.()00.00()

The$180,000,000basevalueissetequaltoanindexvalueof100.

AfterSplit

StockPrice/Share#ofSharesMarketValue

A$1()2,()0(),()0()$20,()0(),()0()

B101,500,00015,00(),()0()

c202,000,00040,000,000

D303,500,000105,000,000

Total$180,000.000

CurrentMarketValue

NewIndexValue=xBeginningIndexValue

BaseValue

180,000,00)

180,000,000

二100

whichispreciselywhatonewouldexpectsincetherehasbeennochangeinpricesother

thanthesplit.

6.Inanunweightedpriceindicatorseries,allstockscarryequalweightirrespectiveoftheir

priceand/ortheirvalue.Onewaytovisualizeanunweightedseriesistoassumethat

equaldollaramountsareinvestedineachstockintheportfolio,forexample,anequal

amountof$1,00()isassumedtobeinvestedineachstock.Therefore,theinvestorwould

own25sharesofGM($40/share)and40sharesofCoorsBrewing($25/share).An

unweightedpriceindexthatconsistsoftheabovethreestockswouldbeconstructedas

follows:

StockPrice/Share#ofSharesMarketValue

GM$4025$1,000

Coors25401,000

Total$2.000

A20%priceincreaseinGM:

StockPrice/Share#ofSharesMarketValue

GM$4825$1,200

Coors25401,000

Total$2.200

A20%priceincreaseinCoors:

StockPrice/Share#ofSharesMarketValue

GM$4025$1,000

Coors30401,200

Total$2200

Therefore,a20%increaseineitherstockwouldhavethesameimpactonthetotalvalue

oftheindex(i.e.,inallcasestheindexincreasesby10%.Analternativetreatmentisto

computepercentagechangesfbreachstockandderivetheaverageofthesepercentage

changes.Inthiscase,theaveragewouldbe10%(20%-10%)).Sointhecaseofan

unweightedprice-indicatorseries,a20%priceincreaseinGMwouldhavethesame

impactontheindexasa20%priceincreaseofCoorsBrewing.

7.Baseduponthesamplefromwhichitisderivedandthefactthatisavalue-weighted

index,theWilshire5000EquityIndexisaweightedcompositeoftheNYSEcomposite

index,theAMEXmarketvalueseries,andtheNASDAQcompositeindex.Wewould

expectittohavethehighestcorrelationwiththeNYSECompositeIndexbecausethe

NYSEhasthehighestmarketvalue.

8.ThehighcorrelationsbetweenreturnsforalternativeNYSEpriceindicatorseriescanbe

attributedtothesourceofthesample(i.e.stocktradedontheNYSE).Thefourseries

differinsamplesize,thatis,theDJIAhas30securities,theS&P400has400securities,

theS&P50()has500securities,andtheNYSECompositeover2,800stocks.TheDJIA

differsincomputationfromtheotherseries,thatis,theDJIAisaprice-weightedseries

wheretheotherthreeseriesarevalue-weighted.Evenso,thereisstrongcorrelation

betweentheseriesbecauseofsimilarityoftypesofcompanies.

9.Sincetheequal-weightedseriesimpliesthatallstockscarrythesameweight,irrespective

ofpriceorvalue,theresultsindicatethatonaverageallstocksintheindexincreasedby

23percent.Ontheotherhand,thepercentagechangeinthevalueofalargecompanyhas

agreaterimpactthanthesamepercentagechangeforasmallcompanyinthevalue

weightedindex.Therefore,thedifferenceinresultsindicatesthatforthisgivenperiod,

thesmallercompaniesintheindexoutperformedthelargercompanies.

10.Thebond-marketseriesaremoredifficulttoconstructduetothewidediversityofbonds

available.Alsobondsarehardtostandardizebecausetheirmaturitiesandmarketyields

areconstantlychanging.Inordertobettersegmentthemarket,youcouldconstructfive

possiblesubindexesbasedoncoupon,quality,industry,maturity,andspecialfeatures

(suchascallfeatures,warrants,convertibility,etc.).

11.SincetheMerrillLynch-WilshireCapitalMarketsindexiscomposedofadistributionof

bondsaswellasstocks,thefactthatthisindexincreasedby15percent,comparedtoa5

percentgainintheWilshire500()Indexindicatesthatbondsoutperformedstocksover

thisperiodoftime.

12.TheRussell1000andRussell2000representtwodifferentsamplesofstocks,segmented

bysize.ThefactthattheRussell2000(whichiscomposedofthesmallest2,000stocksin

theRussell3000)increasedmorethantheRussell1000(composedofthe100()largest

capitalizationU.S.stocks)indicatesthatsmallstocksperformedbetterduringthistime

period.

13.Onewouldexpectthatthelevelofcorrelationbetweenthevariousworldindexesshould

berelativelyhigh.Theseindexestendtoincludethesamecountriesandthelargest

capitalizationstockswithineachcountry.

CHAPTER5

AnswerstoProblems

1(a).Givenathreesecurityseriesandapricechangefromperiodttot+1,thepercentage

changeintheserieswouldbe42.85percent.

PeriodtPeriodt+1

Lauren$60$80

Kayleigh2035

Madison1825

Sum$98$140

Divisor33

Average32.6746.67

c,46.67-32.67

Pereentagechange=--------------------=史型=42.85%

32.6732.67

Kb).Periodt

StockPrice/Share#ofSharesMarketValue

Lauren$601,000,000$60,000,000

Kayleigh2010,000,000200,000,000

Madison1830,000,000540.000.000

Total$800.000.000

Periodt+1

StockPrice/Share#ofSharesMarketValue

Lauren$801,()00,000$8(),00(),()00

Kayleigh351(),000,()0035(),()00,00()

Madison2530,()00,00075(),0()(),()()()

Total$1.18().000000

L180-800380

Pereentagechange=---------------=:——=47.50%

800800

1(c).Thepercentagechangefbrtheprice-weightedseriesisasimpleaverageofthe

differencesinpricefromoneperiodtothenext.Equalweightsareappliedtoeachprice

change.

Thepercentagechangefbrthevalue-weightedseriesisaweightedaverageofthe

differencesinpricefromoneperiodttot+1.Theseweightsaretherelativemarketvalues

fbreachstock.Thus,StockCcarriesthegreatestweightfollowedbyBandthenA.

BecauseStockChadthegreatestpercentageincreaseandthelargestweight,itiseasyto

seethatthepercentagechangewouldbelargerfbrthisseriesthantheprice-weighted

series.

2(a).Periodt

StockPrice/Share#ofSharesMarketValue

Lauren$6016.67$1,000,000

Kayleigh2050.001,000,000

Madison1855.561,000,000

Total$3.000.000

Periodt+1

StockPrice/Share#ofSharesMarketValue

Lauren$8016.67$1,333.60

Kayleigh3550.001,750.00

Madison2555.56L389.00

Total$4.470.60

4.472.6()-3.(XX)1,472.60

Percentagechange=—-------------------=-----------=49.09%

3,(XX)3,(XX)

2(b).

Lauren=80_60="=33.33%

6060

45—15

Kayleigh==—=75.00%

2020

25iQ7

Madison=——=—=38.89%

1818

….33.33%+75.00%+38.89%

Arithmeticaverage=-----------------------------------

147.22%

=49.07%

3

Theanswersarethesame(slightdifferenceduetorounding).Thisiswhatyouwould

expectsincePartArepresentsthepercentagechangeofanequal-weightedseriesandPart

Bappliesanequalweighttotheseparatestocksincalculatingthearithmeticaverage.

2(c).Geometricaverageisthenthrootoftheproductofnitems.

Geometricaverage=[(1.3333)(1.75)(1.3889)^-1

=[3,2407]I/3-1

=1.4798-1

=.4798or47.98%

Thegeometricaverageislessthanthearithmeticaverage.Thisisbecausevariabilityof

returnhasagreateraffectonthearithmeticaveragethanthegeometricaverage.

3.StudentExercise

4(a).

30

DJIA=^Plt/Dadj

i=l

Day1

CompanyPrice/Share

A12

12+23+5287

B23DJIA=—=29

C5233

Day2

(BeforeSplit)(AfterSplit)

CompanyPrice/SharePricc/Share

A1010

B2244

c5555

DJIA小+22+55DJIA=10144155

3X

=包=2929—

3

X

X=3.7586(newdivisor)

Day3

(BeforeSplit)(AfterSplit)

CompanyPrice/SharePrice/Share

A1414

B4646

c5226

14+46+26

14+46+52DJIA=

DJIA=29.798Y

3.7586

11229.798=—

Y

3.7586

Y=2.8861(newdivisor)

Day4

CompanyPrice/Share

A13DJJA=13+47+25

B472.8861

c25

85

=」一=29.452

2.8861

Day5

CompanyPrice/Share

A12DJIA=12+45+20

B452.8861

c26

83

=---------=28.759

2.8861

4(b).Sincetheindexisaprice-weightedaverage,thehigherpricedstockscarrymoreweight.

Butwhenasplitoccurs,thenewdivisorensuresthatthenewvaluefortheseriesisthe

sameasitwouldhavebeenwithoutthesplit.Hence,themaineffectofasplitisjusta

repositioningoftherelativeweightthataparticularstockcarriesindeterminingtheindex.

Forexample,a10%pricechangeforcompanyBwouldcarrymoreweightin

determiningthepercentchangeintheindexinDay3afterthereversesplitthatincreased

itsprice,thanitsweightonDay2.

4(c).StudentExercise

5(a).Base=($12x500)+($23x350)+($52x250)

=$6,000+$8,05()+$13,000=$27,050

Day1=($12x500)+($23x350)+($52x250)

=$6,000+$8,050+$13,000=$27,050

Indexi=($27,050/$27,050)x1()=10

Day2=($10x500)+($22x350)+($55x250)

=$5,000+$7,700+$13,750=$26,450

Index2=($26,450/$27,050)x10=9.778

Day3=($14x500)+($46x175)+($52x250)

=$7,000+$8,050+$13,000=$28,050

Index3=($28,050/$27,050)x10=10.370

Day4=($13x500)+($47x175)+($25x500)

=$6,500+$8,225+$12,500=$27,225

Index4=($27,225/$27,050)x10=10.065

Day5=($12x500)+($45x175)+($26x500)

=$6,000+$7,875+$13,000=$26,875

Index?=($26,875/$27,050)x10=9.935

5(b).Themarketvaluesareunchangedduetosplitsandthusstocksplitshavenoeffect.The

index,however,isweightedbytherelativemarketvalues.

6.Price-weightedindex(PWI)2oo2=(20+80+40)/3=46.67

Toaccountedforstocksplit,anewdivisormustbecalculated:

(20+40+40)/X=46.67

X=2.143(newdivisorafterstocksplit)

Price-weightedindex2003=(32+45+42)/2.143=55.53

VWI2002=20(100,000,000)+80(2,000,000)+40(25,000,000)

=2,000