SOLUTION MANUAL FORg g
FundamentalsgofgInvestmentsgValuationgandgManagement,g10thgEditiongJordan
Chapterg1-21
Chapterg1
AgBriefgHistorygofgRiskgandgReturn
ConceptgQuestions
1. Forgbothgriskgandgreturn,gincreasinggordergisgb,gc,ga,gd.gOngaverage,gtheghighergthegriskgofganginvest
ment,gtheghighergisgitsgexpectedgreturn.
2. Sincegthegpricegdidn’tgchange,gthegcapitalggainsgyieldgwasgzero.gIfgthegtotalgreturngwasgfourgpercent,
gthengthegdividendgyieldgmustgbegfourgpercent.
3. Itgisgimpossiblegtoglosegmoregthang–
100gpercentgofgyourginvestment.gTherefore,greturngdistributionsg aregcutgoffgongtheglowergtailgatg–
100gpercent;gifgreturnsgweregtrulygnormallygdistributed,gyougcouldglosegmuchgmore.
4. Togcalculategangarithmeticgreturn,gyougsumgthegreturnsgandgdividegbygthegnumbergofgreturns.gAsgsuc
h,garithmeticgreturnsgdognotgaccountgforgthegeffectsgofgcompoundingg(and,gingparticular,gthegeffectgo
fgvolatility).gGeometricgreturnsgdogaccountgforgthegeffectsgofgcompoundinggandgforgchangesgingthegb
asegusedgforgeachgyear’sgcalculationgofgreturns.gAsganginvestor,gthegmoregimportantgreturngofgangass
etgisg theggeometricgreturn.
5. Blume’sgformulagusesgthegarithmeticgandggeometricgreturnsgalonggwithgthegnumbergofgobservationsg
togapproximategagholdinggperiodgreturn.gWhengpredictinggagholdinggperiodgreturn,gthegarithmeticgret
urngwillgtendgtogbegtooghighgandgtheggeometricgreturngwillgtendgtogbegtooglow.gBlume’sgformulagadj
ustsgthesegreturnsgforgdifferentgholdinggperiodgexpectedgreturns.
6. T-
billgratesgwereghighestgingthegearlygeightiesgsinceginflationgatgthegtimegwasgrelativelyghigh.gAsgwegdi
scussgingourgchaptergonginterestgrates,gratesgongT-
billsgwillgalmostgalwaysgbegslightlyghighergthangthegexpectedgrategofginflation.
7. Riskgpremiumsgaregaboutgthegsamegregardlessgofgwhethergwegaccountgforginflation.gThegreasongisgth
atgriskgpremiumsgaregthegdifferencegbetweengtwogreturns,gsoginflationgessentiallygnetsgout.
8. Returns,griskgpremiums,gandgvolatilitygwouldgallgbeglowergthangwegestimatedgbecausegaftertaxgretur
nsgaregsmallergthangpretaxgreturns.
9. WeghavegseengthatgT-billsgbarelygkeptgupgwithginflationgbeforegtaxes.gAftergtaxes,ginvestorsgingT-
billsgactuallyglostggroundg(assumingganythinggothergthangagveryglowgtaxgrate).gThus,gangallgT-
billgstrategygwillgprobablyglosegmoneygingrealgdollarsgforgagtaxableginvestor.
10. Itgisgimportantgnotgtoglosegsightgofgthegfactgthatgthegresultsgweghavegdiscussedgcovergoverg80gyears,g
wellgbeyondgtheginvestingglifetimegforgmostgofgus.gThereghavegbeengextendedgperiodsgduringgwhich
gsmallg stocksg haveg doneg terribly.g Thus,g oneg reasong mostg investorsg willg chooseg notg tog pursueg ag
1
©g MCGRAWg HILLg LLC.g ALLg RIGHTSg RESERVED.g NOg REPRODUCTIONg ORg DISTRIBUTIONg WITHOUTg THEg PRIORg WRI
TTENg CONSENTgOFgMCGRAWgHILLgLLC.
, 100
2
©g MCGRAWg HILLg LLC.g ALLg RIGHTSg RESERVED.g NOg REPRODUCTIONg ORg DISTRIBUTIONg WITHOUTg THEg PRIORg WRI
TTENg CONSENTgOFgMCGRAWgHILLgLLC.
, percentgstockg(particularlygsmall-
capgstocks)gstrategygisgthatgmanyginvestorsghavegrelativelygshortghorizons,gandghighgvolatilityginvest
mentsgmaygbegveryginappropriategingsuchgcases.gTheregaregothergreasons,gbutgwegwillgdefergdiscussi
ongofgthesegtoglatergchapters.
11.
SolutionsgtogQuestionsgandgProblems
NOTE:gAllgendgofgchaptergproblemsgweregsolvedgusinggagspreadsheet.gManygproblemsgrequiregmultipleg
steps.gDuegtogspacegandgreadabilitygconstraints,gwhengthesegintermediategstepsgaregincludedgingthisgsolut
ionsgmanual,groundinggmaygappeargtoghavegoccurred.gHowever,gthegfinalganswergforgeachgproblemgisgfo
undgwithoutgroundinggduringganygstepgingthegproblem.
CoregQuestions
1. Totalgdollargreturng=g100($41g–g$37g+g$.28)g=g$428.00
Whethergyougchoosegtogsellgthegstockgdoesgnotgaffectgtheggaingorglossgforgthegyear;gyourgstockgisgwo
rthgwhatgitgwouldgbringgifgyougsoldgit.gWhethergyougchoosegtogdogsogorgnotgisgirrelevantg(ignoringgc
ommissionsgandgtaxes).
2. Capitalggainsgyieldg ($41g – =g .1081,g org10.81%
=
g $37)g/g$37
Dividendgyield =g $.28g/g$3 =g .0076,g org.76%
7
Totalgrategofgretur =g 10.81% +g .76% =g 11.57%
n
3. Dollargreturng=g500($34g–g$37g+g$.28)g=g–$1,360
Capitalggainsgyieldg =g ($34g – –g.0811,g org –g8.11%
g$37)g/g$37g =
Dividendgyield =g $.28g/g$3 =g .0076,g org.76%
7
Totalgrategofgreturng=g–8.11%g+g.76%g=g–7.35%
4.
a. averagegreturng=g6.0%,gaveragegriskgpremiumg=g2.7%
b. averagegreturng=g3.3%,gaveragegriskgpremiumg=g0%
c. averagegreturng=g12.3%,gaveragegriskgpremiumg=g9.0%
d. averagegreturng=g16.3%,gaveragegriskgpremiumg=g13.0%
5. Cherrygaveragegreturng = (17% +g 11%g – +g 3% +g 14%)g/g5 =g 8.60%
g 2%
Strawgaveragegreturng = (16% +g 18%g – +g 1%g + 22%)g/g5 =g 10.20%
g 6%
6. Cherry:gRAg =
3
©g MCGRAWg HILLg LLC.g ALLg RIGHTSg RESERVED.g NOg REPRODUCTIONg ORg DISTRIBUTIONg WITHOUTg THEg PRIORg WRI
TTENg CONSENTgOFgMCGRAWgHILLgLLC.
, 8.60%
Var =g 1g/g42gg(.17g –g .086) +g (.11g –g .086) +g (–.02g –g .086) +g (.03g –g .086) +g (.14g –
2g 2g 2g 2g
=g .00623
g .086)
(.00623)
1/2g
Standardgdeviationg .0789,g org7.89%
= =
Straw:gRBg 10.20%
=
4
©g MCGRAWg HILLg LLC.g ALLg RIGHTSg RESERVED.g NOg REPRODUCTIONg ORg DISTRIBUTIONg WITHOUTg THEg PRIORg WRI
TTENg CONSENTgOFgMCGRAWgHILLgLLC.
FundamentalsgofgInvestmentsgValuationgandgManagement,g10thgEditiongJordan
Chapterg1-21
Chapterg1
AgBriefgHistorygofgRiskgandgReturn
ConceptgQuestions
1. Forgbothgriskgandgreturn,gincreasinggordergisgb,gc,ga,gd.gOngaverage,gtheghighergthegriskgofganginvest
ment,gtheghighergisgitsgexpectedgreturn.
2. Sincegthegpricegdidn’tgchange,gthegcapitalggainsgyieldgwasgzero.gIfgthegtotalgreturngwasgfourgpercent,
gthengthegdividendgyieldgmustgbegfourgpercent.
3. Itgisgimpossiblegtoglosegmoregthang–
100gpercentgofgyourginvestment.gTherefore,greturngdistributionsg aregcutgoffgongtheglowergtailgatg–
100gpercent;gifgreturnsgweregtrulygnormallygdistributed,gyougcouldglosegmuchgmore.
4. Togcalculategangarithmeticgreturn,gyougsumgthegreturnsgandgdividegbygthegnumbergofgreturns.gAsgsuc
h,garithmeticgreturnsgdognotgaccountgforgthegeffectsgofgcompoundingg(and,gingparticular,gthegeffectgo
fgvolatility).gGeometricgreturnsgdogaccountgforgthegeffectsgofgcompoundinggandgforgchangesgingthegb
asegusedgforgeachgyear’sgcalculationgofgreturns.gAsganginvestor,gthegmoregimportantgreturngofgangass
etgisg theggeometricgreturn.
5. Blume’sgformulagusesgthegarithmeticgandggeometricgreturnsgalonggwithgthegnumbergofgobservationsg
togapproximategagholdinggperiodgreturn.gWhengpredictinggagholdinggperiodgreturn,gthegarithmeticgret
urngwillgtendgtogbegtooghighgandgtheggeometricgreturngwillgtendgtogbegtooglow.gBlume’sgformulagadj
ustsgthesegreturnsgforgdifferentgholdinggperiodgexpectedgreturns.
6. T-
billgratesgwereghighestgingthegearlygeightiesgsinceginflationgatgthegtimegwasgrelativelyghigh.gAsgwegdi
scussgingourgchaptergonginterestgrates,gratesgongT-
billsgwillgalmostgalwaysgbegslightlyghighergthangthegexpectedgrategofginflation.
7. Riskgpremiumsgaregaboutgthegsamegregardlessgofgwhethergwegaccountgforginflation.gThegreasongisgth
atgriskgpremiumsgaregthegdifferencegbetweengtwogreturns,gsoginflationgessentiallygnetsgout.
8. Returns,griskgpremiums,gandgvolatilitygwouldgallgbeglowergthangwegestimatedgbecausegaftertaxgretur
nsgaregsmallergthangpretaxgreturns.
9. WeghavegseengthatgT-billsgbarelygkeptgupgwithginflationgbeforegtaxes.gAftergtaxes,ginvestorsgingT-
billsgactuallyglostggroundg(assumingganythinggothergthangagveryglowgtaxgrate).gThus,gangallgT-
billgstrategygwillgprobablyglosegmoneygingrealgdollarsgforgagtaxableginvestor.
10. Itgisgimportantgnotgtoglosegsightgofgthegfactgthatgthegresultsgweghavegdiscussedgcovergoverg80gyears,g
wellgbeyondgtheginvestingglifetimegforgmostgofgus.gThereghavegbeengextendedgperiodsgduringgwhich
gsmallg stocksg haveg doneg terribly.g Thus,g oneg reasong mostg investorsg willg chooseg notg tog pursueg ag
1
©g MCGRAWg HILLg LLC.g ALLg RIGHTSg RESERVED.g NOg REPRODUCTIONg ORg DISTRIBUTIONg WITHOUTg THEg PRIORg WRI
TTENg CONSENTgOFgMCGRAWgHILLgLLC.
, 100
2
©g MCGRAWg HILLg LLC.g ALLg RIGHTSg RESERVED.g NOg REPRODUCTIONg ORg DISTRIBUTIONg WITHOUTg THEg PRIORg WRI
TTENg CONSENTgOFgMCGRAWgHILLgLLC.
, percentgstockg(particularlygsmall-
capgstocks)gstrategygisgthatgmanyginvestorsghavegrelativelygshortghorizons,gandghighgvolatilityginvest
mentsgmaygbegveryginappropriategingsuchgcases.gTheregaregothergreasons,gbutgwegwillgdefergdiscussi
ongofgthesegtoglatergchapters.
11.
SolutionsgtogQuestionsgandgProblems
NOTE:gAllgendgofgchaptergproblemsgweregsolvedgusinggagspreadsheet.gManygproblemsgrequiregmultipleg
steps.gDuegtogspacegandgreadabilitygconstraints,gwhengthesegintermediategstepsgaregincludedgingthisgsolut
ionsgmanual,groundinggmaygappeargtoghavegoccurred.gHowever,gthegfinalganswergforgeachgproblemgisgfo
undgwithoutgroundinggduringganygstepgingthegproblem.
CoregQuestions
1. Totalgdollargreturng=g100($41g–g$37g+g$.28)g=g$428.00
Whethergyougchoosegtogsellgthegstockgdoesgnotgaffectgtheggaingorglossgforgthegyear;gyourgstockgisgwo
rthgwhatgitgwouldgbringgifgyougsoldgit.gWhethergyougchoosegtogdogsogorgnotgisgirrelevantg(ignoringgc
ommissionsgandgtaxes).
2. Capitalggainsgyieldg ($41g – =g .1081,g org10.81%
=
g $37)g/g$37
Dividendgyield =g $.28g/g$3 =g .0076,g org.76%
7
Totalgrategofgretur =g 10.81% +g .76% =g 11.57%
n
3. Dollargreturng=g500($34g–g$37g+g$.28)g=g–$1,360
Capitalggainsgyieldg =g ($34g – –g.0811,g org –g8.11%
g$37)g/g$37g =
Dividendgyield =g $.28g/g$3 =g .0076,g org.76%
7
Totalgrategofgreturng=g–8.11%g+g.76%g=g–7.35%
4.
a. averagegreturng=g6.0%,gaveragegriskgpremiumg=g2.7%
b. averagegreturng=g3.3%,gaveragegriskgpremiumg=g0%
c. averagegreturng=g12.3%,gaveragegriskgpremiumg=g9.0%
d. averagegreturng=g16.3%,gaveragegriskgpremiumg=g13.0%
5. Cherrygaveragegreturng = (17% +g 11%g – +g 3% +g 14%)g/g5 =g 8.60%
g 2%
Strawgaveragegreturng = (16% +g 18%g – +g 1%g + 22%)g/g5 =g 10.20%
g 6%
6. Cherry:gRAg =
3
©g MCGRAWg HILLg LLC.g ALLg RIGHTSg RESERVED.g NOg REPRODUCTIONg ORg DISTRIBUTIONg WITHOUTg THEg PRIORg WRI
TTENg CONSENTgOFgMCGRAWgHILLgLLC.
, 8.60%
Var =g 1g/g42gg(.17g –g .086) +g (.11g –g .086) +g (–.02g –g .086) +g (.03g –g .086) +g (.14g –
2g 2g 2g 2g
=g .00623
g .086)
(.00623)
1/2g
Standardgdeviationg .0789,g org7.89%
= =
Straw:gRBg 10.20%
=
4
©g MCGRAWg HILLg LLC.g ALLg RIGHTSg RESERVED.g NOg REPRODUCTIONg ORg DISTRIBUTIONg WITHOUTg THEg PRIORg WRI
TTENg CONSENTgOFgMCGRAWgHILLgLLC.
