SOLUTION MANUAL FOR g g
FundamentalsgofgInvestmentsgValuationgandgManagementg9thgEditiongBygJord
an
Chapterg1-21
Chapterg1
AgBriefgHistorygofgRiskgandgReturn
ConceptgQuestions
1. Forgbothgriskgandgreturn,gincreasinggordergisgb,gc,ga,gd.gOngaverage,gtheghighergthegriskgofganginvest
ment,gtheghighergisgitsgexpectedgreturn.
2. Sincegthegpricegdidn’tgchange,gthegcapitalggainsgyieldgwasgzero.g Ifgthegtotalgreturngwasgfourgpercent,
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.
Copyrightg2021g©gMcGraw-
HillgEducation.gAllgrightsgreserved.gNogreproductiongorgdistributiongwithout
thegpriorgwrittengconsentgofgMcGraw-HillgEducation.
, 10. Itgisgimportantgnotgtoglosegsightgofgthegfactgthatgthegresultsgweghavegdiscussedgcovergoverg80gyears,g
wellgbeyondgtheginvestingglifetimegforgmostgofgus.gThereghavegbeengextendedgperiodsgduringgwhichg
smallgstocksghavegdonegterribly.gThus,gonegreasongmostginvestorsgwillgchoosegnotgtogpursuegag100gp
ercentgstockg(particularlygsmall-
capgstocks)gstrategygisgthatgmanyginvestorsghavegrelativelygshortghorizons,gandghighgvolatilityginvest
mentsgmaygbegveryginappropriategingsuchgcases.gTheregaregothergreasons,gbutgwegwillgdefergdiscussi
ongofgthesegtoglatergchapters.
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=g($41g–
g$37)/$37g=g.1081,gorg10.81%gDividendgyieldg=g$.28/$3
7g=g.0076,gorg.76%
Totalgrategofgreturng=g10.81%g+g.76%g=g11.57%
3. Dollargreturng=g500($34g–g$37g+g$.28)g=g–$1,360
Capitalggainsgyieldg=g($34g–g$37)/$37g=g–.0811,gorg–
8.11%gDividendgyieldg=g$.28/$37g=g.0076,gorg.76%
Totalgrategofgreturng=g–8.11%g+g.76%g=g–7.35%
4. a.g averagegreturng=g6.2%,gaveragegriskgpremiumg=g2.6%
b. averagegreturng=g3.6%,gaveragegriskgpremiumg=g0%
c. averagegreturng=g11.9%,gaveragegriskgpremiumg=g8.3%
d. averagegreturng=g17.5%,gaveragegriskgpremiumg=g13.9%
5. Cherrygaveragegreturng=g(17%g+g11%g–g2%g+g3%g+g14%)/5g=g8.60%
Strawgaveragegreturng=g(16%g+g18%g–g6%g+g1%g+g22%)/5g=g10.20%
6. Cherry:gRAg=g8.60%
Varg=g1/4[(.17g–g.086)2g+g(.11g–g.086)2g+g(–.02g–g.086)2g+g(.03g–g.086)2g+g(.14g–g.086)2]g=g.00623
Standardgdeviationg=g(.00623)1/2g=g.0789,gorg7.89%
Straw:gRBg=g10.20%
Varg=g1/4[(.16g–g.102)2g+g(.18g–g.102)2g+g(–.06g–g.102)2g+g(.01g–g.102)2g+g(.22g–g.102)2]g=g.01452
Standardgdeviationg=g(.01452)1/2g=g.1205,gorg12.05%
7. Thegcapitalggainsgyieldgisg($59g–g$65)/$65g=g–.0923,gorg–
9.23%g(noticegthegnegativegsign).g Withgagdividendgyieldgofg1.2gpercent,gthegtotalgreturngisg–
Copyrightg2021g©gMcGraw-
HillgEducation.gAllgrightsgreserved.gNogreproductiongorgdistributiongwithout
thegpriorgwrittengconsentgofgMcGraw-HillgEducation.
, 8.03%.
Copyrightg2021g©gMcGraw-
HillgEducation.gAllgrightsgreserved.gNogreproductiongorgdistributiongwithout
thegpriorgwrittengconsentgofgMcGraw-HillgEducation.
, 8. Geometricgreturng=g[(1g+g.17)(1g+g.11)(1g-g.02)(1g+g.03)(1g+g.14)](1/5)g–g1g=g.0837,gorg8.37%
9. Arithmeticgreturng=g(.21g+g.12g+g.07g–.13g–g.04g+g.26)/6g=g.0817,gorg8.17%
Geometricgreturng=g[(1g+g.21)(1g+g.12)(1g+g.07)(1g–g.13)(1g–g.04)(1g+g.26)](1/6)g–g1g=g.0730,gorg7.30%
IntermediategQuestions
10. That’sgplusgorgminusgonegstandardgdeviation,gsogaboutgtwo-
thirdsgofgthegtime,gorgtwogyearsgoutgofgthree.gIngonegyeargoutgofgthree,gyougwillgbegoutsidegthisgrang
e,gimplyinggthatgyougwillgbegbelowgitgonegyeargoutgofgsixgandgabovegitgonegyeargoutgofgsix.
11. Youglosegmoneygifgyoughavegagnegativegreturn.gWithgag12gpercentgexpectedgreturngandgag6gpercentg
standardgdeviation,gagzerogreturngisgtwogstandardgdeviationsgbelowgthegaverage.gThegoddsgofgbeingg
outsideg(abovegorgbelow)gtwogstandardgdeviationsgareg5gpercent;gthegoddsgofgbeinggbelowgareghalfg t
hat,gorg2.5gpercent.g(It’sgactuallyg2.28gpercent.)gYougshouldgexpectgtoglosegmoneygonlyg2.5gyearsgou
tgofgeveryg100.gIt’sgagprettygsafeginvestment.
12. Thegaveragegreturngisg5.9gpercent,gwithgagstandardgdeviationgofg9.8gpercent,gsogProb(Returng<g–
3.9gorgReturng >g15.7g)g≈g1/3,gbutgwegaregonlyginterestedgingonegtail;gProb(Returng<g–
3.9)g≈g1/6,gwhichgisghalfgofg1/3g.
95%: 5.9g±g2σg=g5.9g±g2(9.8)g=g–13.7%gtog25.5%
99%: 5.9g±g3σg=g5.9g±g3(9.8)g=g–23.5%gtog35.3%
13. Expectedgreturng=g17.5%;g σg=g36.3%.gDoublinggyourgmoneygisgag100%greturn,gsogifgthegreturngdist
ributiongisgnormal,gZg=g(100g–g17.5)/36.3g=g2.27gstandardgdeviations;gthisgisgin-
betweengtwogandgthreegstandardgdeviations,gsogthegprobabilitygisgsmall,gsomewheregbetweeng.5%gan
dg2.5%g(why?).gReferringgtogthegnearestgZgtable,gthegactualgprobabilitygisg=g1.152%,gorgaboutgonceg
everyg100gyears.gTriplinggyourgmoneygwouldgbegZg=g(200g–
g17.5)/36.3g=g5.028gstandardgdeviations;gthisgcorrespondsgtogagprobabilitygofg(much)glessgthang0.5%
,gorgoncegeveryg200gyears.g(Thegactualganswergisglessgthangoncegeveryg1gmilliongyears,gsogdon’tghol
dgyourgbreath.)
14. Year Commongstocks T-billgreturn Riskgpremium
1973 –14.69% 7.29% –21.98%
1974 –26.47% 7.99% –34.46%
1975 37.23% 5.87% 31.36%
1796 23.93% 5.07% 18.86%
1977 –7.16% 5.45% –12.61%
sum 12.84% 31.67% –18.83%
a. Annualgriskgpremiumg=gCommongstockgreturng–gT-billgreturng(seegtablegabove).
b. Averagegreturns:gCommongstocksg=g12.84/5g=g.0257,gorg2.57%;g T-
billsg=g31.67/5g=g.0633,gorg6.33%;
Riskgpremiumg=g–18.83/5g=g–.0377,gorg–3.77%
c. Commongstocks:gVarg=g1/4[g(–.1469g–g.0257)2g+g(–.2647g–g.0257)2g+g(.3723g–g.0257)2g+
(.2393g–g.0257)2g+g(–.0716g–g.0257)2]g=g.072337
Standardgdeviationg=g(0.072337)1/2g=g.2690,gorg26.90%
T-bills:g Varg=g1/4[(.0729g–g.0633)2g+g(.0799g–g.0633)2g+g(.0587g–g.0633)2g+g(.0507–.0633)2g+
(.0545g–g.0633)2]g=g.000156
Copyrightg2021g©gMcGraw-
HillgEducation.gAllgrightsgreserved.gNogreproductiongorgdistributiongwithout
thegpriorgwrittengconsentgofgMcGraw-HillgEducation.
FundamentalsgofgInvestmentsgValuationgandgManagementg9thgEditiongBygJord
an
Chapterg1-21
Chapterg1
AgBriefgHistorygofgRiskgandgReturn
ConceptgQuestions
1. Forgbothgriskgandgreturn,gincreasinggordergisgb,gc,ga,gd.gOngaverage,gtheghighergthegriskgofganginvest
ment,gtheghighergisgitsgexpectedgreturn.
2. Sincegthegpricegdidn’tgchange,gthegcapitalggainsgyieldgwasgzero.g Ifgthegtotalgreturngwasgfourgpercent,
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.
Copyrightg2021g©gMcGraw-
HillgEducation.gAllgrightsgreserved.gNogreproductiongorgdistributiongwithout
thegpriorgwrittengconsentgofgMcGraw-HillgEducation.
, 10. Itgisgimportantgnotgtoglosegsightgofgthegfactgthatgthegresultsgweghavegdiscussedgcovergoverg80gyears,g
wellgbeyondgtheginvestingglifetimegforgmostgofgus.gThereghavegbeengextendedgperiodsgduringgwhichg
smallgstocksghavegdonegterribly.gThus,gonegreasongmostginvestorsgwillgchoosegnotgtogpursuegag100gp
ercentgstockg(particularlygsmall-
capgstocks)gstrategygisgthatgmanyginvestorsghavegrelativelygshortghorizons,gandghighgvolatilityginvest
mentsgmaygbegveryginappropriategingsuchgcases.gTheregaregothergreasons,gbutgwegwillgdefergdiscussi
ongofgthesegtoglatergchapters.
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=g($41g–
g$37)/$37g=g.1081,gorg10.81%gDividendgyieldg=g$.28/$3
7g=g.0076,gorg.76%
Totalgrategofgreturng=g10.81%g+g.76%g=g11.57%
3. Dollargreturng=g500($34g–g$37g+g$.28)g=g–$1,360
Capitalggainsgyieldg=g($34g–g$37)/$37g=g–.0811,gorg–
8.11%gDividendgyieldg=g$.28/$37g=g.0076,gorg.76%
Totalgrategofgreturng=g–8.11%g+g.76%g=g–7.35%
4. a.g averagegreturng=g6.2%,gaveragegriskgpremiumg=g2.6%
b. averagegreturng=g3.6%,gaveragegriskgpremiumg=g0%
c. averagegreturng=g11.9%,gaveragegriskgpremiumg=g8.3%
d. averagegreturng=g17.5%,gaveragegriskgpremiumg=g13.9%
5. Cherrygaveragegreturng=g(17%g+g11%g–g2%g+g3%g+g14%)/5g=g8.60%
Strawgaveragegreturng=g(16%g+g18%g–g6%g+g1%g+g22%)/5g=g10.20%
6. Cherry:gRAg=g8.60%
Varg=g1/4[(.17g–g.086)2g+g(.11g–g.086)2g+g(–.02g–g.086)2g+g(.03g–g.086)2g+g(.14g–g.086)2]g=g.00623
Standardgdeviationg=g(.00623)1/2g=g.0789,gorg7.89%
Straw:gRBg=g10.20%
Varg=g1/4[(.16g–g.102)2g+g(.18g–g.102)2g+g(–.06g–g.102)2g+g(.01g–g.102)2g+g(.22g–g.102)2]g=g.01452
Standardgdeviationg=g(.01452)1/2g=g.1205,gorg12.05%
7. Thegcapitalggainsgyieldgisg($59g–g$65)/$65g=g–.0923,gorg–
9.23%g(noticegthegnegativegsign).g Withgagdividendgyieldgofg1.2gpercent,gthegtotalgreturngisg–
Copyrightg2021g©gMcGraw-
HillgEducation.gAllgrightsgreserved.gNogreproductiongorgdistributiongwithout
thegpriorgwrittengconsentgofgMcGraw-HillgEducation.
, 8.03%.
Copyrightg2021g©gMcGraw-
HillgEducation.gAllgrightsgreserved.gNogreproductiongorgdistributiongwithout
thegpriorgwrittengconsentgofgMcGraw-HillgEducation.
, 8. Geometricgreturng=g[(1g+g.17)(1g+g.11)(1g-g.02)(1g+g.03)(1g+g.14)](1/5)g–g1g=g.0837,gorg8.37%
9. Arithmeticgreturng=g(.21g+g.12g+g.07g–.13g–g.04g+g.26)/6g=g.0817,gorg8.17%
Geometricgreturng=g[(1g+g.21)(1g+g.12)(1g+g.07)(1g–g.13)(1g–g.04)(1g+g.26)](1/6)g–g1g=g.0730,gorg7.30%
IntermediategQuestions
10. That’sgplusgorgminusgonegstandardgdeviation,gsogaboutgtwo-
thirdsgofgthegtime,gorgtwogyearsgoutgofgthree.gIngonegyeargoutgofgthree,gyougwillgbegoutsidegthisgrang
e,gimplyinggthatgyougwillgbegbelowgitgonegyeargoutgofgsixgandgabovegitgonegyeargoutgofgsix.
11. Youglosegmoneygifgyoughavegagnegativegreturn.gWithgag12gpercentgexpectedgreturngandgag6gpercentg
standardgdeviation,gagzerogreturngisgtwogstandardgdeviationsgbelowgthegaverage.gThegoddsgofgbeingg
outsideg(abovegorgbelow)gtwogstandardgdeviationsgareg5gpercent;gthegoddsgofgbeinggbelowgareghalfg t
hat,gorg2.5gpercent.g(It’sgactuallyg2.28gpercent.)gYougshouldgexpectgtoglosegmoneygonlyg2.5gyearsgou
tgofgeveryg100.gIt’sgagprettygsafeginvestment.
12. Thegaveragegreturngisg5.9gpercent,gwithgagstandardgdeviationgofg9.8gpercent,gsogProb(Returng<g–
3.9gorgReturng >g15.7g)g≈g1/3,gbutgwegaregonlyginterestedgingonegtail;gProb(Returng<g–
3.9)g≈g1/6,gwhichgisghalfgofg1/3g.
95%: 5.9g±g2σg=g5.9g±g2(9.8)g=g–13.7%gtog25.5%
99%: 5.9g±g3σg=g5.9g±g3(9.8)g=g–23.5%gtog35.3%
13. Expectedgreturng=g17.5%;g σg=g36.3%.gDoublinggyourgmoneygisgag100%greturn,gsogifgthegreturngdist
ributiongisgnormal,gZg=g(100g–g17.5)/36.3g=g2.27gstandardgdeviations;gthisgisgin-
betweengtwogandgthreegstandardgdeviations,gsogthegprobabilitygisgsmall,gsomewheregbetweeng.5%gan
dg2.5%g(why?).gReferringgtogthegnearestgZgtable,gthegactualgprobabilitygisg=g1.152%,gorgaboutgonceg
everyg100gyears.gTriplinggyourgmoneygwouldgbegZg=g(200g–
g17.5)/36.3g=g5.028gstandardgdeviations;gthisgcorrespondsgtogagprobabilitygofg(much)glessgthang0.5%
,gorgoncegeveryg200gyears.g(Thegactualganswergisglessgthangoncegeveryg1gmilliongyears,gsogdon’tghol
dgyourgbreath.)
14. Year Commongstocks T-billgreturn Riskgpremium
1973 –14.69% 7.29% –21.98%
1974 –26.47% 7.99% –34.46%
1975 37.23% 5.87% 31.36%
1796 23.93% 5.07% 18.86%
1977 –7.16% 5.45% –12.61%
sum 12.84% 31.67% –18.83%
a. Annualgriskgpremiumg=gCommongstockgreturng–gT-billgreturng(seegtablegabove).
b. Averagegreturns:gCommongstocksg=g12.84/5g=g.0257,gorg2.57%;g T-
billsg=g31.67/5g=g.0633,gorg6.33%;
Riskgpremiumg=g–18.83/5g=g–.0377,gorg–3.77%
c. Commongstocks:gVarg=g1/4[g(–.1469g–g.0257)2g+g(–.2647g–g.0257)2g+g(.3723g–g.0257)2g+
(.2393g–g.0257)2g+g(–.0716g–g.0257)2]g=g.072337
Standardgdeviationg=g(0.072337)1/2g=g.2690,gorg26.90%
T-bills:g Varg=g1/4[(.0729g–g.0633)2g+g(.0799g–g.0633)2g+g(.0587g–g.0633)2g+g(.0507–.0633)2g+
(.0545g–g.0633)2]g=g.000156
Copyrightg2021g©gMcGraw-
HillgEducation.gAllgrightsgreserved.gNogreproductiongorgdistributiongwithout
thegpriorgwrittengconsentgofgMcGraw-HillgEducation.
