Solution Manual for Fundamentals of Investments Valuation a
l l l l l l l
nd Management, 10th Edition by Bradford Jordan and Thomas
l l l l l l l l
Miller and Steve Dolvin
l l l l
SOLUTION MANUAL FOR l l
FundamentalsloflInvestmentslValuationlandlManagement,l10thlEditionlJordan
Chapterl1-21
Chapterl1
AlBrieflHistoryloflRisklandlReturn
ConceptlQuestions
1. Forlbothlrisklandlreturn,lincreasinglorderlislb,lc,la,ld.lOnlaverage,lthelhigherlthelriskloflanlinvestment,lthel
higherlislitslexpectedlreturn.
2. Sincelthelpriceldidn’tlchange,lthelcapitallgainslyieldlwaslzero.l Ifltheltotallreturnlwaslfourlpercent,lthenlthe
ldividendlyieldlmustlbelfourlpercent.
3. Itlislimpossibleltolloselmorelthanl–
100lpercentloflyourlinvestment.lTherefore,lreturnldistributionslarelcutlofflonlthellowerltaillatl–
100lpercent;liflreturnslwereltrulylnormallyldistributed,lyoulcouldlloselmuchlmore.
4. Tolcalculatelanlarithmeticlreturn,lyoulsumlthelreturnslandldividelbylthelnumberloflreturns.lAslsuch,larith
meticlreturnsldolnotlaccountlforltheleffectsloflcompoundingl(and,linlparticular,ltheleffectloflvolatility).l
Geometriclreturnsldolaccountlforltheleffectsloflcompoundinglandlforlchangeslinlthelbaselusedlforleachly
ear’slcalculationloflreturns.lAslanlinvestor,lthelmorelimportantlreturnloflanlassetlislthelgeometriclreturn.
5. Blume’slformulaluseslthelarithmeticlandlgeometriclreturnslalonglwithlthelnumberloflobservationsltolapp
roximatelalholdinglperiodlreturn.lWhenlpredictinglalholdinglperiodlreturn,lthelarithmeticlreturnlwilllten
dltolbeltoolhighlandlthelgeometriclreturnlwillltendltolbeltoollow.lBlume’slformulaladjustsltheselreturnslforl
differentlholdinglperiodlexpectedlreturns.
6. T-
billlrateslwerelhighestlinlthelearlyleightieslsincelinflationlatltheltimelwaslrelativelylhigh.lAslweldiscussli
nlourlchapterlonlinterestlrates,lrateslonlT-
billslwilllalmostlalwayslbelslightlylhigherlthanlthelexpectedlrateloflinflation.
7. Risklpremiumslarelaboutlthelsamelregardlessloflwhetherlwelaccountlforlinflation.lThelreasonlislthatlriskl
premiumslareltheldifferencelbetweenltwolreturns,lsolinflationlessentiallylnetslout.
8. Returns,lrisklpremiums,landlvolatilitylwouldlalllbellowerlthanlwelestimatedlbecauselaftertaxlreturnslarel
smallerlthanlpretaxlreturns.
1
,Solution Manual for Fundamentals of Investments Valuation a
l l l l l l l
nd Management, 10th Edition by Bradford Jordan and Thomas
l l l l l l l l
Miller and Steve Dolvin
l l l l
9. WelhavelseenlthatlT-billslbarelylkeptluplwithlinflationlbeforeltaxes.lAfterltaxes,linvestorslinlT-
billslactuallyllostlgroundl(assuminglanythinglotherlthanlalveryllowltaxlrate).lThus,lanlalllT-
billlstrategylwilllprobablylloselmoneylinlrealldollarslforlaltaxablelinvestor.
10. Itlislimportantlnotltolloselsightloflthelfactlthatlthelresultslwelhaveldiscussedlcoverloverl80lyears,lwelllbey
ondlthelinvestingllifetimelforlmostloflus.lTherelhavelbeenlextendedlperiodslduringlwhichlsmalllstockslh
aveldonelterribly.lThus,lonelreasonlmostlinvestorslwilllchooselnotltolpursuelal100lpercentlstockl(particul
arlylsmall-
caplstocks)lstrategylislthatlmanylinvestorslhavelrelativelylshortlhorizons,landlhighlvolatilitylinvestmentsl
maylbelverylinappropriatelinlsuchlcases.lTherelarelotherlreasons,lbutlwelwillldeferldiscussionlofltheseltol
laterlchapters.
11.
SolutionsltolQuestionslandlProblems
NOTE:lAlllendloflchapterlproblemslwerelsolvedlusinglalspreadsheet.lManylproblemslrequirelmultiplelsteps.lD
ueltolspacelandlreadabilitylconstraints,lwhenltheselintermediatelstepslarelincludedlinlthislsolutionslmanual,lr
oundinglmaylappearltolhaveloccurred.lHowever,lthelfinallanswerlforleachlproblemlislfoundlwithoutlrounding
lduringlanylsteplinlthelproblem.
CorelQuestions
1. Totalldollarlreturnl=l100($41l–l$37l+l$.28)l=l$428.00
Whetherlyoulchooseltolselllthelstockldoeslnotlaffectlthelgainlorllosslforlthelyear;lyourlstocklislworthlwha
tlitlwouldlbringliflyoulsoldlit.lWhetherlyoulchooseltoldolsolorlnotlislirrelevantl(ignoringlcommissionslan
dltaxes).
2. Capitallgainsl yieldl l $41l–l$37l l /l$37l l.1081,lorl10.81%l Dividendlyieldl l$.28/$37l l.0076,lorl.76%
Totallrateloflreturnl l10.81%l l .76%l l11.57%
3. Dollarlreturnl=l500($34l–l$37l+l$.28)l=l–$1,360
Capitall gainsl yieldl l $34l –l $37 /$37l l –.0811,l orl –
8.11%lDividendlyieldl l $.28/$37l
l .0076,lorl.76%lTotallrateloflreturnl=l–l8.11%l+l.76%l=l–7.35%
4.
a. averagelreturnl=l6.0%,laveragelrisklpremiuml=l2.7%
b. averagelreturnl=l3.3%,laveragelrisklpremiuml=l0%
c. averagelreturnl=l12.3%,laveragelrisklpremiuml=l9.0%
d. averagelreturnl=l16.3%,laveragelrisklpremiuml=l13.0%
2
,Solution Manual for Fundamentals of Investments Valuation a
l l l l l l l
nd Management, 10th Edition by Bradford Jordan and Thomas
l l l l l l l l
Miller and Steve Dolvin
l l l l
5. Cherryl averagel returnl l 17%l l 11%l–l2%l l 3%l l 14% /5l l 8.60%l Strawl averagel returnl
16%l l 18%l–l6%l l1%l l22% /5l l10.20%
6. Cherry:lRAl l 8.60%
2 2 2 2 2
Varl l 1/l4 .17l–l.086 ll
l .11l –l.086 ll
l –.02l –l.086 ll
l .03l –l.086 ll
l .14l –l.086 ll
l l .00623
1/2
l l
Standardldeviationl l .00623 l .0789,lorl7.89%
Straw:lRBl l 10.20%
Varl l 1/l4 .16l–l.102l l2l l l .18l–l.102 2l l –.06l–l.102
l 2l l .01l–l.102
l 2l l .22l–l.102
l 2l
l
.01452l
1/2
l l l
Standardldeviationl l .01452l .1205,lorl12.05%
7. Thelcapitallgainslyieldlisl $59l–l$65l /$65 l –.0923,lorl–
9.23%l(noticelthelnegativelsign).lWithlaldividendlyieldlofl1.2lpercent,ltheltotallreturnlisl–8.03%.
8. Geometriclreturnl l 1l l .17l 1 .11l
l l l 1 .02l
l l l 1 .03l
l l l 1 .14l
l l l l(1/5)l –l1l l .0837,
orl8.37%
9. Arithmeticlreturnl l .21l l.12l l.07l–.13l–l.04l l.26 /l6l l .0817,lorl8.17%
(1/6)
Geometriclreturnl 1l l .21l 1 .12l
l l l 1 .07l
l l l 1 – .13
l l l 1l–l.04l 1 .26
l l l –l 1l
.0730,lorl7.30%
IntermediatelQuestions
10. That’slpluslorlminuslonelstandardldeviation,lsolaboutltwo-
thirdslofltheltime,lorltwolyearsloutloflthree.lInlonelyearloutloflthree,lyoulwilllbeloutsidelthislrange,limplyinglt
hatlyoulwilllbelbelowlitlonelyearloutloflsixlandlabovelitlonelyearloutloflsix.
3
, Solution Manual for Fundamentals of Investments Valuation a
l l l l l l l
nd Management, 10th Edition by Bradford Jordan and Thomas
l l l l l l l l
Miller and Steve Dolvin
l l l l
11. Youlloselmoneyliflyoulhavelalnegativelreturn.lWithlal12lpercentlexpectedlreturnlandlal6lpercentlstandardldev
iation,lalzerolreturnlisltwolstandardldeviationslbelowlthelaverage.lTheloddsloflbeingloutsidel(abovelorlbelow)
ltwolstandardldeviationslarel5lpercent;ltheloddsloflbeinglbelowlarelhalflthat,lorl2.5lpercent.l(It’slactuallyl2.28l
percent.)lYoulshouldlexpectltolloselmoneylonlyl2.5lyearsloutlofleveryl100.lIt’slalprettylsafelinvestment.
12. Thelaveragelreturnlisl6.0lpercent,lwithlalstandardldeviationlofl9.8lpercent,lsolProb(Returnl<l–
3.8lorlReturnl15.8l)l l1/3,lbutlwelarelonlylinterestedlinloneltail;lProb Returnl l –3.9l l l 1/l6
,lwhichlisl halflofl1/3l(orlaboutl16%)l.
95%:l6.0l±l2σl=l6.0l±l2(9.8)l=l–13.6%ltol25.6%
99%:l6.0l±l3σl=l6.0l±l3(9.8)l=l–23.4%ltol35.4%
13. Expectedlreturnl=l 16.4%;lσl =l31.2%.l Doublinglyourl moneylisl al100%lreturn,lsoliflthel returnldistribution
islnormal,lZ l 100l–l16.4l /l31.2l 2.68lstandardldeviations;lthislislin-
betweenltwolandlthreelstandardldeviations,lsolthelprobabilitylislsmall,lsomewherelbetweenl.5%landl2.5%l(w
hy?).lReferringltolthelnearestlZltable,lthelactuallprobabilitylisl=l0.369%,lorllesslthanleveryl100lyears.lTriplin
glyourlmoneylwouldlbel Z
200l–l16.4 /l31.2l
5.88lstandardldeviations;lthislcorrespondsltolalprobabilitylofl(much)llesslthanl0.01%.l(Thelactuallanswerlislle
sslthanlonceleveryl1lmillionlyears,lsoldon’tlholdlyourlbreath.)
14.
Year Commonlstocks T-billlreturn Risklpremium
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. Annuallrisklpremiuml=lCommonlstocklreturnl–lT-billlreturnl(seeltablelabove).
b. Averagelreturns:lCommonlstocksl l12.84/5l l .0257,lorl2.57%;lT-billsl l31.67/5l
l.0633l,lorl6.33%lRisklpremiuml l–18.83/5l l –.0377,lorl–3.77%
2
c. Commonlstocks:lVarl l 1/l4[l –.1469l–l.0257 2
l l –.2647l–l.0257 ll
l .3723l–l.0257
l l2l
.2393l –l.0257 2l l
–.0716l–l.0257
l
2l l l
] .072337
1/2
Standardldeviationl l 0.072337 l l .2690,lorl26.90%
T-bills:lVarl l1/l4 .0729l–l.0633 2l
l .0799l–l.0633
l 2l
l .0587l–l.0633
l l2l
l l .0507l–.0633 2l
.0545l–l.0633l
l
4
l l l l l l l
nd Management, 10th Edition by Bradford Jordan and Thomas
l l l l l l l l
Miller and Steve Dolvin
l l l l
SOLUTION MANUAL FOR l l
FundamentalsloflInvestmentslValuationlandlManagement,l10thlEditionlJordan
Chapterl1-21
Chapterl1
AlBrieflHistoryloflRisklandlReturn
ConceptlQuestions
1. Forlbothlrisklandlreturn,lincreasinglorderlislb,lc,la,ld.lOnlaverage,lthelhigherlthelriskloflanlinvestment,lthel
higherlislitslexpectedlreturn.
2. Sincelthelpriceldidn’tlchange,lthelcapitallgainslyieldlwaslzero.l Ifltheltotallreturnlwaslfourlpercent,lthenlthe
ldividendlyieldlmustlbelfourlpercent.
3. Itlislimpossibleltolloselmorelthanl–
100lpercentloflyourlinvestment.lTherefore,lreturnldistributionslarelcutlofflonlthellowerltaillatl–
100lpercent;liflreturnslwereltrulylnormallyldistributed,lyoulcouldlloselmuchlmore.
4. Tolcalculatelanlarithmeticlreturn,lyoulsumlthelreturnslandldividelbylthelnumberloflreturns.lAslsuch,larith
meticlreturnsldolnotlaccountlforltheleffectsloflcompoundingl(and,linlparticular,ltheleffectloflvolatility).l
Geometriclreturnsldolaccountlforltheleffectsloflcompoundinglandlforlchangeslinlthelbaselusedlforleachly
ear’slcalculationloflreturns.lAslanlinvestor,lthelmorelimportantlreturnloflanlassetlislthelgeometriclreturn.
5. Blume’slformulaluseslthelarithmeticlandlgeometriclreturnslalonglwithlthelnumberloflobservationsltolapp
roximatelalholdinglperiodlreturn.lWhenlpredictinglalholdinglperiodlreturn,lthelarithmeticlreturnlwilllten
dltolbeltoolhighlandlthelgeometriclreturnlwillltendltolbeltoollow.lBlume’slformulaladjustsltheselreturnslforl
differentlholdinglperiodlexpectedlreturns.
6. T-
billlrateslwerelhighestlinlthelearlyleightieslsincelinflationlatltheltimelwaslrelativelylhigh.lAslweldiscussli
nlourlchapterlonlinterestlrates,lrateslonlT-
billslwilllalmostlalwayslbelslightlylhigherlthanlthelexpectedlrateloflinflation.
7. Risklpremiumslarelaboutlthelsamelregardlessloflwhetherlwelaccountlforlinflation.lThelreasonlislthatlriskl
premiumslareltheldifferencelbetweenltwolreturns,lsolinflationlessentiallylnetslout.
8. Returns,lrisklpremiums,landlvolatilitylwouldlalllbellowerlthanlwelestimatedlbecauselaftertaxlreturnslarel
smallerlthanlpretaxlreturns.
1
,Solution Manual for Fundamentals of Investments Valuation a
l l l l l l l
nd Management, 10th Edition by Bradford Jordan and Thomas
l l l l l l l l
Miller and Steve Dolvin
l l l l
9. WelhavelseenlthatlT-billslbarelylkeptluplwithlinflationlbeforeltaxes.lAfterltaxes,linvestorslinlT-
billslactuallyllostlgroundl(assuminglanythinglotherlthanlalveryllowltaxlrate).lThus,lanlalllT-
billlstrategylwilllprobablylloselmoneylinlrealldollarslforlaltaxablelinvestor.
10. Itlislimportantlnotltolloselsightloflthelfactlthatlthelresultslwelhaveldiscussedlcoverloverl80lyears,lwelllbey
ondlthelinvestingllifetimelforlmostloflus.lTherelhavelbeenlextendedlperiodslduringlwhichlsmalllstockslh
aveldonelterribly.lThus,lonelreasonlmostlinvestorslwilllchooselnotltolpursuelal100lpercentlstockl(particul
arlylsmall-
caplstocks)lstrategylislthatlmanylinvestorslhavelrelativelylshortlhorizons,landlhighlvolatilitylinvestmentsl
maylbelverylinappropriatelinlsuchlcases.lTherelarelotherlreasons,lbutlwelwillldeferldiscussionlofltheseltol
laterlchapters.
11.
SolutionsltolQuestionslandlProblems
NOTE:lAlllendloflchapterlproblemslwerelsolvedlusinglalspreadsheet.lManylproblemslrequirelmultiplelsteps.lD
ueltolspacelandlreadabilitylconstraints,lwhenltheselintermediatelstepslarelincludedlinlthislsolutionslmanual,lr
oundinglmaylappearltolhaveloccurred.lHowever,lthelfinallanswerlforleachlproblemlislfoundlwithoutlrounding
lduringlanylsteplinlthelproblem.
CorelQuestions
1. Totalldollarlreturnl=l100($41l–l$37l+l$.28)l=l$428.00
Whetherlyoulchooseltolselllthelstockldoeslnotlaffectlthelgainlorllosslforlthelyear;lyourlstocklislworthlwha
tlitlwouldlbringliflyoulsoldlit.lWhetherlyoulchooseltoldolsolorlnotlislirrelevantl(ignoringlcommissionslan
dltaxes).
2. Capitallgainsl yieldl l $41l–l$37l l /l$37l l.1081,lorl10.81%l Dividendlyieldl l$.28/$37l l.0076,lorl.76%
Totallrateloflreturnl l10.81%l l .76%l l11.57%
3. Dollarlreturnl=l500($34l–l$37l+l$.28)l=l–$1,360
Capitall gainsl yieldl l $34l –l $37 /$37l l –.0811,l orl –
8.11%lDividendlyieldl l $.28/$37l
l .0076,lorl.76%lTotallrateloflreturnl=l–l8.11%l+l.76%l=l–7.35%
4.
a. averagelreturnl=l6.0%,laveragelrisklpremiuml=l2.7%
b. averagelreturnl=l3.3%,laveragelrisklpremiuml=l0%
c. averagelreturnl=l12.3%,laveragelrisklpremiuml=l9.0%
d. averagelreturnl=l16.3%,laveragelrisklpremiuml=l13.0%
2
,Solution Manual for Fundamentals of Investments Valuation a
l l l l l l l
nd Management, 10th Edition by Bradford Jordan and Thomas
l l l l l l l l
Miller and Steve Dolvin
l l l l
5. Cherryl averagel returnl l 17%l l 11%l–l2%l l 3%l l 14% /5l l 8.60%l Strawl averagel returnl
16%l l 18%l–l6%l l1%l l22% /5l l10.20%
6. Cherry:lRAl l 8.60%
2 2 2 2 2
Varl l 1/l4 .17l–l.086 ll
l .11l –l.086 ll
l –.02l –l.086 ll
l .03l –l.086 ll
l .14l –l.086 ll
l l .00623
1/2
l l
Standardldeviationl l .00623 l .0789,lorl7.89%
Straw:lRBl l 10.20%
Varl l 1/l4 .16l–l.102l l2l l l .18l–l.102 2l l –.06l–l.102
l 2l l .01l–l.102
l 2l l .22l–l.102
l 2l
l
.01452l
1/2
l l l
Standardldeviationl l .01452l .1205,lorl12.05%
7. Thelcapitallgainslyieldlisl $59l–l$65l /$65 l –.0923,lorl–
9.23%l(noticelthelnegativelsign).lWithlaldividendlyieldlofl1.2lpercent,ltheltotallreturnlisl–8.03%.
8. Geometriclreturnl l 1l l .17l 1 .11l
l l l 1 .02l
l l l 1 .03l
l l l 1 .14l
l l l l(1/5)l –l1l l .0837,
orl8.37%
9. Arithmeticlreturnl l .21l l.12l l.07l–.13l–l.04l l.26 /l6l l .0817,lorl8.17%
(1/6)
Geometriclreturnl 1l l .21l 1 .12l
l l l 1 .07l
l l l 1 – .13
l l l 1l–l.04l 1 .26
l l l –l 1l
.0730,lorl7.30%
IntermediatelQuestions
10. That’slpluslorlminuslonelstandardldeviation,lsolaboutltwo-
thirdslofltheltime,lorltwolyearsloutloflthree.lInlonelyearloutloflthree,lyoulwilllbeloutsidelthislrange,limplyinglt
hatlyoulwilllbelbelowlitlonelyearloutloflsixlandlabovelitlonelyearloutloflsix.
3
, Solution Manual for Fundamentals of Investments Valuation a
l l l l l l l
nd Management, 10th Edition by Bradford Jordan and Thomas
l l l l l l l l
Miller and Steve Dolvin
l l l l
11. Youlloselmoneyliflyoulhavelalnegativelreturn.lWithlal12lpercentlexpectedlreturnlandlal6lpercentlstandardldev
iation,lalzerolreturnlisltwolstandardldeviationslbelowlthelaverage.lTheloddsloflbeingloutsidel(abovelorlbelow)
ltwolstandardldeviationslarel5lpercent;ltheloddsloflbeinglbelowlarelhalflthat,lorl2.5lpercent.l(It’slactuallyl2.28l
percent.)lYoulshouldlexpectltolloselmoneylonlyl2.5lyearsloutlofleveryl100.lIt’slalprettylsafelinvestment.
12. Thelaveragelreturnlisl6.0lpercent,lwithlalstandardldeviationlofl9.8lpercent,lsolProb(Returnl<l–
3.8lorlReturnl15.8l)l l1/3,lbutlwelarelonlylinterestedlinloneltail;lProb Returnl l –3.9l l l 1/l6
,lwhichlisl halflofl1/3l(orlaboutl16%)l.
95%:l6.0l±l2σl=l6.0l±l2(9.8)l=l–13.6%ltol25.6%
99%:l6.0l±l3σl=l6.0l±l3(9.8)l=l–23.4%ltol35.4%
13. Expectedlreturnl=l 16.4%;lσl =l31.2%.l Doublinglyourl moneylisl al100%lreturn,lsoliflthel returnldistribution
islnormal,lZ l 100l–l16.4l /l31.2l 2.68lstandardldeviations;lthislislin-
betweenltwolandlthreelstandardldeviations,lsolthelprobabilitylislsmall,lsomewherelbetweenl.5%landl2.5%l(w
hy?).lReferringltolthelnearestlZltable,lthelactuallprobabilitylisl=l0.369%,lorllesslthanleveryl100lyears.lTriplin
glyourlmoneylwouldlbel Z
200l–l16.4 /l31.2l
5.88lstandardldeviations;lthislcorrespondsltolalprobabilitylofl(much)llesslthanl0.01%.l(Thelactuallanswerlislle
sslthanlonceleveryl1lmillionlyears,lsoldon’tlholdlyourlbreath.)
14.
Year Commonlstocks T-billlreturn Risklpremium
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. Annuallrisklpremiuml=lCommonlstocklreturnl–lT-billlreturnl(seeltablelabove).
b. Averagelreturns:lCommonlstocksl l12.84/5l l .0257,lorl2.57%;lT-billsl l31.67/5l
l.0633l,lorl6.33%lRisklpremiuml l–18.83/5l l –.0377,lorl–3.77%
2
c. Commonlstocks:lVarl l 1/l4[l –.1469l–l.0257 2
l l –.2647l–l.0257 ll
l .3723l–l.0257
l l2l
.2393l –l.0257 2l l
–.0716l–l.0257
l
2l l l
] .072337
1/2
Standardldeviationl l 0.072337 l l .2690,lorl26.90%
T-bills:lVarl l1/l4 .0729l–l.0633 2l
l .0799l–l.0633
l 2l
l .0587l–l.0633
l l2l
l l .0507l–.0633 2l
.0545l–l.0633l
l
4
