Solution Manual for Fundamentals of Investments Valuation a
k k k k k k k
nd Management, 10th Edition by Bradford Jordan and Thoma
k k k k k k k k
s Miller and Steve Dolvin
k k k k
SOLUTION MANUAL FOR k k
Fundamentals of Investments Valuation and Management, 10th Edition Jordan
k k k k k k k k
Chapter 1-21 k
Chapter 1 k
A Brief History of Risk and Return
k k k k k k
Concept Questions k
1. Forkbothkriskkandkreturn,kincreasingkorderkiskb,kc,ka,kd.kOnkaverage,kthekhigherkthekriskkofkankinvestment,kt
hekhigherkiskitskexpectedkreturn.
2. Sincekthekpricekdidn’tkchange,kthekcapitalkgainskyieldkwaskzero.k Ifkthektotalkreturnkwaskfourkpercent,kthenkt
hekdividendkyieldkmustkbekfourkpercent.
3. Itkiskimpossiblektoklosekmorekthank–
100kpercentkofkyourkinvestment.kTherefore,kreturnkdistributionskarekcutkoffkonktheklowerktailkatk–
100kpercent;kifkreturnskwerektrulyknormallykdistributed,kyoukcouldklosekmuchkmore.
4. Tokcalculatekankarithmetickreturn,kyouksumkthekreturnskandkdividekbyktheknumberkofkreturns.kAsksuch,kari
thmetickreturnskdoknotkaccountkforkthekeffectskofkcompoundingk(and,kinkparticular,kthekeffectkofkvolatilit
y).kGeometrickreturnskdokaccountkforkthekeffectskofkcompoundingkandkforkchangeskinkthekbasekusedkforke
achkyear’skcalculationkofkreturns.kAskankinvestor,kthekmorekimportantkreturnkofkankassetkiskthekgeometrick
return.
5. Blume’skformulakuseskthekarithmetickandkgeometrickreturnskalongkwithktheknumberkofkobservationsktoka
pproximatekakholdingkperiodkreturn.kWhenkpredictingkakholdingkperiodkreturn,kthekarithmetickreturnkwill
ktendktokbektookhighkandkthekgeometrickreturnkwillktendktokbektooklow.kBlume’skformulakadjustskthesekretur
nskforkdifferentkholdingkperiodkexpectedkreturns.
6. T-
billkrateskwerekhighestkinkthekearlykeightiesksincekinflationkatkthektimekwaskrelativelykhigh.kAskwekdiscus
skinkourkchapterkonkinterestkrates,krateskonkT-
billskwillkalmostkalwayskbekslightlykhigherkthankthekexpectedkratekofkinflation.
7. Riskkpremiumskarekaboutktheksamekregardlesskofkwhetherkwekaccountkforkinflation.kThekreasonkiskthatkri
skkpremiumskarekthekdifferencekbetweenktwokreturns,ksokinflationkessentiallyknetskout.
8. Returns,kriskkpremiums,kandkvolatilitykwouldkallkbeklowerkthankwekestimatedkbecausekaftertaxkreturnska
reksmallerkthankpretaxkreturns.
1
,Solution Manual for Fundamentals of Investments Valuation a
k k k k k k k
nd Management, 10th Edition by Bradford Jordan and Thoma
k k k k k k k k
s Miller and Steve Dolvin
k k k k
9. WekhavekseenkthatkT-billskbarelykkeptkupkwithkinflationkbeforektaxes.kAfterktaxes,kinvestorskinkT-
billskactuallyklostkgroundk(assumingkanythingkotherkthankakveryklowktaxkrate).kThus,kankallkT-
billkstrategykwillkprobablyklosekmoneykinkrealkdollarskforkaktaxablekinvestor.
10. Itkiskimportantknotktokloseksightkofkthekfactkthatkthekresultskwekhavekdiscussedkcoverkoverk80kyears,kwellkb
eyondkthekinvestingklifetimekforkmostkofkus.kTherekhavekbeenkextendedkperiodskduringkwhichksmallkstoc
kskhavekdonekterribly.kThus,konekreasonkmostkinvestorskwillkchooseknotktokpursuekak100kpercentkstockk(p
articularlyksmall-
capkstocks)kstrategykiskthatkmanykinvestorskhavekrelativelykshortkhorizons,kandkhighkvolatilitykinvestment
skmaykbekverykinappropriatekinksuchkcases.kTherekarekotherkreasons,kbutkwekwillkdeferkdiscussionkofkthes
ektoklaterkchapters.
11.
SolutionsktokQuestionskandkProblems
NOTE:kAllkendkofkchapterkproblemskwereksolvedkusingkakspreadsheet.kManykproblemskrequirekmultipleksteps.kD
uektokspacekandkreadabilitykconstraints,kwhenkthesekintermediatekstepskarekincludedkinkthisksolutionskmanual,k
roundingkmaykappearktokhavekoccurred.kHowever,kthekfinalkanswerkforkeachkproblemkiskfoundkwithoutkroundi
ngkduringkanykstepkinkthekproblem.
CorekQuestions
1. Totalkdollarkreturnk=k100($41k–k$37k+k$.28)k=k$428.00
Whetherkyoukchoosektoksellkthekstockkdoesknotkaffectkthekgainkorklosskforkthekyear;kyourkstockkiskworthkw
hatkitkwouldkbringkifkyouksoldkit.kWhetherkyoukchoosektokdoksokorknotkiskirrelevantk(ignoringkcommissio
nskandktaxes).
2. Capitalkgainsk yieldk k $41k–k$37k k /k$37k k.1081,kork10.81%kDividendk yieldk k $.28/$37k k.0076,kork.76%
Totalkratekofkreturnk k10.81%k k .76%k k11.57%
3. Dollarkreturnk=k500($34k–k$37k+k$.28)k=k–$1,360
Capitalk gainsk yieldk k $34k –k $37 /$37k k –.0811,k ork –
8.11%kDividendkyieldk k $.28/$37k
k .0076,kork.76%kTotalkratekofkreturnk=k–k8.11%k+k.76%k=k–7.35%
4.
a. averagekreturnk=k6.0%,kaveragekriskkpremiumk=k2.7%
b. averagekreturnk=k3.3%,kaveragekriskkpremiumk=k0%
c. averagekreturnk=k12.3%,kaveragekriskkpremiumk=k9.0%
d. averagekreturnk=k16.3%,kaveragekriskkpremiumk=k13.0%
2
,Solution Manual for Fundamentals of Investments Valuation a
k k k k k k k
nd Management, 10th Edition by Bradford Jordan and Thoma
k k k k k k k k
s Miller and Steve Dolvin
k k k k
5. Cherrykaveragek returnk k 17%k k 11%k –k 2%k k 3%k k 14% /5k k 8.60%k Strawk averagek returnk
16%k k 18%k–k6%k k1%k k22% /5k k10.20%
6. Cherry:kRAk k 8.60%
2 2 2 2 2
Vark k 1/k4 .17k–k.086 k k
k .11k –k.086 k k
k –.02k –k.086 k k
k .03k –k.086 k k
k .14k –k.086 k k
k k .00623
1/2
Standardkdeviationk k .00623 k k
k .0789,kork7.89%
Straw:kRBk k 10.20%
Vark k 1/k4 .16k–k.102k k 2k
k .18k–k.102
k
2k k –.06k–k.102
k
2k k .01k–k.102
k
2k k .22k–k.102
k
2k
k
.01452k
1/2
Standardkdeviationk k .01452k k k
k .1205,kork12.05%
7. Thekcapitalkgainskyieldkisk $59k–k$65k /$65 k –.0923,kork–
9.23%k(noticektheknegativeksign).kWithkakdividendkyieldkofk1.2kpercent,kthektotalkreturnkisk–8.03%.
8. Geometrickreturnk k 1k k .17k k 1k k .11k k1k k .02k k 1k k .03k k 1k k .14k k(1/5)k
–k1k k .0837,
ork8.37%
9. Arithmetickreturnk k .21k k.12k k.07k–.13k–k.04k k.26 /k6k k .0817,kork8.17%
(1/6)
Geometrickreturnk 1k k .21k k 1k k .12k k 1k k .07k k 1k–k.13 1k–k.04k k 1k k .26 –k 1k
.0730,kork7.30%
IntermediatekQuestions
10. That’skpluskorkminuskonekstandardkdeviation,ksokaboutktwo-
thirdskofkthektime,korktwokyearskoutkofkthree.kInkonekyearkoutkofkthree,kyoukwillkbekoutsidekthiskrange,kimplyin
gkthatkyoukwillkbekbelowkitkonekyearkoutkofksixkandkabovekitkonekyearkoutkofksix.
3
, Solution Manual for Fundamentals of Investments Valuation a
k k k k k k k
nd Management, 10th Edition by Bradford Jordan and Thoma
k k k k k k k k
s Miller and Steve Dolvin
k k k k
11. Youklosekmoneykifkyoukhavekaknegativekreturn.kWithkak12kpercentkexpectedkreturnkandkak6kpercentkstandardkd
eviation,kakzerokreturnkisktwokstandardkdeviationskbelowkthekaverage.kThekoddskofkbeingkoutsidek(abovekorkbe
low)ktwokstandardkdeviationskarek5kpercent;kthekoddskofkbeingkbelowkarekhalfkthat,kork2.5kpercent.k(It’skactual
lyk2.28kpercent.)kYoukshouldkexpectktoklosekmoneykonlyk2.5kyearskoutkofkeveryk100.kIt’skakprettyksafekinvest
ment.
12. Thekaveragekreturnkisk6.0kpercent,kwithkakstandardkdeviationkofk9.8kpercent,ksokProb(Returnk<k–
3.8korkReturnk15.8k)k k1/3,kbutkwekarekonlykinterestedkinkonektail;kProb Returnk k –3.9k k k 1/k6
,kwhichkisk halfkofk1/3k(orkaboutk16%)k.
95%:k6.0k±k2σk=k6.0k±k2(9.8)k=k–13.6%ktok25.6%
99%:k6.0k±k3σk=k6.0k±k3(9.8)k=k–23.4%ktok35.4%
13. Expectedkreturnk=k 16.4%;kσk =k31.2%.k Doublingkyourk moneykisk ak100%kreturn,ksokifkthek returnkdistribution
isknormal,kZ k 100k–k16.4k /k31.2k 2.68kstandardkdeviations;kthiskiskin-
betweenktwokandkthreekstandardkdeviations,ksokthekprobabilitykisksmall,ksomewherekbetweenk.5%kandk2.5%k(
why?).kReferringktoktheknearestkZktable,kthekactualkprobabilitykisk=k0.369%,korklesskthankeveryk100kyears.kTri
plingkyourkmoneykwouldkbek Z
200k–k16.4 /k31.2k
5.88kstandardkdeviations;kthiskcorrespondsktokakprobabilitykofk(much)klesskthank0.01%.k(Thekactualkanswerkisk
lesskthankoncekeveryk1kmillionkyears,ksokdon’tkholdkyourkbreath.)
14.
Year Commonkstocks T-billkreturn Riskkpremium
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. Annualkriskkpremiumk=kCommonkstockkreturnk–kT-billkreturnk(seektablekabove).
b. Averagekreturns:kCommonkstocksk k12.84/5k k .0257,kork2.57%;kT-billsk k31.67/5k
k .0633k,kork6.33%kRiskkpremiumk k–18.83/5k k –.0377,kork–3.77%
2
c. Commonkstocks:kVark k 1/k4[k –.1469k–k.0257 2
k k –.2647k–k.0257 k k
k .3723k–k.0257
k
k2k
.2393k –k.0257 2k k –.0716k–k.0257
k
2k
]k k .072337
1/2
Standardkdeviationk k 0.072337 k k .2690,kork26.90%
T-bills:k Vark k1/k4 .0729k–k.0633 2k
k .0799k–k.0633
k
2k
k .0587k–k.0633
k
k2k
k k .0507k–.0633 2k
k.0545k–k.0633k
4
k k k k k k k
nd Management, 10th Edition by Bradford Jordan and Thoma
k k k k k k k k
s Miller and Steve Dolvin
k k k k
SOLUTION MANUAL FOR k k
Fundamentals of Investments Valuation and Management, 10th Edition Jordan
k k k k k k k k
Chapter 1-21 k
Chapter 1 k
A Brief History of Risk and Return
k k k k k k
Concept Questions k
1. Forkbothkriskkandkreturn,kincreasingkorderkiskb,kc,ka,kd.kOnkaverage,kthekhigherkthekriskkofkankinvestment,kt
hekhigherkiskitskexpectedkreturn.
2. Sincekthekpricekdidn’tkchange,kthekcapitalkgainskyieldkwaskzero.k Ifkthektotalkreturnkwaskfourkpercent,kthenkt
hekdividendkyieldkmustkbekfourkpercent.
3. Itkiskimpossiblektoklosekmorekthank–
100kpercentkofkyourkinvestment.kTherefore,kreturnkdistributionskarekcutkoffkonktheklowerktailkatk–
100kpercent;kifkreturnskwerektrulyknormallykdistributed,kyoukcouldklosekmuchkmore.
4. Tokcalculatekankarithmetickreturn,kyouksumkthekreturnskandkdividekbyktheknumberkofkreturns.kAsksuch,kari
thmetickreturnskdoknotkaccountkforkthekeffectskofkcompoundingk(and,kinkparticular,kthekeffectkofkvolatilit
y).kGeometrickreturnskdokaccountkforkthekeffectskofkcompoundingkandkforkchangeskinkthekbasekusedkforke
achkyear’skcalculationkofkreturns.kAskankinvestor,kthekmorekimportantkreturnkofkankassetkiskthekgeometrick
return.
5. Blume’skformulakuseskthekarithmetickandkgeometrickreturnskalongkwithktheknumberkofkobservationsktoka
pproximatekakholdingkperiodkreturn.kWhenkpredictingkakholdingkperiodkreturn,kthekarithmetickreturnkwill
ktendktokbektookhighkandkthekgeometrickreturnkwillktendktokbektooklow.kBlume’skformulakadjustskthesekretur
nskforkdifferentkholdingkperiodkexpectedkreturns.
6. T-
billkrateskwerekhighestkinkthekearlykeightiesksincekinflationkatkthektimekwaskrelativelykhigh.kAskwekdiscus
skinkourkchapterkonkinterestkrates,krateskonkT-
billskwillkalmostkalwayskbekslightlykhigherkthankthekexpectedkratekofkinflation.
7. Riskkpremiumskarekaboutktheksamekregardlesskofkwhetherkwekaccountkforkinflation.kThekreasonkiskthatkri
skkpremiumskarekthekdifferencekbetweenktwokreturns,ksokinflationkessentiallyknetskout.
8. Returns,kriskkpremiums,kandkvolatilitykwouldkallkbeklowerkthankwekestimatedkbecausekaftertaxkreturnska
reksmallerkthankpretaxkreturns.
1
,Solution Manual for Fundamentals of Investments Valuation a
k k k k k k k
nd Management, 10th Edition by Bradford Jordan and Thoma
k k k k k k k k
s Miller and Steve Dolvin
k k k k
9. WekhavekseenkthatkT-billskbarelykkeptkupkwithkinflationkbeforektaxes.kAfterktaxes,kinvestorskinkT-
billskactuallyklostkgroundk(assumingkanythingkotherkthankakveryklowktaxkrate).kThus,kankallkT-
billkstrategykwillkprobablyklosekmoneykinkrealkdollarskforkaktaxablekinvestor.
10. Itkiskimportantknotktokloseksightkofkthekfactkthatkthekresultskwekhavekdiscussedkcoverkoverk80kyears,kwellkb
eyondkthekinvestingklifetimekforkmostkofkus.kTherekhavekbeenkextendedkperiodskduringkwhichksmallkstoc
kskhavekdonekterribly.kThus,konekreasonkmostkinvestorskwillkchooseknotktokpursuekak100kpercentkstockk(p
articularlyksmall-
capkstocks)kstrategykiskthatkmanykinvestorskhavekrelativelykshortkhorizons,kandkhighkvolatilitykinvestment
skmaykbekverykinappropriatekinksuchkcases.kTherekarekotherkreasons,kbutkwekwillkdeferkdiscussionkofkthes
ektoklaterkchapters.
11.
SolutionsktokQuestionskandkProblems
NOTE:kAllkendkofkchapterkproblemskwereksolvedkusingkakspreadsheet.kManykproblemskrequirekmultipleksteps.kD
uektokspacekandkreadabilitykconstraints,kwhenkthesekintermediatekstepskarekincludedkinkthisksolutionskmanual,k
roundingkmaykappearktokhavekoccurred.kHowever,kthekfinalkanswerkforkeachkproblemkiskfoundkwithoutkroundi
ngkduringkanykstepkinkthekproblem.
CorekQuestions
1. Totalkdollarkreturnk=k100($41k–k$37k+k$.28)k=k$428.00
Whetherkyoukchoosektoksellkthekstockkdoesknotkaffectkthekgainkorklosskforkthekyear;kyourkstockkiskworthkw
hatkitkwouldkbringkifkyouksoldkit.kWhetherkyoukchoosektokdoksokorknotkiskirrelevantk(ignoringkcommissio
nskandktaxes).
2. Capitalkgainsk yieldk k $41k–k$37k k /k$37k k.1081,kork10.81%kDividendk yieldk k $.28/$37k k.0076,kork.76%
Totalkratekofkreturnk k10.81%k k .76%k k11.57%
3. Dollarkreturnk=k500($34k–k$37k+k$.28)k=k–$1,360
Capitalk gainsk yieldk k $34k –k $37 /$37k k –.0811,k ork –
8.11%kDividendkyieldk k $.28/$37k
k .0076,kork.76%kTotalkratekofkreturnk=k–k8.11%k+k.76%k=k–7.35%
4.
a. averagekreturnk=k6.0%,kaveragekriskkpremiumk=k2.7%
b. averagekreturnk=k3.3%,kaveragekriskkpremiumk=k0%
c. averagekreturnk=k12.3%,kaveragekriskkpremiumk=k9.0%
d. averagekreturnk=k16.3%,kaveragekriskkpremiumk=k13.0%
2
,Solution Manual for Fundamentals of Investments Valuation a
k k k k k k k
nd Management, 10th Edition by Bradford Jordan and Thoma
k k k k k k k k
s Miller and Steve Dolvin
k k k k
5. Cherrykaveragek returnk k 17%k k 11%k –k 2%k k 3%k k 14% /5k k 8.60%k Strawk averagek returnk
16%k k 18%k–k6%k k1%k k22% /5k k10.20%
6. Cherry:kRAk k 8.60%
2 2 2 2 2
Vark k 1/k4 .17k–k.086 k k
k .11k –k.086 k k
k –.02k –k.086 k k
k .03k –k.086 k k
k .14k –k.086 k k
k k .00623
1/2
Standardkdeviationk k .00623 k k
k .0789,kork7.89%
Straw:kRBk k 10.20%
Vark k 1/k4 .16k–k.102k k 2k
k .18k–k.102
k
2k k –.06k–k.102
k
2k k .01k–k.102
k
2k k .22k–k.102
k
2k
k
.01452k
1/2
Standardkdeviationk k .01452k k k
k .1205,kork12.05%
7. Thekcapitalkgainskyieldkisk $59k–k$65k /$65 k –.0923,kork–
9.23%k(noticektheknegativeksign).kWithkakdividendkyieldkofk1.2kpercent,kthektotalkreturnkisk–8.03%.
8. Geometrickreturnk k 1k k .17k k 1k k .11k k1k k .02k k 1k k .03k k 1k k .14k k(1/5)k
–k1k k .0837,
ork8.37%
9. Arithmetickreturnk k .21k k.12k k.07k–.13k–k.04k k.26 /k6k k .0817,kork8.17%
(1/6)
Geometrickreturnk 1k k .21k k 1k k .12k k 1k k .07k k 1k–k.13 1k–k.04k k 1k k .26 –k 1k
.0730,kork7.30%
IntermediatekQuestions
10. That’skpluskorkminuskonekstandardkdeviation,ksokaboutktwo-
thirdskofkthektime,korktwokyearskoutkofkthree.kInkonekyearkoutkofkthree,kyoukwillkbekoutsidekthiskrange,kimplyin
gkthatkyoukwillkbekbelowkitkonekyearkoutkofksixkandkabovekitkonekyearkoutkofksix.
3
, Solution Manual for Fundamentals of Investments Valuation a
k k k k k k k
nd Management, 10th Edition by Bradford Jordan and Thoma
k k k k k k k k
s Miller and Steve Dolvin
k k k k
11. Youklosekmoneykifkyoukhavekaknegativekreturn.kWithkak12kpercentkexpectedkreturnkandkak6kpercentkstandardkd
eviation,kakzerokreturnkisktwokstandardkdeviationskbelowkthekaverage.kThekoddskofkbeingkoutsidek(abovekorkbe
low)ktwokstandardkdeviationskarek5kpercent;kthekoddskofkbeingkbelowkarekhalfkthat,kork2.5kpercent.k(It’skactual
lyk2.28kpercent.)kYoukshouldkexpectktoklosekmoneykonlyk2.5kyearskoutkofkeveryk100.kIt’skakprettyksafekinvest
ment.
12. Thekaveragekreturnkisk6.0kpercent,kwithkakstandardkdeviationkofk9.8kpercent,ksokProb(Returnk<k–
3.8korkReturnk15.8k)k k1/3,kbutkwekarekonlykinterestedkinkonektail;kProb Returnk k –3.9k k k 1/k6
,kwhichkisk halfkofk1/3k(orkaboutk16%)k.
95%:k6.0k±k2σk=k6.0k±k2(9.8)k=k–13.6%ktok25.6%
99%:k6.0k±k3σk=k6.0k±k3(9.8)k=k–23.4%ktok35.4%
13. Expectedkreturnk=k 16.4%;kσk =k31.2%.k Doublingkyourk moneykisk ak100%kreturn,ksokifkthek returnkdistribution
isknormal,kZ k 100k–k16.4k /k31.2k 2.68kstandardkdeviations;kthiskiskin-
betweenktwokandkthreekstandardkdeviations,ksokthekprobabilitykisksmall,ksomewherekbetweenk.5%kandk2.5%k(
why?).kReferringktoktheknearestkZktable,kthekactualkprobabilitykisk=k0.369%,korklesskthankeveryk100kyears.kTri
plingkyourkmoneykwouldkbek Z
200k–k16.4 /k31.2k
5.88kstandardkdeviations;kthiskcorrespondsktokakprobabilitykofk(much)klesskthank0.01%.k(Thekactualkanswerkisk
lesskthankoncekeveryk1kmillionkyears,ksokdon’tkholdkyourkbreath.)
14.
Year Commonkstocks T-billkreturn Riskkpremium
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. Annualkriskkpremiumk=kCommonkstockkreturnk–kT-billkreturnk(seektablekabove).
b. Averagekreturns:kCommonkstocksk k12.84/5k k .0257,kork2.57%;kT-billsk k31.67/5k
k .0633k,kork6.33%kRiskkpremiumk k–18.83/5k k –.0377,kork–3.77%
2
c. Commonkstocks:kVark k 1/k4[k –.1469k–k.0257 2
k k –.2647k–k.0257 k k
k .3723k–k.0257
k
k2k
.2393k –k.0257 2k k –.0716k–k.0257
k
2k
]k k .072337
1/2
Standardkdeviationk k 0.072337 k k .2690,kork26.90%
T-bills:k Vark k1/k4 .0729k–k.0633 2k
k .0799k–k.0633
k
2k
k .0587k–k.0633
k
k2k
k k .0507k–.0633 2k
k.0545k–k.0633k
4
