SOLUTION MANUAL FORm m
Fundamentals of Investments Valuation and Management 9th Edition By Jor
m m m m m m m m m
dan
Chapter 1-21
m
Chapter 1 m
A Brief History of Risk and Return
m m m m m m
ConceptmQuestions
1. Formboth mrisk mand mreturn,mincreasingmordermismb,mc,ma,md.mOn maverage,mthemhighermthemrisk mof man minves
tment,mthemhighermismitsmexpected mreturn.
2. Sincemthempricemdidn’tmchange,mthemcapitalmgainsmyield mwasmzero.m If mthemtotalmreturn mwasmfourmperce
nt,mthen mthemdividend myield mmustmbemfourmpercent.
3. Itmismimpossible mto mlosemmoremthan m–
100 mpercentmof myourminvestment.mTherefore,mreturn mdistributionsm aremcutmoff monmthemlowermtailmatm–
100 mpercent;mif mreturnsmweremtruly mnormally mdistributed,myou mcould mlosemmuch mmore.
4. To mcalculate man marithmeticmreturn,myou msummthemreturnsmand mdividemby mthemnumbermof mreturns.mAsmsu
ch,marithmetic mreturnsmdo mnotmaccountmformthemeffectsmof mcompoundingm(and,min mparticular,mthemeffect
mof mvolatility). mGeometric mreturns mdo maccountmformthe meffects mof mcompoundingmand mformchanges min mth
embasemused mformeach myear’smcalculation mof mreturns.mAsman minvestor,mthemmoremimportantmreturn mof ma
n massetmism themgeometric mreturn.
5. Blume’smformulamusesmthemarithmeticmand mgeometricmreturnsmalongmwith mthemnumbermof mobservations
mto mapproximate ma mholdingmperiod mreturn. mWhen mpredictingma mholdingmperiod mreturn, mthe marithmetic mr
eturn mwillmtend mto mbemtoo mhigh mand mthemgeometricmreturn mwillmtend mto mbemtoo mlow.mBlume’smformulam
adjustsmthesemreturnsmformdifferentmholdingmperiod mexpected mreturns.
6. T-
billmratesmweremhighestmin mthemearly meightiesmsinceminflation matmthemtimemwasmrelatively mhigh.mAsmwem
discussmin mourmchaptermon minterestmrates,mratesmon mT-
billsmwillmalmostmalwaysmbemslightly mhighermthan mthemexpected mratemof minflation.
7. Risk mpremiumsmaremaboutmthemsamemregardlessmof mwhethermwemaccountmforminflation.mThemreason mismt
hatmrisk mpremiumsmaremthemdifference mbetween mtwo mreturns,mso minflation messentially mnetsmout.
8. Returns,mrisk mpremiums,mand mvolatility mwould mallmbemlowermthan mwemestimated mbecausemaftertax mretu
rnsmaremsmallermthan mpretax mreturns.
9. Wemhavemseen mthatmT-billsmbarely mkeptmup mwith minflation mbeforemtaxes.mAftermtaxes,minvestorsmin mT-
billsmactually mlostmground m(assumingmanythingmothermthan mamvery mlowmtax mrate).mThus,man mallmT-
billmstrategy mwillmprobably mlosemmoney min mrealmdollarsmformamtaxable minvestor.
Copyrightm2021m© mMcGraw-
Hillm Education.m Allm rightsm reserved.m Nomreproduction m ormdistribution mwithout
them priorm writtenm consentm ofm McGraw-Hillm Education.
, 10. Itmismimportantmnotmto mlosemsightmof mthemfactmthatmthemresultsmwemhavemdiscussed mcovermoverm80 myears
,m wellmbeyond mtheminvestingmlifetimemformmostmof mus.mTheremhavembeen mextended mperiodsmduringmwh
ich msmallmstocksmhavemdonemterribly.mThus,monemreason mmostminvestorsmwillmchoose mnotmto mpursue mam
100 mpercentmstock m(particularly msmall-
cap mstocks)mstrategy mismthatmmany minvestorsmhavemrelatively mshortmhorizons,mand mhigh mvolatility minve
stmentsmmay mbemvery minappropriate min msuch mcases.mTheremaremothermreasons,mbutmwemwillmdefermdiscu
ssion mof mthesemto mlatermchapters.
Solutionsmto mQuestionsmandmProblems
NOTE:mAllmend mofmchaptermproblemsmweremsolved musing ma mspreadsheet.mManymproblemsmrequiremmultiplem
steps.mDuemtomspacemandmreadabilitymconstraints,mwhen mthesemintermediate mstepsmaremincluded min mthismsolu
tionsmmanual,mroundingmmaymappearmtomhavemoccurred.mHowever,mthemfinalmanswermformeach mproblemmismf
ound mwithoutmrounding mduring manymstep min mthemproblem.
CoremQuestions
1. Totalmdollarmreturn m=m100($41 m– m$37 m+m$.28)m=m$428.00
Whethermyou mchoosemto msellmthemstock mdoesmnotmaffectmthemgain mormlossmformthemyear;myourmstock mism
worth mwhatmitmwould mbringmif myou msold mit.mWhethermyou mchoosemto mdo mso mormnotmismirrelevantm(ignori
ngmcommissionsmand mtaxes).
2. Capitalmgainsmyield m=m($41 m–
m$37)/$37 m=m.1081, morm10.81%mDividend myieldm=m$.28/$3
7 m=m.0076,morm.76%
Totalmratemof mreturn m=m10.81% m+m.76% m=m11.57%
3. Dollarmreturn m=m500($34 m– m$37 m+m$.28)m=m–$1,360
Capitalmgainsmyield m=m($34 m– m$37)/$37 m=m–.0811,morm–
8.11% mDividend myield m=m$.28/$37 m=m.0076,morm.76%
Totalmratemof mreturn m=m–8.11% m+m.76% m=m–7.35%
4. a.m average mreturn m=m6.2%,maverage mrisk mpremium m=m2.6%
b. average mreturn m=m3.6%,maverage mrisk mpremium m=m0%
c. average mreturn m=m11.9%,maverage mrisk mpremium m=m8.3%
d. average mreturn m=m17.5%,maverage mrisk mpremium m=m13.9%
5. Cherry maveragemreturnm=m(17% m+m11%m–m2%m+m3%m+m14%)/5m=m8.60%
Strawmaverage mreturn m=m(16% m+m18% m– m6% m+m1% m+m22%)/5 m=m10.20%
6. Cherry:mRA m=m8.60%
Varm=m1/4[(.17 m– m.086)2 m+m(.11 m– m.086)2 m+m(–.02 m– m.086)2 m+m(.03 m– m.086)2 m+m(.14 m– m.086)2 ]m=m.00623
Standard mdeviation m=m(.00623)1/2 m=m.0789,morm7.89%
Straw:mRBm=m10.20%
Varm=m1/4[(.16 m– m.102)2 m+m(.18 m– m.102)2 m+m(–.06 m– m.102)2 m+m(.01 m– m.102)2 m+m(.22 m– m.102)2 ]m=m.01452
Standard mdeviation m=m(.01452)1/2 m=m.1205,morm12.05%
7. Themcapitalmgainsmyield mism($59 m– m$65)/$65 m=m–.0923,morm–
9.23% m(noticemthemnegativemsign).m Withmamdividend myield mof m1.2 mpercent,mthemtotalmreturn mism–
Copyrightm2021m© mMcGraw-
Hillm Education.m Allm rightsm reserved.m Nomreproduction m ormdistribution mwithout
them priorm writtenm consentm ofm McGraw-Hillm Education.
, 8.03%.
Copyrightm2021m© mMcGraw-
Hillm Education.m Allm rightsm reserved.m Nomreproduction m ormdistribution mwithout
them priorm writtenm consentm ofm McGraw-Hillm Education.
, 8. Geometric mreturn m=m[(1 m+m.17)(1 m+m.11)(1 m-m.02)(1 m+m.03)(1 m+m.14)](1/5)m– m1 m=m.0837,morm8.37%
9. Arithmetic mreturn m=m(.21 m+m.12 m+m.07 m–.13 m– m.04 m+m.26)/6 m=m.0817,morm8.17%
Geometric mreturn m=m[(1 m+m.21)(1 m+m.12)(1 m+m.07)(1 m– m.13)(1 m– m.04)(1 m+m.26)](1/6)m– m1 m=m.0730,morm7.30%
Intermediate mQuestions
10. That’smplusmormminusmonemstandard mdeviation,mso maboutmtwo-
thirdsmof mthemtime,mormtwo myearsmoutmof mthree.mIn monemyearmoutmof mthree,myou mwillmbemoutside mthismra
nge,mimplyingmthatmyou mwillmbembelowmitmonemyearmoutmof msix mand mabovemitmonemyearmoutmof msix.
11. You mlosemmoney mif myou mhavemamnegativemreturn.mWith mam12 mpercentmexpected mreturn mand mam6 mpercen
tmstandard mdeviation,mamzero mreturn mismtwo mstandard mdeviationsmbelowmthemaverage.mThemoddsmof mbei
ngmoutside m(abovemormbelow)mtwo mstandard mdeviationsmarem5 mpercent;mthemoddsmof mbeingmbelowmaremh
alf m that,morm2.5 mpercent.m(It’smactually m2.28 mpercent.)mYou mshould mexpectmto mlosemmoney monly m2.5 mye
arsmoutmof mevery m100.mIt’smampretty msafeminvestment.
12. Themaveragemreturnmism5.9mpercent,mwith mamstandardmdeviation mof m9.8 mpercent,mso mProb(Return m<m–
3.9 mormReturn m >m15.7 m)m≈m1/3 ,mbutmwemaremonly minterested min monemtail;mProb(Return m<m–
3.9)m≈m1/6 ,mwhich mismhalf mof m1/3 m.
95%: 5.9 m±m2σm=m5.9 m±m2(9.8)m=m–13.7% mto m25.5%
99%: 5.9 m±m3σm=m5.9 m±m3(9.8)m=m–23.5% mto m35.3%
13. Expected mreturn m=m17.5%;m σm=m36.3%.mDoublingmyourmmoney mismam100% mreturn,mso mif mthemreturn mdi
stribution mismnormal,mZm=m(100 m– m17.5)/36.3 m=m2.27 mstandard mdeviations;mthismismin-
between mtwo mand mthreemstandard mdeviations,mso mthemprobability mismsmall,msomewhere mbetween m.5% ma
nd m2.5% m(why?).mReferringmto mthemnearestmZmtable,mthemactualmprobability mism=m1.152%,mormaboutmon
cemevery m100 myears.mTriplingmyourmmoney mwould mbemZm=m(200 m–
m17.5)/36.3 m=m5.028 mstandard mdeviations;mthismcorresponds mto ma mprobability mof m(much)mless mthan m0.5
%,mormoncemevery m200 myears.m(Themactualmanswermismlessmthan moncemevery m1 mmillion myears,mso mdon’tm
hold myourmbreath.)
14. Year Common mstocks T-billmreturn Risk mpremium
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. Annualmrisk mpremium m=mCommon mstock mreturn m– mT-billmreturn m(seemtablemabove).
b. Average mreturns:mCommon mstocksm=m12.84/5 m=m.0257,morm2.57%;m T-
billsm=m31.67/5 m=m.0633,morm6.33%;
Risk mpremium m=m–18.83/5 m=m–.0377,morm–3.77%
c. Common mstocks:mVarm=m1/4[m(–.1469 m– m.0257)2 m+m(–.2647 m– m.0257)2 m+m(.3723 m– m.0257)2 m+
(.2393 m– m.0257)2 m+m(–.0716 m– m.0257)2 ]m=m.072337
Standard mdeviation m=m(0.072337)1/2 m=m.2690,morm26.90%
T-bills:m Varm=m1/4[(.0729 m– m.0633)2 m+m(.0799 m– m.0633)2 m+m(.0587 m– m.0633)2 m+m(.0507–.0633)2 m+
(.0545 m– m.0633)2 ]m=m.000156
Copyrightm2021m© mMcGraw-
Hillm Education.m Allm rightsm reserved.m Nomreproduction m ormdistribution mwithout
them priorm writtenm consentm ofm McGraw-Hillm Education.
Fundamentals of Investments Valuation and Management 9th Edition By Jor
m m m m m m m m m
dan
Chapter 1-21
m
Chapter 1 m
A Brief History of Risk and Return
m m m m m m
ConceptmQuestions
1. Formboth mrisk mand mreturn,mincreasingmordermismb,mc,ma,md.mOn maverage,mthemhighermthemrisk mof man minves
tment,mthemhighermismitsmexpected mreturn.
2. Sincemthempricemdidn’tmchange,mthemcapitalmgainsmyield mwasmzero.m If mthemtotalmreturn mwasmfourmperce
nt,mthen mthemdividend myield mmustmbemfourmpercent.
3. Itmismimpossible mto mlosemmoremthan m–
100 mpercentmof myourminvestment.mTherefore,mreturn mdistributionsm aremcutmoff monmthemlowermtailmatm–
100 mpercent;mif mreturnsmweremtruly mnormally mdistributed,myou mcould mlosemmuch mmore.
4. To mcalculate man marithmeticmreturn,myou msummthemreturnsmand mdividemby mthemnumbermof mreturns.mAsmsu
ch,marithmetic mreturnsmdo mnotmaccountmformthemeffectsmof mcompoundingm(and,min mparticular,mthemeffect
mof mvolatility). mGeometric mreturns mdo maccountmformthe meffects mof mcompoundingmand mformchanges min mth
embasemused mformeach myear’smcalculation mof mreturns.mAsman minvestor,mthemmoremimportantmreturn mof ma
n massetmism themgeometric mreturn.
5. Blume’smformulamusesmthemarithmeticmand mgeometricmreturnsmalongmwith mthemnumbermof mobservations
mto mapproximate ma mholdingmperiod mreturn. mWhen mpredictingma mholdingmperiod mreturn, mthe marithmetic mr
eturn mwillmtend mto mbemtoo mhigh mand mthemgeometricmreturn mwillmtend mto mbemtoo mlow.mBlume’smformulam
adjustsmthesemreturnsmformdifferentmholdingmperiod mexpected mreturns.
6. T-
billmratesmweremhighestmin mthemearly meightiesmsinceminflation matmthemtimemwasmrelatively mhigh.mAsmwem
discussmin mourmchaptermon minterestmrates,mratesmon mT-
billsmwillmalmostmalwaysmbemslightly mhighermthan mthemexpected mratemof minflation.
7. Risk mpremiumsmaremaboutmthemsamemregardlessmof mwhethermwemaccountmforminflation.mThemreason mismt
hatmrisk mpremiumsmaremthemdifference mbetween mtwo mreturns,mso minflation messentially mnetsmout.
8. Returns,mrisk mpremiums,mand mvolatility mwould mallmbemlowermthan mwemestimated mbecausemaftertax mretu
rnsmaremsmallermthan mpretax mreturns.
9. Wemhavemseen mthatmT-billsmbarely mkeptmup mwith minflation mbeforemtaxes.mAftermtaxes,minvestorsmin mT-
billsmactually mlostmground m(assumingmanythingmothermthan mamvery mlowmtax mrate).mThus,man mallmT-
billmstrategy mwillmprobably mlosemmoney min mrealmdollarsmformamtaxable minvestor.
Copyrightm2021m© mMcGraw-
Hillm Education.m Allm rightsm reserved.m Nomreproduction m ormdistribution mwithout
them priorm writtenm consentm ofm McGraw-Hillm Education.
, 10. Itmismimportantmnotmto mlosemsightmof mthemfactmthatmthemresultsmwemhavemdiscussed mcovermoverm80 myears
,m wellmbeyond mtheminvestingmlifetimemformmostmof mus.mTheremhavembeen mextended mperiodsmduringmwh
ich msmallmstocksmhavemdonemterribly.mThus,monemreason mmostminvestorsmwillmchoose mnotmto mpursue mam
100 mpercentmstock m(particularly msmall-
cap mstocks)mstrategy mismthatmmany minvestorsmhavemrelatively mshortmhorizons,mand mhigh mvolatility minve
stmentsmmay mbemvery minappropriate min msuch mcases.mTheremaremothermreasons,mbutmwemwillmdefermdiscu
ssion mof mthesemto mlatermchapters.
Solutionsmto mQuestionsmandmProblems
NOTE:mAllmend mofmchaptermproblemsmweremsolved musing ma mspreadsheet.mManymproblemsmrequiremmultiplem
steps.mDuemtomspacemandmreadabilitymconstraints,mwhen mthesemintermediate mstepsmaremincluded min mthismsolu
tionsmmanual,mroundingmmaymappearmtomhavemoccurred.mHowever,mthemfinalmanswermformeach mproblemmismf
ound mwithoutmrounding mduring manymstep min mthemproblem.
CoremQuestions
1. Totalmdollarmreturn m=m100($41 m– m$37 m+m$.28)m=m$428.00
Whethermyou mchoosemto msellmthemstock mdoesmnotmaffectmthemgain mormlossmformthemyear;myourmstock mism
worth mwhatmitmwould mbringmif myou msold mit.mWhethermyou mchoosemto mdo mso mormnotmismirrelevantm(ignori
ngmcommissionsmand mtaxes).
2. Capitalmgainsmyield m=m($41 m–
m$37)/$37 m=m.1081, morm10.81%mDividend myieldm=m$.28/$3
7 m=m.0076,morm.76%
Totalmratemof mreturn m=m10.81% m+m.76% m=m11.57%
3. Dollarmreturn m=m500($34 m– m$37 m+m$.28)m=m–$1,360
Capitalmgainsmyield m=m($34 m– m$37)/$37 m=m–.0811,morm–
8.11% mDividend myield m=m$.28/$37 m=m.0076,morm.76%
Totalmratemof mreturn m=m–8.11% m+m.76% m=m–7.35%
4. a.m average mreturn m=m6.2%,maverage mrisk mpremium m=m2.6%
b. average mreturn m=m3.6%,maverage mrisk mpremium m=m0%
c. average mreturn m=m11.9%,maverage mrisk mpremium m=m8.3%
d. average mreturn m=m17.5%,maverage mrisk mpremium m=m13.9%
5. Cherry maveragemreturnm=m(17% m+m11%m–m2%m+m3%m+m14%)/5m=m8.60%
Strawmaverage mreturn m=m(16% m+m18% m– m6% m+m1% m+m22%)/5 m=m10.20%
6. Cherry:mRA m=m8.60%
Varm=m1/4[(.17 m– m.086)2 m+m(.11 m– m.086)2 m+m(–.02 m– m.086)2 m+m(.03 m– m.086)2 m+m(.14 m– m.086)2 ]m=m.00623
Standard mdeviation m=m(.00623)1/2 m=m.0789,morm7.89%
Straw:mRBm=m10.20%
Varm=m1/4[(.16 m– m.102)2 m+m(.18 m– m.102)2 m+m(–.06 m– m.102)2 m+m(.01 m– m.102)2 m+m(.22 m– m.102)2 ]m=m.01452
Standard mdeviation m=m(.01452)1/2 m=m.1205,morm12.05%
7. Themcapitalmgainsmyield mism($59 m– m$65)/$65 m=m–.0923,morm–
9.23% m(noticemthemnegativemsign).m Withmamdividend myield mof m1.2 mpercent,mthemtotalmreturn mism–
Copyrightm2021m© mMcGraw-
Hillm Education.m Allm rightsm reserved.m Nomreproduction m ormdistribution mwithout
them priorm writtenm consentm ofm McGraw-Hillm Education.
, 8.03%.
Copyrightm2021m© mMcGraw-
Hillm Education.m Allm rightsm reserved.m Nomreproduction m ormdistribution mwithout
them priorm writtenm consentm ofm McGraw-Hillm Education.
, 8. Geometric mreturn m=m[(1 m+m.17)(1 m+m.11)(1 m-m.02)(1 m+m.03)(1 m+m.14)](1/5)m– m1 m=m.0837,morm8.37%
9. Arithmetic mreturn m=m(.21 m+m.12 m+m.07 m–.13 m– m.04 m+m.26)/6 m=m.0817,morm8.17%
Geometric mreturn m=m[(1 m+m.21)(1 m+m.12)(1 m+m.07)(1 m– m.13)(1 m– m.04)(1 m+m.26)](1/6)m– m1 m=m.0730,morm7.30%
Intermediate mQuestions
10. That’smplusmormminusmonemstandard mdeviation,mso maboutmtwo-
thirdsmof mthemtime,mormtwo myearsmoutmof mthree.mIn monemyearmoutmof mthree,myou mwillmbemoutside mthismra
nge,mimplyingmthatmyou mwillmbembelowmitmonemyearmoutmof msix mand mabovemitmonemyearmoutmof msix.
11. You mlosemmoney mif myou mhavemamnegativemreturn.mWith mam12 mpercentmexpected mreturn mand mam6 mpercen
tmstandard mdeviation,mamzero mreturn mismtwo mstandard mdeviationsmbelowmthemaverage.mThemoddsmof mbei
ngmoutside m(abovemormbelow)mtwo mstandard mdeviationsmarem5 mpercent;mthemoddsmof mbeingmbelowmaremh
alf m that,morm2.5 mpercent.m(It’smactually m2.28 mpercent.)mYou mshould mexpectmto mlosemmoney monly m2.5 mye
arsmoutmof mevery m100.mIt’smampretty msafeminvestment.
12. Themaveragemreturnmism5.9mpercent,mwith mamstandardmdeviation mof m9.8 mpercent,mso mProb(Return m<m–
3.9 mormReturn m >m15.7 m)m≈m1/3 ,mbutmwemaremonly minterested min monemtail;mProb(Return m<m–
3.9)m≈m1/6 ,mwhich mismhalf mof m1/3 m.
95%: 5.9 m±m2σm=m5.9 m±m2(9.8)m=m–13.7% mto m25.5%
99%: 5.9 m±m3σm=m5.9 m±m3(9.8)m=m–23.5% mto m35.3%
13. Expected mreturn m=m17.5%;m σm=m36.3%.mDoublingmyourmmoney mismam100% mreturn,mso mif mthemreturn mdi
stribution mismnormal,mZm=m(100 m– m17.5)/36.3 m=m2.27 mstandard mdeviations;mthismismin-
between mtwo mand mthreemstandard mdeviations,mso mthemprobability mismsmall,msomewhere mbetween m.5% ma
nd m2.5% m(why?).mReferringmto mthemnearestmZmtable,mthemactualmprobability mism=m1.152%,mormaboutmon
cemevery m100 myears.mTriplingmyourmmoney mwould mbemZm=m(200 m–
m17.5)/36.3 m=m5.028 mstandard mdeviations;mthismcorresponds mto ma mprobability mof m(much)mless mthan m0.5
%,mormoncemevery m200 myears.m(Themactualmanswermismlessmthan moncemevery m1 mmillion myears,mso mdon’tm
hold myourmbreath.)
14. Year Common mstocks T-billmreturn Risk mpremium
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. Annualmrisk mpremium m=mCommon mstock mreturn m– mT-billmreturn m(seemtablemabove).
b. Average mreturns:mCommon mstocksm=m12.84/5 m=m.0257,morm2.57%;m T-
billsm=m31.67/5 m=m.0633,morm6.33%;
Risk mpremium m=m–18.83/5 m=m–.0377,morm–3.77%
c. Common mstocks:mVarm=m1/4[m(–.1469 m– m.0257)2 m+m(–.2647 m– m.0257)2 m+m(.3723 m– m.0257)2 m+
(.2393 m– m.0257)2 m+m(–.0716 m– m.0257)2 ]m=m.072337
Standard mdeviation m=m(0.072337)1/2 m=m.2690,morm26.90%
T-bills:m Varm=m1/4[(.0729 m– m.0633)2 m+m(.0799 m– m.0633)2 m+m(.0587 m– m.0633)2 m+m(.0507–.0633)2 m+
(.0545 m– m.0633)2 ]m=m.000156
Copyrightm2021m© mMcGraw-
Hillm Education.m Allm rightsm reserved.m Nomreproduction m ormdistribution mwithout
them priorm writtenm consentm ofm McGraw-Hillm Education.
