Solution Manual for Fundamentals of Investments: Valuation and Management, 10th Edition – Complete Chapter Solutions (Chapters 1–12)

SOLUTION MANUAL FOR j j


Fundamentals of Investments Valuation and Management, 10th Edition Jordan
j j j j j j j j



Chapter 1-21 j




Chapter 1 j


A Brief History of Risk and Return
j j j j j j




Concept Questions j




1. Forjbothjriskjandjreturn,jincreasingjorderjisjb,jc,ja,jd.jOnjaverage,jthejhigherjthejriskjofjanjinvestment,jthej
higherjisjitsjexpectedjreturn.

2. Sincejthejpricejdidn’tjchange,jthejcapitaljgainsjyieldjwasjzero.jIfjthejtotaljreturnjwasjfourjpercent,jthenjthej
dividendjyieldjmustjbejfourjpercent.

3. Itjisjimpossiblejtojlosejmorejthanj–
100jpercentjofjyourjinvestment.jTherefore,jreturnjdistributionsj arejcutjoffjonjthejlowerjtailjatj–
100jpercent;jifjreturnsjwerejtrulyjnormallyjdistributed,jyoujcouldjlosejmuchjmore.

4. Tojcalculatejanjarithmeticjreturn,jyoujsumjthejreturnsjandjdividejbyjthejnumberjofjreturns.jAsjsuch,jarith
meticjreturnsjdojnotjaccountjforjthejeffectsjofjcompoundingj(and,jinjparticular,jthejeffectjofjvolatility).jGe
ometricjreturnsjdojaccountjforjthejeffectsjofjcompoundingjandjforjchangesjinjthejbasejusedjforjeachjyear’s
jcalculationjofjreturns.jAsjanjinvestor,jthejmorejimportantjreturnjofjanjassetjisj thejgeometricjreturn.



5. Blume’sjformulajusesjthejarithmeticjandjgeometricjreturnsjalongjwithjthejnumberjofjobservationsjtojappr
oximatejajholdingjperiodjreturn.jWhenjpredictingjajholdingjperiodjreturn,jthejarithmeticjreturnjwilljtendjt
ojbejtoojhighjandjthejgeometricjreturnjwilljtendjtojbejtoojlow.jBlume’sjformulajadjustsjthesejreturnsjforjdif
ferentjholdingjperiodjexpectedjreturns.

6. T-
billjratesjwerejhighestjinjthejearlyjeightiesjsincejinflationjatjthejtimejwasjrelativelyjhigh.jAsjwejdiscussjinj
ourjchapterjonjinterestjrates,jratesjonjT-
billsjwilljalmostjalwaysjbejslightlyjhigherjthanjthejexpectedjratejofjinflation.

7. Riskjpremiumsjarejaboutjthejsamejregardlessjofjwhetherjwejaccountjforjinflation.jThejreasonjisjthatjriskjp
remiumsjarejthejdifferencejbetweenjtwojreturns,jsojinflationjessentiallyjnetsjout.

8. Returns,jriskjpremiums,jandjvolatilityjwouldjalljbejlowerjthanjwejestimatedjbecausejaftertaxjreturnsjarejs
mallerjthanjpretaxjreturns.

9. WejhavejseenjthatjT-billsjbarelyjkeptjupjwithjinflationjbeforejtaxes.jAfterjtaxes,jinvestorsjinjT-
billsjactuallyjlostjgroundj(assumingjanythingjotherjthanjajveryjlowjtaxjrate).jThus,janjalljT-
billjstrategyjwilljprobablyjlosejmoneyjinjrealjdollarsjforjajtaxablejinvestor.

10. Itjisjimportantjnotjtojlosejsightjofjthejfactjthatjthejresultsjwejhavejdiscussedjcoverjoverj80jyears,j welljbeyo
ndjthejinvestingjlifetimejforjmostjofjus.jTherejhavejbeenjextendedjperiodsjduringjwhichjsmallj stocksj hav
ej donej terribly.j Thus,j onej reasonj mostj investorsj willj choosej notj toj pursuej aj 100

1
©j MCGRAWj HILLj LLC.j ALLj RIGHTSj RESERVED.j NOj REPRODUCTIONj ORj DISTRIBUTIONj WITHOUTj THEj PRIORj WRITTENj C
ONSENTjOFjMCGRAWjHILLjLLC.

, percentjstockj(particularlyjsmall-
capjstocks)jstrategyjisjthatjmanyjinvestorsjhavejrelativelyjshortjhorizons,jandjhighjvolatilityjinvestmentsj
mayjbejveryjinappropriatejinjsuchjcases.jTherejarejotherjreasons,jbutjwejwilljdeferjdiscussionjofjthesejtojl
aterjchapters.

11.

SolutionsjtojQuestionsjandjProblems

NOTE:jAlljendjofjchapterjproblemsjwerejsolvedjusingjajspreadsheet.jManyjproblemsjrequirejmultiplejsteps.jD
uejtojspacejandjreadabilityjconstraints,jwhenjthesejintermediatejstepsjarejincludedjinjthisjsolutionsjmanual,jro
undingjmayjappearjtojhavejoccurred.jHowever,jthejfinaljanswerjforjeachjproblemjisjfoundjwithoutjroundingjd
uringjanyjstepjinjthejproblem.

CorejQuestions

1. Totaljdollarjreturnj=j100($41j–j$37j+j$.28)j=j$428.00
Whetherjyoujchoosejtojselljthejstockjdoesjnotjaffectjthejgainjorjlossjforjthejyear;jyourjstockjisjworthjwhatjit
jwouldjbringjifjyoujsoldjit.jWhetherjyoujchoosejtojdojsojorjnotjisjirrelevantj(ignoringjcommissionsjandjtax

es).

2. Capitaljgainsjyieldj  $41j –j $37j/j$37 j .1081,j orj10.81%
Dividendjyield j $.28j/j$37 j .0076,j orj.76%
Totaljratejofjreturn j 10.81% j .76% j 11.57%
3. Dollarjreturnj=j500($34j–j$37j+j$.28)j=j–$1,360
Capitaljgainsjyieldj j $34j –j $37/j j$37j  –j.0811,j orj –j8.11%
Dividendjyield j $.28j/j$37 j .0076,j orj.76%
Totaljratejofjreturnj=j–8.11%j+j.76%j=j–7.35%

4.
a. averagejreturnj=j6.0%,javeragejriskjpremiumj=j2.7%
b. averagejreturnj=j3.3%,javeragejriskjpremiumj=j0%
c. averagejreturnj=j12.3%,javeragejriskjpremiumj=j9.0%
d. averagejreturnj=j16.3%,javeragejriskjpremiumj=j13.0%

5. Cherryjaveragejreturnj  17%  11% – 2% j j j j 3% j 14%j/j5 j 8.60%
Strawjaveragejreturnj  16%  18% – 6%
j j j j 1%j  22%j/j5 j 10.20%

6. Cherry:jRAj  8.60%
Var j 1j/j4j.17j –j .086 j .11j –j .086 j –.02j –j .086 j .03j –j .086 j .14j –j .086 
2j 2j 2j 2j 2j
j .00623
 
.00623
1/2j
Standardjdeviationj   .0789,j orj7.89%

Straw:jRBj  10.20%



2
©j MCGRAWj HILLj LLC.j ALLj RIGHTSj RESERVED.j NOj REPRODUCTIONj ORj DISTRIBUTIONj WITHOUTj THEj PRIORj WRITTENj C
ONSENTjOFjMCGRAWjHILLjLLC.

, Var j 1j/j4j.16j –j .102  .18 – .102  –.06 – .102  .01 – .102  .22 – .102  j.01452
2j 2j 2j 2j 2j


j j j j j j j j



Standardjdeviationj  .01452  .1205,j orj12.05%
1/j2j




7. Thej capitalj gainsj yieldj isj $59j –j $65j/j$65j  – .0923j,j orj –9.23%j (noticej thej negativej sign).
Withjajdividendjyieldjofj1.2jpercent,jthejtotaljreturnjisj–8.03%.

Geometricjreturnj  1jj .171jj .111jj .021jj .031j .14
(1/5)j
8. –j1j  .0837,jorj8.37%

9. Arithmeticjreturnj  .21 
j .12 j .07j –j.13j –j .04 j .26j/j6 j .0817,j orj8.17%
Geometricjreturn j1j .211j  .121j  .071j –j .131j –j .041j  .26
(1/6)j
–j 1j  .0730,j orj7.30%

IntermediatejQuestions

10. That’sjplusjorjminusjonejstandardjdeviation,jsojaboutjtwo-
thirdsjofjthejtime,jorjtwojyearsjoutjofjthree.jInjonejyearjoutjofjthree,jyoujwilljbejoutsidejthisjrange,jimplyin
gjthatjyoujwilljbejbelowjitjonejyearjoutjofjsixjandjabovejitjonejyearjoutjofjsix.

11. Youjlosejmoneyjifjyoujhavejajnegativejreturn.jWithjaj12jpercentjexpectedjreturnjandjaj6jpercentjstandardj
deviation,jajzerojreturnjisjtwojstandardjdeviationsjbelowjthejaverage.jThejoddsjofjbeingjoutsidej(abovejorj
below)jtwojstandardjdeviationsjarej5jpercent;jthejoddsjofjbeingjbelowjarejhalfj that,jorj2.5jpercent.j(It’sjac
tuallyj2.28jpercent.)jYoujshouldjexpectjtojlosejmoneyjonlyj2.5jyearsjoutjofjeveryj100.jIt’sjajprettyjsafejinv
estment.

12. Thejaveragejreturnjisj6.0jpercent,jwithjajstandardjdeviationjofj9.8jpercent,jsojProb(Returnj<j–3.8jor
Return  15.8j) j 1/j3j,jbutjwejarejonlyjinterestedjinjonejtail;j ProbjReturnj  – 3.9 j 1/ j6
,jwhichjisjhalfjofj 1/ j3j (orjaboutj16%)j.
95%:j6.0j±j2σj=j6.0j±j2(9.8)j=j–13.6%jtoj25.6%
99%:j6.0j±j3σj=j6.0j±j3(9.8)j=j–23.4%jtoj35.4%

13. Expectedj returnj =j 16.4%;j σj =j 31.2%.j Doublingj yourj moneyj isj aj 100%j return,j soj ifj thej return
distributionjisjnormal,j Zj j 100j –j 16.4/j j31.2j j 2.68j standardjdeviations;jthisjisjin-betweenjtwo
andjthreejstandardjdeviations,jsojthejprobabilityjisjsmall,jsomewherejbetweenj.5%jandj2.5%j(why?).jRef
erringj toj thej nearestj Zj table,j thej actualj probabilityj isj =j 0.369%,j orj lessj thanj everyj 100j years.
Triplingj j yourj j moneyj j wouldj j be Zj j 200j –j 16.4j/j31.2j j 5.88j j standardj j deviations;j j this
correspondsjtojajprobabilityjofj(much)jlessjthanj0.01%.j(Thejactualjanswerjisjlessjthanjoncejeveryj1jmillio
njyears,jsojdon’tjholdjyourjbreath.)

14.
Year Commonjstocks T-billjreturn Riskjpremium
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%

3
©j MCGRAWj HILLj LLC.j ALLj RIGHTSj RESERVED.j NOj REPRODUCTIONj ORj DISTRIBUTIONj WITHOUTj THEj PRIORj WRITTENj C
ONSENTjOFjMCGRAWjHILLjLLC.

, a. Annualjriskjpremiumj=jCommonjstockjreturnj–jT-billjreturnj(seejtablejabove).
b. Averagejreturns:jCommonjstocksj j 12.84j/j5j j .0257,j orj2.57%;j T-billsj j 31.67j/j5j j .0633,j orj6.33%
Riskjpremiumj j –18.83j/j5j j –.0377,j orj –j3.77%
Commonjstocks:jVarj j 1/ j4[j j–.1469j –j .0257 j –.2647j –j .0257 j .3723j –j .0257 
2j 2j 2j
c.

.2393 – .0257 j –.0716j –j .0257 ]j j .072337
2j 2j
j j



Standardjdeviationj j 0.072337 j .2690,j orj26.90%
1/j2j



T-bills:jVarj j1/j4j .0729j –j.0633 j .0799j –j.0633 j .0587j –j.0633 j .0507j–j.0633 j .0545j –j .063
2j 2j 2j 2j


Standardjdeviationj j .000156 j .0125,j orj1.25%
1/j2j



Riskjpremium:jVarj j 1/j4[–.2198j –j –.0377 j –.3446j –j –.0377 j .3136j –j –.0377 
2j 2j 2j



.1886 – –.0377  –.1261 – –.0377 ]  .077446
2j 2j
j j j j j j j



Standardjdeviationj j .077446 j .2783,j orj27.83%
1/j2j




d. Beforejthejfact,jforjmostjassetsjthejriskjpremiumjwilljbejpositive;jinvestorsjdemandjcompensationjov
erjandjabovejthejrisk-
freejreturnjtojinvestjtheirjmoneyjinjthejriskyjasset.jAfterjthejfact,jthejobservedjriskjpremiumjcanjbejne
gativejifjthejasset’sjnominaljreturnjisjunexpectedlyjlow,jthejrisk-
freejreturnjisjunexpectedlyjhigh,jorjanyjcombinationjofjthesejtwojevents.

$324,000/$1,000 –j 1j j .1226,j orj12.26%
1/50j
15. j j j j




$324,000/$1,000 –j 1j j .1226,j orj12.26%
1/50j
16. j j j j




17. 5jyearjestimatej j 5j –j 1/j j40j –j 1j j10.24%j j 40j –j 5/j j40j –j 1j j12.60%j j 12.36%
10jyearjestimatej j10j –j 1j/j40j –j 1j j10.24%j j 40j –j 10j/j40j –j 1j j12.60%j j 12.06%
20jyearjestimatejj20j–j1/j j40j –j1j j10.24%jj 40j–j 20/j j40j –j1j j12.60%j j11.45%

18. Small-companyjstocksj j$29,j781.01/j$1 –j 1j j .1171,j orj11.71%
1/93j



Large-companyjstocksj j $6,j462.39j/j$1 –j 1j j .0989,j orj9.89%
1/93j



Long-termjgovernmentjbondsj j $129.95j/j$1 –j 1j j .0537,j orj5.37%
1/93j



Treasuryjbillsj j $23.05j/j$1 –j 1j j .0343,j orj3.43%
1/93j



Inflationj j $14.03j/j$1 –j 1j j .0288,j orj2.88%
1/90j




19. RAj j –.09j j .17j j .09j j .14j –j .04j/j5j j .0540,j orj5.40%1/5j
R j j 1j –j .091j j .171j j .091j j .141j j .04 –j 1j j .0490,j orj 4.90%
G  


4
©j MCGRAWj HILLj LLC.j ALLj RIGHTSj RESERVED.j NOj REPRODUCTIONj ORj DISTRIBUTIONj WITHOUTj THEj PRIORj WRITTENj C
ONSENTjOFjMCGRAWjHILLjLLC.