SOLUTION MANUAL FOR #z #z
Fundamentals of Investments Valuation and Management 9th Edition By
#z #z #z #z #z #z #z #z
Jordan
#z
Chapter 1-21
#z
Chapter 1 #z
A Brief History of Risk and Return
#z #z #z #z #z #z
Concept #zQuestions
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an
investment, the higher is its expected return.
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four percent,
then the dividend yield must be four percent.
3. It is impossible to lose more than –100 percent of your investment. Therefore, return distributions
are cut off on the lower tail at –100 percent; if returns were truly normally distributed, you could lose
much more.
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns. As such,
arithmetic returns do not account for the effects of compounding (and, in particular, the effect of
volatility). Geometric returns do account for the effects of compounding and for changes in the base
used for each year’s calculation of returns. As an investor, the more important return of an asset is
the geometric return.
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observations to
approximate a holding period return. When predicting a holding period return, the arithmetic return
will tend to be too high and the geometric return will tend to be too low. Blume’s formula adjusts
these returns for different holding period expected returns.
6. T-bill rates were highest in the early eighties since inflation at the time was relatively high. As we
discuss in our chapter on interest rates, rates on T-bills will almost always be slightly higher than the
expected rate of inflation.
7. Risk premiums are about the same regardless of whether we account for inflation. The reason is that
risk premiums are the difference between two returns, so inflation essentially nets out.
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns
are smaller than pretax returns.
9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-bills
actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-bill strategy
will probably lose money in real dollars for a taxable investor.
Copyright #z2021 #z© #zMcGraw-Hill #zEducation. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution
#zwithout
the #zprior #zwritten #zconsent #zof #zMcGraw-Hill #zEducation.
, 10. It #zis #zimportant #znot #zto #zlose #zsight #zof #zthe #zfact #zthat #zthe #zresults #zwe #zhave #zdiscussed #zcover #zover
#z80 #zyears, # z well #zbeyond #zthe #zinvesting #zlifetime #zfor #zmost #zof #zus. #zThere #zhave #zbeen #zextended
#zperiods #zduring #zwhich #zsmall #zstocks #zhave #zdone #zterribly. #zThus, #zone #zreason #zmost #zinvestors
#zwill #zchoose #znot #zto #zpursue #za #z100 #zpercent #zstock #z(particularly #zsmall-cap #zstocks) #zstrategy #zis
#zthat #zmany #zinvestors #zhave #zrelatively #zshort #zhorizons, #zand #zhigh #zvolatility #zinvestments #zmay #zbe
#zvery #zinappropriate #zin #zsuch #zcases. #zThere #zare #zother #zreasons, #zbut #zwe #zwill #zdefer #zdiscussion #zof
#zthese #zto #zlater #zchapters.
Solutions #zto #zQuestions #zand #zProblems
NOTE: #zAll #zend #zof #zchapter #zproblems #zwere #zsolved #zusing #za #zspreadsheet. #zMany #zproblems #zrequire
#zmultiple #zsteps. #zDue #zto #zspace #zand #zreadability #zconstraints, #zwhen #zthese #zintermediate #zsteps #zare
#zincluded #zin #zthis #zsolutions #zmanual, #zrounding #zmay #zappear #zto #zhave #zoccurred. #zHowever, #zthe #zfinal
#zanswer #zfor #zeach #zproblem #zis #zfound #zwithout #zrounding #zduring #zany #zstep #zin #zthe #zproblem.
Core #zQuestions
1. Total #zdollar #zreturn #z= #z100($41 #z– #z$37 #z+ #z$.28) #z= #z$428.00
Whether #zyou #zchoose #zto #zsell #zthe #zstock #zdoes #znot #zaffect #zthe #zgain #zor #zloss #zfor #zthe #zyear; #zyour
#zstock #zis #zworth #zwhat #zit #zwould #zbring #zif #zyou #zsold #zit. #zWhether #zyou #zchoose #zto #zdo #zso #zor #znot
#zis #zirrelevant #z(ignoring #zcommissions #zand #ztaxes).
2. Capital #zgains #zyield #z= #z($41 #z– #z$37)/$37 #z= #z.1081, #zor
#z10.81% #zDividend #zyield #z= #z$.28/$37 #z= #z.0076, #zor
#z.76%
Total #zrate #zof #zreturn #z= #z10.81% #z+ #z.76% #z= #z11.57%
3. Dollar #zreturn #z= #z500($34 #z– #z$37 #z+ #z$.28) #z= #z–$1,360
Capital #zgains #zyield #z= #z($34 #z– #z$37)/$37 #z= #z–.0811, #zor #z–
8.11% #zDividend #zyield #z= #z$.28/$37 #z= #z.0076, #zor #z.76%
Total #zrate #zof #zreturn #z= #z–8.11% #z+ #z.76% #z= #z–7.35%
4. a. # z average #zreturn #z= #z6.2%, #zaverage #zrisk #zpremium #z= #z2.6%
b. average #zreturn #z= #z3.6%, #zaverage #zrisk #zpremium #z= #z0%
c. average #zreturn #z= #z11.9%, #zaverage #zrisk #zpremium #z= #z8.3%
d. average #zreturn #z= #z17.5%, #zaverage #zrisk #zpremium #z= #z13.9%
5. Cherry #zaverage #zreturn #z= #z(17% #z+ #z11% #z– #z2% #z+ #z3% #z+ #z14%)/5 #z=
#z8.60%
Straw #zaverage #zreturn #z= #z(16% #z+ #z18% #z– #z6% #z+ #z1% #z+ #z22%)/5 #z= #z10.20%
6. Cherry: #zRA #z= #z8.60%
Var #z= #z1/4[(.17 #z– #z.086)2 #z+ #z(.11 #z– #z.086)2 #z+ #z(–.02 #z– #z.086)2 #z+ #z(.03 #z– #z.086)2 #z+ #z(.14 #z– #z.086)2] #z= #z.00623
Standard #zdeviation #z= #z(.00623)1/2 #z= #z.0789, #zor #z7.89%
Straw: #zRB #z= #z10.20%
Var #z= #z1/4[(.16 #z– #z.102)2 #z+ #z(.18 #z– #z.102)2 #z+ #z(–.06 #z– #z.102)2 #z+ #z(.01 #z– #z.102)2 #z+ #z(.22 #z– #z.102)2] #z= #z.01452
Standard #zdeviation #z= #z(.01452)1/2 #z= #z.1205, #zor #z12.05%
7. The #zcapital #zgains #zyield #zis #z($59 #z– #z$65)/$65 #z= #z–.0923, #zor #z–9.23% #z(notice #zthe #znegative
Copyright #z2021 #z© #zMcGraw-Hill #zEducation. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution
#zwithout
the #zprior #zwritten #zconsent #zof #zMcGraw-Hill #zEducation.
, sign). # z With #za #zdividend #zyield #zof #z1.2 #zpercent, #zthe #ztotal #zreturn #zis #z–8.03%.
#z
8. Geometric #zreturn #z= #z[(1 #z+ #z.17)(1 #z+ #z.11)(1 #z- #z.02)(1 #z+ #z.03)(1 #z+ #z.14)](1/5) #z– #z1 #z= #z.0837, #zor #z8.37%
9. Arithmetic #zreturn #z= #z(.21 #z+ #z.12 #z+ #z.07 #z–.13 #z– #z.04 #z+ #z.26)/6 #z= #z.0817, #zor #z8.17%
Geometric #zreturn #z= #z[(1 #z+ #z.21)(1 #z+ #z.12)(1 #z+ #z.07)(1 #z– #z.13)(1 #z– #z.04)(1 #z+ #z.26)](1/6) #z– #z1 #z= #z.0730, #zor #z7.30%
Intermediate #zQuestions
10. That’s #zplus #zor #zminus #zone #zstandard #zdeviation, #zso #zabout #ztwo-thirds #zof #zthe #ztime, #zor #ztwo #zyears
#zout #zof #zthree. #zIn #zone #zyear #zout #zof #zthree, #zyou #zwill #zbe #zoutside #zthis #zrange, #zimplying #zthat #zyou
#zwill #zbe #zbelow #zit #zone #zyear #zout #zof #zsix #zand #zabove #zit #zone #zyear #zout #zof #zsix.
11. You #zlose #zmoney #zif #zyou #zhave #za #znegative #zreturn. #zWith #za #z12 #zpercent #zexpected #zreturn #zand #za #z6
#zpercent #zstandard #zdeviation, #za #zzero #zreturn #zis #ztwo #zstandard #zdeviations #zbelow #zthe #zaverage.
#zThe #zodds #zof #zbeing #zoutside #z(above #zor #zbelow) #ztwo #zstandard #zdeviations #zare #z5 #zpercent; #zthe
#zodds #zof #zbeing #zbelow #zare #zhalf # z that, #zor #z2.5 #zpercent. #z(It’s #zactually #z2.28 #zpercent.) #zYou
#zshould #zexpect #zto #zlose #zmoney #zonly #z2.5 #zyears #zout #zof #zevery #z100. #zIt’s #za #zpretty #zsafe
#zinvestment.
12. The #zaverage #zreturn #zis #z5.9 #zpercent, #zwith #za #zstandard #zdeviation #zof #z9.8 #zpercent, #zso #zProb(Return
#z< #z–3.9 #zor #zReturn # z > #z15.7 #z) #z≈ #z1/3, #zbut #zwe #zare #zonly #zinterested #zin #zone #ztail; #zProb(Return #z<
#z–3.9) #z≈ #z1/6, #zwhich #zis #zhalf #zof #z1/3 #z.
95%: 5.9 #z± #z2σ #z= #z5.9 #z± #z2(9.8) #z= #z–13.7% #zto #z25.5%
99%: 5.9 #z± #z3σ #z= #z5.9 #z± #z3(9.8) #z= #z–23.5% #zto #z35.3%
13. Expected #zreturn #z= #z17.5%; # z σ #z= #z36.3%. #zDoubling #zyour #zmoney #zis #za #z100% #zreturn, #zso #zif #zthe
#zreturn #zdistribution #zis #znormal, #zZ #z= #z(100 #z– #z17.5)/36.3 #z= #z2.27 #zstandard #zdeviations; #zthis #zis #zin-
between #ztwo #zand #zthree #zstandard #zdeviations, #zso #zthe #zprobability #zis #zsmall, #zsomewhere #zbetween
#z.5% #zand #z2.5% #z(why?). #zReferring #zto #zthe #znearest #zZ #ztable, #zthe #zactual #zprobability #zis #z=
#z1.152%, #zor #zabout #zonce #zevery #z100 #zyears. #zTripling #zyour #zmoney #zwould #zbe #zZ #z= #z(200 #z–
#z17.5)/36.3 #z= #z5.028 #zstandard #zdeviations; #zthis #zcorresponds #zto #za #zprobability #zof #z(much) #zless
#zthan #z0.5%, #zor #zonce #zevery #z200 #zyears. #z(The #zactual #zanswer #zis #zless #zthan #zonce #zevery #z1 #zmillion
#zyears, #zso #zdon’t #zhold #zyour #zbreath.)
14. Year Common #zstocks T-bill #zreturn Risk #zpremium
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. Annual #zrisk #zpremium #z= #zCommon #zstock #zreturn #z– #zT-bill #zreturn #z(see #ztable #zabove).
b. Average #zreturns: #zCommon #zstocks #z= #z12.84/5 #z= #z.0257, #zor #z2.57%; # z T-bills #z= #z31.67/5 #z=
#z.0633, #zor #z6.33%;
Risk #zpremium #z= #z–18.83/5 #z= #z–.0377, #zor #z–3.77%
c. Common #zstocks: #zVar #z= #z1/4[ #z(–.1469 #z– #z.0257)2 #z+ #z(–.2647 #z– #z.0257)2 #z+ #z(.3723 #z– #z.0257)2 #z+
(.2393 #z– #z.0257)2 #z+ #z(–.0716 #z– #z.0257)2] #z= #z.072337
Standard #zdeviation #z= #z(0.072337)1/2 #z= #z.2690, #zor #z26.90%
Copyright #z2021 #z© #zMcGraw-Hill #zEducation. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution
#zwithout
the #zprior #zwritten #zconsent #zof #zMcGraw-Hill #zEducation.
, T-bills: # z Var #z= #z1/4[(.0729 #z– #z.0633)2 #z+ #z(.0799 #z– #z.0633)2 #z+ #z(.0587 #z– #z.0633)2 #z+ #z(.0507–.0633)2 #z+
(.0545 #z– #z.0633)2] #z= #z.000156
Standard #zdeviation #z= #z(.000156)1/2 #z= #z.0125, #zor #z1.25%
Risk #zpremium: # z Var #z= #z1/4[(–.2198 #z– #z(–.0377))2 #z+ #z(–.3446 #z– #z(–.0377))2 #z+ #z(.3136 #z– #z(–.0377))2 #z+
(.1886 #z– #z(–.0377))2 #z+ #z(–.1261 #z– #z(–.0377))2] #z= #z.077446
Standard #zdeviation #z= #z(.077446)1/2 #z= #z.2783, #zor #z27.83%
d. Before #zthe #zfact, #zfor #zmost #zassets #zthe #zrisk #zpremium #zwill #zbe #zpositive; #zinvestors #zdemand
#zcompensation #zover #zand #zabove #zthe #zrisk-free #zreturn #zto #zinvest #ztheir #zmoney #zin #zthe #zrisky
#zasset. #zAfter #zthe #zfact, #zthe #zobserved #zrisk #zpremium #zcan #zbe #znegative #zif #zthe #zasset’s #znominal
#zreturn #zis #zunexpectedly #zlow, #zthe #zrisk- #zfree #zreturn #zis #zunexpectedly #zhigh, #zor #zany
#zcombination #zof #zthese #ztwo #zevents.
15. ($324,000/$1,000)1/50 #z– #z1 #z= #z.1226, #zor #z12.26%
16. 5 #zyear #zestimate #z= #z[(5 #z– #z1)/(40 #z– #z1)] #z× #z10.24% #z+ #z[(40 #z– #z5)/(40 #z– #z1)] #z× #z12.60% #z= #z12.36%
10 #zyear #zestimate #z= #z[(10 #z– #z1)/(40 #z– #z1)] #z× #z10.24% #z+ #z[(40 #z– #z10)/(40 #z– #z1)] #z× #z12.60% #z= #z12.06%
20 #zyear #zestimate #z= #z[(20 #z– #z1)/(40 #z– #z1)] #z× #z10.24% #z+ #z[(40 #z– #z20)/(40 #z– #z1)] #z× #z12.60% #z= #z11.45%
17. Small-company #zstocks #z= #z($29,781.01/$1)1/93 #z– #z1 #z= #z.1171, #zor
#z– #z1 #z=
1/93
#z11.71% #zLarge-company #zstocks #z= #z($6,462.39/$1)
1/93
#z.0989, #zor #z9.89% #zLong-term #zgovernment #zbonds #z= #z($129.95/$1)
#z– #z1 #z= #z.0537, #zor #z5.37% #zTreasury #zbills #z= #z($23.05/$1) #z– #z1 #z=
1/93
#z.0343, #zor #z3.43%
Inflation #z= #z($14.03/$1)1/90 #z– #z1 #z= #z.0288, #zor #z2.88%
18. RA #z= #z(–.09 #z+ #z.17 #z+ #z.09 #z+ #z.14 #z– #z.04)/5 #z= #z.0540, #zor #z5.40%
RG #z= #z[(1 #z– #z.09)(1 #z+ #z.17)(1 #z+ #z.09)(1 #z+ #z.14)(1 #z- #z.04)]1/5 #z– #z1 #z= #z.0490, #zor #z4.90%
19. R1 #z= #z($15.61 #z– #z$13.25 #z+ #z$.15)/$13.25 #z= #z.1894, #zor
#z18.94% #zR2 #z= #z($16.72 #z– #z$15.61 #z+ #z$.18)/$15.61 #z=
#z.0826, #zor #z8.26% #zR3 #z= #z($15.18 #z– #z$16.72 #z+
#z$.20)/$16.72 #z= #z–.0801, #zor #z–8.01% #zR4 #z= #z($17.12 #z–
#z$15.18 #z+ #z$.24)/$15.18 #z= #z.1436, #zor #z14.36% #zR5 #z=
#z($20.43 #z– #z$17.12 #z+ #z$.28)/$17.12 #z= #z.2097, #zor
#z20.97%
RA #z= #z(.1894 #z+ #z.0826 #z– #z.0801 #z+ #z.1436 #z+ #z.2097)/5 #z= #z.1090, #zor #z10.90%
RG #z= #z[(1 #z+ #z.1894)(1 #z+ #z.0826)(1 #z– #z.0801)(1 #z+ #z.1436)(1 #z+ #z.2097)]1/5 #z– #z1 #z= #z.1038, #zor #z10.38%
20. Stock #zA: #zRA #z= #z(.08 #z+ #z.08 #z+ #z.08 #z+ #z.08 #z+ #z.08)/5 #z= #z.0800, #zor #z8.00%
Var #z= #z1/4[(.08 #z– #z.08)2 #z+ #z(.08 #z– #z.08)2 #z+ #z(.08 #z– #z.08)2 #z+ #z(.08 #z– #z.08)2 #z+ #z(.08 #z– #z.08)2] #z= #z.000000
Standard #zdeviation #z= #z(.000)1/2 #z= #z.000, #zor #z0.00%
RG #z= #z[(1 #z+ #z.08)(1 #z+ #z.08)(1 #z+ #z.08)(1 #z+.08)(1 #z+ #z.08)]1/5 #z– #z1 #z= #z.0800, #zor #z8.00%
Stock #zB: #zRA #z= #z(.03 #z+ #z.13 #z+ #z.07 #z+ #z.05 #z+ #z.12)/5 #z= #z.0800, #zor #z8.00%
Var #z= #z1/4[(.03 #z– #z.08)2 #z+ #z(.13 #z– #z.08)2 #z+ #z(.07 #z– #z.08)2 #z+ #z(.05 #z– #z.08)2 #z+ #z(.12 #z– #z.08)2] #z= #z.001900
Standard #zdeviation #z= #z(.001900)1/2 #z= #z.0436, #zor #z4.36%
RG #z= #z[(1 #z+ #z.03)(1 #z+ #z.13)(1 #z+ #z.07)(1 #z+ #z.05)(1 #z+ #z.12)]1/5 #z– #z1 #z= #z.0793, #zor #z7.93%
Stock #zC: #zRA #z= #z(–.24 #z+ #z.37 #z+ #z.14 #z+ #z.09 #z+ #z.04)/5 #z= #z.0800. #zor #z8.00%
Copyright #z2021 #z© #zMcGraw-Hill #zEducation. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution
#zwithout
the #zprior #zwritten #zconsent #zof #zMcGraw-Hill #zEducation.
Fundamentals of Investments Valuation and Management 9th Edition By
#z #z #z #z #z #z #z #z
Jordan
#z
Chapter 1-21
#z
Chapter 1 #z
A Brief History of Risk and Return
#z #z #z #z #z #z
Concept #zQuestions
1. For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an
investment, the higher is its expected return.
2. Since the price didn’t change, the capital gains yield was zero. If the total return was four percent,
then the dividend yield must be four percent.
3. It is impossible to lose more than –100 percent of your investment. Therefore, return distributions
are cut off on the lower tail at –100 percent; if returns were truly normally distributed, you could lose
much more.
4. To calculate an arithmetic return, you sum the returns and divide by the number of returns. As such,
arithmetic returns do not account for the effects of compounding (and, in particular, the effect of
volatility). Geometric returns do account for the effects of compounding and for changes in the base
used for each year’s calculation of returns. As an investor, the more important return of an asset is
the geometric return.
5. Blume’s formula uses the arithmetic and geometric returns along with the number of observations to
approximate a holding period return. When predicting a holding period return, the arithmetic return
will tend to be too high and the geometric return will tend to be too low. Blume’s formula adjusts
these returns for different holding period expected returns.
6. T-bill rates were highest in the early eighties since inflation at the time was relatively high. As we
discuss in our chapter on interest rates, rates on T-bills will almost always be slightly higher than the
expected rate of inflation.
7. Risk premiums are about the same regardless of whether we account for inflation. The reason is that
risk premiums are the difference between two returns, so inflation essentially nets out.
8. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns
are smaller than pretax returns.
9. We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-bills
actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-bill strategy
will probably lose money in real dollars for a taxable investor.
Copyright #z2021 #z© #zMcGraw-Hill #zEducation. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution
#zwithout
the #zprior #zwritten #zconsent #zof #zMcGraw-Hill #zEducation.
, 10. It #zis #zimportant #znot #zto #zlose #zsight #zof #zthe #zfact #zthat #zthe #zresults #zwe #zhave #zdiscussed #zcover #zover
#z80 #zyears, # z well #zbeyond #zthe #zinvesting #zlifetime #zfor #zmost #zof #zus. #zThere #zhave #zbeen #zextended
#zperiods #zduring #zwhich #zsmall #zstocks #zhave #zdone #zterribly. #zThus, #zone #zreason #zmost #zinvestors
#zwill #zchoose #znot #zto #zpursue #za #z100 #zpercent #zstock #z(particularly #zsmall-cap #zstocks) #zstrategy #zis
#zthat #zmany #zinvestors #zhave #zrelatively #zshort #zhorizons, #zand #zhigh #zvolatility #zinvestments #zmay #zbe
#zvery #zinappropriate #zin #zsuch #zcases. #zThere #zare #zother #zreasons, #zbut #zwe #zwill #zdefer #zdiscussion #zof
#zthese #zto #zlater #zchapters.
Solutions #zto #zQuestions #zand #zProblems
NOTE: #zAll #zend #zof #zchapter #zproblems #zwere #zsolved #zusing #za #zspreadsheet. #zMany #zproblems #zrequire
#zmultiple #zsteps. #zDue #zto #zspace #zand #zreadability #zconstraints, #zwhen #zthese #zintermediate #zsteps #zare
#zincluded #zin #zthis #zsolutions #zmanual, #zrounding #zmay #zappear #zto #zhave #zoccurred. #zHowever, #zthe #zfinal
#zanswer #zfor #zeach #zproblem #zis #zfound #zwithout #zrounding #zduring #zany #zstep #zin #zthe #zproblem.
Core #zQuestions
1. Total #zdollar #zreturn #z= #z100($41 #z– #z$37 #z+ #z$.28) #z= #z$428.00
Whether #zyou #zchoose #zto #zsell #zthe #zstock #zdoes #znot #zaffect #zthe #zgain #zor #zloss #zfor #zthe #zyear; #zyour
#zstock #zis #zworth #zwhat #zit #zwould #zbring #zif #zyou #zsold #zit. #zWhether #zyou #zchoose #zto #zdo #zso #zor #znot
#zis #zirrelevant #z(ignoring #zcommissions #zand #ztaxes).
2. Capital #zgains #zyield #z= #z($41 #z– #z$37)/$37 #z= #z.1081, #zor
#z10.81% #zDividend #zyield #z= #z$.28/$37 #z= #z.0076, #zor
#z.76%
Total #zrate #zof #zreturn #z= #z10.81% #z+ #z.76% #z= #z11.57%
3. Dollar #zreturn #z= #z500($34 #z– #z$37 #z+ #z$.28) #z= #z–$1,360
Capital #zgains #zyield #z= #z($34 #z– #z$37)/$37 #z= #z–.0811, #zor #z–
8.11% #zDividend #zyield #z= #z$.28/$37 #z= #z.0076, #zor #z.76%
Total #zrate #zof #zreturn #z= #z–8.11% #z+ #z.76% #z= #z–7.35%
4. a. # z average #zreturn #z= #z6.2%, #zaverage #zrisk #zpremium #z= #z2.6%
b. average #zreturn #z= #z3.6%, #zaverage #zrisk #zpremium #z= #z0%
c. average #zreturn #z= #z11.9%, #zaverage #zrisk #zpremium #z= #z8.3%
d. average #zreturn #z= #z17.5%, #zaverage #zrisk #zpremium #z= #z13.9%
5. Cherry #zaverage #zreturn #z= #z(17% #z+ #z11% #z– #z2% #z+ #z3% #z+ #z14%)/5 #z=
#z8.60%
Straw #zaverage #zreturn #z= #z(16% #z+ #z18% #z– #z6% #z+ #z1% #z+ #z22%)/5 #z= #z10.20%
6. Cherry: #zRA #z= #z8.60%
Var #z= #z1/4[(.17 #z– #z.086)2 #z+ #z(.11 #z– #z.086)2 #z+ #z(–.02 #z– #z.086)2 #z+ #z(.03 #z– #z.086)2 #z+ #z(.14 #z– #z.086)2] #z= #z.00623
Standard #zdeviation #z= #z(.00623)1/2 #z= #z.0789, #zor #z7.89%
Straw: #zRB #z= #z10.20%
Var #z= #z1/4[(.16 #z– #z.102)2 #z+ #z(.18 #z– #z.102)2 #z+ #z(–.06 #z– #z.102)2 #z+ #z(.01 #z– #z.102)2 #z+ #z(.22 #z– #z.102)2] #z= #z.01452
Standard #zdeviation #z= #z(.01452)1/2 #z= #z.1205, #zor #z12.05%
7. The #zcapital #zgains #zyield #zis #z($59 #z– #z$65)/$65 #z= #z–.0923, #zor #z–9.23% #z(notice #zthe #znegative
Copyright #z2021 #z© #zMcGraw-Hill #zEducation. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution
#zwithout
the #zprior #zwritten #zconsent #zof #zMcGraw-Hill #zEducation.
, sign). # z With #za #zdividend #zyield #zof #z1.2 #zpercent, #zthe #ztotal #zreturn #zis #z–8.03%.
#z
8. Geometric #zreturn #z= #z[(1 #z+ #z.17)(1 #z+ #z.11)(1 #z- #z.02)(1 #z+ #z.03)(1 #z+ #z.14)](1/5) #z– #z1 #z= #z.0837, #zor #z8.37%
9. Arithmetic #zreturn #z= #z(.21 #z+ #z.12 #z+ #z.07 #z–.13 #z– #z.04 #z+ #z.26)/6 #z= #z.0817, #zor #z8.17%
Geometric #zreturn #z= #z[(1 #z+ #z.21)(1 #z+ #z.12)(1 #z+ #z.07)(1 #z– #z.13)(1 #z– #z.04)(1 #z+ #z.26)](1/6) #z– #z1 #z= #z.0730, #zor #z7.30%
Intermediate #zQuestions
10. That’s #zplus #zor #zminus #zone #zstandard #zdeviation, #zso #zabout #ztwo-thirds #zof #zthe #ztime, #zor #ztwo #zyears
#zout #zof #zthree. #zIn #zone #zyear #zout #zof #zthree, #zyou #zwill #zbe #zoutside #zthis #zrange, #zimplying #zthat #zyou
#zwill #zbe #zbelow #zit #zone #zyear #zout #zof #zsix #zand #zabove #zit #zone #zyear #zout #zof #zsix.
11. You #zlose #zmoney #zif #zyou #zhave #za #znegative #zreturn. #zWith #za #z12 #zpercent #zexpected #zreturn #zand #za #z6
#zpercent #zstandard #zdeviation, #za #zzero #zreturn #zis #ztwo #zstandard #zdeviations #zbelow #zthe #zaverage.
#zThe #zodds #zof #zbeing #zoutside #z(above #zor #zbelow) #ztwo #zstandard #zdeviations #zare #z5 #zpercent; #zthe
#zodds #zof #zbeing #zbelow #zare #zhalf # z that, #zor #z2.5 #zpercent. #z(It’s #zactually #z2.28 #zpercent.) #zYou
#zshould #zexpect #zto #zlose #zmoney #zonly #z2.5 #zyears #zout #zof #zevery #z100. #zIt’s #za #zpretty #zsafe
#zinvestment.
12. The #zaverage #zreturn #zis #z5.9 #zpercent, #zwith #za #zstandard #zdeviation #zof #z9.8 #zpercent, #zso #zProb(Return
#z< #z–3.9 #zor #zReturn # z > #z15.7 #z) #z≈ #z1/3, #zbut #zwe #zare #zonly #zinterested #zin #zone #ztail; #zProb(Return #z<
#z–3.9) #z≈ #z1/6, #zwhich #zis #zhalf #zof #z1/3 #z.
95%: 5.9 #z± #z2σ #z= #z5.9 #z± #z2(9.8) #z= #z–13.7% #zto #z25.5%
99%: 5.9 #z± #z3σ #z= #z5.9 #z± #z3(9.8) #z= #z–23.5% #zto #z35.3%
13. Expected #zreturn #z= #z17.5%; # z σ #z= #z36.3%. #zDoubling #zyour #zmoney #zis #za #z100% #zreturn, #zso #zif #zthe
#zreturn #zdistribution #zis #znormal, #zZ #z= #z(100 #z– #z17.5)/36.3 #z= #z2.27 #zstandard #zdeviations; #zthis #zis #zin-
between #ztwo #zand #zthree #zstandard #zdeviations, #zso #zthe #zprobability #zis #zsmall, #zsomewhere #zbetween
#z.5% #zand #z2.5% #z(why?). #zReferring #zto #zthe #znearest #zZ #ztable, #zthe #zactual #zprobability #zis #z=
#z1.152%, #zor #zabout #zonce #zevery #z100 #zyears. #zTripling #zyour #zmoney #zwould #zbe #zZ #z= #z(200 #z–
#z17.5)/36.3 #z= #z5.028 #zstandard #zdeviations; #zthis #zcorresponds #zto #za #zprobability #zof #z(much) #zless
#zthan #z0.5%, #zor #zonce #zevery #z200 #zyears. #z(The #zactual #zanswer #zis #zless #zthan #zonce #zevery #z1 #zmillion
#zyears, #zso #zdon’t #zhold #zyour #zbreath.)
14. Year Common #zstocks T-bill #zreturn Risk #zpremium
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. Annual #zrisk #zpremium #z= #zCommon #zstock #zreturn #z– #zT-bill #zreturn #z(see #ztable #zabove).
b. Average #zreturns: #zCommon #zstocks #z= #z12.84/5 #z= #z.0257, #zor #z2.57%; # z T-bills #z= #z31.67/5 #z=
#z.0633, #zor #z6.33%;
Risk #zpremium #z= #z–18.83/5 #z= #z–.0377, #zor #z–3.77%
c. Common #zstocks: #zVar #z= #z1/4[ #z(–.1469 #z– #z.0257)2 #z+ #z(–.2647 #z– #z.0257)2 #z+ #z(.3723 #z– #z.0257)2 #z+
(.2393 #z– #z.0257)2 #z+ #z(–.0716 #z– #z.0257)2] #z= #z.072337
Standard #zdeviation #z= #z(0.072337)1/2 #z= #z.2690, #zor #z26.90%
Copyright #z2021 #z© #zMcGraw-Hill #zEducation. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution
#zwithout
the #zprior #zwritten #zconsent #zof #zMcGraw-Hill #zEducation.
, T-bills: # z Var #z= #z1/4[(.0729 #z– #z.0633)2 #z+ #z(.0799 #z– #z.0633)2 #z+ #z(.0587 #z– #z.0633)2 #z+ #z(.0507–.0633)2 #z+
(.0545 #z– #z.0633)2] #z= #z.000156
Standard #zdeviation #z= #z(.000156)1/2 #z= #z.0125, #zor #z1.25%
Risk #zpremium: # z Var #z= #z1/4[(–.2198 #z– #z(–.0377))2 #z+ #z(–.3446 #z– #z(–.0377))2 #z+ #z(.3136 #z– #z(–.0377))2 #z+
(.1886 #z– #z(–.0377))2 #z+ #z(–.1261 #z– #z(–.0377))2] #z= #z.077446
Standard #zdeviation #z= #z(.077446)1/2 #z= #z.2783, #zor #z27.83%
d. Before #zthe #zfact, #zfor #zmost #zassets #zthe #zrisk #zpremium #zwill #zbe #zpositive; #zinvestors #zdemand
#zcompensation #zover #zand #zabove #zthe #zrisk-free #zreturn #zto #zinvest #ztheir #zmoney #zin #zthe #zrisky
#zasset. #zAfter #zthe #zfact, #zthe #zobserved #zrisk #zpremium #zcan #zbe #znegative #zif #zthe #zasset’s #znominal
#zreturn #zis #zunexpectedly #zlow, #zthe #zrisk- #zfree #zreturn #zis #zunexpectedly #zhigh, #zor #zany
#zcombination #zof #zthese #ztwo #zevents.
15. ($324,000/$1,000)1/50 #z– #z1 #z= #z.1226, #zor #z12.26%
16. 5 #zyear #zestimate #z= #z[(5 #z– #z1)/(40 #z– #z1)] #z× #z10.24% #z+ #z[(40 #z– #z5)/(40 #z– #z1)] #z× #z12.60% #z= #z12.36%
10 #zyear #zestimate #z= #z[(10 #z– #z1)/(40 #z– #z1)] #z× #z10.24% #z+ #z[(40 #z– #z10)/(40 #z– #z1)] #z× #z12.60% #z= #z12.06%
20 #zyear #zestimate #z= #z[(20 #z– #z1)/(40 #z– #z1)] #z× #z10.24% #z+ #z[(40 #z– #z20)/(40 #z– #z1)] #z× #z12.60% #z= #z11.45%
17. Small-company #zstocks #z= #z($29,781.01/$1)1/93 #z– #z1 #z= #z.1171, #zor
#z– #z1 #z=
1/93
#z11.71% #zLarge-company #zstocks #z= #z($6,462.39/$1)
1/93
#z.0989, #zor #z9.89% #zLong-term #zgovernment #zbonds #z= #z($129.95/$1)
#z– #z1 #z= #z.0537, #zor #z5.37% #zTreasury #zbills #z= #z($23.05/$1) #z– #z1 #z=
1/93
#z.0343, #zor #z3.43%
Inflation #z= #z($14.03/$1)1/90 #z– #z1 #z= #z.0288, #zor #z2.88%
18. RA #z= #z(–.09 #z+ #z.17 #z+ #z.09 #z+ #z.14 #z– #z.04)/5 #z= #z.0540, #zor #z5.40%
RG #z= #z[(1 #z– #z.09)(1 #z+ #z.17)(1 #z+ #z.09)(1 #z+ #z.14)(1 #z- #z.04)]1/5 #z– #z1 #z= #z.0490, #zor #z4.90%
19. R1 #z= #z($15.61 #z– #z$13.25 #z+ #z$.15)/$13.25 #z= #z.1894, #zor
#z18.94% #zR2 #z= #z($16.72 #z– #z$15.61 #z+ #z$.18)/$15.61 #z=
#z.0826, #zor #z8.26% #zR3 #z= #z($15.18 #z– #z$16.72 #z+
#z$.20)/$16.72 #z= #z–.0801, #zor #z–8.01% #zR4 #z= #z($17.12 #z–
#z$15.18 #z+ #z$.24)/$15.18 #z= #z.1436, #zor #z14.36% #zR5 #z=
#z($20.43 #z– #z$17.12 #z+ #z$.28)/$17.12 #z= #z.2097, #zor
#z20.97%
RA #z= #z(.1894 #z+ #z.0826 #z– #z.0801 #z+ #z.1436 #z+ #z.2097)/5 #z= #z.1090, #zor #z10.90%
RG #z= #z[(1 #z+ #z.1894)(1 #z+ #z.0826)(1 #z– #z.0801)(1 #z+ #z.1436)(1 #z+ #z.2097)]1/5 #z– #z1 #z= #z.1038, #zor #z10.38%
20. Stock #zA: #zRA #z= #z(.08 #z+ #z.08 #z+ #z.08 #z+ #z.08 #z+ #z.08)/5 #z= #z.0800, #zor #z8.00%
Var #z= #z1/4[(.08 #z– #z.08)2 #z+ #z(.08 #z– #z.08)2 #z+ #z(.08 #z– #z.08)2 #z+ #z(.08 #z– #z.08)2 #z+ #z(.08 #z– #z.08)2] #z= #z.000000
Standard #zdeviation #z= #z(.000)1/2 #z= #z.000, #zor #z0.00%
RG #z= #z[(1 #z+ #z.08)(1 #z+ #z.08)(1 #z+ #z.08)(1 #z+.08)(1 #z+ #z.08)]1/5 #z– #z1 #z= #z.0800, #zor #z8.00%
Stock #zB: #zRA #z= #z(.03 #z+ #z.13 #z+ #z.07 #z+ #z.05 #z+ #z.12)/5 #z= #z.0800, #zor #z8.00%
Var #z= #z1/4[(.03 #z– #z.08)2 #z+ #z(.13 #z– #z.08)2 #z+ #z(.07 #z– #z.08)2 #z+ #z(.05 #z– #z.08)2 #z+ #z(.12 #z– #z.08)2] #z= #z.001900
Standard #zdeviation #z= #z(.001900)1/2 #z= #z.0436, #zor #z4.36%
RG #z= #z[(1 #z+ #z.03)(1 #z+ #z.13)(1 #z+ #z.07)(1 #z+ #z.05)(1 #z+ #z.12)]1/5 #z– #z1 #z= #z.0793, #zor #z7.93%
Stock #zC: #zRA #z= #z(–.24 #z+ #z.37 #z+ #z.14 #z+ #z.09 #z+ #z.04)/5 #z= #z.0800. #zor #z8.00%
Copyright #z2021 #z© #zMcGraw-Hill #zEducation. #zAll #zrights #zreserved. #zNo #zreproduction #zor #zdistribution
#zwithout
the #zprior #zwritten #zconsent #zof #zMcGraw-Hill #zEducation.
