SOLUTION MANUAL FOR . .
Fundamentals of Investments Valuation and Management 9th Edition By Jordan
. . . . . . . . .
Chapter 1-21
.
Chapter 1 .
A Brief History of Risk and Return
. . . . . .
Concept.Questions
1. For.both.risk.and.return,.increasing.order.is.b,.c,.a,.d..On.average,.the.higher.the.risk.of.an.investment,.the.h
igher.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,.arithm
etic.returns.do.not.account.for.the.effects.of.compounding.(and,.in.particular,.the.effect.of.volatility)..Geo
metric.returns.do.account.for.the.effects.of.compounding.and.for.changes.in.the.base.used.for.each.year’s.c
alculation.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.appr
oximate.a.holding.period.return..When.predicting.a.holding.period.return,.the.arithmetic.return.will.tend.t
o.be.too.high.and.the.geometric.return.will.tend.to.be.too.low..Blume’s.formula.adjusts.these.returns.for.dif
ferent.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.o
ur.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.pr
emiums.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.s
maller.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.2021.©.McGraw-Hill.Education..All.rights.reserved..No.reproduction.or.distribution.without
the.prior.written.consent.of.McGraw-Hill.Education.
,10. It.is.important.not.to.lose.sight.of.the.fact.that.the.results.we.have.discussed.cover.over.80.years,. well.beyo
nd.the.investing.lifetime.for.most.of.us..There.have.been.extended.periods.during.which.small.stocks.have.
done.terribly..Thus,.one.reason.most.investors.will.choose.not.to.pursue.a.100.percent.stock.(particularly.s
mall-
cap.stocks).strategy.is.that.many.investors.have.relatively.short.horizons,.and.high.volatility.investments.
may.be.very.inappropriate.in.such.cases..There.are.other.reasons,.but.we.will.defer.discussion.of.these.to.la
ter.chapters.
Solutions.to.Questions.and.Problems
NOTE:.All.end.of.chapter.problems.were.solved.using.a.spreadsheet..Many.problems.require.multiple.steps..D
ue.to.space.and.readability.constraints,.when.these.intermediate.steps.are.included.in.this.solutions.manual,.ro
unding.may.appear.to.have.occurred..However,.the.final.answer.for.each.problem.is.found.without.rounding.du
ring.any.step.in.the.problem.
Core.Questions
1. Total.dollar.return.=.100($41.–.$37.+.$.28).=.$428.00
Whether.you.choose.to.sell.the.stock.does.not.affect.the.gain.or.loss.for.the.year;.your.stock.is.worth.what.it.
would.bring.if.you.sold.it..Whether.you.choose.to.do.so.or.not.is.irrelevant.(ignoring.commissions.and.taxe
s).
2. Capital.gains.yield.=.($41.–
.$37)/$37.=..1081,.or.10.81%.Dividend.yield.=.$.28/$37.=..0
076,.or..76%
Total.rate.of.return.=.10.81%.+..76%.=.11.57%
3. Dollar.return.=.500($34.–.$37.+.$.28).=.–$1,360
Capital.gains.yield.=.($34.–.$37)/$37.=.–.0811,.or.–
8.11%.Dividend.yield.=.$.28/$37.=..0076,.or..76%
Total.rate.of.return.=.–8.11%.+..76%.=.–7.35%
4. a.. average.return.=.6.2%,.average.risk.premium.=.2.6%
b. average.return.=.3.6%,.average.risk.premium.=.0%
c. average.return.=.11.9%,.average.risk.premium.=.8.3%
d. average.return.=.17.5%,.average.risk.premium.=.13.9%
5. Cherry.average.return.=.(17%.+.11%.–.2%.+.3%.+.14%)/5.=.8.60%
Straw.average.return.=.(16%.+.18%.–.6%.+.1%.+.22%)/5.=.10.20%
6. Cherry:.RA.=.8.60%
Var.=.1/4[(.17.–..086)2.+.(.11.–..086)2.+.(–.02.–..086)2.+.(.03.–..086)2.+.(.14.–..086)2].=..00623
Standard.deviation.=.(.00623)1/2.=..0789,.or.7.89%
Straw:.RB.=.10.20%
Var.=.1/4[(.16.–..102)2.+.(.18.–..102)2.+.(–.06.–..102)2.+.(.01.–..102)2.+.(.22.–..102)2].=..01452
Standard.deviation.=.(.01452)1/2.=..1205,.or.12.05%
7. The.capital.gains.yield.is.($59.–.$65)/$65.=.–.0923,.or.–
9.23%.(notice.the.negative.sign).. With.a.dividend.yield.of.1.2.percent,.the.total.return.is.–8.03%.
Copyright.2021.©.McGraw-Hill.Education..All.rights.reserved..No.reproduction.or.distribution.without
the.prior.written.consent.of.McGraw-Hill.Education.
,8. Geometric.return.=.[(1.+..17)(1.+..11)(1.-..02)(1.+..03)(1.+..14)](1/5).–.1.=..0837,.or.8.37%
9. Arithmetic.return.=.(.21.+..12.+..07.–.13.–..04.+..26)/6.=..0817,.or.8.17%
Geometric.return.=.[(1.+..21)(1.+..12)(1.+..07)(1.–..13)(1.–..04)(1.+..26)](1/6).–.1.=..0730,.or.7.30%
Intermediate.Questions
10. That’s.plus.or.minus.one.standard.deviation,.so.about.two-
thirds.of.the.time,.or.two.years.out.of.three..In.one.year.out.of.three,.you.will.be.outside.this.range,.implying
.that.you.will.be.below.it.one.year.out.of.six.and.above.it.one.year.out.of.six.
11. You.lose.money.if.you.have.a.negative.return..With.a.12.percent.expected.return.and.a.6.percent.standard.d
eviation,.a.zero.return.is.two.standard.deviations.below.the.average..The.odds.of.being.outside.(above.or.b
elow).two.standard.deviations.are.5.percent;.the.odds.of.being.below.are.half. that,.or.2.5.percent..(It’s.actu
ally.2.28.percent.).You.should.expect.to.lose.money.only.2.5.years.out.of.every.100..It’s.a.pretty.safe.invest
ment.
12. The.average.return.is.5.9.percent,.with.a.standard.deviation.of.9.8.percent,.so.Prob(Return.<.–
3.9.or.Return. >.15.7.).≈.1/3,.but.we.are.only.interested.in.one.tail;.Prob(Return.<.–
3.9).≈.1/6,.which.is.half.of.1/3..
95%: 5.9.±.2σ.=.5.9.±.2(9.8).=.–13.7%.to.25.5%
99%: 5.9.±.3σ.=.5.9.±.3(9.8).=.–23.5%.to.35.3%
13. Expected.return.=.17.5%;. σ.=.36.3%..Doubling.your.money.is.a.100%.return,.so.if.the.return.distribution.i
s.normal,.Z.=.(100.–.17.5)/36.3.=.2.27.standard.deviations;.this.is.in-
between.two.and.three.standard.deviations,.so.the.probability.is.small,.somewhere.between..5%.and.2.5%.
(why?)..Referring.to.the.nearest.Z.table,.the.actual.probability.is.=.1.152%,.or.about.once.every.100.years..
Tripling.your.money.would.be.Z.=.(200.–
.17.5)/36.3.=.5.028.standard.deviations;.this.corresponds.to.a.probability.of.(much).less.than.0.5%,.or.once
.every.200.years..(The.actual.answer.is.less.than.once.every.1.million.years,.so.don’t.hold.your.breath.)
14. Year Common.stocks T-bill.return Risk.premium
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.risk.premium.=.Common.stock.return.–.T-bill.return.(see.table.above).
b. Average.returns:.Common.stocks.=.12.84/5.=..0257,.or.2.57%;. T-
bills.=.31.67/5.=..0633,.or.6.33%;
Risk.premium.=.–18.83/5.=.–.0377,.or.–3.77%
c. Common.stocks:.Var.=.1/4[.(–.1469.–..0257)2.+.(–.2647.–..0257)2.+.(.3723.–..0257)2.+
(.2393.–..0257)2.+.(–.0716.–..0257)2].=..072337
Standard.deviation.=.(0.072337)1/2.=..2690,.or.26.90%
T-bills:. Var.=.1/4[(.0729.–..0633)2.+.(.0799.–..0633)2.+.(.0587.–..0633)2.+.(.0507–.0633)2.+
(.0545.–..0633)2].=..000156
Standard.deviation.=.(.000156)1/2.=..0125,.or.1.25%
Copyright.2021.©.McGraw-Hill.Education..All.rights.reserved..No.reproduction.or.distribution.without
the.prior.written.consent.of.McGraw-Hill.Education.
, Risk.premium:. Var.=.1/4[(–.2198.–.(–.0377))2.+.(–.3446.–.(–.0377))2.+.(.3136.–.(–.0377))2.+
(.1886.–.(–.0377))2.+.(–.1261.–.(–.0377))2].=..077446
Standard.deviation.=.(.077446)1/2.=..2783,.or.27.83%
d. Before.the.fact,.for.most.assets.the.risk.premium.will.be.positive;.investors.demand.compensation.over.
and.above.the.risk-
free.return.to.invest.their.money.in.the.risky.asset..After.the.fact,.the.observed.risk.premium.can.be.nega
tive.if.the.asset’s.nominal.return.is.unexpectedly.low,.the.risk-
.free.return.is.unexpectedly.high,.or.any.combination.of.these.two.events.
15. ($324,000/$1,000)1/50.–.1.=..1226,.or.12.26%
16. 5.year.estimate.=.[(5.–.1)/(40.–.1)].×.10.24%.+.[(40.–.5)/(40.–.1)].×.12.60%.=.12.36%
10.year.estimate.=.[(10.–.1)/(40.–.1)].×.10.24%.+.[(40.–.10)/(40.–.1)].×.12.60%.=.12.06%
20.year.estimate.=.[(20.–.1)/(40.–.1)].×.10.24%.+.[(40.–.20)/(40.–.1)].×.12.60%.=.11.45%
17. Small-company.stocks.=.($29,781.01/$1)1/93.–
1/93
.1.=..1171,.or.11.71%.Large-company.stocks.=.($6,462.39/$1) .–
1/93
.1.=..0989,.or.9.89%.Long-term.government.bonds.=.($129.95/$1) .–
1/93
.1.=..0537,.or.5.37%.Treasury.bills.=.($23.05/$1) .–.1.=..0343,.or.3.43%
Inflation.=.($14.03/$1)1/90.–.1.=..0288,.or.2.88%
18. RA.=.(–.09.+..17.+..09.+..14.–..04)/5.=..0540,.or.5.40%
RG.=.[(1.–..09)(1.+..17)(1.+..09)(1.+..14)(1.-..04)]1/5.–.1.=..0490,.or.4.90%
19. R1.=.($15.61.–
.$13.25.+.$.15)/$13.25.=..1894,.or.18.94%.R2.=.($16.72.–
.$15.61.+.$.18)/$15.61.=..0826,.or.8.26%.R3.=.($15.18.–
.$16.72.+.$.20)/$16.72.=.–.0801,.or.–8.01%.R4.=.($17.12.–
.$15.18.+.$.24)/$15.18.=..1436,.or.14.36%.R5.=.($20.43.–
.$17.12.+.$.28)/$17.12.=..2097,.or.20.97%
RA.=.(.1894.+..0826.–..0801.+..1436.+..2097)/5.=..1090,.or.10.90%
RG.=.[(1.+..1894)(1.+..0826)(1.–..0801)(1.+..1436)(1.+..2097)]1/5.–.1.=..1038,.or.10.38%
20. Stock.A:.RA.=.(.08.+..08.+..08.+..08.+..08)/5.=..0800,.or.8.00%
Var.=.1/4[(.08.–..08)2.+.(.08.–..08)2.+.(.08.–..08)2.+.(.08.–..08)2.+.(.08.–..08)2].=..000000
Standard.deviation.=.(.000)1/2.=..000,.or.0.00%
RG.=.[(1.+..08)(1.+..08)(1.+..08)(1.+.08)(1.+..08)]1/5.–.1.=..0800,.or.8.00%
Stock.B:.RA.=.(.03.+..13.+..07.+..05.+..12)/5.=..0800,.or.8.00%
Var.=.1/4[(.03.–..08)2.+.(.13.–..08)2.+.(.07.–..08)2.+.(.05.–..08)2.+.(.12.–..08)2].=..001900
Standard.deviation.=.(.001900)1/2.=..0436,.or.4.36%
RG.=.[(1.+..03)(1.+..13)(1.+..07)(1.+..05)(1.+..12)]1/5.–.1.=..0793,.or.7.93%
Stock.C:.RA.=.(–.24.+..37.+..14.+..09.+..04)/5.=..0800..or.8.00%
Var.=.1/4[(–.24.–..08)2.+.(.37.–..08)2.+.(.14.–..08)2.+.(.09.–..08)2.+.(.04.–..08)2].=..047950
Standard.deviation.=.(.047950)1/2.=..2190,.or.21.90%
RG.=.[(1.–..24)(1.+..37)(1.+..14)(1.+..09)(1.+..04)]1/5.–.1.=..0612,.or.6.12%
The.larger.the.standard.deviation,.the.greater.will.be.the.difference.between.the.arithmetic.return.and.geo
Copyright.2021.©.McGraw-Hill.Education..All.rights.reserved..No.reproduction.or.distribution.without
the.prior.written.consent.of.McGraw-Hill.Education.
Fundamentals of Investments Valuation and Management 9th Edition By Jordan
. . . . . . . . .
Chapter 1-21
.
Chapter 1 .
A Brief History of Risk and Return
. . . . . .
Concept.Questions
1. For.both.risk.and.return,.increasing.order.is.b,.c,.a,.d..On.average,.the.higher.the.risk.of.an.investment,.the.h
igher.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,.arithm
etic.returns.do.not.account.for.the.effects.of.compounding.(and,.in.particular,.the.effect.of.volatility)..Geo
metric.returns.do.account.for.the.effects.of.compounding.and.for.changes.in.the.base.used.for.each.year’s.c
alculation.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.appr
oximate.a.holding.period.return..When.predicting.a.holding.period.return,.the.arithmetic.return.will.tend.t
o.be.too.high.and.the.geometric.return.will.tend.to.be.too.low..Blume’s.formula.adjusts.these.returns.for.dif
ferent.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.o
ur.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.pr
emiums.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.s
maller.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.2021.©.McGraw-Hill.Education..All.rights.reserved..No.reproduction.or.distribution.without
the.prior.written.consent.of.McGraw-Hill.Education.
,10. It.is.important.not.to.lose.sight.of.the.fact.that.the.results.we.have.discussed.cover.over.80.years,. well.beyo
nd.the.investing.lifetime.for.most.of.us..There.have.been.extended.periods.during.which.small.stocks.have.
done.terribly..Thus,.one.reason.most.investors.will.choose.not.to.pursue.a.100.percent.stock.(particularly.s
mall-
cap.stocks).strategy.is.that.many.investors.have.relatively.short.horizons,.and.high.volatility.investments.
may.be.very.inappropriate.in.such.cases..There.are.other.reasons,.but.we.will.defer.discussion.of.these.to.la
ter.chapters.
Solutions.to.Questions.and.Problems
NOTE:.All.end.of.chapter.problems.were.solved.using.a.spreadsheet..Many.problems.require.multiple.steps..D
ue.to.space.and.readability.constraints,.when.these.intermediate.steps.are.included.in.this.solutions.manual,.ro
unding.may.appear.to.have.occurred..However,.the.final.answer.for.each.problem.is.found.without.rounding.du
ring.any.step.in.the.problem.
Core.Questions
1. Total.dollar.return.=.100($41.–.$37.+.$.28).=.$428.00
Whether.you.choose.to.sell.the.stock.does.not.affect.the.gain.or.loss.for.the.year;.your.stock.is.worth.what.it.
would.bring.if.you.sold.it..Whether.you.choose.to.do.so.or.not.is.irrelevant.(ignoring.commissions.and.taxe
s).
2. Capital.gains.yield.=.($41.–
.$37)/$37.=..1081,.or.10.81%.Dividend.yield.=.$.28/$37.=..0
076,.or..76%
Total.rate.of.return.=.10.81%.+..76%.=.11.57%
3. Dollar.return.=.500($34.–.$37.+.$.28).=.–$1,360
Capital.gains.yield.=.($34.–.$37)/$37.=.–.0811,.or.–
8.11%.Dividend.yield.=.$.28/$37.=..0076,.or..76%
Total.rate.of.return.=.–8.11%.+..76%.=.–7.35%
4. a.. average.return.=.6.2%,.average.risk.premium.=.2.6%
b. average.return.=.3.6%,.average.risk.premium.=.0%
c. average.return.=.11.9%,.average.risk.premium.=.8.3%
d. average.return.=.17.5%,.average.risk.premium.=.13.9%
5. Cherry.average.return.=.(17%.+.11%.–.2%.+.3%.+.14%)/5.=.8.60%
Straw.average.return.=.(16%.+.18%.–.6%.+.1%.+.22%)/5.=.10.20%
6. Cherry:.RA.=.8.60%
Var.=.1/4[(.17.–..086)2.+.(.11.–..086)2.+.(–.02.–..086)2.+.(.03.–..086)2.+.(.14.–..086)2].=..00623
Standard.deviation.=.(.00623)1/2.=..0789,.or.7.89%
Straw:.RB.=.10.20%
Var.=.1/4[(.16.–..102)2.+.(.18.–..102)2.+.(–.06.–..102)2.+.(.01.–..102)2.+.(.22.–..102)2].=..01452
Standard.deviation.=.(.01452)1/2.=..1205,.or.12.05%
7. The.capital.gains.yield.is.($59.–.$65)/$65.=.–.0923,.or.–
9.23%.(notice.the.negative.sign).. With.a.dividend.yield.of.1.2.percent,.the.total.return.is.–8.03%.
Copyright.2021.©.McGraw-Hill.Education..All.rights.reserved..No.reproduction.or.distribution.without
the.prior.written.consent.of.McGraw-Hill.Education.
,8. Geometric.return.=.[(1.+..17)(1.+..11)(1.-..02)(1.+..03)(1.+..14)](1/5).–.1.=..0837,.or.8.37%
9. Arithmetic.return.=.(.21.+..12.+..07.–.13.–..04.+..26)/6.=..0817,.or.8.17%
Geometric.return.=.[(1.+..21)(1.+..12)(1.+..07)(1.–..13)(1.–..04)(1.+..26)](1/6).–.1.=..0730,.or.7.30%
Intermediate.Questions
10. That’s.plus.or.minus.one.standard.deviation,.so.about.two-
thirds.of.the.time,.or.two.years.out.of.three..In.one.year.out.of.three,.you.will.be.outside.this.range,.implying
.that.you.will.be.below.it.one.year.out.of.six.and.above.it.one.year.out.of.six.
11. You.lose.money.if.you.have.a.negative.return..With.a.12.percent.expected.return.and.a.6.percent.standard.d
eviation,.a.zero.return.is.two.standard.deviations.below.the.average..The.odds.of.being.outside.(above.or.b
elow).two.standard.deviations.are.5.percent;.the.odds.of.being.below.are.half. that,.or.2.5.percent..(It’s.actu
ally.2.28.percent.).You.should.expect.to.lose.money.only.2.5.years.out.of.every.100..It’s.a.pretty.safe.invest
ment.
12. The.average.return.is.5.9.percent,.with.a.standard.deviation.of.9.8.percent,.so.Prob(Return.<.–
3.9.or.Return. >.15.7.).≈.1/3,.but.we.are.only.interested.in.one.tail;.Prob(Return.<.–
3.9).≈.1/6,.which.is.half.of.1/3..
95%: 5.9.±.2σ.=.5.9.±.2(9.8).=.–13.7%.to.25.5%
99%: 5.9.±.3σ.=.5.9.±.3(9.8).=.–23.5%.to.35.3%
13. Expected.return.=.17.5%;. σ.=.36.3%..Doubling.your.money.is.a.100%.return,.so.if.the.return.distribution.i
s.normal,.Z.=.(100.–.17.5)/36.3.=.2.27.standard.deviations;.this.is.in-
between.two.and.three.standard.deviations,.so.the.probability.is.small,.somewhere.between..5%.and.2.5%.
(why?)..Referring.to.the.nearest.Z.table,.the.actual.probability.is.=.1.152%,.or.about.once.every.100.years..
Tripling.your.money.would.be.Z.=.(200.–
.17.5)/36.3.=.5.028.standard.deviations;.this.corresponds.to.a.probability.of.(much).less.than.0.5%,.or.once
.every.200.years..(The.actual.answer.is.less.than.once.every.1.million.years,.so.don’t.hold.your.breath.)
14. Year Common.stocks T-bill.return Risk.premium
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.risk.premium.=.Common.stock.return.–.T-bill.return.(see.table.above).
b. Average.returns:.Common.stocks.=.12.84/5.=..0257,.or.2.57%;. T-
bills.=.31.67/5.=..0633,.or.6.33%;
Risk.premium.=.–18.83/5.=.–.0377,.or.–3.77%
c. Common.stocks:.Var.=.1/4[.(–.1469.–..0257)2.+.(–.2647.–..0257)2.+.(.3723.–..0257)2.+
(.2393.–..0257)2.+.(–.0716.–..0257)2].=..072337
Standard.deviation.=.(0.072337)1/2.=..2690,.or.26.90%
T-bills:. Var.=.1/4[(.0729.–..0633)2.+.(.0799.–..0633)2.+.(.0587.–..0633)2.+.(.0507–.0633)2.+
(.0545.–..0633)2].=..000156
Standard.deviation.=.(.000156)1/2.=..0125,.or.1.25%
Copyright.2021.©.McGraw-Hill.Education..All.rights.reserved..No.reproduction.or.distribution.without
the.prior.written.consent.of.McGraw-Hill.Education.
, Risk.premium:. Var.=.1/4[(–.2198.–.(–.0377))2.+.(–.3446.–.(–.0377))2.+.(.3136.–.(–.0377))2.+
(.1886.–.(–.0377))2.+.(–.1261.–.(–.0377))2].=..077446
Standard.deviation.=.(.077446)1/2.=..2783,.or.27.83%
d. Before.the.fact,.for.most.assets.the.risk.premium.will.be.positive;.investors.demand.compensation.over.
and.above.the.risk-
free.return.to.invest.their.money.in.the.risky.asset..After.the.fact,.the.observed.risk.premium.can.be.nega
tive.if.the.asset’s.nominal.return.is.unexpectedly.low,.the.risk-
.free.return.is.unexpectedly.high,.or.any.combination.of.these.two.events.
15. ($324,000/$1,000)1/50.–.1.=..1226,.or.12.26%
16. 5.year.estimate.=.[(5.–.1)/(40.–.1)].×.10.24%.+.[(40.–.5)/(40.–.1)].×.12.60%.=.12.36%
10.year.estimate.=.[(10.–.1)/(40.–.1)].×.10.24%.+.[(40.–.10)/(40.–.1)].×.12.60%.=.12.06%
20.year.estimate.=.[(20.–.1)/(40.–.1)].×.10.24%.+.[(40.–.20)/(40.–.1)].×.12.60%.=.11.45%
17. Small-company.stocks.=.($29,781.01/$1)1/93.–
1/93
.1.=..1171,.or.11.71%.Large-company.stocks.=.($6,462.39/$1) .–
1/93
.1.=..0989,.or.9.89%.Long-term.government.bonds.=.($129.95/$1) .–
1/93
.1.=..0537,.or.5.37%.Treasury.bills.=.($23.05/$1) .–.1.=..0343,.or.3.43%
Inflation.=.($14.03/$1)1/90.–.1.=..0288,.or.2.88%
18. RA.=.(–.09.+..17.+..09.+..14.–..04)/5.=..0540,.or.5.40%
RG.=.[(1.–..09)(1.+..17)(1.+..09)(1.+..14)(1.-..04)]1/5.–.1.=..0490,.or.4.90%
19. R1.=.($15.61.–
.$13.25.+.$.15)/$13.25.=..1894,.or.18.94%.R2.=.($16.72.–
.$15.61.+.$.18)/$15.61.=..0826,.or.8.26%.R3.=.($15.18.–
.$16.72.+.$.20)/$16.72.=.–.0801,.or.–8.01%.R4.=.($17.12.–
.$15.18.+.$.24)/$15.18.=..1436,.or.14.36%.R5.=.($20.43.–
.$17.12.+.$.28)/$17.12.=..2097,.or.20.97%
RA.=.(.1894.+..0826.–..0801.+..1436.+..2097)/5.=..1090,.or.10.90%
RG.=.[(1.+..1894)(1.+..0826)(1.–..0801)(1.+..1436)(1.+..2097)]1/5.–.1.=..1038,.or.10.38%
20. Stock.A:.RA.=.(.08.+..08.+..08.+..08.+..08)/5.=..0800,.or.8.00%
Var.=.1/4[(.08.–..08)2.+.(.08.–..08)2.+.(.08.–..08)2.+.(.08.–..08)2.+.(.08.–..08)2].=..000000
Standard.deviation.=.(.000)1/2.=..000,.or.0.00%
RG.=.[(1.+..08)(1.+..08)(1.+..08)(1.+.08)(1.+..08)]1/5.–.1.=..0800,.or.8.00%
Stock.B:.RA.=.(.03.+..13.+..07.+..05.+..12)/5.=..0800,.or.8.00%
Var.=.1/4[(.03.–..08)2.+.(.13.–..08)2.+.(.07.–..08)2.+.(.05.–..08)2.+.(.12.–..08)2].=..001900
Standard.deviation.=.(.001900)1/2.=..0436,.or.4.36%
RG.=.[(1.+..03)(1.+..13)(1.+..07)(1.+..05)(1.+..12)]1/5.–.1.=..0793,.or.7.93%
Stock.C:.RA.=.(–.24.+..37.+..14.+..09.+..04)/5.=..0800..or.8.00%
Var.=.1/4[(–.24.–..08)2.+.(.37.–..08)2.+.(.14.–..08)2.+.(.09.–..08)2.+.(.04.–..08)2].=..047950
Standard.deviation.=.(.047950)1/2.=..2190,.or.21.90%
RG.=.[(1.–..24)(1.+..37)(1.+..14)(1.+..09)(1.+..04)]1/5.–.1.=..0612,.or.6.12%
The.larger.the.standard.deviation,.the.greater.will.be.the.difference.between.the.arithmetic.return.and.geo
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