湖南工业大学《风险投资学》课件-第六章

单元1：资本资产定价模型(CAPM)假设单元2：资本资产定价模型(CAPM)推导单元3：证券市场线(SML)单元4：证券市场线与资本市场线(CML)比较单元5：指数模型(Index

Model)主题六：重要投资理论(I)2单元1：资本资产定价模型(CAPM)假设单元2：资本资产定价模型(CAPM)推导单元3：证券市场线(SML)单元4：证券市场线与资本市场线(CML)比较单元5：指数模型(Index

Model)主题六：重要投资理论(I)3Capital

Asset

Pricing

Model

(CAPM)4•

It

is

the

equilibrium

model

that

underlies

allmodern

financial

theory.•

Derived

using

principles

of

diversification

withsimplified

assumptions.•

Markowitz,

Sharpe,

Lintner

and

Mossin

areresearchers

credited

with

its

development.CAPM假设5•

除了财富与风险趋避程度，其余皆一模一样1.

Relatively

small

endowment

(wealth);

Individualinvestors

are

price

takers.

投资人行为不足以影响价格(完全竞争市场假设)2.

Myopic

(短视近利);

Single-period

investmenthorizon.3.

Investments

are

limited

to

traded

financial

assets.不能投资

non

traded

assetsCAPM假设

(续)64.

No

taxes

and

transaction

costs.税会影响投资种类(交易税、资本利得税、利息税)，所以没税及交易成本(佣金)5.

Information

is

costless

and

available

to

allinvestors.

即没有信息不对称6.

Investors

are

rational

mean-variance

optimizers.𝑈

=

𝐸

𝑟

−

0.5𝐴𝜎2CAPM假设

(续)77.

There

are

homogeneous

expectations.齐一预期以相同的方式分析证券，对于经济表示有相同观点，对未来现金流量机率分配有相同预期。CAPM假设

(续)8

TotalWealthABCRiskyRisklessRiskyRisklessRiskyRisklessResulting

Equilibrium

Conditions9All

investors

will

hold

the

same

portfolio

for

riskyassets

–

market

portfolio:•

因为投资期间相同、投资种类相同、效用函数相同、对未来资产价格变化的预期也相同，所以所有人都持有相同的投资组合。所有投资人只有risky

assets形成的投资组合(不持无风险性资产):•

因为将所有人的投资组合加总，无风险资产借贷会

相消，所以整个经济体的财富就是所有风险性资产

的加总。而风险性资产的加总即为市场投资组合。Resulting

Equilibrium

Conditions10•

Market

portfolio

contains

all

securities

and

theproportion

of

each

security

is

its

market

value

asa

percentage

of

total

market

value.•

(Market

value=price

per

share*number

of

sharesoutstanding)Resulting

Equilibrium

Conditions

(cont.)11•

Risk

premium

on

the

the

market

depends

on

theaverage

risk

aversion

of

all

market

participants.E(rM

)

rf

A

M

2𝑦

=

,𝑌

=𝐴𝜎𝑀𝐴𝜎𝑀12Resulting

Equilibrium

Conditions

(cont.)𝑀𝑎𝑥

𝑈

=

𝐸

𝑟

−

0.5𝐴𝜎2s.t𝐹.𝑂.𝐶=1

𝐸𝑟𝑀

−𝑟

𝑓

𝐸𝑟𝑀

−𝑟

𝑓

2

2→

𝐸

𝑟𝑀

−

𝑟

𝑓

=

𝐴𝜎𝑀2

𝐸(𝑟

𝑝)

=

𝑟

𝑓

+

𝑦

𝐸

𝑟𝑀

−

𝑟

𝑓𝜎𝑝2

=

𝑦2𝜎𝑀2单元1：资本资产定价模型(CAPM)假设单元2：资本资产定价模型(CAPM)推导单元3：证券市场线(SML)单元4：证券市场线与资本市场线(CML)比较单元5：指数模型(Index

Model)主题六：重要投资理论(I)13

Resulting

Equilibrium

Conditions

(cont.)•

Risk

premium

on

an

individual

security

is

a

function

of

its

covariance

with

the

market.•

Expected

return-beta

relationship

14

E(rME(ri)

rf

Cov(ri,rM

)

2

M)

rf

i

E(rM

)

rfExplanation•GE’s

contribution

to

the

variance

of

the

market

M

2

:

wGE[w1cov(r

1,rGE)

...

wGE

cov(rGE,rGE)

...

wn

cov(rn,rGE)]

wGE

cov(rM,rGE)•

GE’s

contribution

to

the

risk

premium

of

the

market

E(rM

)

rf

:

wGE[E(r

GE)-rf]

15

M16Explanation•

Reward

to

risk

ratio

in

GE:•

Reward

to

risk

ratio

in

the

market:[E(rGE)

rf]

cov(rM,rGE)

wGE[E(rGE)

rf]wGE

cov(rM,rGE)[E(rM)

rf]

2

[E(rM)

rf]

cov(rM,rM)

M

Explanation•

All

offer

the

same

reward-to-risk

ratio

when

equilibrium

exists:cov(rM,rGE)

2

M[E(rM

)

rf]

[E(rGE)

rf]

[E(rM

)

rf]

2

[E(rGE)

rf]

cov(rM,rGE)

GE[E(rM

)

rf]

17Return

and

Risk

For

Individual

Securities18••The

risk

premium

on

individual

securities

is

a

function

ofthe

individual

security’s

contribution

to

the

risk

of

themarket

portfolio.

GE代表该资产本身对于市场风险的贡献度An

individual

security’s

risk

premium

is

a

function

of

thecovariance

of

returns

with

the

assets

that

make

up

themarket

portfolio.

GE

呈现资产本身报酬与市场报酬的共变异关系cov(rM,rGE)

M

2

GE

19Expected

return-beta

relationship•

对个别资产成立对投资组合也成立

::

wnE(rn)

wnrf

wn

n

E(rM

)

rf

E(rP)

rf

P

E(rM

)

rf

w1E(r

1)

w1rf

w1

1

E(rM

)

rfQuestion20•

The

market

risk

premium

is

8%.•

What

is

the

risk

premium

on

a

portfolio

with

25%in

GN

and

75%

in

Ford?

Ford

1.25

GN

1.1Question21What

is

the

risk

premium

on

a

portfolio

with

25%

inGN

and

75%

in

Ford?𝐸

𝑟𝐺𝑁

−

𝑟

𝑓

=

1.1

×

8%

=

8.8%𝐸

𝑟𝐹𝑜𝑟𝑑

−

𝑟

𝑓

=

1.25

×

8%

=

10%∴

𝐸

𝑟

𝑝

−

𝑟

𝑓

=

0.25

×

8.8%

+

0.75

×

10%=

2.2%

+

7.5%=

9.7%或

𝛽𝑝

=

1.1

×

0.25

+

1.25

×

0.75

=

1.2125→

𝐸

𝑟

𝑝

−

𝑟

𝑓

=

𝛽𝑝

𝐸

𝑟

𝑚

−

𝑟

𝑓

=

1.2125

×

8%=

9.7%单元1：资本资产定价模型(CAPM)假设单元2：资本资产定价模型(CAPM)推导单元3：证券市场线(SML)单元4：证券市场线与资本市场线(CML)比较单元5：指数模型(Index

Model)主题六：重要投资理论(I)22

M

M23Expected

return-beta

relationship•

对个别资产成立对投资组合也成立

E(rP)

rf

P

E(rM

)

rf

E(rM)

rf

M

E(rM

)

rf

M

1

或是

1

cov(rM,rM

)

2

M

2

2

M

24rf

Security

Market

Line

E(r)

E(r)

SML

E(rM)rf

M=

1.0SML

Relationships25

=

[Cov(ri,rm)]

/

m2Slope

SML

=

E(rm)

-

rf=

market

risk

premiumSML

=

rf+

[E(rm)

-

rf]Sample

Calculations

for

SMLE(rm)

-

rf

=

0.08rf=

0.03

x=

1.25E(rx)

=

0.03

+

1.25(0.08)

=

0.13

or

13%

y

=

0.6E(ry)

=

0.03

+

0.6(0.08)

=

0.078

or

7.8%

2627Rx=13%Graph

of

Sample

Calculations

E(r)

SML1.0Rm=11%

Ry=7.8%

3%

1.25

x0.6

y0.08Disequilibrium

Example28E(r)

SML15%

Rm=11%rf=3%1.0

1.25Disequilibrium

Example

(cont.)29••••Suppose

a

security

with

a

of

1.25

is

offering

expectedreturn

of

15%.According

to

SML,

it

should

be

13%.Expected

return-CAPM

return=Alpha=15%-13%=2%

(+)Under-priced:

offering

too

high

of

a

rate

of

return

for

itslevel

of

risk.30Disequilibrium

Example

(cont.)•

Actual

expected

return

>

required

rate

of

return

(fair

expected

rate

of

return)

underpriced,

buy

more

𝛼:

Actual

expected

return-

fair

expected

return

+

𝛼:𝑏𝑢𝑦𝑚𝑜𝑟𝑒,

−

𝛼:𝑠𝑒𝑙𝑙

𝑚𝑜𝑟𝑒•

Capital

budgeting:•

𝑟

𝑓

=

8%,𝐸

𝑟𝑀

=

16%,𝛽

=

1.3,𝐸

𝑟

=

8%

+

(16%

−

8%)

×

1.3

=

18.4%•

若IRR(内部报酬率)>18.4%，则可接受投资计划0=𝑡

𝐶𝐹𝑖𝑖=1

(1+𝐼𝑅𝑅)𝑖单元1：资本资产定价模型(CAPM)假设单元2：资本资产定价模型(CAPM)推导单元3：证券市场线(SML)单元4：证券市场线与资本市场线(CML)比较单元5：指数模型(Index

Model)主题六：重要投资理论(I)3132

)Security

Market

Line

E(r)

SML

E(r

M)

rr

ff

M=

1.0SML

Relationships

=Slope

SML

=[COV(ri,rm)]

/

m2E(rm)

-

rf

=

market

risk

premiumSML

=

rf+

[E(rm)

-

rf]

3334E(rM)

rfMCapital

Market

Line

E(r)

CML

m

M35Slope

and

Market

Risk

Premium

E(rp)

rf

M

rfE(rM)

-

rf===Market

portfolioRisk

free

rateMarket

risk

premiumMarket

price

of

riskSlope

of

the

CML[E(rM)

rf]

=

=𝐶𝑀𝐿:𝐸

𝑟

𝑐

=

𝑟

𝑓

+𝜎𝑐

[]Slope

and

Market

Risk

Premium36𝑆𝑀𝐿:𝐸

𝑟𝑖

=

𝑟

𝑓

+

𝛽[𝐸(𝑟𝑀)

−

𝑟

𝑓](可以是个别资产或投资组合)𝐸(𝑟𝑀)−𝑟𝑓𝜎𝑀(只对efficient

portfolio

成立)SMLCMLMeasureofriskUsesystematicrisk(non-diversifiablerisk)Usestandarddeviation(totalrisk)ApplicationUsedtodeterminetheappropriateexpected(benchmark)returnsforsecuritiesUsedtodeterminetheappropriateassetallocation(betweenrisk-freeassetandthemarketportfolio)fortheinvestorDefinitionGraphoftheCAPMGraphoftheefficientfrontierSlopeMarketriskpremiumMarketportfolioSharperatioKey

difference

between

the

SML

and

the

CML37Relaxing

the

assumptions••••Zero-beta

version

of

the

CAPMNontraded

assetsMultiperiodTransaction

Cost

and

liquidity

premium•

Heterogeneous

expectations:

there

is

no

single

SML.

Investors

will

disagree

about

the

intercept

and

slope

of

the

SML.

SML

will

be

a

thick

band.•

Tax:

there

is

no

single

SML.

Investors

will

disagree

about

the

intercept

and

slope

of

the

SML

due

to

their

tax

bracket.

SML

will

be

a

thick

band.

38Zero-beta

version

of

the

CAPM39•

If

risk-free

borrowing

and

lending

doesn’t

exist,

a

portfolioof

risky

securities

must

be

created

such

that

the

portfoliobeta

equals

zero.•

SML

with

equal

risk-free

borrowing

and

lending:rf+

[E(rm)

-

rf]•

SML

without

equal

risk-free

borrowing

and

lending:E(r0)+

[E(rm)

-

E(r0)]•

Because

E(r0)>

rf

,

SML

has

a

higher

intercept

and

aflatter

slope.Liquidity

premium40•

Transaction

Cost

and

liquidity

premiumLiquidity

流通性：资产变现的成本与容易程度、资产报酬与流通性有关，属于系统风险，应给予补贴。人们偏好流动性高，交易成本低的资产，所以低流动性的资产，要求报酬率较高。单元1：资本资产定价模型(CAPM)假设单元2：资本资产定价模型(CAPM)推导单元3：证券市场线(SML)单元4：证券市场线与资本市场线(CML)比较单元5：指数模型(Index

Model)主题六：重要投资理论(I)41Difficulties

in

applying

the

CAPM42•

Cannot

identify

the

unobserved

market

portfolio.•

Only

describes

the

equilibrium

relationship

for

unobservedexpected

returns.•

Only

describes

the

equilibrium

relationship

betweenreturns

and

unobserved

beta,

which

needs

to

beestimated.Index

model43•

A

regression

model

specifying

the

relationship

betweenrealized

returns

for

stocks

and

an

observable

market

index.•

The

observed

index

serves

as

a

proxy

for

the

marketportfolio.•

Index

model

uses

observed

realized

returns.•

Index

model

provides

a

way

to

estimate

asset

betas.•

Single

index

model:Ri

Rf

i

i(Rmkt

Rf)

iAlpha44•

Alpha

=

realized

average

return-CAPM

required

return•

说明:

i

E(Ri)

CAPM

requiredreturn𝑅𝑖

−

𝑅𝑓

=

𝛼𝑖

+

𝛽𝑖

𝑅𝑚

−

𝑅𝑓

+

𝜀𝑖→

E(𝑅𝑖)

=

𝑅𝑓

+

𝛼𝑖

+

𝛽𝑖[𝐸(𝑅𝑚)

−

𝑅𝑓]=

𝛼𝑖

+

CAPM

required

return∴

𝛼𝑖

=

E(𝑅𝑖)

−

CAPM

required

returnRisk

Reduction

with

Diversification45Number

ofSecuritiesSt.

DeviationMarket

RiskUnique

RiskTwo

sources

of

uncertainty

•

Total

risk=

systematic

risk+

nonsystematic

risk•

Market

risk:

systematic

risk;

nondiversifiable

risk•

Unique

risk:

firm-specific

risk;

nonsystematic

risk;

diversifiable

risk•

R-square:a.

measure

of

systematic

riskb.

the

proportion

which

can

be

explained

by

the

market

index

46

Ri

Rf

i

i(Rmkt

Rf)

i