Chap007 Optimal Risky Portfolios 博迪投资学课件

Investments,

8th

editionBodie,

Kane

and

MarcusSlides

by

Susan

HineMc

Graw-

Hill/

IrwinCopyright

©

2009

by

The

Mc

Graw-

HillCompanies,

Inc.

All

rights

reserved.CHAPTER

7Optimal

RiskyPortfoliosDiversification

and

Portfolio

Risk7-2Market

riskSystematic

or

nondiversifiableFirm-specific

riskDiversifiable

or

nonsystematicFigure

7.1

Portfolio

Risk

as

a

Function

of

theNumber

of

Stocks

in

the

Portfolio7-3Figure

7.2

Portfolio

Diversification7-4Covariance

and

Correlation

Portfolio

risk

depends

on

the

correlationbetweenthe

returns

of

the

assets

in

theportfolio

Covariance

and

the

correlation

coefficienprovide

a

measure

of

the

way

returns

twoassets

vary7-5Two-Security

Portfolio:

Return7-6Two-Security

Portfolio:

RiskwE=

Variance

of

Security

D=

Variance

of

Security

E=

Covariance

of

returns

forSecurity

D

and

Security

E7-7Two-Security

Portfolio:

RiskContinued

Another

way

to

express

variance

of

theportfolio:7-8D,E

=

Correlation

coefficient

ofreturnsD

=

Standard

deviation

ofreturns

for

Security

DE

=

Standard

deviation

ofreturns

for

Security

E7-9Cov(rD,rE)

=DE

D

ECovarianceRange

of

values

for+

1.0

>

r

>

-1.07-101,2If

r

=

1.0,

the

securities

would

be

perfpositively

correlatedIf

r

=

-

1.0,

the

securities

would

beperfectly

negatively

correlatedCorrelation

Coefficients:

Possible

ValuesTable

7.1

Descriptive

Statistics

for

TwoMutual

Funds7-112p

=

w12

1+2

w22

1232Cov(r1,r2)Cov(r1,r3)Cov(r2,r3)+

2w1w2+

2w1w3+

2w2w3+

w32Three-Security

Portfolio7-12Table

7.2

Computation

of

PortfolioVariance

From

the

Covariance

Matrix7-13Table

7.3

Expected

Return

and

StandardDeviation

with

Various

CorrelationCoefficients7-14Figure

7.3

Portfolio

Expected

Return

asa

Function

of

Investment

Proportions7-15Figure

7.4

Portfolio

Standard

Deviationas

a

Function

of

Investment

Proportions7-16Minimum

Variance

Portfolio

as

Depictedin

Figure

7.47-17

Standard

deviation

is

smaller

than

that

ofeither

of

the

individual

component

assets

Figure

7.3

and

7.4

combined

demonstratethe

relationship

between

portfolio

riskFigure

7.5

Portfolio

Expected

Return

asa

Function

of

Standard

Deviation7-18

The

relationship

depends

on

the

correlationcoefficient-1.0

<

<

+1.0

The

smaller

the

correlation,

the

greater

therisk

reduction

potentialIf

r

=

+1.0,

no

risk

reduction

is

possible7-19Correlation

EffectsFigure

7.6

The

Opportunity

Set

of

theDebt

and

Equity

Funds

and

TwoFeasible

CALs7-20The

Sharpe

Ratio

Maximize

the

slope

of

the

CAL

for

anypossible

portfolio,

pThe

objective

function

is

the

slope:7-21Figure

7.7

The

Opportunity

Set

of

theDebt

and

Equity

Funds

with

the

OptimalCAL

and

the

Optimal

Risky

Portfolio7-22Figure

7.8

Determination

of

the

OptimalOverall

Portfolio7-23Figure

7.9

The

Proportions

of

theOptimal

Overall

Portfolio7-24Markowitz

Portfolio

Selection

Model7-25Security

SelectionFirst

step

is

to

determine

the

risk-returnopportunities

availableAll

portfolios

that

lie

on

the

minimum-variance

frontier

from

the

global

minimum-variance

portfolioand

upward

provide

thebest

risk-return

combinationsFigure

7.10

The

Minimum-VarianceFrontier

of

Risky

Assets7-26Markowitz

Portfolio

Selection

ModelContinued7-27

We

now

search

for

the

CAL

with

the

highestreward-to-variability

ratioFigure

7.11

The

Efficient

Frontier

ofRisky

Assets

with

the

Optimal

CAL7-28Markowitz

Portfolio

Selection

ModelContinued

Now

the

individual

chooses

the

appropriatemix

between

the

optimal

risky

portfolio

P

andT-bills

as

in

Figure

7.87-29Figure

7.12

The

Efficient

Portfolio

Set7-30Capital

Allocation

and

the

SeparationProperty7-31

The

separation

property

tells

us

that

theportfolio

choice

problem

may

be

separatedinto

two

independent

tasksDetermination

of

the

optimal

risky

portfoliis

purely

technicalAllocation

of

the

complete

portfolio

to

T-bills

versus

the

risky

portfolio

depends

onpersonal

preferenceFigure

7.13

Capital

Allocation

Lines

witVarious

Portfolios

from

the

Efficient

Se7-32The

Power

of

DiversificationRemember:

If

we

define

the

average

variance

andaverage

covariance

of

the

securities

as:We

can

then

express

portfolio

variance

as:7-33Table

7.4

Risk

Reduction

of

EquallyWeighted

Portfolios

in

Correlated

andUncorrelated

Universes7-34Risk

Pooling,

Risk

Sharing

and

Risk

intheLong

RunConsider

the

following:1

−

p

=

.999p

=

.001Loss:

payout

=

$100,000No

Loss:

payout

=

07-35Risk

Pooling

and

the

Insurance

PrincipleConsider

the

variance

of

the

portfolio: