博迪投資學(xué)Chap010章節(jié)(314KB)

Arbitrage

PricingTheory

andMultifactor

Modelsof

Risk

and

ReturnCHAPTER

10Single

Factor

ModelReturns

on

a

security

come

from

two

sourcesCommon

macro-economic

factorFirm

specific

eventsPossible

common

macro-economic

factorsGross

Domestic

Product

GrowthInterest

RatesSingle

Factor

Model

Equationri

=Return

for

security

I=

Factor

sensitivity

or

factor

loading

or

factobetaF

=

Surprise

in

macro-economic

factor(F

could

be

positive,

negative

or

zero)ei

=

Firm

specific

eventsMultifactor

Models

Use

more

than

one

factor

in

addition

tomarket

returnExamples

include

gross

domestic

product,expected

inflation,

interest

rates

etc.Estimate

a

beta

or

factor

loading

for

eachfactor

using

multiple

regression.MultifactorModelEquationri

=

E(ri)

+

GDP

GDP

+

IR

IR

+

eiri

=

Return

for

security

iGDP=

Factor

sensitivity

for

GDPIR

=

Factor

sensitivity

for

Interest

Rateei

=

Firm

specific

eventsMultifactor

SML

ModelsE(r)

=

rf

+GDPRPGDP

+

IRRPIRGDP

=

Factor

sensitivity

for

GDPRPGDP

=

Risk

premium

for

GDPIR

=

Factor

sensitivity

for

Interest

RateRPIR

=

Risk

premium

for

Interest

RateArbitrage

Pricing

TheoryArbitrage

-

arises

if

an

investor

can

construct

azero

investment

portfolio

with

a

sure

profit

Since

no

investment

is

required,

an

investorcan

create

large

positions

to

secure

largelevels

of

profit

In

efficient

markets,

profitable

arbitrageopportunities

will

quickly

disappearAPT

&

Well-Diversified

PortfoliosrP

=

E

(rP)

+

bPF

+

ePF

=

some

factorFor

a

well-diversified

portfolio:eP

approaches

zeroSimilar

to

CAPM,Figure

10.1

Returns

as

a

Function

of

theSystematic

FactorFigure

10.2

Returns

as

a

Function

of

theSystematic

Factor:

An

ArbitrageOpportunityFigure

10.3

An

Arbitrage

OpportunityFigure

10.4

The

Security

Market

Line

APT

applies

to

well

diversified

portfolios

andnot

necessarily

to

individual

stocks

With

APT

it

is

possible

for

some

individualstocks

to

be

mispriced

-

not

lie

on

the

SML

APT

is

more

general

in

that

it

gets

to

anexpected

return

and

beta

relationship

withoutthe

assumption

of

the

market

portfolioAPT

can

be

extended

to

multifactor

modelsAPT

and

CAPM

ComparedMultifactor

APTUse

of

more

than

a

single

factorRequires

formation

of

factor

portfoliosWhat

factors?Factors

that

are

important

to

performanceof

the

general

economyFama-French

Three

Factor

ModelTwo-Factor

Model

The

multifactor

APR

is

similar

to

the

one-factor

caseBut

need

to

think

in

terms

of

a

factor

portfoliWell-diversifiedBeta

of

1

for

one

factorBeta

of

0

for

any

otherExample

of

the

Multifactor

ApproachWork

of

Chen,

Roll,

and

Ross–

Chose

a

set

of

factors

based

on

the

abilityof

the

factors

to

paint

a

broad

picture

of

themacro-economyFama-French

Three-Factor

Model The

factors

chosen

are

variables

that

onpast

evidence

seem

to

predict

averagereturns

well

and

may

capture

the

riskpremiumsWhere:

SMB

=

Small

Minus

Big,

i.e.,

the

return

of

a

portfolio

of

small

stocks

iexcess

of

the

return

on

a

portfolio

of

large

stocks

HML

=

High

Minus

Low,

i.e.,

the

return

of

a

portfolio

of

stocks

with

ahigh

book

to-market

ratio

in

excess

of

the

return

on

a

portfolio

of

stocwith

a

low

book-to-market

ratioThe

Multifactor

CAPM

and

the

APM

A

multi-index

CAPM

will

inherit

its

ri