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Investment Analysis and

Portfolio Management

by Frank K. Reilly & Keith C. Brown

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An Introduction to

Asset Pricing Models Ca!ital Market "heory# An $verview

"he Ca!ital Asset Pri%ing Model

Relaing the Ass'm!tions

(m!iri%al "ests of the CAPM

"he Market Portfolio# "heory vs.

Pra%ti%e

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Capital Market Theory: An Overview

, Ca!ital market theory etends !ortfolio theoryand develo!s a model for !ri%ing all risky

assets- while %a!ital asset !ri%ing model

CAPM/ will allow yo' to determine the

re0'ired rate of ret'rn for any risky asset, Fo'r Areas

Ba%kgro'nd for Ca!ital Market "heory

1evelo!ing the Ca!ital Market 2ine Risk- 1iversifi%ation- and the Market Portfolio

Investing with the CM2# An (am!le

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Background for Capital Market Theory

, Ass'm!tions of Ca!ital Market "heory All investors are Markowit4 effi%ient investors who

want to target !oints on the effi%ient frontier

Investors %an borrow or lend any amo'nt of money

at the risk*free rate of ret'rn RFR/ All investors have homogeneo's e!e%tations5 that

is- they estimate identi%al !robability distrib'tions

for f't're rates of ret'rn

All investors have the same one*!eriod timehori4on s'%h as one*month- si months- or one

year

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, Ass'm!tions Contin'ed/ All investments are infinitely divisible- whi%h means

that it is !ossible to b'y or sell fra%tional shares of

any asset or !ortfolio

"here are no taes or transa%tion %osts involved inb'ying or selling assets

"here is no inflation or any %hange in interest rates-

or inflation is f'lly anti%i!ated

Ca!ital markets are in e0'ilibri'm- im!lying that allinvestments are !ro!erly !ri%ed in line with their

risk levels

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, 1evelo!ment of Ca!ital Market "heory "he ma8or fa%tor that allowed !ortfolio theory to

develo! into %a!ital market theory is the %on%e!t of

a risk*free asset

, An asset with 4ero standard deviation

, 9ero %orrelation with all other risky assets

, Provides the risk*free rate of ret'rn RFR/

, :ill lie on the verti%al ais of a !ortfolio gra!h

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eveloping the Capital Market !ine

, Covarian%e with a Risk*Free Asset Covarian%e between two sets of ret'rns is

Be%a'se the ret'rns for the risk free asset are

%ertain- th's Ri < (Ri/- and Ri * (Ri/ < =- whi%h means that

the %ovarian%e between the risk*free asset and any

risky asset or !ortfolio will always be 4ero

>imilarly- the %orrelation between any risky asset

and the risk*free asset wo'ld be 4ero too sin%e r RF-i<

CovRF- I ? @RF @i

∑=

=n

1i

j jiiij )]/nE(R -)][R E(R -[R Cov

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, Combining a Risk*Free Asset with a RiskyPortfolio- M

(!e%ted ret'rn# It is the weighted average of the

two ret'rns

>tandard deviation# A!!lying the two*asset

standard deviation form'la- we will have

>in%e @RF

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, "he Ca!ital Market 2ine :ith these res'lts- we %an develo! the riskret'rn

relationshi! between E R !ort/ and σ !ort

"his relationshi! holds for every %ombination of the

risk*free asset with any %olle%tion of risky assets

owever- when the risky !ortfolio- M- is the market!ortfolio %ontaining all risky assets held anywhere in

the market!la%e- this linear relationshi! is %alled the

Ca!ital Market 2ine (hibit )./

D(.RERFR/(.R M!ort M

port RFRσ

σ −

+= )

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"#hi$it 8%&

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, Risk*Ret'rn Possibilities with 2everage $ne %an attain a higher e!e%ted ret'rn than is

available at !oint M

$ne %an invest along the effi%ient frontier beyond

!oint M- s'%h as !oint 1 :ith the risk*free asset- one %an add leverage tothe !ortfolio by borrowing money at the risk*freerate and investing in the risky !ortfolio at !oint M toa%hieve a !oint like (

Clearly- !oint ( dominates !oint 1 >imilarly- one %an red'%e the investment risk by

lending money at the risk*free asset to rea%h !ointslike C see (hibit ).+/


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"#hi$it 8%'

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(isk) iversification * the Market Portfolio

, "he Market Portfolio Be%a'se !ortfolio M lies at the !oint of tangen%y- ithas the highest !ortfolio !ossibility line

(verybody will want to invest in Portfolio M andborrow or lend to be somewhere on the CM2

It m'st in%l'de A22 RI>KG A>>(">

>in%e the market is in e0'ilibri'm- all assets in this!ortfolio are in !ro!ortion to their market val'es

Be%a'se it %ontains all risky assets- it is a

%om!letely diversified !ortfolio- whi%h means that

all the 'ni0'e risk of individ'al assets 'nsystemati%

risk/ is diversified away

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, >ystemati% Risk $nly systemati% risk remains in the market !ortfolio

>ystemati% risk is the variability in all risky assets

%a'sed by ma%roe%onomi% variables

, Hariability in growth of money s'!!ly, Interest rate volatility

, Hariability in fa%tors like / ind'strial !rod'%tion +/

%or!orate earnings 3/ %ash flow

>ystemati% risk %an be meas'red by the standarddeviation of ret'rns of the market !ortfolio and %an

%hange over time

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, ow to Meas're 1iversifi%ation All !ortfolios on the CM2 are !erfe%tly !ositively

%orrelated with ea%h other and with the %om!letely

diversified market Portfolio M

"hat is- a %om!letely diversified !ortfolio wo'ldhave a %orrelation with the market !ortfolio of .==

"he reason is that %om!lete risk diversifi%ation

means the elimination of all the 'nsystemati% or

'ni0'e risk and the systemati% risk %orrelates!erfe%tly with the market !ortfolio

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, 1iversifi%ation and the (limination ofJnsystemati% Risk

"he !'r!ose of diversifi%ation is to red'%e the

standard deviation of the total !ortfolio

"his ass'mes that im!erfe%t %orrelations eistamong se%'rities

As yo' add se%'rities- yo' e!e%t the average

%ovarian%e for the !ortfolio to de%line

ow many se%'rities m'st yo' add to obtain a%om!letely diversified !ortfolio

>ee (hibit ).3

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"#hi$it 8%+

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, "he CM2 and the >e!aration "heorem "he CM2 leads all investors to invest in the M

!ortfolio

Individ'al investors sho'ld differ in !osition on the

CM2 de!ending on risk !referen%es ow an investor gets to a !oint on the CM2 is

based on finan%ing de%isions

Risk averse investors will lend at the risk*free rate

while investors !referring more risk might borrowf'nds at the RFR and invest in the market !ortfolio

"he investment de%ision of %hoosing the !oint on

CM2 is se!arate from the finan%ing de%ision of

rea%hing there thro'gh either lending or borrowing

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, A Risk Meas're for the CM2 "he Markowit4 !ortfolio model %onsiders the

average %ovarian%e with all other assets

"he only im!ortant %onsideration is the assetLs

%ovarian%e with the market !ortfolio Covarian%e with the market !ortfolio is the

systemati% risk of an asset

Harian%e of a risky asset i

Har Rit/< Har biRMt/ Har/ ystemati% Harian%e Jnsystemati% Harian%e

where bi< slo!e %oeffi%ient for asset i

< random error term

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Investing with the CM!: An "#a,ple

>'!!ose yo' have a riskless se%'rity at 6N and a market!ortfolio with a ret'rn of N and a standard deviation of=N. ow sho'ld yo' go abo't investing yo'r money sothat yo'r investment will have a risk level of 7N

, Portfolio Ret'rn

(R!ort/

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The Capital Asset Pricing Model

, A Con%e!t'al 1evelo!ment of the CAPM "he eisten%e of a risk*free asset res'lted in

deriving a %a!ital market line CM2/ that be%ame

the relevant frontier

owever- CM2 %annot be 'sed to meas're thee!e%ted ret'rn on an individ'al asset

For individ'al asset or any !ortfolio/- the relevant

risk meas're is the assetLs %ovarian%e with the

market !ortfolio "hat is- for an individ'al asset i- the relevant risk is

not @i- b't rather @i r iM- where r iM is the %orrelation

%oeffi%ient between the asset and the market

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A!!lying the CM2 'sing this relevant risk meas're

2et i

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, "he >e%'rity Market 2ine >M2/ "he >M2 is a gra!hi%al form of the CAPM

(hibit ).7 shows the relationshi! between the

e!e%ted or re0'ired rate of ret'rn and the

systemati% risk on a risky asset "he e!e%ted rate of ret'rn of a risk asset is

determined by the RFR !l's a risk !remi'm for the

individ'al asset

"he risk !remi'm is determined by the systemati%risk of the asset beta/ and the !revailing market

risk !remi'm RM*RFR/

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"#hi$it 8%-

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, 1etermining the (!e%ted Rate of Ret'rn Risk*free rate is 7N and the market ret'rn is N

>to%k A B C 1 (

Beta =.= .== .7 .6= *=.3=

A!!lying

(R A/ < =.=7 =.= =.=*=.=7/ < =.=) < .)N

(RB

/ < =.=7 .== =.=*=.=7/ < =.== < =.=N

(RC/ < =.=7 .7 =.=*=.=7/ < =.=; < =.;N

(R1/ < =.=7 .6= =.=*=.=7/ < =.=; < =.;N

(R(/ < =.=7 *=.3= =.=*=.=7/ < =.=3) < =3.)N

])[ RFRi

−+= Mi (.RRFR/(.R β

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, Identifying Jnderval'ed & $verval'ed Assets In e0'ilibri'm- all assets and all !ortfolios of

assets sho'ld !lot on the >M2

Any se%'rity with an estimated ret'rn that !lots

above the >M2 is 'nder!ri%ed

Any se%'rity with an estimated ret'rn that !lots

below the >M2 is over!ri%ed

A s'!erior investor m'st derive val'e estimates forassets that are %onsistently s'!erior to the

%onsens's market eval'ation to earn better risk*

ad8'sted rates of ret'rn than the average investor

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Com!are the re0'ired rate of ret'rn to theestimated rate of ret'rn for a s!e%ifi% risky asset

'sing the >M2 over a s!e%ifi% investment hori4on

to determine if it is an a!!ro!riate investment

(hibit ).) shows A- C and ( are 'nder!ri%ed b't

B and 1 are over !ri%ed be%a'se

>to%k Re0'ired Ret'rn (stimated Ret'rn

A .)N ).=N

B .=N ;.+N

C .;N 7.7N

1 =.;N 7.7N

( 3.)N ;.=N

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"#hi$it 8%8

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, Cal%'lating >ystemati% Risk "he form'la

"he %hara%teristi% line

, A regression line between the ret'rns to the se%'rity R it/

over time and the ret'rns R Mt/ to the market !ortfolio

, "he slo!e of the regression line is beta

, >ee (hibit ).=

2

),(

M

M i

iM

M

i

i

R RCovr

ε β α ++= tM,iiti, R R

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"#hi$it 8%&.

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, "he Im!a%t of the "ime Interval "he n'mber of observations and time interval 'sedin regression vary- %a'sing beta to vary

"here is no Q%orre%t interval for analysis

Hal'e 2ine Investment >ervi%es H2/ 'ses weeklyrates of ret'rn over five years

Merrill 2yn%h- Pier%e- Fenner & >mith M2/ 'ses

monthly ret'rn over five years

"he ret'rn time interval makes a differen%e- and itsim!a%t in%reases as the firmLs si4e de%lines

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, "he (ffe%t of the Market Proy "heoreti%ally- the market !ortfolio sho'ld in%l'deall J.>. and non*J.>. sto%ks and bonds- real

estate- %oins- stam!s- art- anti0'es- and any other

marketable risky asset from aro'nd the world

Most !eo!le 'se the >tandard & PoorLs 7==

Com!osite Inde as the !roy d'e to

, It %ontains large !ro!ortion of the total market val'e

of J.>. sto%ks

, It is a val'e weighted inde

Jsing a different !roy for the market !ortfolio will

lead to a different beta val'e

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(ela#ing the Assu,ptions

, 1ifferential Borrowing and 2ending Rates :hen borrowing rate- R b- is higher than RFR- the

>M2 will be Qbroken into two lines

>ee (hibit ).+

, 9ero Beta Model Instead of a risk*free rate- a 4ero*beta !ortfolio

'n%orrelated with the market !ortfolio/ %an be

'sed to draw the Q>M2 line

>in%e the 4ero*beta !ortfolio is likely to have a

higher ret'rn than the risk*free rate- this Q>M2 will

have a less stee! slo!e

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"#hi$it 8%&'

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(ela#ing the Assu,ptions

, "ransa%tion Costs :ith transa%tions %osts- the >M2 will be a band ofse%'rities- rather than a straight line

, eterogeneo's (!e%tations and Planning

Periods eterogeneo's e!e%tations will %reate a set band/

of lines with a breadth determined by the

divergen%e of e!e%tations

"he im!a%t of !lanning !eriods is similar , "aes

1ifferential ta rates %o'ld %a'se ma8or differen%es

in the CM2 and >M2 among investors

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",pirical Tests of the CAPM

, Relationshi! between >ystemati% Risk andRet'rn

(ffe%t of >kewness on Relationshi!

, Investors !refer sto%ks with high !ositive skewness

that !rovide an o!!ort'nity for very large ret'rns (ffe%t of >i4e- P?(- and 2everage

, >i4e- and P?( have an inverse im!a%t on ret'rns after

%onsidering the CAPM. Finan%ial 2everage also

hel!s e!lain %ross*se%tion of ret'rns

(ffe%t of Book*to*Market Hal'e

, Fama and Fren%h +/ fo'nd the BH?MH ratio to be

a key determinant of ret'rns

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Market Portfolio: Theory vs% Practice

, "he tr'e market !ortfolio sho'ld

In%l'ded all the risky assets in the world

In e0'ilibri'm- the assets wo'ld be in%l'ded in the

!ortfolio in !ro!ortion to their market val'e.

, "here is no 'nanimity abo't whi%h !roy to 'seand different !roies have been 'sed

An in%orre%t market !roy will affe%t both the beta risk

meas'res and the !osition and slo!e of the >M2 that

is 'sed to eval'ate !ortfolio !erforman%e

(hibit ).) ill'strates the im!a%t of time !eriod and

!roies on beta meas'res

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"#hi$it 8%&8

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/u,,ary

,"he ass'm!tion of %a!ital market theorye!and on those of the Markowit4 !ortfolio

model and in%l'de %onsideration of the risk*

free rate of ret'rn

, "he dominant investment o!!ort'nity is theline tangent to the effi%ient frontier at the

market !ortfolio- known as the CM2

, Investors %an move along the CM2 by

investing in both risk*free rate and the market

!ortfolio thro'gh either lending or borrowing

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/u,,ary

, "he relevant risk meas're for an individ'alrisky asset is its systemati% risk or %ovarian%e

with the market !ortfolio

, >M2 is derived to show the relationshi!

between the re0'ired ret'rn and its systemati%risk for any risky asset

, Ass'ming se%'rity markets are not always

%om!letely effi%ient- yo' %an identify'nderval'ed and overval'ed se%'rities by

%om!aring yo'r estimate of the rate of ret'rn

on an investment to its re0'ired rate of ret'rn

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/u,,ary

,:hen we rela several of the ma8orass'm!tions of the CAPM- the re0'ired

modifi%ations are relatively minor and do not

%hange the overall %on%e!t of the model

, Betas of individ'al sto%ks are not stable while!ortfolio betas are stable

, "here is a %ontroversy abo't the relationshi!

between beta and rate of ret'rn on sto%ks

, Changing the !roy for the market !ortfolio

res'lts in signifi%ant differen%es in betas-

>M2s- and e!e%ted ret'rns

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http://www.valueline.com/http://www.wsharpe.com/http://gsb.uchicago.edu/fac/eugene.fama/http://www.moneychimp.com/http://www.moneychimp.com/http://gsb.uchicago.edu/fac/eugene.fama/http://www.wsharpe.com/http://www.valueline.com/

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