54274499 the Capital Asset Pricing Model CAPM

7/23/2019 54274499 the Capital Asset Pricing Model CAPM

http://slidepdf.com/reader/full/54274499-the-capital-asset-pricing-model-capm 1/21

The Capital Asset Pricing ModelThe Capital Asset Pricing Model(CAPM)(CAPM)



Underlying AssumptionUnderlying Assumption

•Market EfciencyMarket Efciency

•Risk aversion and mean varianceRisk aversion and mean variance

optimizationoptimization•Homogeneous expectationsHomogeneous expectations

•

Single time periodSingle time period•Risk-ree rateRisk-ree rate



The Capital Asset Pricing ModelThe Capital Asset Pricing ModelWhat is it?What is it?

– CAPM is a model that provides a framework toCAPM is a model that provides a framework to

determine the reuired rate of return on andetermine the reuired rate of return on an

asset and indicates the relationship !etweenasset and indicates the relationship !etween

return and risk of the asset"return and risk of the asset"



CAPMCAPM

An hypothesis !y An hypothesis !y Professor William #"$harpeProfessor William #"$harpe

– %ypothesi&es that investors reuire higher%ypothesi&es that investors reuire higher

rates of return for greater levels of relevantrates of return for greater levels of relevant

risk"risk"

' There are no prices on the model( instead itThere are no prices on the model( instead ithypothesi&es the relationship !etween riskhypothesi&es the relationship !etween risk

and return for individual securities"and return for individual securities"

')t is often used( however( the price)t is often used( however( the pricesecurities and investments"securities and investments"



The Capital Asset Pricing ModelThe Capital Asset Pricing Model%ow is it Used?%ow is it Used?

– Uses include*Uses include*' +etermining the cost of euity capital"+etermining the cost of euity capital"

' The relevant risk in the dividend discount model to estimate a stock,s intrinsicThe relevant risk in the dividend discount model to estimate a stock,s intrinsic

-inherent economic worth. value"-inherent economic worth. value" -As illustrated !elow.-As illustrated !elow.

Estimate Investment’s

Risk (Beta Coefficient)

etermine Investment’s

Re!"ired Ret"rn

Estimate the

Investment’s Intrinsic

#al"e

Compare to the act"al

stock price in the

market

2i

M

i,M

σ

COV =β )( i M i RF ER RF k β −+=

g k D P c −

=1

0)s the stock

fairly priced?



The Capital Asset Pricing ModelThe Capital Asset Pricing Model/0pected and 1euired 1ates of 1eturn/0pected and 1euired 1ates of 1eturn

A is an

undervalued

portfolio" /0pected

return is greater

than the reuired

return"+emand for

Portfolio A will

increase driving up

the price( and

therefore the

e0pected return will

fall until e0pectedeuals reuired

-market euili!rium

condition is

achieved".

1euired

return on A

/0pected

return on A

B is a portfolio that

offers and e0pected

return eual to the

reuired return"

$%

ER

R&

B

C

A

CM'

C is an overvalued

portfolio" /0pected

return is less than

the reuired return"

$elling pressure

will cause the priceto fall and the yield

to rise until

e0pected euals

the reuired return"

1euired

1eturn on C

/0pected

1eturn on C



CAPM and Market 1iskCAPM and Market 1isk

The apital !sset "ricing Model The apital !sset "ricing Model



+iversifia!le and 2on3+iversifia!le 1isk+iversifia!le and 2on3+iversifia!le 1isk

• M# applies to efcient portoliosM# applies to efcient portolios

• $olatility %risk& o$olatility %risk& o individual security returnsindividual security returns are caused 'y t(o di)erent actors*are caused 'y t(o di)erent actors*

– 2on3diversifia!le risk -system wide changes in the2on3diversifia!le risk -system wide changes in the

economy and markets that affect all securities ineconomy and markets that affect all securities in

varying degrees.varying degrees.

– +iversifia!le risk -company3specific factors that affect+iversifia!le risk -company3specific factors that affect

the returns of only one security.the returns of only one security.



The CAPM and Market 1iskThe CAPM and Market 1iskPortfolio 1isk and +iversificationPortfolio 1isk and +iversification

2um!er of $ecurities

Total 1isk -4.

Uniue -2on3systematic. 1isk

Market -$ystematic. 1isk

Market or

sstematic

risk is riskthat cannot

e eliminated

from the

portfolio

investing the

portfolio into

more and

differentsec"rities*



1elevant 1isk1elevant 1isk+rawing a Conclusion from #igure+rawing a Conclusion from #igure

• +igure demonstrates that an individual securities,+igure demonstrates that an individual securities,

volatility o return comes rom t(o actors*volatility o return comes rom t(o actors*

– $ystematic factors$ystematic factors

– Company3specific factorsCompany3specific factors

• hen com'ined into portolios. company-speci/c riskhen com'ined into portolios. company-speci/c riskis diversi/ed a(ay0is diversi/ed a(ay0

• Since all investors are 1diversi/ed, then in an efcientSince all investors are 1diversi/ed, then in an efcient

market. no-one (ould 'e (illing to pay a 1premium,market. no-one (ould 'e (illing to pay a 1premium,

or company-speci/c risk0or company-speci/c risk0• Relevant risk to diversi/ed investors then is systematicRelevant risk to diversi/ed investors then is systematic

risk0risk0

• Systematic risk is measured using the 2eta oefcient0Systematic risk is measured using the 2eta oefcient0



Measuring $ystematic 1iskMeasuring $ystematic 1isk

The 5eta CoefficientThe 5eta Coefficient


%!"M&%!"M&



The 5eta CoefficientThe 5eta CoefficientWhat is the 5eta Coefficient?What is the 5eta Coefficient?

• ! measure o systematic %non-diversi/a'le&! measure o systematic %non-diversi/a'le&

riskrisk

• !s a 1coefcient, the 'eta is a pure num'er!s a 1coefcient, the 'eta is a pure num'erand has no units o measure0and has no units o measure0



The 5eta CoefficientThe 5eta Coefficient%ow Can We /stimate the 6alue of the 5eta Coefficient?%ow Can We /stimate the 6alue of the 5eta Coefficient?

• There are t(o 'asic approaches to There are t(o 'asic approaches to

estimating the 'eta coefcient*estimating the 'eta coefcient*

7"7" Using a formula -and su!8ective forecasts.Using a formula -and su!8ective forecasts.

9"9" Use of regression -using past holding period returns.Use of regression -using past holding period returns.



The CAPM and Market 1iskThe CAPM and Market 1iskThe Characteristic :ine for $ecurity AThe Characteristic :ine for $ecurity A

;

<

9

=

39

3<

3;

+ec"rit A Ret"rns (,)

3; 3< 39 = 9 < ; >

M a r k e t R e t " r n s ( , ) The slope of

the regression

line is eta*

The line of

est fit is

kno-n in

finance as thecharacteristic

line*

The plottedpoints are the

coincident

rates of ret"rn

earned on the

investment

and the market

portfolio overpast periods*



The #ormula for the 5eta CoefficientThe #ormula for the 5eta Coefficient

5eta is eual to the covariance of the returns of the5eta is eual to the covariance of the returns of the

stock with the returns of the market( divided !y thestock with the returns of the market( divided !y the

variance of the returns of the market*variance of the returns of the market*

,

2i

M

i M i

M

i,M

σ

COV

σ

σ ρ β ==



The 5eta CoefficientThe 5eta Coefficient%ow is the 5eta Coefficient )nterpreted?%ow is the 5eta Coefficient )nterpreted?

• The 'eta o the market portolio is !#!3S 4 506 The 'eta o the market portolio is !#!3S 4 506

• The 'eta o a security compares the volatility o its returns to the The 'eta o a security compares the volatility o its returns to thevolatility o the market returns*volatility o the market returns*

ss @ 7"= @ 7"= 33 the security has the same volatility as the marketthe security has the same volatility as the marketas a wholeas a whole

ss 7"= 7"= 33 aggressive investment with volatility of returnsaggressive investment with volatility of returnsgreater than the marketgreater than the market

ss B 7"= B 7"= 33 defensive investment with volatility of returnsdefensive investment with volatility of returns

less than the marketless than the market

ss B ="= B ="= 33 an investment with returns that are negativelyan investment with returns that are negativelycorrelated with the returns of the marketcorrelated with the returns of the market



The $ecurity Market :ineThe $ecurity Market :ine


%!"M&%!"M&



The CAPM and Market 1iskThe CAPM and Market 1iskThe $ecurity Market :ine -$M:.The $ecurity Market :ine -$M:.

– The $M: is the hypothesi&ed relationship !etween return -theThe $M: is the hypothesi&ed relationship !etween return -thedependent varia!le. and systematic risk -the !eta coefficient."dependent varia!le. and systematic risk -the !eta coefficient."

– )t is a straight line relationship defined !y the following formula*)t is a straight line relationship defined !y the following formula*

– Where*Where*

k k i i = the required return on security ‘i’ = the required return on security ‘i’ ER ER M M – RF = market premium for risk – RF = market premium for risk

ΒΒii = the beta coefficient for security ‘i’ = the beta coefficient for security ‘i’

)( i M i

RF ER RF k β −+=



.A

ER

R&

.

B

A

.B

+M'

The CAPM and Market 1iskThe CAPM and Market 1iskThe $M: and $ecurity 6aluationThe $M: and $ecurity 6aluation

i M i RF ER RF k β )( −+=

1euired returns

are forecast using

this euation"

ou can see thatthe reuired return

on any security is

a function of its

systematic risk -.

and market

factors -RF andmarket premium

for risk)

A is an

undervalued

security !ecause

its e0pected return

is greater than the

reuired return"

)nvestors will

Dflock, to A and !id

up the price

causing e0pectedreturn to fall till it

euals the

reuired return"

1euired

1eturn A

/0pected

1eturn A

$imilarly( 5 is an

overvalued

security"

)nvestor,s will sellto lock in gains(

!ut the selling

pressure will

cause the market

price to fall(

causing thee0pected return to

rise until it euals

the reuired

return"



The CAPM in $ummaryThe CAPM in $ummaryThe $M: and CM:The $M: and CM:

– The CAPM is well entrenched and widely used !yThe CAPM is well entrenched and widely used !y

investors( managers and financial institutions"investors( managers and financial institutions"

– )t is a single factor model !ecause it !ased on the)t is a single factor model !ecause it !ased on the

hypothesis that reuired rate of return can !ehypothesis that reuired rate of return can !e

predicted using one factor – systematic riskpredicted using one factor – systematic risk

– The $M: is used to price individual investments andThe $M: is used to price individual investments and

uses the !eta coefficient as the measure of risk"uses the !eta coefficient as the measure of risk"

– The CM: is used with diversified portfolios and usesThe CM: is used with diversified portfolios and uses

the standard deviation as the measure of risk"the standard deviation as the measure of risk"



Challenges to CAPMChallenges to CAPM

• Empirical tests suggest*Empirical tests suggest* – CAPM does not hold well in practice*CAPM does not hold well in practice*

' /0 post $M: is an upward sloping line/0 post $M: is an upward sloping line' /0 ante/0 ante y (ertica!)y (ertica!) – intercept is higher that 1# – intercept is higher that 1#' $lope is less than what is predicted !y theory$lope is less than what is predicted !y theory

– 5eta possesses no e0planatory power for predicting stock returns5eta possesses no e0planatory power for predicting stock returns-#ama and #rench( 7EE9.-#ama and #rench( 7EE9.

• !"M remains in (idespread use despite the oregoing0!"M remains in (idespread use despite the oregoing0 – Advantages include – relative simplicity and intuitive logic" Advantages include – relative simplicity and intuitive logic"

• 2ecause o the pro'lems (ith !"M. other models have2ecause o the pro'lems (ith !"M. other models have'een developed including*'een developed including* – #ama3#rench -##. Model#ama3#rench -##. Model – Ar!itrage Pricing Theory -APT. Ar!itrage Pricing Theory -APT. – %amada Model%amada Model

Documents

54274499 the Capital Asset Pricing Model CAPM