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CAPM Examples

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The Capital Asset PricingModel

What is it?

An hypothesis by Professor William harpe !ypothesi"es that in#estors re$%ire higher rates of ret%rn for greater

le#els of rele#ant ris&'

There are no prices on the model( instead it hypothesi"es therelationship bet)een ris& and ret%rn for indi#id%al sec%rities'

*t is often %sed( ho)e#er( the price sec%rities and in#estments'

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The Capital Asset PricingModel

!o) is it ,sed?

,ses incl%de .etermining the cost of e$%ity capital'

The rele#ant ris& in the di#idend disco%nt model to estimate a

stoc&/s intrinsic 0inherent economic )orth1 #al%e'0As ill%stratedbelo)1

EstimateInvestments Risk(Beta Coefcient)

DetermineInvestmentsRequired Return

Estimate theInvestmentsIntrinsic Value

Compare to theactual stock price inthe market

*s the stoc&fairlypriced?

2i

M

i,M

COV= )(

iMi RFERRFk +=

gkDPc

= 1

0

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Mar&et Portfolio and Capital Mar&et3ine

The ass%mptions ha#e the follo)ingimplications

4' The 5optimal6 ris&y portfolio is the one

that is tangent to the e7cient frontier ona line that is dra)n from 8' Thisportfolio )ill be the same for allin#estors'

2' This optimal ris&y portfolio )ill be themarket portfolio0M1 )hich contains allris&y sec%rities'

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The Capital Asset PricingModelAss%mptions

CAPM is based on the follo)ing ass%mptions4' All in#estors ha#e identical expectations abo%t expected

ret%rns( standard de#iations( and correlation coe7cientsfor all sec%rities'

2' All in#estors ha#e the same one-period in#estment timehori"on'

+' All in#estors can borro) or lend money at the ris&-freerate of ret%rn 081'

' There are no transaction costs'

:' There are no personal income taxes so that in#estors are

indi;erent bet)een capital gains an di#idends'

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The Capital sset !ricin" #odel $ De%nition

*n >nance( one of the most important things toremember is that ret%rn is a f%nction of ris&'

This means that the more ris& yo% ta&e( the higheryo%r potential ret%rn sho%ld be to o;set yo%r

increased chance for loss' ne tool that >nance professionals %se to calc%late

the ret%rn that an in#estment sho%ld bring is theCapital sset !ricin" #odel0CAPM from no) on1'

CAPM calc%lates a re$%ired ret%rn based on a ris&meas%rement' To do this( the model relies on a riskmultiplier called the beta coefcient( )hich )e)ill disc%ss in the next section'

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Main Ass%mptions of CAPMModel

All Investors are Efcient Investors$ *n#estors follo) Mar&o)it" idea ofthe e7cient frontier and choose to in#est in portfolios along the frontier'Investors Borrow/Lend Money at the Risk-ree Rate -This rate remainsstatic for any amo%nt of money'!he !ime "ori#on is e$ual %or All Investors - When choosingin#estments( in#estors ha#e e$%al time hori"ons for the chosen in#estments'

All Assets are In&nitely 'ivisible -This indicates that fractional shares canbe p%rchased and the stoc&s can be in>nitely di#isible'(o !a)es and !ransaction *osts -ass%me that in#estors@ res%lts are nota;ected by taxes and transaction costs'All Investors "ave the +ame ,robability %or utcomes -Whendetermining the expected ret%rn( ass%me that all in#estors ha#e the sameprobability for o%tcomes'

(o In.ation E)ists $ 8et%rns are not a;ected by the ination rate in acapital mar&et as none exists in capital mar&et theory'!here is (o Mispricin 0ithin the *apital Markets - Ass%me the mar&etsare e7cient and that no mispricings )ithin the mar&ets exist'

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CAPM orm%la

The capital asset pricing model 0CAPM1is a model that calc%lates expectedret%rn based on expected rate of

ret%rn on the mar&et( the ris&-free rateand the beta coe7cient of the stoc&'

E081 B 8f D0 8mar&et - 8f 1

http://www.investopedia.com/terms/c/capm.asphttp://www.investopedia.com/terms/c/capm.asp

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Meas%ring ystematic 8is&

The eta Coe7cientThe Capital Asset Pricing

Model 0CAPM1

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C!APTE8 9 F The CapitalAsset Pricing Model0CAPM1

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The eta Coe7cientWhat is the eta Coe7cient?

A meas%re of systematic 0non-di#ersi>able1 ris&

As a Hcoe7cient/ the beta is a p%ren%mber and has no %nits of meas%re'

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C!APTE8 9 F The CapitalAsset Pricing Model0CAPM1

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The eta Coe7cient!o) Can We Estimate the Ial%e of the eta Coe7cient?

There are t)o basic approaches toestimating the beta coe7cient

4' ,sing a form%la 0and s%bJecti#e forecasts1

2' ,se of regression 0%sing past holding

period ret%rns1

(Figure 9 8 on the following slide illustrates the characteristic line used toestimate the beta coecient)

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C!APTE8 9 F The CapitalAsset Pricing Model0CAPM1

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The CAPM and Mar&et 8is&The Characteristic 3ine for ec%rity A

& $ 'I*RE