an introduction to asset pricing models

8/8/2019 An Introduction to Asset Pricing Models

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An Introduction to AssetAn Introduction to Asset

Pricing ModelsPricing Models


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Chapter ObjectivesChapter Objectives

CAPMCAPM assumptionsassumptions

risk/return structurerisk/return structure CAPM equationCAPM equation

betabeta

Security Market LineSecurity Market Line

Empirical use of modelEmpirical use of model time intervalstime intervals

variablesvariables


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Capital Market Theory:Capital Market Theory:

An OverviewAn Overview Capital market theory extends portfolioCapital market theory extends portfolio

theory and develops a model for pricing alltheory and develops a model for pricing allrisky assetsrisky assets

Capital assetpricing model (CAPM) willCapital assetpricing model (CAPM) willallow you to determine the required rateallow you to determine the required rate

of return for any risky assetof return for any risky asset


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Assumptions ofCMTAssumptions ofCMT

1.1. All investors are Markowitz efficient investors whoAll investors are Markowitz efficient investors whowant to targetpoints on the efficient frontier.want to targetpoints on the efficient frontier.

2.2. Investors can borrow or lend any amount of money atInvestors can borrow or lend any amount of money atthe riskthe risk--free rate of return (RFR).free rate of return (RFR).

3.3. All investors have homogeneous expectations.All investors have homogeneous expectations.

4.4. All investors have the same oneAll investors have the same one--period time horizon.period time horizon.

5.5. All investments are infinitely divisible.All investments are infinitely divisible.

6.6. There are no taxes or transaction costs.There are no taxes or transaction costs.7.7. There is no inflation or any change in interest rates.There is no inflation or any change in interest rates.

8.8. Capital markets are in equilibrium.Capital markets are in equilibrium.


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RiskRisk--Free AssetFree Asset

An asset with zero varianceAn asset with zero variance

Zero correlation withall other risky assetsZero correlation withall other risky assets Provides the riskProvides the risk--free rate of return (RFR)free rate of return (RFR)

Will lie on the vertical axis ofaportfolioWill lie on the vertical axis ofaportfoliographgraph


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RiskRisk--Free AssetFree Asset

Covariance between two sets of returns isCovariance between two sets of returns is

!!

n

1ijjiiij )]/nE(R-)][RE(R-[RCov

Because the returns for the risk free asset are certain,

0RF!W Thus Ri = E(Ri), and Ri - E(Ri) = 0

Consequently, the covariance of the risk-free asset with any

risky asset or portfolio will always equal zero. Similarly the

correlation between any risky asset and the risk-free asset

would be zero.


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Market PortfolioMarket Portfolio

Under CAPM, in equilibrium eachassethasUnder CAPM, in equilibrium eachassethasnonzero proportion in Mnonzero proportion in M

All assets included in risky portfolio MAll assets included in risky portfolio M All investors buy MAll investors buy M

If M does not involve a security, then nobody isIf M does not involve a security, then nobody isinvesting in the securityinvesting in the security

If no one is investing, then no demand for securitiesIf no one is investing, then no demand for securities If no demand, then price fallsIf no demand, then price falls

Falls to point where security is attractive and peopleFalls to point where security is attractive and peoplebuy and so it is in Mbuy and so it is in M


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CML and the Separation TheoremCML and the Separation Theorem CML represents new EFCML represents new EF

all investors have the same EF but chooseall investors have the same EF but choosedifferentportfolios based on risk tolerancesdifferentportfolios based on risk tolerances

investor spreads money among risky assets ininvestor spreads money among risky assets insame relative proportions and then borrows/lendssame relative proportions and then borrows/lends

separation theoremseparation theorem optimal combination of risky assets for investoroptimal combination of risky assets for investor

can be determined without knowledge ofcan be determined without knowledge of

investors preferences toward risk and returninvestors preferences toward risk and return investment decisioninvestment decision

financing decisionfinancing decision


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The CML and the SeparationThe CML and the Separation

TheoremTheorem

The decision of both investors is to investThe decision of both investors is to investin portfolio M along the CML (thein portfolio M along the CML (the

investment decision)investment decision)

M

CML

PFR

B

A

( )port

E R

portW


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Number ofStocks in a Portfolio and theNumber ofStocks in a Portfolio and the

Standard Deviation of Portfolio ReturnStandard Deviation of Portfolio ReturnFigure 9.3

Standard Deviation of Return

Number of Stocks in the Portfolio

Standard Deviation of

the Market Portfolio

(systematic risk)Systematic Risk

Total

Risk

Unsystematic

(diversifiable)

Risk


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A Risk Measure for the CMLA Risk Measure for the CML

Covariance with the M portfolio is the systematicCovariance with the M portfolio is the systematicrisk ofan assetrisk ofan asset

The Markowitz portfolio model considers theThe Markowitz portfolio model considers theaverage covariance withall other assets in theaverage covariance withall other assets in theportfolioportfolio

The only relevantportfolio is the M portfolioThe only relevantportfolio is the M portfolio

Because all individual risky assets are part of theBecause all individual risky assets are part of theM portfolio, an assets return in relation to theM portfolio, an assets return in relation to thereturn for the M portfolio may be described asreturn for the M portfolio may be described asfollows:follows: I! Miiiit RbaR


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The Capital Asset Pricing Model:The Capital Asset Pricing Model:

Expected Return and RiskExpected Return and Risk The existence ofa riskThe existence ofa risk--free asset resulted infree asset resulted in

deriving a capital market line (CML) that becamederiving a capital market line (CML) that became

the relevant frontierthe relevant frontier An assets covariance with the marketportfolioAn assets covariance with the marketportfolio

is the relevant risk measureis the relevant risk measure

This can be used to determine an appropriateThis can be used to determine an appropriateexpected rate of return on a risky assetexpected rate of return on a risky asset -- thethecapital assetpricing model (CAPM)capital assetpricing model (CAPM)


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The Capital Asset Pricing Model:The Capital Asset Pricing Model:

Expected Return and RiskExpected Return and Risk CAPM indicates what should be the expected orCAPM indicates what should be the expected or

required rates of return on risky assetsrequired rates of return on risky assets

This helps to value an asset by providing anThis helps to value an asset by providing anappropriate discount rate to use in dividendappropriate discount rate to use in dividendvaluation modelsvaluation models

You can compare an estimated rate of return toYou can compare an estimated rate of return tothe required rate of return implied by CAPMthe required rate of return implied by CAPM --over/ under valued ?over/ under valued ?


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The Security Market Line (SML)The Security Market Line (SML)

The relevant risk measure for an individualThe relevant risk measure for an individualrisky asset is its covariance with therisky asset is its covariance with the

marketportfolio (Covmarketportfolio (Covi,mi,m)) This is shown as the risk measureThis is shown as the risk measure

The return for the marketportfolio shouldThe return for the marketportfolio should

be consistent with its own risk, which isbe consistent with its own risk, which isthe covariance of the market with itselfthe covariance of the market with itself --or its variance:or its variance:

2

mW


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Determining the ExpectedDetermining the Expected

Return for a Risky AssetReturn for a Risky Asset

The expected rate of return ofa risk asset isThe expected rate of return ofa risk asset is

determined by the RFR plus a riskdetermined by the RFR plus a riskpremium for the individual assetpremium for the individual asset

The risk premium is determined by theThe risk premium is determined by the

systematic risk of the asset (beta) and thesystematic risk of the asset (beta) and theprevailing market risk premium (Rprevailing market risk premium (RMM--RFR)RFR)

RFR)-(RRFR)E(R Mi iF!


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Return for a Risky AssetReturn for a Risky AssetAssume:Assume: RFR = 5% (0.05)RFR = 5% (0.05)RRMM = 9% (0.09)= 9% (0.09)

Implied market risk premiumImplied market risk premium = 4% (0.04)= 4% (0.04)

Stock Beta

A 0.70

B 1.00

C 1.15

D 1.40

E -0.30RFR)-(RRFR)E(R Mi iF!

E(RA) = 0.05 + 0.70 (0.09-0.05) = 0.078 = 7.8%

E(RB

) = 0.05 + 1.00 (0.09-0.05) = 0.090 = 09.0%

E(RC) = 0.05 + 1.15 (0.09-0.05) = 0.096 = 09.6%

E(RD) = 0.05 + 1.40 (0.09-0.05) = 0.106 = 10.6%

E(RE) = 0.05 + -0.30 (0.09-0.05) = 0.038 = 03.8%


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Return for a Risky AssetReturn for a Risky AssetIn equilibrium, all assets and all portfolios ofIn equilibrium, all assets and all portfolios ofassets should plot on the SMLassets should plot on the SML

Any security withan estimated return thatplotsAny security withan estimated return thatplots

above the SML is underpricedabove the SML is underpricedAny security withan estimated return thatplotsAny security withan estimated return thatplots

below the SML is overpricedbelow the SML is overpriced

A superior investor must derive value estimatesA superior investor must derive value estimates

for assets thatare consistently superior to thefor assets thatare consistently superior to theconsensus market evaluation to earn betterconsensus market evaluation to earn betterriskrisk--adjusted rates of return than the averageadjusted rates of return than the averageinvestorinvestor


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Price, Dividend, andPrice, Dividend, and

Rate of Return EstimatesRate of Return Estimates

Stock (Pi) Expected Price (Pt+1) (Dt+1) of Return (Percent)

A 25 27 0.50 10.0 %

B 40 42 0.50 6.2

C 33 39 1.00 21.2

D 64 65 1.10 3.3

E 50 54 0.00 8.0

Current Price Expected Dividend Expected Future Rate

Table 9.1


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Comparison of Required Rate ofComparison of Required Rate of

Return to Estimated Rate of ReturnReturn to Estimated Rate of Return

S E(Ri) Es im d R urn Minus E(Ri) Ev lu i n

A 0. 0 10.2% 10.0 -0.2 Properly Valued

1.00 12.0% 6.2 -5.8 Overvalued

1.15 12.9% 21.2 8. Undervalued

1. 0 14.4% . -11.1 Overvalued

E -0. 0 4.2% 8.0 3.8 Undervalued

R quir d R urn Es im d R urn

Table 9.2


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Plot of Estimated ReturnsPlot of Estimated Returns

on SML Graphon SML Graph Figure 9.7)E i

Beta.

m SML

.20 .40 .60 .80 1.20 1.40 1.60 1.80-.40 -.20

.22

.20

.18

.16

.14

.12

Rm.10

.08

.06

.04

.02

A

B

C

D

E


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Calculating Systematic Risk:Calculating Systematic Risk:

The Characteristic LineThe Characteristic LineThe systematic risk input ofan individual asset is derivedThe systematic risk input ofan individual asset is derived

from a regression model, referred to as the assetsfrom a regression model, referred to as the assetscharacteristic line with the model portfolio:characteristic line with the model portfolio:

IFE ! tM,iiti, RRwhere:Ri,t = the rate of return for asset i during period t

RM,t = the rate of return for the market portfolio M during t

miii R-R FE !

2,ov

W

F !i

error termrandomthe!I


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Scatter Plot of Rates of ReturnScatter Plot of Rates of ReturnFigure 9.8

RM

RiThe characteristic

line is the regression

line of the best fit

through a scatter plotof rates of return


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Empirical Tests of the CAPMEmpirical Tests of the CAPM

Stability of BetaStability of Beta

Comparability of Published Estimates of BetaComparability of Published Estimates of Beta Number of observations and time interval used inNumber of observations and time interval used in

regression varyregression vary

Value Line InvestmentServices (VL) uses weekly rates ofValue Line InvestmentServices (VL) uses weekly rates ofreturn over five yearsreturn over five years

Merrill Lynch (ML) uses monthly return over five yearsMerrill Lynch (ML) uses monthly return over five years

There is no correct interval for analysisThere is no correct interval for analysis

Weak relationship between VL & ML betas due toWeak relationship between VL & ML betas due to

difference in intervals useddifference in intervals used Interval effect impacts smaller firms moreInterval effect impacts smaller firms more

MarketportfolioMarketportfolio


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The Market Portfolio:The Market Portfolio:

Theory versus PracticeTheory versus Practice

There is a controversy over the marketThere is a controversy over the market

portfolio. Hence, proxies are usedportfolio. Hence, proxies are used There is no unanimity about whichproxyThere is no unanimity about whichproxy

to useto use


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MicroeconomicMicroeconomic--Based RiskBased Risk

Factor ModelsFactor Models Specify the risk in microeconomic terms usingSpecify the risk in microeconomic terms using

certain characteristics of the underlying sample ofcertain characteristics of the underlying sample ofsecuritiessecurities

ittititmtiititeHMLbSMBbRFRRbaRFRR !

321)()(

ittitititmtiititeYRPRbHMLbSMBbRFRRbaRFRR ! 1)()( 4321

extension of Fama-French 3-factor model includes a fourth factor thatthataccounts for firms withpositive past return to produce positivefuture return - momentum


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SummarySummary

When you combine the riskWhen you combine the risk--free assetfree asset

withany risky asset on the Markowitzwithany risky asset on the Markowitzefficient frontier, you derive a set ofefficient frontier, you derive a set of

straightstraight--line portfolio possibilitiesline portfolio possibilities


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SummarySummary

The dominant line is tangent to theThe dominant line is tangent to theefficient frontierefficient frontier

Referred to as the capital market lineReferred to as the capital market line(CML)(CML)

All investors should targetpoints alongAll investors should targetpoints alongthis line depending on their riskthis line depending on their riskpreferencespreferences


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SummarySummary

All investors want to invest in the riskyAll investors want to invest in the risky

portfolio, so this marketportfolio mustportfolio, so this marketportfolio must

contain all risky assetscontain all risky assets

The investment decision and financing decisionThe investment decision and financing decision

can be separatedcan be separated

Everyone wants to invest in the marketportfolioEveryone wants to invest in the marketportfolio

Investors finance based on risk preferencesInvestors finance based on risk preferences


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SummarySummary

The relevant risk measure for anThe relevant risk measure for anindividual risky asset is its systematicindividual risky asset is its systematicrisk or covariance with the marketrisk or covariance with the market

portfolioportfolio

Once you have determined this BetaOnce you have determined this Betameasure and a security market line, youmeasure and a security market line, you

can determine the required return on acan determine the required return on asecurity based on its systematic risksecurity based on its systematic risk


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SummarySummary

Assuming security markets are notAssuming security markets are notalways completely efficient, you canalways completely efficient, you canidentify undervalued and overvaluedidentify undervalued and overvaluedsecurities by comparing your estimatesecurities by comparing your estimateof the rate of return on an investmentof the rate of return on an investmentto its required rate of returnto its required rate of return

an introduction to asset pricing models

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