CHAPTER NINE

Capital Market Theory

CHAPTER NINE

Capital Market Theory

Cleary / Jones

Investments: Analysis and Management

Learning ObjectivesLearning ObjectivesLearning ObjectivesLearning Objectives

To explain capital market theory To explain capital market theory and the Capital Asset Pricing Modeland the Capital Asset Pricing Model

To discuss the importance and To discuss the importance and composition of the market portfoliocomposition of the market portfolio

To describe two important To describe two important relationships in CAPM as relationships in CAPM as represented by the capital market represented by the capital market line and the security market lineline and the security market line

Learning ObjectivesLearning ObjectivesLearning ObjectivesLearning Objectives

To describe how betas are To describe how betas are estimated and how beta is usedestimated and how beta is used

To discuss the Arbitrage Pricing To discuss the Arbitrage Pricing Theory as an alternative to the Theory as an alternative to the Capital Asset Pricing ModelCapital Asset Pricing Model

Capital Asset Pricing Capital Asset Pricing ModelModel

Capital Asset Pricing Capital Asset Pricing ModelModel

Focus on the equilibrium Focus on the equilibrium relationship between the risk and relationship between the risk and expected return on risky assetsexpected return on risky assets

Builds on Markowitz portfolio Builds on Markowitz portfolio theorytheory

Each investor is assumed to Each investor is assumed to diversify his or her portfolio diversify his or her portfolio according to the Markowitz modelaccording to the Markowitz model

CAPM AssumptionsCAPM AssumptionsCAPM AssumptionsCAPM Assumptions

All investors:All investors:– Use the same Use the same

information to information to generate an generate an efficient frontier efficient frontier

– Have the same Have the same one-period time one-period time horizonhorizon

– Can borrow or lend Can borrow or lend money at the risk-money at the risk-free rate of returnfree rate of return

No transaction No transaction costs, no personal costs, no personal income taxes, no income taxes, no inflationinflation

No single investor No single investor can affect the can affect the price of a stockprice of a stock

Capital markets Capital markets are in equilibrium are in equilibrium

Market PortfolioMarket PortfolioMarket PortfolioMarket Portfolio

Most important implication of the CAPM Most important implication of the CAPM – All investors hold the same optimal All investors hold the same optimal

portfolio of risky assetsportfolio of risky assets– The optimal portfolio is at the highest point The optimal portfolio is at the highest point

of tangency between RF and the efficient of tangency between RF and the efficient frontier frontier

– The portfolio of The portfolio of allall risky assets is the risky assets is the optimal risky portfoliooptimal risky portfolio

Called the market portfolioCalled the market portfolio

Characteristics of the Characteristics of the Market PortfolioMarket Portfolio

Characteristics of the Characteristics of the Market PortfolioMarket Portfolio

All risky assets must be in portfolio, so All risky assets must be in portfolio, so it is completely diversifiedit is completely diversified– Contains only systematic riskContains only systematic risk

All securities included in proportion to All securities included in proportion to their market valuetheir market value

Unobservable, but proxied by TSE 300Unobservable, but proxied by TSE 300 In theory, should contain all risky In theory, should contain all risky

assets worldwideassets worldwide

Capital Market LineCapital Market LineCapital Market LineCapital Market Line

Line from RF to L is Line from RF to L is capital market line capital market line (CML)(CML)

x = risk premium x = risk premium = E(R = E(RMM) - RF) - RF

y = risk = y = risk = MM

Slope = x/ySlope = x/y

= [E(R= [E(RMM) - RF]/) - RF]/MM

y-intercept = RFy-intercept = RF

E(RM)

RF

RiskM

L

M

y

x

Capital Market LineCapital Market LineCapital Market LineCapital Market Line

Slope of the CML is the market Slope of the CML is the market price of risk for efficient portfolios, price of risk for efficient portfolios, or the equilibrium price of risk in or the equilibrium price of risk in the marketthe market

Relationship between risk and Relationship between risk and expected return for portfolio P expected return for portfolio P (Equation for CML):(Equation for CML):

pM

Mp

RF)R(ERF)R(E

Security Market LineSecurity Market LineSecurity Market LineSecurity Market Line

CML Equation only applies to markets in CML Equation only applies to markets in equilibrium and efficient portfoliosequilibrium and efficient portfolios

The Security Market Line depicts the The Security Market Line depicts the tradeoff between risk and expected tradeoff between risk and expected return for individual securitiesreturn for individual securities

Under CAPM, all investors hold the Under CAPM, all investors hold the market portfoliomarket portfolio– How does an individual security contribute to How does an individual security contribute to

the risk of the market portfolio? the risk of the market portfolio?

Security Market LineSecurity Market LineSecurity Market LineSecurity Market Line

Equation for expected return for an Equation for expected return for an individual stock similar to CML individual stock similar to CML EquationEquation

RF)R(ERF

RF)R(ERF)R(E

Mi

M

M,i

M

Mi

Security Market LineSecurity Market LineSecurity Market LineSecurity Market Line

Beta = 1.0 implies Beta = 1.0 implies as risky as marketas risky as market

Securities A and B Securities A and B are more risky than are more risky than the marketthe market– Beta > 1.0Beta > 1.0

Security C is less Security C is less risky than the risky than the marketmarket– Beta < 1.0Beta < 1.0

AB

C

E(RM)

RF

0 1.0 2.00.5 1.5

SML

BetaM

E(R)

Security Market LineSecurity Market LineSecurity Market LineSecurity Market Line

Beta measures systematic riskBeta measures systematic risk– Measures relative risk compared to Measures relative risk compared to

the market portfolio of all stocksthe market portfolio of all stocks– Volatility different than marketVolatility different than market

All securities should lie on the SMLAll securities should lie on the SML– The expected return on the security The expected return on the security

should be only that return needed to should be only that return needed to compensate for systematic riskcompensate for systematic risk

CAPM’s Expected Return-CAPM’s Expected Return-Beta RelationshipBeta Relationship

CAPM’s Expected Return-CAPM’s Expected Return-Beta RelationshipBeta Relationship

Required rate of return on an asset (kRequired rate of return on an asset (kii) ) is composed ofis composed of– risk-free rate (RF)risk-free rate (RF)

– risk premium (risk premium (ii [ E(R [ E(RMM) - RF ])) - RF ]) Market risk premium adjusted for specific Market risk premium adjusted for specific

securitysecurity

kkii = RF + = RF +ii [ E(R [ E(RMM) - RF ]) - RF ]– The greater the systematic risk, the The greater the systematic risk, the

greater the required returngreater the required return

Estimating the SMLEstimating the SMLEstimating the SMLEstimating the SML

Treasury Bill rate used to estimate RFTreasury Bill rate used to estimate RF Expected market return unobservableExpected market return unobservable

– Estimated using past market returns and Estimated using past market returns and taking an expected valuetaking an expected value

Estimating individual security betas Estimating individual security betas difficultdifficult– Only company-specific factor in CAPMOnly company-specific factor in CAPM– Requires asset-specific forecastRequires asset-specific forecast

Estimating BetaEstimating BetaEstimating BetaEstimating Beta

Market modelMarket model– Relates the return on each stock to the Relates the return on each stock to the

return on the market, assuming a linear return on the market, assuming a linear relationshiprelationship

RRii = =ii + +i i RRMM +e +eii

Characteristic lineCharacteristic line– Line fit to total returns for a security Line fit to total returns for a security

relative to total returns for the market relative to total returns for the market indexindex

How Accurate Are Beta How Accurate Are Beta Estimates?Estimates?

How Accurate Are Beta How Accurate Are Beta Estimates?Estimates?

Betas change with a company’s Betas change with a company’s situationsituation– Not stationary over time Not stationary over time

Estimating a Estimating a futurefuture beta beta– May differ from the historical betaMay differ from the historical beta

RRMM represents the total of all marketable represents the total of all marketable assets in the economyassets in the economy– Approximated with a stock market indexApproximated with a stock market index– Approximates return on all common stocksApproximates return on all common stocks

No one correct number of No one correct number of observations and time periods for observations and time periods for calculating betacalculating beta

The regression calculations of the The regression calculations of the true true and and from the characteristic from the characteristic line are subject to estimation errorline are subject to estimation error

Portfolio betas more reliable than Portfolio betas more reliable than individual security betasindividual security betas

How Accurate Are Beta How Accurate Are Beta Estimates?Estimates?

How Accurate Are Beta How Accurate Are Beta Estimates?Estimates?

Arbitrage Pricing TheoryArbitrage Pricing TheoryArbitrage Pricing TheoryArbitrage Pricing Theory

Based on the Law of One PriceBased on the Law of One Price– Two otherwise identical assets cannot Two otherwise identical assets cannot

sell at different pricessell at different prices– Equilibrium prices adjust to eliminate Equilibrium prices adjust to eliminate

all arbitrage opportunitiesall arbitrage opportunities Unlike CAPM, APT does Unlike CAPM, APT does notnot assume assume

– single-period investment horizon, single-period investment horizon, absence of personal taxes, riskless absence of personal taxes, riskless borrowing or lending, mean-variance borrowing or lending, mean-variance decisionsdecisions

FactorsFactorsFactorsFactors

APT assumes returns generated by a APT assumes returns generated by a factor modelfactor model

Factor CharacteristicsFactor Characteristics– Each risk must have a pervasive Each risk must have a pervasive

influence on stock returnsinfluence on stock returns– Risk factors must influence expected Risk factors must influence expected

return and have nonzero pricesreturn and have nonzero prices– Risk factors must be unpredictable to Risk factors must be unpredictable to

the marketthe market

APT ModelAPT ModelAPT ModelAPT Model

Most important are the deviations of Most important are the deviations of the factors from their expected valuesthe factors from their expected values

The expected return-risk relationship The expected return-risk relationship for the APT can be described as:for the APT can be described as:

E(RE(Rii) =RF +b) =RF +bi1 i1 (risk premium for factor 1) (risk premium for factor 1) +b+bi2i2 (risk premium for factor 2) +… (risk premium for factor 2) +… +b+binin (risk premium for factor n) (risk premium for factor n)

Problems with APTProblems with APTProblems with APTProblems with APT

Factors are not well specified ex anteFactors are not well specified ex ante– To implement the APT model, the To implement the APT model, the

factors that account for the differences factors that account for the differences among security returns are requiredamong security returns are required

CAPM identifies market portfolio as single CAPM identifies market portfolio as single factorfactor

Neither CAPM or APT has been Neither CAPM or APT has been proven superiorproven superior– Both rely on unobservable expectationsBoth rely on unobservable expectations