Chapter 9

Chapter 9Chapter 9

AN INTRODUCTION TO ASSET AN INTRODUCTION TO ASSET PRICING MODELSPRICING MODELS

Chapter 9 QuestionsChapter 9 Questions

• What are the assumptions of the capital What are the assumptions of the capital asset pricing model?asset pricing model?

• What is a risk-free asset and what are its What is a risk-free asset and what are its risk-return characteristics?risk-return characteristics?

• What is the covariance and correlation What is the covariance and correlation between the risk-free asset and a risky asset between the risk-free asset and a risky asset or portfolio of risky assets?or portfolio of risky assets?

• What is the expected return when we What is the expected return when we combine the risk-free assets and a portfolio combine the risk-free assets and a portfolio of risky assets?of risky assets?


• What is the standard deviation when we What is the standard deviation when we combine the risk-free asset and a portfolio of combine the risk-free asset and a portfolio of risky assets?risky assets?

• When you combine the risk-free asset and a When you combine the risk-free asset and a portfolio of risky assets on the Markowitz portfolio of risky assets on the Markowitz efficient frontier, what does the set of efficient frontier, what does the set of possible portfolios look like?possible portfolios look like?

• Given the initial set of portfolio possibilities Given the initial set of portfolio possibilities with a risk-free asset, what happens when with a risk-free asset, what happens when you add financial leverage (that is, borrow)?you add financial leverage (that is, borrow)?


• What is the market portfolio, what assets are What is the market portfolio, what assets are included, and what are the relative weights?included, and what are the relative weights?

• What is the capital market line (CML)?What is the capital market line (CML)?• What do we mean by complete What do we mean by complete

diversification?diversification?• How do we measure diversification for an How do we measure diversification for an

individual portfolio?individual portfolio?• What are systematic and unsystematic risk?What are systematic and unsystematic risk?


• Given the capital market line (CML), what is Given the capital market line (CML), what is the separation theorem?the separation theorem?

• Given the CML, what is the relevant risk Given the CML, what is the relevant risk measure for an individual risky asset?measure for an individual risky asset?

• What is the security market line (SML) and What is the security market line (SML) and how does it differ from the CML?how does it differ from the CML?

• What is beta and why is it referred to as a What is beta and why is it referred to as a standardized measure of systematic risk?standardized measure of systematic risk?


• How can we use the SML to determine the How can we use the SML to determine the expected (required) rate of return for a risky expected (required) rate of return for a risky asset?asset?

• Using the SML, what do we mean by an Using the SML, what do we mean by an undervalued and overvalued security, and undervalued and overvalued security, and how do we determine whether an asset is how do we determine whether an asset is undervalued or overvalued?undervalued or overvalued?

• What is an asset’s characteristic line and how What is an asset’s characteristic line and how do we compute the characteristic line for an do we compute the characteristic line for an asset?asset?


• What is the impact on the characteristic What is the impact on the characteristic line when we compute it using different line when we compute it using different return intervals (such as weekly versus return intervals (such as weekly versus monthly) and when we employ different monthly) and when we employ different proxies (that is, benchmarks) for the proxies (that is, benchmarks) for the market portfolio (for example, the S&P market portfolio (for example, the S&P 500 versus a global stock index)?500 versus a global stock index)?


• What is the basic conceptual difference What is the basic conceptual difference between the CAPM and the several between the CAPM and the several multifactor models currently available?multifactor models currently available?

• When dealing with multifactor models, When dealing with multifactor models, what is the difference between what is the difference between macroeconomic and microeconomic macroeconomic and microeconomic models?models?

Capital Market Theory:Capital Market Theory: An Overview An Overview

• Capital market theory extends portfolio theory Capital market theory extends portfolio theory and seeks to develops a model for pricing all and seeks to develops a model for pricing all risky assets based on their relevant risksrisky assets based on their relevant risks

• Asset Pricing ModelsAsset Pricing Models– Capital asset pricing model (CAPM) allows for the Capital asset pricing model (CAPM) allows for the

calculation of the required rate of return for any calculation of the required rate of return for any risky asset based on the security’s betarisky asset based on the security’s beta

– Alternative asset pricing models allow for multiple Alternative asset pricing models allow for multiple factors in determining the required rate of returnfactors in determining the required rate of return

Assumptions of Assumptions of Capital Market TheoryCapital Market Theory

• All investors are Markowitz efficient investors All investors are Markowitz efficient investors who invest on the efficient frontier. who invest on the efficient frontier.

• Investors can borrow or lend any amount of Investors can borrow or lend any amount of money at the risk-free rate of return (RFR). money at the risk-free rate of return (RFR).

• Investors have homogeneous expectations; Investors have homogeneous expectations; that is, they estimate identical probability that is, they estimate identical probability distributions for future rates of return.distributions for future rates of return.

• All investors have the same one-period time All investors have the same one-period time horizon such as one-month, six months, or horizon such as one-month, six months, or one year. one year.

Assumptions of Assumptions of Capital Market TheoryCapital Market Theory

• All investments are infinitely divisible, which All investments are infinitely divisible, which means that it is possible to buy or sell means that it is possible to buy or sell fractional shares of any asset or portfolio. fractional shares of any asset or portfolio.

• There are no taxes or transaction costs There are no taxes or transaction costs involved in buying or selling assets. involved in buying or selling assets.

• There is no inflation or any change in interest There is no inflation or any change in interest rates, or inflation is fully anticipated.rates, or inflation is fully anticipated.

• Capital markets are in equilibrium.Capital markets are in equilibrium.

Making AssumptionsMaking Assumptions

• Some of these assumptions are clearly Some of these assumptions are clearly unrealisticunrealistic

• Relaxing many of these assumptions would Relaxing many of these assumptions would have only minor influence on the model and have only minor influence on the model and would not change its main implications or would not change its main implications or conclusions.conclusions.

• The primary way to judge a theory is on how The primary way to judge a theory is on how well it explains and helps predict behavior, well it explains and helps predict behavior, not on its assumptions.not on its assumptions.

Capital Market Theory and Capital Market Theory and a Risk-Free Asseta Risk-Free Asset

Perhaps surprisingly, there are rather large Perhaps surprisingly, there are rather large implications for capital market theory when a implications for capital market theory when a risk-free asset exists.risk-free asset exists.

• What is a risk-free asset?What is a risk-free asset?– An asset with zero varianceAn asset with zero variance– Provides the risk-free rate of return (RFR)Provides the risk-free rate of return (RFR)– It will be an “intercept” value on a portfolio graph It will be an “intercept” value on a portfolio graph

between expected return and standard deviation.between expected return and standard deviation.

• Since it has zero variance, it will also have Since it has zero variance, it will also have zero correlation with all other risky assetszero correlation with all other risky assets

Risk-Free AssetRisk-Free Asset

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

n

1ijjiiij 1-)]}/nE(R-)][RE(R-[R{Cov

Because the returns for the risk free asset are certain,

0RF 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.

Combining a Risk-Free Combining a Risk-Free Asset with a PortfolioAsset with a Portfolio

Expected return is the weighted average Expected return is the weighted average of the two returnsof the two returns

))E(RW-(1(RFR)W)E(R iRFRFport

This is a linear relationship


Standard deviation: Standard deviation: The expected variance for a The expected variance for a two-asset portfolio istwo-asset portfolio is

211,22122

22

21

21

2port rww2ww)E(

Substituting the risk-free asset for Security 1, and the risky asset for Security 2, this formula would become

iRFiRF iRF,RFRF22

RF22

RF2port )rw-(1w2)w1(w)E(

Since we know that the variance of the risk-free asset is zero and the correlation between the risk-free asset and any risky asset i is zero we can adjust the formula

22RF

2port )w1()E( i


Given the variance formulaGiven the variance formula22

RF2port )w1()E( i

22RFport )w1()E( i the standard deviation is

i)w1( RF

Therefore, the standard deviation of a portfolio that combines the risk-free asset with risky assets is the linear proportion of the standard deviation of the risky asset portfolio.


Since both the expected return Since both the expected return andand the the standard deviation of return for such a standard deviation of return for such a portfolio are linear combinations, a portfolio are linear combinations, a graph of possible portfolio returns and graph of possible portfolio returns and risks looks like a straight line between risks looks like a straight line between the two assets.the two assets.

Portfolio Possibilities Combining the Portfolio Possibilities Combining the Risk-Free Asset and Risky Portfolios Risk-Free Asset and Risky Portfolios

on the Efficient Frontieron the Efficient Frontier

)E( port

)E(R port

RFR

M

C

AB

D

Risk-Return Possibilities Risk-Return Possibilities with Leveragewith Leverage

• To attain a higher expected return than is To attain a higher expected return than is available at point M (in exchange for available at point M (in exchange for accepting higher risk)accepting higher risk)

• Either invest along the efficient frontier Either invest along the efficient frontier beyond point M, such as point Dbeyond point M, such as point D

• Or, add leverage to the portfolio by borrowing Or, add leverage to the portfolio by borrowing money at the risk-free rate and investing in money at the risk-free rate and investing in the risky portfolio at point Mthe risky portfolio at point M

Portfolio Possibilities Combining the Portfolio Possibilities Combining the Risk-Free Asset and Risky Portfolios Risk-Free Asset and Risky Portfolios

on the Efficient Frontieron the Efficient Frontier

)E( port

)E(R port

RFR

M

CML

Borrowing

Lending

The Market PortfolioThe Market Portfolio

• Portfolio M lies at the point of tangency, so it Portfolio M lies at the point of tangency, so it has the highest portfolio possibility linehas the highest portfolio possibility line

• This line of tangency is called the Capital This line of tangency is called the Capital Market Line (CML)Market Line (CML)

• Everybody will want to invest in Portfolio M Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the and borrow or lend to be somewhere on the CML (the CML is a new efficient frontier)CML (the CML is a new efficient frontier)– Therefore this portfolio must include all risky Therefore this portfolio must include all risky

assets (or else some assets would have no assets (or else some assets would have no demand)demand)

The Market PortfolioThe Market Portfolio

• Because the market is in equilibrium, all Because the market is in equilibrium, all assets are included in this portfolio in assets are included in this portfolio in proportion to their market valueproportion to their market value

• Because it contains all risky assets, it is Because it contains all risky assets, it is a completely diversified portfolio, which a completely diversified portfolio, which means that all the unique risk of means that all the unique risk of individual assets (unsystematic risk) is individual assets (unsystematic risk) is diversified awaydiversified away

Systematic RiskSystematic Risk

• Only systematic risk remains in the market Only systematic risk remains in the market portfolioportfolio

• Systematic risk is the variability in all risky Systematic risk is the variability in all risky assets caused by macroeconomic variablesassets caused by macroeconomic variables

• Systematic risk can be measured by the Systematic risk can be measured by the standard deviation of returns of the market standard deviation of returns of the market portfolio and can change over timeportfolio and can change over time

Factors Affecting Factors Affecting Systematic RiskSystematic Risk

• Systematic risk factors are those Systematic risk factors are those macroeconomic variables that affect the macroeconomic variables that affect the valuation of all risky assetsvaluation of all risky assets– Variability in growth of the money supplyVariability in growth of the money supply– Interest rate volatilityInterest rate volatility– Variability in aggregate industrial Variability in aggregate industrial

productionproduction

How to Measure How to Measure DiversificationDiversification

• All portfolios on the CML are perfectly All portfolios on the CML are perfectly positively correlated with each other positively correlated with each other and with the completely diversified and with the completely diversified market Portfolio Mmarket Portfolio M

• A completely diversified portfolio would A completely diversified portfolio would have a correlation with the market have a correlation with the market portfolio of +1.00portfolio of +1.00

Diversifying Away Diversifying Away Unsystematic RiskUnsystematic Risk

• The purpose of diversification is to reduce the The purpose of diversification is to reduce the standard deviation of the total portfoliostandard deviation of the total portfolio

• As you add securities, you expect the As you add securities, you expect the average covariance for the portfolio to average covariance for the portfolio to decline, but not to disappear since decline, but not to disappear since correlations are not perfectly negative.correlations are not perfectly negative.

• About how many securities must you add to About how many securities must you add to obtain a completely diversified portfolio?obtain a completely diversified portfolio?– About 90% of the benefit after 12-18 stocksAbout 90% of the benefit after 12-18 stocks– Maximum benefit needs between 30 and 40Maximum benefit needs between 30 and 40

The Portfolio Standard The Portfolio Standard DeviationDeviation

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

The CML and the The CML and the Separation TheoremSeparation Theorem

• The CML leads all investors to invest in the M The CML leads all investors to invest in the M portfolio (The Investment Decision)portfolio (The Investment Decision)

• Individual investors should differ in position Individual investors should differ in position on the CML depending on risk preferences on the CML depending on risk preferences (which leads to the Financing Decision)(which leads to the Financing Decision)– Risk averse investors will lend part of the portfolio Risk averse investors will lend part of the portfolio

at the risk-free rate and invest the remainder in at the risk-free rate and invest the remainder in the market portfolio (points left of M)the market portfolio (points left of M)

– Aggressive investors would borrow funds at the Aggressive investors would borrow funds at the RFR and invest everything in the market portfolio RFR and invest everything in the market portfolio (points to the right of M)(points to the right of M)

A Risk Measure for the A Risk Measure for the CMLCML

If…If…the relevant risk in a portfolio is the average the relevant risk in a portfolio is the average

covariance with all other assets in the portfolio,covariance with all other assets in the portfolio,

and …and …the only relevant portfolio is the market portfolio (M),the only relevant portfolio is the market portfolio (M),

then it follows that …then it follows that …the covariance with the market portfolio is the the covariance with the market portfolio is the

relevant (systematic) risk of an asset.relevant (systematic) risk of an asset.

A Risk Measure for the A Risk Measure for the CMLCML

Because all individual risky assets are part of the M portfolio, Because all individual risky assets are part of the M portfolio, an asset’s rate of return in relation to the return for the M an asset’s rate of return in relation to the return for the M portfolio may be described using the following linear portfolio may be described using the following linear model:model:

RRitit = a = aii +b +biiRRMtMt + +where: where:

RRitit = return for asset i during period t = return for asset i during period t

aaii = constant term for asset i = constant term for asset i

bbii = slope coefficient for asset i = slope coefficient for asset i

RRMtMt = return for the M portfolio during period t = return for the M portfolio during period t

=random error term=random error term

The Capital Asset Pricing The Capital Asset Pricing ModelModel

• The existence of a risk-free asset resulted in The existence of a risk-free asset resulted in deriving a capital market line (CML) that deriving a capital market line (CML) that became the relevant frontierbecame the relevant frontier

• An asset’s covariance with the market An asset’s covariance with the market portfolio is the relevant risk measureportfolio is the relevant risk measure

• This can be used to determine an appropriate This can be used to determine an appropriate required rate of return on a risky asset - the required rate of return on a risky asset - the capital asset pricing model (CAPM)capital asset pricing model (CAPM)

The Capital Asset Pricing The Capital Asset Pricing ModelModel

• CAPM indicates what should be the expected CAPM indicates what should be the expected or required rates of return on risky assetsor required rates of return on risky assets

• This helps to value an asset by providing an This helps to value an asset by providing an appropriate discount rate to use in dividend appropriate discount rate to use in dividend valuation modelsvaluation models

• You can compare an expected rate of return You can compare an expected rate of return to the required rate of return implied by to the required rate of return implied by CAPM - over/ under valued?CAPM - over/ under valued?

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

• The relevant risk measure for an The relevant risk measure for an individual risky asset is its covariance individual risky asset is its covariance with the market portfolio (Covwith the market portfolio (Covi,mi,m))

• This is shown as the risk measureThis is shown as the risk measure• The return for the market portfolio The return for the market portfolio

should be consistent with its own risk, should be consistent with its own risk, which is the covariance of the market which is the covariance of the market with itself - or its variancewith itself - or its variance

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

)Cov(RFR-R

RFR)E(R Mi,2M

Mi

RFR)-R(Cov

RFR M2M

Mi,

2M

Mi,Cov

We then define as beta

RFR)-(RRFR)E(R Mi i

)( i

Graph of SMLGraph of SML

)E(R i

)Beta(Cov 2Mim/0.1

mR

SML

0

Negative Beta

RFR

Determining the Expected Determining the Expected ReturnReturn

• The expected rate of return of a risk The expected rate of return of a risk asset is determined by the RFR plus a asset is determined by the RFR plus a risk premium for the individual assetrisk premium for the individual asset

• The risk premium is determined by the The risk premium is determined by the systematic risk of the asset (beta) and systematic risk of the asset (beta) and the prevailing market risk premium the prevailing market risk premium (R(RMM-RFR)-RFR)

RFR)-(RRFR)E(R Mi i

Determining the Expected Determining the Expected ReturnReturn

• In equilibrium, all assets and all portfolios of In equilibrium, all assets and all portfolios of assets should plot on the SMLassets should plot on the SML– The SML gives the market “going rate of return” or The SML gives the market “going rate of return” or

what you should earn as a return for a securitywhat you should earn as a return for a security– Any security with an expected return that plots Any security with an expected return that plots

above the SML is underpricedabove the SML is underpriced– Any security with an expected return that plots Any security with an expected return that plots

below the SML is overpricedbelow the SML is overpriced

Identifying Undervalued Identifying Undervalued and Overvalued Assetsand Overvalued Assets

• Compare the required rate of return to Compare the required rate of return to the expected rate of return for a specific the expected rate of return for a specific risky asset using the SML over a risky asset using the SML over a specific investment horizon to specific investment horizon to determine if it is an appropriate determine if it is an appropriate investmentinvestment

• Independent estimates of expected Independent estimates of expected return for the securities provide price return for the securities provide price and dividend outlooksand dividend outlooks

Calculating Beta: The Calculating Beta: The Characteristic LineCharacteristic Line

The systematic risk input of an individual asset is derived The systematic risk input of an individual asset is derived from a regression model, referred to as the asset’s from a regression model, referred to as the asset’s characteristic line with the model portfolio:characteristic line with the model portfolio:

tM,iiti, RRwhere: Ri,t = the rate of return for asset i during period tRM,t = the rate of return for the market portfolio M during t

miii R-R

2M

Mi,Cov

i

error term random the

Issues in Beta EstimationIssues in Beta Estimation

• The Impact of the Time IntervalThe Impact of the Time Interval– Number of observations and time interval used in Number of observations and time interval used in

regression varyregression vary• Value Line Investment Services (VL) uses weekly rates Value Line Investment Services (VL) uses weekly rates

of return over five yearsof return over five years• Merrill Lynch, Pierce, Fenner & Smith (ML) uses monthly Merrill Lynch, Pierce, Fenner & Smith (ML) uses monthly

return over five yearsreturn over five years

– There is no “correct” interval for analysisThere is no “correct” interval for analysis– Weak relationship between VL & ML betas due to Weak 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

Issues in Beta EstimationIssues in Beta Estimation

• The Effect of the Market ProxyThe Effect of the Market Proxy– A measure of the market portfolio is neededA measure of the market portfolio is needed– S&P 500 Composite Index is most often usedS&P 500 Composite Index is most often used

• Includes a large proportion of the total market value of Includes a large proportion of the total market value of U.S. stocksU.S. stocks

• Value weighted seriesValue weighted series

– Weaknesses of Using S&P 500Weaknesses of Using S&P 500as the Market Proxyas the Market Proxy

• Includes only U.S. stocks Includes only U.S. stocks • The theoretical market portfolio should include all types The theoretical market portfolio should include all types

of assets from all around the worldof assets from all around the world

Multifactor Models of Risk Multifactor Models of Risk and Returnand Return

• CAPM is criticized because of the CAPM is criticized because of the difficulties in selecting a proxy for the difficulties in selecting a proxy for the market portfolio as a benchmarkmarket portfolio as a benchmark

• An initial alternative pricing theory with An initial alternative pricing theory with fewer assumptions was developed:fewer assumptions was developed:– Arbitrage Pricing TheoryArbitrage Pricing Theory

Multifactor Pricing ModelsMultifactor Pricing Models

• Arbitrage Pricing TheoryArbitrage Pricing Theory– A practical problem with implementation is A practical problem with implementation is

that neither the identity nor the exact that neither the identity nor the exact number of risk factors are part of the number of risk factors are part of the theory, so the risk factor specification is ad theory, so the risk factor specification is ad hochoc

– An alternative approach, similar to the APT An alternative approach, similar to the APT is to directly specify the risk factors to is to directly specify the risk factors to model (the F’s in the slide that follows)model (the F’s in the slide that follows)


= return on asset = return on asset ii during a specified time period during a specified time period= expected return for asset = expected return for asset ii= = reaction in asset reaction in asset jj’s returns to movements in a ’s returns to movements in a

common factorcommon factor= a common factor influences the returns on all assets= a common factor influences the returns on all assets

= a unique effect on asset = a unique effect on asset ii’s return that, by ’s return that, by assumption, is completely diversifiable in large assumption, is completely diversifiable in large portfolios and has a mean of zeroportfolios and has a mean of zero

jtktjktjtjjjt FFFaR ...2211

Rjt

Ei

jk

kF

jt


Theory does not suggest a particular set Theory does not suggest a particular set of factors to price; two general of factors to price; two general approaches have been employed.approaches have been employed.

• Macroeconomic-Based Risk Factor Macroeconomic-Based Risk Factor ModelsModels

• Microeconomic-Based Risk Factor Microeconomic-Based Risk Factor ModelsModels

Macroeconomic-Based Macroeconomic-Based Risk Factor ModelsRisk Factor Models

• Chen, Roll, and RossChen, Roll, and RossDeveloped a return model based on:Developed a return model based on:– Return on a value-weighted NYSE indexReturn on a value-weighted NYSE index– Monthly growth in U.S. industrial productionMonthly growth in U.S. industrial production– Change in inflationChange in inflation– Difference between actual and expected inflationDifference between actual and expected inflation– Unanticipated change in the bond credit spreadUnanticipated change in the bond credit spread– Unanticipated term structure shiftUnanticipated term structure shift


Chen, Roll, and RossChen, Roll, and RossGeneral Findings:General Findings:– Significance of various risk factors Significance of various risk factors

changes over timechanges over time– The stock market index factor is never The stock market index factor is never

significantsignificant


• Burmeister, Roll, And RossBurmeister, Roll, And RossIdentify five risk exposures:Identify five risk exposures:– Confidence riskConfidence risk– Time horizon riskTime horizon risk– Inflation riskInflation risk– Business cycle riskBusiness cycle risk– Market timing riskMarket timing risk

Microeconomic-Based Risk Microeconomic-Based Risk Factor ModelsFactor Models

Fama and FrenchFama and French• Characteristic-based approach explaining Characteristic-based approach explaining

returns based on:returns based on:– Excess return on a stock market portfolioExcess return on a stock market portfolio– SMB (Small minus big)SMB (Small minus big)

• The return on a small-cap portfolio less the return on a The return on a small-cap portfolio less the return on a large-cap portfoliolarge-cap portfolio

– HML (High minus low)HML (High minus low)• The return of a high book-to-market value portfolio less The return of a high book-to-market value portfolio less

the return on a low book-to-market value portfoliothe return on a low book-to-market value portfolio

Microeconomic-Based Risk Microeconomic-Based Risk Factor ModelsFactor Models

Fama and FrenchFama and French• Compared the performance of stocks sorted Compared the performance of stocks sorted

into P/E quintilesinto P/E quintiles– The estimated beta from a single-factor model The estimated beta from a single-factor model

varies greatly between high and low P/E stocksvaries greatly between high and low P/E stocks– Low P/E stocks tend to be positively correlated Low P/E stocks tend to be positively correlated

with the small-firm premiumwith the small-firm premium– Low P/E stocks tend to have low book-to-market Low P/E stocks tend to have low book-to-market

ratios and high P/E stocks tend to have high book-ratios and high P/E stocks tend to have high book-to-market ratiosto-market ratios

Microeconomic-Based Risk Microeconomic-Based Risk Factor Models: ExtensionsFactor Models: Extensions

• CarhartCarhart– Extends the Fama/French model to include Extends the Fama/French model to include

a fourth factor related to momentuma fourth factor related to momentum

• Other characteristic-based models use Other characteristic-based models use index portfolios as common factorsindex portfolios as common factors

• Barra approach utilizes many firm and Barra approach utilizes many firm and industry variablesindustry variables

Using Multifactor ModelsUsing Multifactor Models

• To estimate returns for individual stocks, use To estimate returns for individual stocks, use the following steps:the following steps:– Identify a specific set of common risk factorsIdentify a specific set of common risk factors– Estimate the risk premiums for the factorsEstimate the risk premiums for the factors– Estimate the sensitivities of the individual stock to Estimate the sensitivities of the individual stock to

each factoreach factor– Calculate the expected return by applying the Calculate the expected return by applying the

model with the appropriate values of each model with the appropriate values of each common risk factorcommon risk factor

Chapter 9

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