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Chapter 13

Capital Asset Pricing

Theory

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CHAPTER 13 OVERVIEW

13.1 Portfolio Theory

13.2 Capital Asset Pricing Model

13.3 Expected Return and Risk

13.4 Empirical Criticisms of Beta

13.5 Arbitrage Pricing Theory

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Portfolio Theory

� Investment Portfolio:

collection of securities that

together provide an investor

with an attractive trade-off

between risk and return

� Portfolio Theory: concept of

making security choices based

on portfolio expected returns

and risks

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PORTFOLIO THEORY

Basic Assumptions

� Expected Return: anticipated profit over some

relevant holding period

� Risk: return dispersion, usually measured by

standard deviation of returns

� Probability Distribution: apportionment of likely

occurrences

�

Utility: positive benefit� Disutility: psychic loss

� Risk Averse: desire to avoid risk

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PORTFOLIO THEORYThree Fundamental Assertions

� Investors seek to maximize utility.

� Investors are risk averse: Utility rises withexpected return and falls with an increase in

volatility.

� The optimal portfolio has the highest expectedreturn for a given level of risk, or the lowest level

of risk for a given expected return.

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Portfolio Expected Rate of Return and

Risk

Expected rate of return:

Standard deviation (risk):Standard deviation (risk):

E R W E Rp i ii

N !

!

§1

§§§! !!

vvv!N

i

N

j

jijii

N

i

p COV W W VASD W 1 11

2

1

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INVES TM EN T OPPORTU NI TY FU NDAM EN TALS

Expected Rate of Return & Risk Expected Rate of Return & Risk

Figure 13.2 (c)Figure 13.2 (c)

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Portfolio risk increases with the volatilityof individual holdings and the extent to

which holding have high covariance.

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Optimal Portfolio Choice

� Zero-Risk Portfolio: constant return portfolio

� Efficient Portfolio: portfolio with maximum expectedreturn for a given level of risk, or minimum risk for agiven expected return

� Efficient Frontier: collection of all efficient portfolios

� Optimal Portfolio: collection of securities that providesan investor with the highest level of expected utility

� Market Portfolio: all tradable assets

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C apital Asset Pricing Model ( C APM)

Method for predicting

how investment returnsare determined in an

efficient capital market

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KEY TERMS

C apital Asset Pricing Model

� capital market line (CML)

� security market line (SML)

� systematic risk

� unsystematic risk

� diversifiable risk

� nondiversifiable risk

� security characteristic line(SCL)

� positive abnormal returns

� negative abnormal return

� market index bias

� model specification bias

� time interval bias

� nonstationary beta problem

� arbitrage pricing theory (APT)

� arbitrage

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C AP I TAL ASSE T PR I C ING MODE LBasic Assumptions

� Investors hold efficient portfolios; higher expectedreturns involve higher risk.

� Unlimited borrowing and lending are available at the risk-

free rate.� Investors have homogeneous expectations.

� There is a one-period time horizon.

� Investments are infinitely divisible.

�

No taxes or transaction costs exist.� Inflation is fully anticipated.

� Capital markets are in equilibrium.

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CAPM & Market Efficiency

� CAPM can test Efficient Market Hypothesis.

� Market is efficient if only risk-free assets give risk-

free rates of return (e.g., Treasury bills).

�

Deviations may indicate opportunities.

� Modeling predictions can suggest improvements to

market functioning.

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Lending & Borrowing Under the

CPM� Assumption of unlimited lending and borrowing at

risk-free rate.

� Lending if portion of portfolio held in risk-freeassets.

� Borrowing (leverage) if more than 100% of portfoliois invested in risky assets.

� Superior returns made possible with lending andborrowing; creates spectrum of risk preference fordifferent investors.

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C AP I TAL ASSE T PR I C ING MODE L

Three Linear Relationshi ps

� Capital Market Line: linear risk-return trade-off for

all investment portfolios

� Security Market Line: linear risk-return trade-off for

individual stocks

� Security Characteristic Line: linear relation between

the return on individual securities and the overall

market at every point in time

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� Capital Market Line: linear risk-return trade-off for

all investment portfolios

Standard Deviation (total portfolio risk)

E(R)

M

Rf

W = market W

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EX P E C T ED R E TUR N & R ISK The C apital Market Line ( C ML)

Linear risk-return trade-off for all investment portfolios given by

? A

E R RE R R

SD RSD R

R SDR

SD RE R R

P F

M F

M

P

F P

M

M F

!

!

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EX P E C T ED R E TUR N & R ISK

TheC

ap

ital Market Line ( C

ML)

Figure 13.4Figure 13.4

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Security Market Line (SML)


individual stocks

� Systematic Risk: return volatility tied to overall market;

also called nondiversifiable risk

� Unsystematic Risk: return volatility tied specifically to

an individual company; also called diversifiable risk

� Beta: sensitivity of a securitys returns to the

systematic market risk factor

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all individual stocks

Systematic Risk

E(R)

M

Rf

F = 1

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The BETA Factor

Figure 13.5 Figure 13.5

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The Security Characteristic Line

� Linear relation between the return on individual securities and

the overall market at every point in time, given by:

ZZ Positive Abnormal Returns:Positive Abnormal Returns: aboveabove--average returns that cant be explained asaverage returns that cant be explained ascompensation for added riskcompensation for added risk

ZZ Negative Abnormal Returns:Negative Abnormal Returns: belowbelow--average returns that cannot be explained byaverage returns that cannot be explained bybelowbelow--market riskmarket risk

R Rit i i M t i! �E F

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Empirical Implications of CAPM

� Optimal portfolio choice depends on market risk-return trade-

offs and individual investors differences in risk preferences.

� Relation between expected return and risk is linear for all

portfolios and individual assets.

� Expected rate of return is risk-free rate plus relative risk (ßp)

times market risk premium.

± High beta portfolios earn high risk premiums.

± Low beta portfolios earn low risk premiums.

� Stock price F measures relevant risk for all securities.

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E MP I R I C AL C R I T I C IS M S OF BE TAMODE L S P E C I F I C AT I ON PROBLE M S

� CAPM provides only incomplete description of return

volatilityvolatility in individual issues can only be described

as a function of overall market volatility.

� Overall market volatility very difficult to measure

± Market Index Bias: distortion to beta estimates due to fact that

indexes are imperfect proxies for overall market

± No single index includes all capital assets, including stocks,

bonds, real estate, collectibles, etc.

�Model Specification Bias: distortion to beta estimates becauseSCL fails to include other important systematic influences on

stock market volatility

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E MP I R I C AL C R I T I C IS M S OF BE TAData I nterval & N onstationary Beta

Problems

� Data Interval Problem: beta

estimation problem derived

from the fact that beta

estimates depend on data

interval studied

� Nonstationary Beta Problem:

difficulty tied to the fact that

betas are inherently unstable

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Testable Limitations Of CAPM

� ß, the slope of the regression of a securitys return on

the market return, is the only risk factor needed to

explain expected return.

� ß captures a positive expected return premium for risk.

� Other risk factors emerge:

± firm size

±low P/E, price/cash flow, P/B, and sales growth

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APT vs. CPM

� Volatile returns attributable to six-factor APT

models are very unstableexplain very little of

variation in average returns.

� Though both CAPM and APT theory and

evidence confirm relationship between risk andreturn, neither approach gives precise

estimates.

� Neither provides foolproof test of EMF.

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KEY TERMS

Capital Asset Pricing

� investment portfolio

�

portfolio theory� expected return

� risk

� probability distribution

� utility

�

disutility

� risk averse

� zero-risk portfolio

� efficient portfolio

� efficient frontier

� optimal portfolio

� market portfolio

� capital asset pricing

model

capm 2011

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