Bodi Kane Marcus Ch 5

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The Capital Asset Pricing Model

Chapter 9

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•Equilibrium model that underlies all modern financial theory

•Derived using principles of diversification with simplified assumptions

•Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development

Capital Asset Pricing Model (CAPM)

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•Individual investors are price takers•Single-period investment horizon•Investments are limited to traded

financial assets•No taxes, and transaction costs

Assumptions

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•Information is costless and available to all investors

•Investors are rational mean-variance optimizers

•Homogeneous expectations

Assumptions (cont’d)

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•All investors will hold the same portfolio for risky assets – market portfolio

•Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value

Resulting Equilibrium Conditions

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•Risk premium on the market depends on the average risk aversion of all market participants

•Risk premium on an individual security is a function of its covariance with the market

Resulting Equilibrium Conditions (cont’d)

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Capital Market Line

E(r)

E(rM)

rf

MCML

m

Problem 9-7,8,9,12; p313

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M = Market portfoliorf = Risk free rateE(rM) - rf = Market risk premium

E(rM) - rf = Market price of risk

= Slope of the CAPMM

Slope and Market Risk Premium

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•The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio

•Individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio

Expected Return and Risk on Individual Securities

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Security Market LineE(r)

E(rM)

rf

SML

M

ß= 1.0

Problem 9-6,10,11

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6

E( rA ) < E( rB )

A > B

impossible

Bodi Kane Marcus Ch 5

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10

E( rA ) < E( rM )

A > M

impossible

Bodi Kane Marcus Ch 5

13

11

E( rA ) < E( rM )

A < M

possible

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= [COV(ri,rm)] / m2

Slope SML = E(rm) - rf

= market risk premium SML = rf + [E(rm) - rf]

Betam = [Cov (ri,rm)] / sm2

= sm2 / sm

2 = 1

SML Relationships

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RPM=E(rm) - rf = .08 rf = .03

x = 1.25

E(rx) = .03 + 1.25(.08) = .13 or 13%

y = .6

e(ry) = .03 + .6 (.08) = .078 or 7.8%

Sample Calculations for SML

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Graph of Sample CalculationsE(r)

Rx=13%

SML

m

ß

ß1.0

Rm=11%

Ry=7.8%

3%

xß

1.25

yß.6

.08

Exercise 9.6 - 9.12

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Disequilibrium ExampleE(r)

15%

SML

ß1.0

Rm=11%

rf=3%

1.25

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•Suppose a security with a of 1.25 is offering expected return of 15%

•According to SML, it should be 13%•Underpriced: offering too high of a rate

of return for its level of risk

Disequilibrium Example

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Black’s Zero Beta Model p.301

•Absence of a risk-free asset•Combinations of portfolios on the

efficient frontier are efficient•All frontier portfolios have companion

portfolios that are uncorrelated•Returns on individual assets can be

expressed as linear combinations of efficient portfolios

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Black’s Zero Beta Model Formulation

),(

),(),()()()()(

2QPP

QPPiQPQi rrCov

rrCovrrCovrErErErE

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Efficient Portfolios and Zero Companions

Q

P

Z(Q)Z(P)

E[rz (Q)]

E[rz (P)]

E(r)

s

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Zero Beta Market Model

2)()(

),()()()()(

M

MiMZMMZi

rrCovrErErErE

CAPM with E(rz (m)) replacing rf

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CAPM & Liquidity

•Liquidity•Illiquidity Premium•Research supports a premium for

illiquidity▫Amihud and Mendelson

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CAPM with a Liquidity Premium

)()()( ifiifi cfrrErrE

f (ci) = liquidity premium for security i

f (ci) increases at a decreasing rate

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Illiquidity and Average Returns

Average monthly return(%)

Bid-ask spread (%)

Bodi Kane Marcus Ch 5

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