capital asset pricing model and arbitrage pricing theory: empirical
The Capital Asset Pricing Model
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Transcript of The Capital Asset Pricing Model
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
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10
E( rA ) < E( rM )
A > M
impossible
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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 (%)
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