The Capital Asset Pricing Model

1
Chapter 9

• The Capital Asset Pricing Model

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Capital Asset Pricing Model (CAPM)

• It is the 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.

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Assumptions

• Individual investors are price takers.
• Single-period investment horizon.
• Investments are limited to traded financial
  assets.
• No taxes and transaction costs.

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Assumptions (contd)

• Information is costless and available to all
  investors.
• Investors are rational mean-variance optimizers.
• There are homogeneous expectations.

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Resulting Equilibrium Conditions

• 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.

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Resulting Equilibrium Conditions (contd)

• Risk premium on the 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.

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Capital Market Line
E(r)
CML
M
E(rM)
rf
?
?m
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Slope and Market Risk Premium

• M Market portfolio rf Risk free
  rate E(rM) - rf Market risk premium E(rM) -
  rf Market price of risk
• Slope of the CAPM

?
M
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Return and Risk For Individual Securities

• The risk premium on individual securities is a
  function of the individual securitys
  contribution to the risk of the market portfolio.
• An individual securitys risk premium is a
  function of the covariance of returns with the
  assets that make up the market portfolio.

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Security Market Line
E(r)
SML
E(rM)
rf
b
bM 1.0
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SML Relationships

• ???????????????????? COV(ri,rm) / ?m2
• Slope SML E(rm) - rf
• market risk premium
• SML rf ?E(rm) - rf
• Betam Cov (ri,rm) / sm2
• sm2 / sm2 1

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Sample Calculations for SML

• 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

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Graph of Sample Calculations
E(r)
SML
Rx13
.08
Rm11
Ry7.8
3
b
1.0
1.25 bx
.6 by
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Disequilibrium Example
E(r)
SML
15
Rm11
rf3
b
1.25
1.0
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Disequilibrium Example (cont.)

• Suppose a security with a ? of 1.25 is offering
  expected return of 15.
• According to SML, it should be 13.
• Under-priced offering too high of a rate of
  return for its level of risk.

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Blacks Zero Beta Model

• 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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Blacks Zero Beta Model Formulation
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Efficient Portfolios and Zero Companions
E(r)
Q
P
Erz (Q)
Z(Q)
Z(P)
Erz (P)
s
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Zero Beta Market Model
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
f (ci) liquidity premium for security i f (ci)
increases at a decreasing rate
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Liquidity and Average Returns
Average monthly return()
Bid-ask spread ()