The Capital Asset Pricing Model

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Chapter 9

• The Capital AssetPricing Model

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Capital Asset Pricing Model (CAPM)

• 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
• 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 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
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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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Expected Return and Risk on Individual Securities

• The risk premium on individual securities is a
  function of the individual securitys
  contribution to the risk of the market portfolio
• 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
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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
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Disequilibrium Example
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Disequilibrium Example

• 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

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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
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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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Illiquidity and Average Returns
Average monthly return()
Bid-ask spread ()