CHAPTER 7: CAPM CAPITAL ASSET PRICING MODEL

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CHAPTER 7 CAPM(CAPITAL ASSET PRICING MODEL)
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Why CAPM?

• Predicts the return of a stock
• If expected return gt CAPM return
• Stock is underpriced
• If expected return lt CAPM return
• Stock is overpriced

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Chapter Summary

• Objective To present the basic version of the
  model and its applicability.
• Assumptions
• Result (ie. Equilibrium Conditions)
• The Security Market Line (SML)

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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 free and available to all
  investors
• Investors are rational and are risk averse
• Investors have homogeneous expectations

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Summary Reminder

• Objective To present the basic version of the
  model and its applicability.
• Assumptions
• Result (ie. Equilibrium Conditions)
• The Security Market Line (SML)

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Resulting Equilibrium Conditions

• All investors will hold the same portfolio of
  risky assets ie. market portfolio
• Market portfolio contains all securities and the
  proportion of each security is its market value
  as a percentage of total market value of all
  stocks
• The market portfolio is on the efficient frontier
  and, moreover, is the tangency portfolio to the
  CAL

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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. This
  is represented by BETA.

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Capital Market Line
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Slope and Market Risk Premium

• M The market portfolio rf Risk free
  rate E(rM) - rf Market risk premium
• Slope of the CML

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Summary Reminder

• Objective To present the basic version of the
  model and its applicability.
• Assumptions
• Resulting Equilibrium Conditions
• The Security Market Line (SML)

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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
E(r)
SML
E(rM)
rf
ß
ß
1.0
M
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SML Relationships

• ??????????????????? ? Cov(ri,rm) / ?m2
• Slope SML E(rm) - rf
• market risk premium
• E(r)SML rf ?E(rm) - rf
• Note B is different for each stock and changes
  through time

b
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Sample Calculations for SML

• E(rm) - rf .08 rf .03
• a) ?x 1.25
• E(rx) .03 1.25(.08) .13 or 13
• b) ?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
• Under-priced offering too high of a rate of
  return for its level of risk

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Multifactor models

• Arbitrage pricing theory (APT)
• E(r)SML rf ?1E(rm) - rf ?2E(r2) - rf
• ?3E(r3) - rf .
• Where factors 2, 3, 4,etc are different factors