The Capital Asset Pricing Model

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Chapter 8
The Capital Asset Pricing Model
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Chapter Summary

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

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Demand for Stocks and Equilibrium Prices

• Imagine a world where all investors face the same
  opportunity set
• Each investor computes his/her optimal (tangency)
  portfolio as in Chapter 6
• The demand of this investor for a particular
  firms shares comes from this tangency portfolio

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Demand for Stocks and Equilibrium Prices (contd)

• As the price of the shares falls, the demand for
  the shares increases (income, substitution
  effects)
• The supply of shares is vertical, fixed and
  independent of the share price
• The CAPM shows the conditions that prevail when
  supply and demand are equal for all firms in
  investors opportunity set

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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)
• Blacks Zero Beta Model
• CAPM and Liquidity

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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
  (use Markowitz model)
• There are homogeneous expectations

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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)
• Blacks Zero Beta Model
• CAPM and Liquidity

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Resulting Equilibrium Conditions

• All investors will hold the same portfolio of
  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
• The market portfolio is on the efficient frontier
  and, moreover, it is the tangency portfolio

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Resulting Equilibrium Conditions (contd)

• Risk premium on the market depends on the average
  risk aversion of all market participants
  E(rM)-rfAs2M
• Risk premium on an individual security is a
  function of its covariance with the market
  biCov(ri,rM)/s2M
• E(ri)-rf(Cov(ri,rM)/s2M)E(rM)-rf

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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)
• Blacks Zero Beta Model
• CAPM and Liquidity

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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
• Derive CAPM!

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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
• BetaM Cov (rM,rM) / sM2
• sM2 / sM2 1

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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 (fair)
• According to SML, it should be 13 (actually
  expected)
• Under-priced offering too high of a rate of
  return for its level of risk
• Alpha2

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Figure 8.4 Frequency Distribution of Alphas
(mutual funds 1945-1964)
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The CAPM and Reality

• Is the condition of zero alphas for all stocks as
  implied by the CAPM met?
• Not perfect but one of the best available
• Is the CAPM testable?
• Proxies must be used for the market portfolio
• CAPM is still considered the best available
  description of security pricing and is widely
  accepted

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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)
• Blacks Zero Beta Model
• CAPM and Liquidity

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Extensions of the CAPM

• Zero-Beta Model
• Helps to explain positive alphas on low beta
  stocks and negative alphas on high beta stocks
• Consideration of labor income and non-traded
  assets
• Mertons Multiperiod Model and hedge portfolios
• Incorporation of the effects of changes in the
  real rate of interest and inflation

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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 (no borrowing)
CAPM with E(rz (M)) replacing rf
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Zero Beta Market Model (no borrowing)
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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)
• Blacks Zero Beta Model
• CAPM and Liquidity

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CAPM Liquidity

• Liquidity cost or ease with which an asset can
  be sold
• 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
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CAPM Summary