Capital Asset Pricing Model

1
Capital Asset Pricing Model

• CAPM
• Security Market Line
• CAPM and Market Efficiency
• Alpha (a) vs. Beta (b)

2
CAPM

• Capital Asset Pricing Model
• An equilibrium model underlying modern finance
  theory
• Based on diversification principle and simplified
  assumptions
• Who developed it?
• Markowitz Nobel Prize
• Sharpe Nobel Prize
• Treynor, Lintner and Mossin

3
CAPM

• Assumptions
• Individual investors are price takers
• Individuals action inconsequential to stock
  prices
• Single-period investment horizon
• Investors maximize expected utility
• Homogeneous expectations
• Investors do not know the actual outcome
• Investors agree on the likelihood of each outcome
• Investors risk aversion may be different
• Market is frictionless
• No taxes, and transaction costs

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CAPM

• Resulting Equilibrium Outcome
• All investors will hold the same portfolio for
  risky assets the market portfolio
• Market portfolio contains all securities and the
  proportion of each security is its market value
  as a percentage of total market value
• 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

5
CAPM

• Capital Market Line

ErP
CML
M
ErM
rf
?P
?M
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CAPM a Single Factor Model

• CAPM is just a single factor model!

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CAPM

• Expected return on individual security
• The risk premium on individual securities
• is equal to its expected return above the risk
  free rate of return
• depends on its contribution to the risk of the
  market portfolio
• depends on its level of systematic risk
• The systematic risk
• is a function of the covariance of returns with
  the assets that make up the market portfolio
• is equal to one for market portfolio

8
Security Market Line (SML)

• Math and Graphical Representation

E(ri)
SML
E(rM)
rf
bi
bM
1.0
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Security Market Line (SML)

• Sample calculations
• Market risk premium is 8, risk free rate is 3,
  security x and y have beta of 1.25 and 0.6, what
  is the expected return of each based on CAPM?
• Solution
• Security x
• Security y

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Security Market Line (SML)

• Graph of Samples

E(r)
SML
rx13
rM11
ry7.8
Market risk premium 8
rf3
?
?M1.0
?x1.25
?y0.6
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CAPM Estimation

• How to find beta?
• Find the return data of individual stocks
• Find the market return data
• Find the T-bill data
• Calculate the excess return of
• Individual stocks
• Market
• Run the regression

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CAPM Estimation

• GM Example (is it such a good stock?)

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CAPM and Market Efficiency

• If markets are perfectly efficient, there would
  be no non-zero alphas!
• Did this stop people in search for alpha?

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CAPM, Alpha, and Market Efficiency

• Non-zero alphas show up as deviations from the
  SML for individual securities

SML
Eri
15
? 2
rm11
rf3
?
1.0
1.25
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Investments - It Is All about Alpha!

• Investments Active vs. Passive
• Alpha (a) vs. Beta (b)
• Beta is easy it is the market
• Beta should be free!
• Alpha is hard, but does it require frequent
  trading?
• Not necessarily it is about taking right
  long-term positions, and identifying underpriced
  factors
• Good old Buy Low Sell High always works!!!
• Not having too many constraints helps

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Application - Disequilibrium Example

• Suppose a security with ? 1.25 is offering
  expected return of 15, whats your decision?
• Solution
• According to SML (CAPM), it should offer 13
• ? 15 132
• Under-priced offering too high a rate of return
  for its level of risk, what to do?
• What is then over-priced? It is the market
  index!!!
• Long a portfolio C of similar stocks and short a
  market portfolio!

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Arbitrage How to Get It Done

• How does it work?
• Market portfolio aM 0, and ßM 1
• If portfolio C has aC 2, ßC 1.25
• Show me the money
• Long 100 of portfolio C
• Short 125 of the market portfolio
• Net payoff
• Risk-free two bucks? Ill take it anytime!

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Application

• Graph of disequilibrium

SML
Eri
15
? 2
rm11
rf3
?
1.0
1.25
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Wrap-up

• What is CAPM?
• Market risk premium
• beta
• What does CAPM tell us?
• How to capture the excess risk adjusted return
  (non-zero ?)?