1. Capital Asset Pricing Model
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Capital Asset Pricing Model
CAPM
Security Market Line
CAPM and Market Efficiency
Alpha (a) vs. Beta (b)

2. CAPM Capital Asset Pricing Model Who developed it?
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
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3. CAPM Assumptions Individual investors are price takers
Individual’s 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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4. 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
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5. CAPM
Capital Market Line
E[rP]
CML M
E[rM] rf P M
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6. CAPM – a Single Factor Model
CAPM is just a single factor model!
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7. 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
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8. Security Market Line (SML)
Math and Graphical Representation
E(ri)
SML
E(rM) rf bi bM
= 1.0
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9. 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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10. Security Market Line (SML)
Graph of Samples
E(r)
SML
rx=13%
rM=11%
ry=7.8%
Market risk premium: 8%
rf=3% 
y=0.6
M=1.0
x=1.25
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11. 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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12. CAPM Estimation
GM Example (is it such a good stock?)
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13. 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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14. CAPM, Alpha, and Market Efficiency
Non-zero alphas show up as deviations from the SML for individual securities
SML
E[ri]
15%
 = 2%
rm=11%
rf=3% 
1.0
1.25
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15. 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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16. Application - Disequilibrium Example
Suppose a security with  = 1.25 is offering expected return of 15%, what’s your decision?
Solution:
According to SML (CAPM), it should offer 13%
 = 15% – 13%=2%
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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17. Arbitrage – How to Get It Done
How does it work?
Market portfolio: αM = 0, and βM = 1
If portfolio C has αC = 2%, βC = 1.25
Show me the money
Long $100 of portfolio C
Short $125 of the market portfolio
Net payoff
Risk-free two bucks? I’ll take it anytime!
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18. Application Graph of disequilibrium  SML E[ri] 15%  = 2% rm=11%
rf=3% 
1.0
1.25
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19. Wrap-up What is CAPM? What does CAPM tell us?
Market risk premium
beta
What does CAPM tell us?
How to capture the excess risk adjusted return (non-zero )?
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