1. Capital Asset Pricing and
Arbitrage Pricing Theory
Prof. Karim Mimouni
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2. Capital Asset Pricing Model
(CAPM)
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3. 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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4. Assumptions (cont.)
• Information is costless and available to all
investors
• Homogeneous expectations
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5. 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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6. The Efficient Frontier and the
Capital Market Line
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7. 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
σM
= Slope of the CML
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8. Expected Return and Risk
on Individual Securities
E (ri ) − rf = β i ( E (rM ) − rf )
M = Market portfolio
rf = Risk free rate
E(ri) - rf = Risk premium on security i
E(rM) - rf = Market risk premium
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9. The Security Market Line and
Positive Alpha Stock
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10. • Determine the equation of the SML and plot it
when:
( E (r
M ) − rf ) = 0.08
and
rf = 0.03
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11. Application
• You are in an economy where Rf=9%,
E(Rm)=20%.
• Determine the equation of the SML line in
this economy.
• A stock has a beta=1.5. Determine the
required rate of return. Give your
recommendation when you think its
expected return will be 22%.
• Do the same analysis when beta=-0.5 and
investor expect the return to be 7% 11

12. Estimating the Index Model
• Using historical data on T-bills, S&P 500
and individual securities
• Regress risk premiums for individual
stocks against the risk premiums for the
S&P 500
• Slope is the beta for the individual stock
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13. Characteristic Line for GM
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14. Security Characteristic
Line for GM: Summary Output
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15. Multifactor Models
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16. • Limitations for CAPM
• Market Portfolio is not directly observable
• Research shows that other factors affect
returns
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17. Fama French Research
• Returns are related to factors other than market
returns
• Size
• Book value relative to market value
• Three factor model better describes returns
• Example : GM
E (rGM ) − r f = β GM , M ( E (rM ) − rf ) + β GM ,SMB ( E (rSMB ) − rf ) + β GM , HML ( E (rHML ) − rf )
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18. Regression Statistics for the Single-
index and FF Three-factor Model
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19. Arbitrage Pricing Theory
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20. • Arbitrage - arises if an investor can
construct a zero beta investment portfolio
with a return greater than the risk-free rate
• If two portfolios are mispriced, the investor
could buy the low-priced portfolio and sell
the high-priced portfolio
• In efficient markets, profitable arbitrage
opportunities will quickly disappear
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21. Security
Line Characteristics
E (rP ) − rf = β P ( E (rM ) − rf )
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22. APT and CAPM Compared
• APT applies to well diversified portfolios and not
necessarily to individual stocks
• With APT it is possible for some individual stocks
to be mispriced - not lie on the SML
• APT is more general in that it gets to an
expected return and beta relationship without the
assumption of the market portfolio
• APT can be extended to multifactor models
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