Lecture 6
Topic:
Capital Asset Pricing Model and
Market Efficient Hypothesis
Agenda:
I.
Fundamentals of CAPM
II.
Multifactor models and CAPM
III.
Stock Market Efficiency
I. Fundamentals of CAPM:
• Quantify the relationship between risk and return
Total risk =
Firm specific risk
+ Market risk
Ri =
Rf
+ Market Risk Premium × Units of Market Risk
Ri =
Rf
+
Ri -Rf =
(Rm - Rf )
× βi
(Rm - Rf ) × βi
Excess return of i = excess return of the market portfolio × Units of Market Risk
associated with i
Example 1: Calculation of required rate of return
Risk-free rate (3-m T-Bill)
Expected Market Return
Market Risk Premium
Beta of IBM
4.77%
10.50%
5.73%
1.85
Required rate of return
15.37%
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• Quantify Units of Market Risk (βi):
1) Formula: βi = Cov(ri,rm)/Var(rm)
2) Regression: regress (Ri - Rf) on (Rm - Rf).
ri = α + βi rm + ei
ri : Ri - Rf
rm: Rm - Rf
In this regression, we use the equity market movement to explain the stock
return.
Example 2: Calculation of beta.
a) Formula: βi = Cov(ri,rm)/Var(rm)
Prob.
Ret(A)
Ret(M)
Ret(A) E(A)
Ret(M) E(M)
Prob. * (Ret(A) - E(A)) * (Ret(M) * E(M))
10%
20%
40%
20%
10%
-5.00%
0.00%
5.00%
10.00%
15.00%
-2.00%
1.00%
3.00%
4.00%
5.00%
-10.00%
-5.00%
0.00%
5.00%
10.00%
-4.50%
-1.50%
0.50%
1.50%
2.50%
0.05%
0.02%
0.00%
0.02%
0.03%
E(R )
Variance
Stdev
5.00%
0.30%
5.48%
2.50%
0.04%
1.91%
Beta
2.74
Covariance
Correlation
b) Regression: regress (Ri - Rf) on (Rm - Rf).
ri = α + βi rm + ei
2
0.10%
95.56%
• Implication of the regression:
Total risk =
Market risk
+
Firm specific risk
Var(ri) =
=
Variance from market risk
βi2 × Var(rm)
+
+
variance from firm specific risk
Var(ei)
The proportion of the total risk from market risk =( βi2 × Var(rm) ) / Var(ri).
It measures how much total risk could be explained by the market risk.
Example 3:
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II. Multifactor models and CAPM:
• Background:
In reality, systematic risk (market risk) is not due to one source, but instead
derives from uncertainty in many economywide factors such as:
Busyness cycle
Interest rate risk
Energy price risk
• Definition:
Models of security returns positing that returns respond to several systematic
factors
• Illustration:
~ A two factor model:
ri = α + βim× rm + βiTB × rTB + ei
ri : Ri - Rf
rm: Rm - Rf
rTB: RTB - Rf
=== capture the sensitivity to the market index
=== capture the sensitivity to interest rate risk
In this regression, we use the equity market movement and interest
rate risk to explain the stock return.
Example 4:
~ A three factor model:
ri = α + βim× rm + βsize × r SMB + βB/M ×r HML + ei
r SMB
r HML L
=== capture the size premium
=== capture the book-to-market premium
Implication of the three factor model:
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III. Stock Market Efficiency
• Definition:
Stock markets are efficient, if stock prices can instantly and correctly reflect all
the available information in the markets.
All information: past, public, and inside information
Strong form
Public and past information
Semi-strong form
Past information
Weak form
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• Weak form test:
~ Short-term returns (daily to quarterly returns):
Continuation pattern leads to momentum trading strategy.
~ Long-term returns (yearly returns):
Reversal pattern leads to contrarian investment strategy.
• Semi-strong form test:
~ January effect
~ P/E
~ B/M
~ Post-earnings announcement price drift
• Strong form test:
~ Inside information
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