The Inefficient
Stock Market
Chapter 2:
Estimating Expected Return
with the
Theories of Modern Finance
Asset Pricing Theories
Estimating
expected return with the
Asset Pricing Models of Modern
Finance
CAPM: strong assumption -- strong prediction.
Corresponding Security Market Line
Market Index on Efficient Set
Expected
Return
C
B
Expected
Return
Market
Index
A
x
Risk
(Return Variability)
x
xx
x
x
xx
x
x
xx
x
x
x
x
x
xx
x
x
xx
Market
Beta
x
Market Index Inside Efficient Set
Expected
Return
Corresponding Security Market Cloud
Expected
Return
Market
Index
Risk
(Return Variability)
Market Beta
Asset Pricing Theories
Estimating
expected return with the
Asset Pricing Models of Modern
Finance
CAPM: strong assumption -- strong prediction.
APT: weak assumption -- weak prediction.
The Arbitrage Pricing Theory
Estimating the macro-economic betas.
Obtain
a characteristic line for each risk factor
Regress return on stock against risk factor
Relationship Between Return to General
Electric and Changes in Interest Rates
Return to G.E.
25%
20%
15%
10%
Line of Best Fit
5%
0%
April, 1987
-5%
-10%
-15%
-20%
-25%
-10%
-5%
0%
5%
10%
Percentage Change in Yield on Long-term Govt. Bond
The Arbitrage Pricing Theory
Estimating the macro-economic betas.
No-arbitrage condition for asset pricing.
If
risk-return relationship is non-linear, you
can arbitrage.
Curved Relationship Between Expected Return and Interest Rate Beta
Expected Return
35%
25%
C
A
-3
D
E F
15%
B
5%
-1
-5%
-15%
1
3
Interest Rate Beta
The Arbitrage Pricing Theory
Two stocks:
A: E(r) = 4%; Interest-rate beta = -2.20
B: E(r) = 26%; Interest-rate beta = 1.83
Invest 54.54% in E and 45.46% in A.
Portfolio E(r) = .5454 * 26% + .4546 * 4% =
16%
Portfolio beta = .5454 * 1.83 + .4546 * -2.20 = 0
With many combinations like this, you can
create a risk-free portfolio with a 16% expected
return.
The Arbitrage Pricing Theory
Two different stocks:
C: E(r) = 15%; Interest-rate beta = -1.00
D: E(r) = 25%; Interest-rate beta = 1.00
Invest 50.00% in E and 50.00% in A.
Portfolio E(r) = .5000 * 25% + .4546 * 15% =
20%
Portfolio beta = .5000 * 1.00 + .5000 * -1.00 = 0
With many combinations like this, you can
create a risk-free portfolio with a 20% expected
return. Then sell-short the 16% and invest the
proceeds in the 20% to arbitrage.
The Arbitrage Pricing Theory
No-arbitrage condition for asset pricing.
If
risk-return relationship is non-linear, you
can arbitrage.
Attempts to arbitrage will force linearity in
relationship between risk and return.
APT Relationship Between Expected Return and Interest Rate Beta
Expected Return
35%
E
25%
F
D
15%
C
5%
A B
-3
-1
-5%
-15%
1
3
Interest Rate Beta
The Arbitrage Pricing Theory
But, in the real world …
Finite
samples and fat-tailed distributions
preclude the formation of the riskless
hedges that are necessary to ensure that the
theory holds
E.g., LTCM
Future topics
Chapter 7
• Importance of Efficient Capital Markets
• Alternative Efficient Market Hypotheses
• Efficient Markets and
– Technical Analysis
– Fundamental Analysis
– Portfolio Management
• “Shift Happens” - Mauboussin
• “The Wrong 20-Yard Line” - Haugen
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