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