The Inefficient Market
What Pays Off and Why
Part 1: What Pays Off
Prentice Hall 1999
Visit our web-site at HaugenSystems.com
Background

The evolution of academic finance
The Evolution of Academic Finance
The Old Finance
1930’s
40’s
50’s
60’s
70’s
80’s
90’s
beyond
The Old Finance
Theme:
Analysis of Financial Statements and the Nature of Financial Claims
Paradigms: Security Analysis
(Graham & Dodd)
Foundation: Accounting and Law
Uses and Rights of Financial Claims
(Dewing)
The Evolution of Academic Finance
The Old Finance
1930’s
40’s
Bob goes
to college
50’s
60’s
70’s
80’s
90’s
beyond
Modern Finance
Modern Finance
Theme:
Valuation Based on Rational Economic Behavior
Paradigms:
Optimization
(Markowitz)
Irrelevance
(Modigliani & Miller)
Foundation: Financial Economics
CAPM
EMH
(Sharpe, Lintner & Mossen) (Fama)
The Evolution of Academic Finance
The Old Finance
1930’s
40’s
50’s
Bob goes
to college
60’s
70’s
The New Finance
80’s
90’s
beyond
Modern Finance
The New Finance
Theme:
Inefficient Markets
Paradigms:
Inductive ad hoc Factor Models
Expected Return
(Haugen)
Risk
(Chen, Roll & Ross)
Foundation: Statistics, Econometrics, and Psychology
Behavioral Models
(Kahneman & Tversky)
Background


The evolution of academic finance
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
Background


The evolution of academic finance
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
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
What Pays Off.
Probability Distribution For Returns to a Portfolio
Probability
Variance of Return
Expected
Return
Possible Rates
of Returns
Risk Factor Models

The variance of stock returns can be split
into two components:

Variance = systematic risk + diversifiable risk

Systematic risk is computed using the
following spreadsheet:
Risk Factor Models

Factor betas are estimated by relating stock
returns to (unexpected) percentage changes
in the factor over a period where the stock’s
character is similar to the present.
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
Spreadsheet for Computing Systematic Risk
Portfolio Beta
(Inflation)
Portfolio Beta
Portfolio Beta
(Inflation)
(Oil Price)
1.00
Correlation Between
Inflation and Oil Price
Portfolio Beta Correlation Between
(Oil Price) Inflation and Oil Price
1.00
Risk Factor Models

Factor correlations can be estimated over a
longer period because they are, presumably,
more stable over time.

This may increase the predictive accuracy of
factor models relative to more naïve historical
estimates.
Relationship Between Rate of Inflation and
Percentage Change in Price of Oil
Monthly Percentage
Change in Price of Oil
140
120
100
80
60
40
Line of Best Fit
20
0
-20
-40
-1
-0.5
0
0.5
1
1.5
2
Monthly Rate
of Inflation
Computing Portfolio Systematic Risk
Portfolio Beta * Portfolio Beta * 1.00
(Inflation)
(Inflation)
+
Portfolio Beta * Portfolio Beta * Correlation Between
(Oil Price)
Inflation and Oil Price
(Inflation)
+
Portfolio Beta * Portfolio Beta * 1.00
(Oil Price)
(Oil Price)
+
Portfolio Beta * Portfolio Beta * Correlation Between
Inflation and Oil Price
(Oil Price)
(Inflation)
=
Portfolio Systematic Risk
Risk Factor Models

If your factors have truly captured the
structure behind the correlations between
stock returns, then portfolio diversifiable risk
can be estimated by summing the products
of:
– The diversifiable risk of each stock
– The square of its portfolio weight.
Diversifiable Risk Decreases with the Number of Stocks in a Portfolio
.10
.09
Diversifiable Risk
.08
.07
.06
.05
.04
.03
.02
.01
.00
1
4
7
10
13
16
19
22
25
Number of Stocks in Portfolio
28
31
34
37
40
Study by Fedenia
University of Wisconsin

Study covers all NYSE stocks (1963-94).

Goal is to find lowest volatility portfolio for next 12
months for 100 randomly selected stocks.

The naïve estimate finds the low volatility portfolio over
the previous 60 months.

Creates a risk model using, as factors, 5 portfolios that
account for the correlations between the 100 stocks.

Finds the lowest volatility portfolio with risk model

Repeats process 270 times for each year.
Study by Fedenia
University of Wisconsin

Average annualized volatility in the next
year using the naïve estimate: 12.32%.

Average annualized volatility in the next
year using the risk factor model: 11.93%.
Expected Return Factor Models

The factors in an expected return model
represent the character of the companies.

They might include the history of their stock
prices, its size, financial condition, cheapness
or dearness of prices in the market, etc.

Factor payoffs are estimated by relating
individual stock returns to individual stock
characteristics over the cross-section of a
stock population (here the largest 3000 U.S.
stocks).
Five Factor Families





Risk
Liquidity
Price level
Growth potential
Price history
Relationship Between Total Return and Book to Price Ratio
January, 1981
100%
Total Return
50%
0%
Line of Best Fit
-50%
-100%
-1.5
-1.0
-0.5
0.0
0.5
1.0
Book to Price
1.5
2.0
2.5
3.0
The Most Important Factors


The monthly slopes (payoffs) are averages
over the period 1979 through mid 1986.
“T” statistics on the averages are
computed, and the stocks are ranked by
the absolute values of the “Ts”.
Most Important Factors
1979/01 through
1986/06
1986/07 through 1993/12
Factor
Mean
Confidence
Mean
Confidence
One-month excess return
-0.97%
99%
-0.72%
99%
0.52%
99%
0.52%
99%
Trading volume/market
cap
-0.35%
99%
-0.20%
98%
Two-month excess return
-0.20%
99%
-0.11%
99%
Earnings to price
0.27%
99%
0.26%
99%
Return on equity
0.24%
99%
0.13%
97%
Book to price
0.35%
99%
0.39%
99%
-0.10%
99%
-0.09%
99%
Six-month excess return
0.24%
99%
0.19%
99%
Cash flow to price
0.13%
99%
0.26%
99%
Twelve-month excess
return
Trading volume trend
Projecting Expected Return

The components of expected return are
obtained by multiplying the projected payoff to
each factor (here the average of the past 12)
by the stock’s current exposure to the factor.

Exposures are measured in standard
deviations from the cross-sectional mean.

The individual components are then summed
to obtain the aggregate expected return for
the next period (here a month).
Estimating Expected Stock Returns
Factor
Exposure
Book\Price
1.5 S.D.
x
20 B.P.
=
30 B.P.
Short-Term Reversal 1.0 S.D.
.
.
.
.
.
.
.
.
.
.
.
.
x
-10 B.P.
.
.
.
.
.
.
=
-10 B.P.
.
.
.
.
.
.
x
-20 B.P.
=
40 B.P.
Trading Volume
-2 S.D.
Payoff
Total Excess Return
Component
80 B.P.
The Model’s Out-of-sample
Predictive Power

The 3000 stocks are ranked by expected
return and formed into deciles (decile 10
highest).

The performance of the deciles is observed in
the next month.

The expected returns are re-estimated, and
the deciles are re-ranked.

The process continues through 1993.
Logarithm of Cumulative Decile Performance
2.5
10
2
9
8
7
6
1.5
5
4
1
3
0.5
2
0
1
-0.5
-1
80Q1 81Q1 82Q1 83Q1 84Q1 85Q1 86Q1 87Q1 88Q1 89Q1 90Q1 91Q1 92Q1 93Q1 94Q1 95Q1 96Q1 97Q1 98Q1
Date
Realized Return for 1984 by Decile
Realized Return
30%
20%
10%
(Y/X = 5.5%)
0%
Y
-10%
X
-20%
-30%
-40%
0
1
2
3
4
5
6
7
8
9
10
Decile
Extension of Study to Other Periods
Nardin Baker

The same family of factors is used on a
similar stock population.

Years before and after initial study period are
examined to determine slopes and spreads
between decile 1 and 10.
Slope and Spread
100%
90%
difference
slope
80%
70%
60%
50%
40%
30%
20%
10%
0%
1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1998
Years
Decile Risk Characteristics

The characteristics reflect the character of the
deciles over the period 1979-1993.
Fama-French
Three- Factor Model

Monthly decile returns are regressed on
monthly differences in the returns to the
following:
– S&P 500 and T bills
– The 30% of stocks that are smallest and
largest
– The 30% of stocks with highest book-to-price
and the lowest.
Sensitivities (Betas) to Market Returns
Market Beta
1.25
1.2
1.15
1.1
1.05
Decile
1
1
0.95
2
3
4
5
6
7
8
9
10
Sensitivities (Betas) to Relative Performance of Small and Large Stocks
Size Beta
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9
10
Decile
Sensitivities (Betas) to Relative
Performance of Value and Growth Stocks
Value/Growth
Beta
0.3
0.2
0.1
8
0
1
-0.1
-0.2
2
3
4
5
6
7
9
10
Decile
Fundamental
Characteristics
Averaged over all stocks in
each decile and over all months
(1979-83).
Risk
Decile Risk Characteristics
Interest Coverage
Market Beta
Debt to Equity
Stock
Volatility
50%
8
7
Coverage
41.42%
6.63
40%
6
33.22%
5
Volatility
30%
4
20%
3
2
1
1.76
10%
Beta
1.21
1.03
1.00
Debt to Equity
0.85
0%
0
1
2
3
4
5
6
Decile
7
8
9
10
Liquidity
Size and Liquidity Characteristics
Stock Price
Size
Trading Volume
$70
$1,100
$60.89
$60
Trading Volume
$1011
$50
$1,000
$900
$42.42
$40
$800
Size
$30
$20
$30.21
Price
$14.93
$700
$600
$10
$500
$470
$0
$400
1
2
3
4
5
Decile
6
7
8
9
10
Price History
Technical History
Excess Return
30.01%
30%
12 months
16.60%
20%
6 months
10%
0%
-10%
-20%
3 months
8.83%
0.09%
2 months
1.21%
-1.80%
1 month
-0.14%
-6.89%
-12.14%
-15.74%
1
2
3
4
5
Decile
6
7
8
9
10
Profitability
Current Profitability
Profit Margin
Return on Assets
Return on Equity
Earnings Growth
Asset Turnover
Asset Turnover
20%
115%
120%
Return on Equity
15.39%
10%
0%
Profit Margin
7.86%
Return on Assets
6.50%
110%
100%
Earnings Growth 0.95%
90%
-10%
80%
1
2
3
4
5
6
Decile
7
8
9
10
Trends in
Profitability
Profitability Trends
(Growth In)
5 Year
Trailing Growth
Asset Turnover
0.0%
-0.13%
Profit Margin
-0.5%
Return on Assets
-0.95%
-1.0%
-1.11%
Return on Equity
-1.18%
-1.5%
1
2
3
4
5
Decile
6
7
8
9
10
Cheapness in
Stock Price
Price Level
Cash Flow-to-Price
Earnings-to-Price
Dividend-to-Price
Sales-to-Price
Book-to-Price
20%
214%
Sales-to-Price
207%
17%
Cash Flow-to-Price
10%
150%
Earnings-to-Price
10%
6%
3.69%
Dividend-to-Price
2.19%
0% 81%
200%
100%
80%
Book-to-Price
50%
-1.55%
-10%
0%
1
2
3
4
5
6
Decile
7
8
9
10
Simulation of
Investment Performance

Efficient portfolios are constructed
quarterly, assuming 2% round-trip
transactions costs within the Russell 1000
population.
–
–
–
–
–
Turnover controlled to 20% to 40% per annum.
Maximum stock weight is 5%.
No more that 3X S&P 500 cap weight in any stock.
Industry weight to within 3% of S&P 500.
Turnover controlled to within 20% to 40%.
Annualized total return
Optimized Portfolios in the Russell 1000 Population
1979-1993
H
20%
I
18%
G
1000
Index
16%
14%
12%
L
10%
12%
13%
14%
15%
16%
17%
18%
Annualized volatility of return
Possible Sources of Bias

Survival bias:
– Excluding firms that go inactive during test
period.

Look-ahead bias:
– Using data that was unavailable when you trade.
Bid-asked bounce:
– If this month’s close is a bid, there is 1 chance in
4 that next and last month’s close will be at an
asked, showing reversals.
Data snooping:
– Using the results of prior studies as a guide and
then testing with their data.
Data mining:
– Spinning the computer.



Using the Ad Hoc Expected Return
Factor Model Internationally


The most important factors across the 5
largest stock markets (1985-93).
Simulating investment performance:
– Within countries, constraints are those stated
previously.
– Positions in countries are in accord with
relative total market capitalization.
Mean Payoffs and Confidence Probabilities for the
Twelve Most Important Factors of the World (1985-93)
United States
Mean
Germany
Confidence Mean
Level
Confidence
France
United
Kingdom
Japan
Mean
Confidence Mean
Confidence Mean
Confidence
-0.33%
Level
(Different
From Zero)
99%
-0.22%
Level
(Different
From Zero)
99%
-0.39%
Level
(Different
From Zero)
99%
One-month stock return
-0.32%
99%
-0.26%
Level
(Different
From Zero)
99%
Book to price
0.14%
99%
0.16%
99%
0.18%
99%
0.12%
99%
0.12%
99%
Twelve-month stock return
0.23%
99%
0.08%
99%
0.12%
99%
0.21%
99%
0.04%
86%
Cash flow to price
0.18%
99%
0.08%
99%
0.15%
99%
0.09%
99%
0.05%
91%
Earnings to price
0.16%
99%
0.04%
83%
0.13%
99%
0.08%
99%
0.05%
94%
Sales to price
0.08%
99%
0.10%
99%
0.05%
99%
0.05%
91%
0.13%
99%
Three-month stock return
-0.01%
38%
-0.14%
99%
-0.08%
99%
-0.08%
99%
-0.26%
99%
Debt to equity
-0.06%
96%
-0.06%
96%
-0.09%
99%
-0.10%
99%
-0.01%
31%
Variance of total return
-0.06%
94%
-0.04%
83%
-0.12%
99%
-0.01%
38%
-0.11%
99%
Residual variance
-0.08%
99%
-0.04%
80%
-0.09%
99%
-0.03%
77%
0.00%
8%
Five-year stock return
-0.01%
31%
-0.02%
51%
-0.06%
94%
-0.06%
96%
-0.07%
98%
Return on equity
0.11%
99%
0.01%
31%
0.10%
99%
0.04%
80%
0.05%
92%
(Different
From Zero)
Optimization in France, Germany, U. K., Japan and across
the five largest countries. 1985-1994
19.0%
17.0%
H
five largest
countries
(including U.S.)
15.0%
Annualized
total
return
G

H France  H


France
I
I
index
u
G
U. K.
G
index
I
U. K.
index of
five largest
countries
n
Japan
H
13.0%

Germany

I

G
11.0%
9.0%
H
I
Germany
t
index


G
7.0%
5.0%
10%
12%
14%
16%
18%
Annualized volatility of return
20%
22%
Japan
index
24%
Expansion of the
1996 Study
Nardin Baker
Performance In Different Countries
1985 - 1998 (September)
30%
25%
20%
Return
15%
10%
5%
0%
12%
14%
16%
18%
20%
22%
24%
26%
28%
30%
32%
Volatility
AUS
GBR
BEL
HKG
CAN
ITA
CHE
JPN
DEU
NLD
ESP
SWE
FRA
USA
Actual
Performance
Industrifinans Forvaltning
Global Fund
180%
160%
140%
170.65%
Industrifinans World
144.04%
Morgan Stanley World NOK
120%
100%
80%
60%
40%
20%
0%
-20%
jan.95 apr
jul
oct jan.96 apr
jul
oct jan.97 apr
jul
oct jan.98 apr
jul
oct jan.99 apr
Cumulative return since inception (31 October 1994 )
Industrifinans Contact: Ole Jakob Wold +47.22.473300
Past performance is not a guarantee of future results
Performance before fees, after transactions costs and includes reinvested dividends
Measured in Norwegian Krone (NOK), Managed to stay neutral in country and sector weights
Managed using modified (Haugen-Baker) JFE Expected Return Model by Baker at Grantham Mayo Van Otterloo, Inc.
Industrifinans Forvaltning
Probability that the expected return to the Global Fund
has been higher than the Morgan Stanley World Index
100%
92.2%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
dec.94mar jun
sep dec.95mar jun
sep dec.96mar jun
sep dec.97mar jun
sep dec.98mar
Probability of out-performing the Morgan Stanley World Index since inception (31 October 1994)
Performance measured before fees, after transactions costs and includes reinvested dividends
Industrifinans Contact: Ole Jakob Wold +47.22.473300
Measured in Norwegian Krone (NOK), Managed to stay neutral in country and sector weights
Past performance is not a guarantee of future results Managed using modified (Haugen-Baker) JFE Expected Return Model by Baker at Grantham Mayo Van Otterloo, Inc.
140%
Analytic Investors
Enhanced Equity Institutional Composite
130.31%
120%
100%
Institutional Composite
S&P 500
102.73%
80%
60%
40%
20%
0%
nov.96jan.97 mar may
jul
sep
nov jan.98 mar may
jul
sep
nov jan.99 mar
Cumulative return since inception (30 Sep 1996)
AI Contact: Dennis Bein 213.688.3015
Past performance is not a guarantee of future results
Performance before fees, after transactions costs and includes reinvested dividends
Managed using Haugen expected return model & Barra optimizer & risk model
Analytic Investors
Probability that the expected return to the Enhanced Equity
Institutional Composite has been higher than the S&P 500 Index
100%
93.3%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
nov.96
feb.97
may
aug
nov
feb.98
may
aug
nov
feb.99
Probability of out-performing the S&P 500 Index since inception (30 Sep 1996)
AI Contact: Dennis Bein 213.688.3015
Past performance is not a guarantee of future results
Performance before fees, after transactions costs and includes reinvested dividends
Managed using Haugen expected return model & Barra optimizer & risk model
Performance of 413 Mutual Funds
10/96 - 9/98


“T” stat. on mean monthly out-performance
to S&P 500.
Large funds with highest correlation with
S&P with a 36 month history.
Three Year Out-(Under)-Performance T-Distribution
25%
Percent of sample
20%
15%
10%
5%
0%
to -5.0 -5.0 to -4.5 to -4.0 to -3.5 to -3.0 to -2.5 to -2.0 to -1.5 to -1.0 to -0.5 to 0.0 to
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
0.5 to
1.0
1.0 to
1.5
T-statistics for mean out-(under) performance
1.5 to
2.0
2.0 to
Why.
Will return to “why”
later on.
But first …
A Test of Relative
Predictive Power
1980 -1997
Model employing factors
exploiting the market’s tendencies
to over- and under-react
vs.
Models employing risk factors
only.
The Ad Hoc Expected
Return Factor Model






Risk
Liquidity
Profitability
Price level
Price history
Earnings revision and surprise
Decile Returns for the Ad Hoc Factor Model
(1980 through mid 1997)
Average
Annualized
Return
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
Decile
1
2
3
4
5
6
7
8
9
10
The Capital Asset
Pricing Model


Market beta measured over the trailing
3 to 5-year periods).
Stocks ranked by beta and formed into
deciles monthly.
Decile Returns for CAPM Model
Average
Annualized
Return
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
1
2
3
4
5
6
7
8
9
10
Decile
The Arbitrage Pricing Theory

Macroeconomic Factors
–
–
–
–
–

Monthly T-bill returns
Long-term T-bond returns less short-term
T-bond returns less low-grade
Monthly inflation
Monthly change in industrial production
Beta Estimation
– Betas re-estimated monthly by regressing stock
returns on economic factors over trailing 3-5
years

Payoff Projection
– Next month’s payoff is average of trailing 12
months
Average Returns for APT Model
Average
Annualized
Return
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
1
2
3
4
5
6
7
8
9
10 Decile
Overall Results

Ad Hoc Expected Return Factor Model
– Average Annualized Spread Between Deciles 1 & 10
– Years with Negative Spreads

46.04%
0 years
Models Based on MODERN FINANCE
– CAPM
• Average Annualized Spread Between Deciles 1 & 10
• Years with Negative Spreads
– APT
• Average Annualized Spread Between Deciles 1 & 10
• Years with Negative Spreads
-6.94%
13 years
6.06%
6 years
Getting to Heaven
and Hell in the
Stock Market
The Position of Portfolios in Abnormal Profit Space
True Abnormal Profit
Super Stocks
Priced Abnormal Profit
Stupid Stocks
The Position of Portfolios in Abnormal Profit Space
True Abnormal Profit
Investment
Heaven
Priced Abnormal Profit
Stupid Stocks
The Position of Portfolios in Abnormal Profit Space
True Abnormal Profit
Investment
Heaven
Priced Abnormal Profit
Investment
Hell
The Position of Portfolios in Abnormal Profit Space
True Abnormal Profit
Investment
Heaven
Can’t get
to heaven
by going
around
the corner
You
must
go
directly
to
heaven
Priced Abnormal Profit
Investment
Hell
How do you get to
Investment Heaven?
Three main steps:
– Use risk factor models to estimate
variances and covariances
– Use ad hoc expected return factor
models to estimate expected returns
– Combine this information into optimal
portfolios through Markowitz optimization