The Inefficient Market

The Inefficient Market
What Pays Off and Why Part 1: What Pays Off Abridged 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 Uses and Rights of Financial Claims (Graham & Dodd) (Dewing) Foundation: Accounting and Law

Old Finance Best investment strategy =
Stock-picking / value-investing approach, such as Warren Buffett uses

The Old Finance Bob goes to college 1930’s 40’s 50’s 60’s 70’s 80’s 90’s beyond Modern Finance Modern Finance Theme: Valuation Based on Rational Economic Behavior Paradigms: Optimization Irrelevance CAPM EMH (Markowitz) (Modigliani & Miller) (Sharpe, Lintner & Mossen) (Fama) Foundation: Financial Economics

Modern Finance Optimal investment strategy =
Invest in index funds, try to match market as closely as possible at as low a cost as possible

The Old Finance Bob goes to college The New Finance 1930’s 40’s 50’s 60’s 70’s 80’s 90’s beyond Modern Finance The New Finance Theme: Inefficient Markets Paradigms: Inductive ad hoc Factor Models Behavioral Models Expected Return Risk (Haugen) (Chen, Roll & Ross) (Kahneman & Tversky) Foundation: Statistics, Econometrics, and Psychology

New Finance Market is inefficient, but hard to beat nonetheless
Optimal investment approach = Use Markowitz optimization to create optimal portfolios APT Risk-factor model to model risk Ad hoc inductive expected return factor model to model expected returns Quantitative hedge fund, such as Enhanced index fund Long / short fund

Hedge Fund Risk/Return Profile
Ten Years Ending 2/03

Rest of Book Part I: Describes one approach to developing a quantitative hedge fund Focus of this class Part II: Discusses why that approach works Chapters 9 – 12 won’t be covered in class, but can read for own pleasure

Part I: What Pays Off

Probability Distribution For Returns to a Portfolio
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 modeled using an APT-type risk-factor model Measures extent to which stocks’ returns [jointly] move up and down over time Estimated using time-series data Diversifiable risk is reduced through optimal diversification

Expected Return Factor Models
Expected return factor models measure / predict the extent to which the stocks’ returns are different from each other within a given period of time.

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. Unlike CAPM and APT, not only risk factors such as market beta or APT betas are included 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 Profitability
Market and APT betas, TIE, debt ratio, etc., values and trends thereof Liquidity Market cap., price, trading volume, etc. Price level E/P, B/P, Sales/P, CF/P, Div/P Profitability Profit margin, ROE, ROA, earnings surprise, etc. Price history (technical factors) Excess return over past 1, 2, 3, 6, 12, 24, & 60 months

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 One-month excess return -0.97% 99% -0.72% return Twelve-month excess 0.52% 99% Trading volume/market cap -0.35% 99% -0.20% 98% Two-month excess return -0.20% 99% -0.11% Earnings to price 0.27% 99% 0.26% Return on equity 0.24% 99% 0.13% 97% Book to price 0.35% 99% 0.39% Trading volume trend -0.10% 99% -0.09% Six-month excess return 0.24% 99% 0.19% Cash flow to price 0.13% 99% 0.26%

The Most Important Factors
Among the factors that are significant (i.e., that can be used to distinguish between which companies will have higher returns and which will have lower returns) are: A number of liquidity factors Various fundamental factors, indicating value with growth Technical factors, indicating short-term reversals and intermediate term momentum Suggest that technical factors provide marginal value when used in conjunction with fundamental analysis Notably, no CAPM or APT risk factors are included!

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 Payoff Component Book\Price 1.5 S.D. x 20 B.P. = 30 B.P. Short-Term Reversal 1.0 S.D. x -10 B.P. = . . . . . . Trading Volume -2 S.D. x -20 B.P. = 40 B.P. Total Excess Return 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

Realized Return for 1984 by Decile
3 4 5 6 7 8 9 10 Decile -40% -30% -20% -10% 0% 10% 20% 30% 1 2 Realized Return (Y/X = 5.5%) Y X

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 Years 1997 0% 10% 20% 30% 40% 50% 60% 70% 80% 90%
100% 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 Years 1998 difference slope

Decile Risk Characteristics
The characteristics reflect the character of the deciles over the period

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
10 Decile 1 2 3 4 5 6 7 8 9 0.95 1.05 1.1 1.15 1.2 1.25 Market Beta

Sensitivities (Betas) to Relative Performance of Small and Large Stocks
2 3 4 5 6 7 8 9 10 Decile 0.1 0.2 0.3 0.4 0.5 1 Size Beta

Sensitivities (Betas) to Relative
Performance of Value and Growth Stocks Decile 8 9 10 1 2 3 4 5 6 7 -0.2 -0.1 0.1 0.2 0.3 Value/Growth Beta

Fundamental Characteristics
Averaged over all stocks in each decile and over all months ( ).

Decile Risk Characteristics
Stock Volatility 1 2 3 4 5 6 7 8 9 10 Decile 0% Interest Coverage Market Beta Debt to Equity 10% 20% 30% 40% 50% Coverage 1.76 6.63 Volatility 41.42% 33.22% Beta 1.00 1.21 Debt to Equity 1.03 0.85

Liquidity

Size and Liquidity Characteristics
$0 $10 $20 $30 $40 $50 $60 $70 1 2 3 4 5 6 7 8 9 10 Decile Stock Price Trading Volume $400 $500 $600 $700 $800 $900 $1,000 $1,100 Size $42.42 $60.89 Trading Volume $470 $1011 Size $14.93 $30.21 Price

Price History

Technical History Decile Excess Return 1 2 3 4 5 6 7 8 9 10 -20% -10%
30% Excess Return 12 months -15.74% 30.01% 6 months -12.14% 16.60% 3 months -6.89% 8.83% 2 months -1.80% 1.21% 1 month 0.09% -0.14%

Profitability

Current Profitability
90% 100% 110% 120% Asset Turnover 2 3 4 5 6 7 8 9 10 Decile 80% -10% 0% 10% 20% 1 Profit Margin Return on Assets Return on Equity Earnings Growth Asset Turnover 115% Return on Equity 15.39% Profit Margin 7.86% Return on Assets 6.50% Earnings Growth 0.95%

Trends in Profitability

Profitability Trends (Growth In) 5 Year Trailing Growth Decile 1 2 3 4
6 7 8 9 10 Decile 5 Year Trailing Growth -1.5% -1.0% -0.5% 0.0% Return on Assets -1.11% Asset Turnover -0.13% Profit Margin -0.95% Return on Equity -1.18%

Cheapness in Stock Price

Price Level Sales-to-Price Book-to-Price Decile Cash Flow-to-Price
50% 100% 150% 200% Sales-to-Price Book-to-Price 3 4 5 6 7 8 9 10 Decile 0% -10% 10% 20% 1 2 Cash Flow-to-Price Earnings-to-Price Dividend-to-Price Sales-to-Price 214% 207% Cash Flow-to-Price 6% 17% Earnings-to-Price -1.55% 10% Dividend-to-Price 2.19% 3.69% Book-to-Price 81% 80%

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%.

Optimized Portfolios in the Russell 1000 Population
H 20% I 18% G 1000 Index 16% Annualized total return 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 ( ). 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 ( ) United Kingdom Mean Confidence Level (Different From Zero) -0.22% 99% 0.12% 0.21% 0.09% 0.08% 0.05% 91% -0.08% -0.10% -0.01% 38% -0.03% 77% -0.06% 96% 0.04% 80% United States Mean Confidence Level (Different From Zero) -0.32% 99% 0.14% 0.23% 0.18% 0.16% 0.08% -0.01% 38% -0.06% 96% 94% -0.08% 31% 0.11% Germany Mean Confidence Level (Different From Zero) -0.26% 99% 0.16% 0.08% 0.04% 83% 0.10% -0.14% -0.06% 96% -0.04% 80% -0.02% 51% 0.01% 31% France Mean Confidence Level (Different From Zero) -0.33% 99% 0.18% 0.12% 0.15% 0.13% 0.05% -0.08% -0.09% -0.12% -0.06% 94% 0.10% Japan Mean Confidence Level (Different From Zero) -0.39% 99% 0.12% 0.04% 86% 0.05% 91% 94% 0.13% -0.26% -0.01% 31% -0.11% 0.00% 8% -0.07% 98% 92% One-month stock return Book to price Twelve-month stock return Cash flow to price Earnings to price Sales to price Three-month stock return Debt to equity Variance of total return Residual variance Five-year stock return Return on equity

Optimization in France, Germany, U. K
Optimization in France, Germany, U. K., Japan and across the five largest countries 19.0% 17.0% 15.0% 13.0% 11.0% 9.0% 7.0% 5.0% l five largest countries (including U.S.) H I G n index of l G I H France France index u l U. K. H I G index Annualized total return l Japan H I G Japan index l t Germany Germany index H I G 10% 12% 14% 16% 18% 20% 22% 24% Annualized volatility of return

Expansion of the 1996 Study Nardin Baker

Performance In Different Countries
(September) 30% 25% 20% Return 15% 10% 5% 0% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 32% Volatility AUS BEL CAN CHE DEU ESP FRA GBR HKG ITA JPN NLD SWE USA

Actual Performance

Industrifinans Forvaltning
Global Fund -20% 0% 20% 40% 60% 80% 100% 120% 140% 160% 180% 170.65% Industrifinans World jan.95 apr jul oct jan.96 jan.97 jan.98 jan.99 Cumulative return since inception (31 October 1994) Morgan Stanley World NOK 144.04% Performance before fees, after transactions costs and includes reinvested dividends Industrifinans Contact: Ole Jakob Wold 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.

Probability that the expected return to the Global Fund
Industrifinans Forvaltning Probability that the expected return to the Global Fund has been higher than the Morgan Stanley World Index 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Performance measured before fees, after transactions costs and includes reinvested dividends Industrifinans Contact: Ole Jakob Wold 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. dec.94 mar jun sep dec.95 dec.96 dec.97 dec.98 Probability of out-performing the Morgan Stanley World Index since inception (31 October 1994) 92.2%

Enhanced Equity Institutional Composite
Analytic Investors Enhanced Equity Institutional Composite 0% 20% 40% 60% 80% 100% 120% 140% AI Contact: Dennis Bein Performance before fees, after transactions costs and includes reinvested dividends Past performance is not a guarantee of future results Managed using Haugen expected return model & Barra optimizer & risk model nov.96 jan.97 mar may jul sep nov jan.98 jan.99 Cumulative return since inception (30 Sep 1996) 130.31% Institutional Composite 102.73% S&P 500

Probability that the expected return to the Enhanced Equity
Analytic Investors Probability that the expected return to the Enhanced Equity Institutional Composite has been higher than the S&P 500 Index 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% AI Contact: Dennis Bein Performance before fees, after transactions costs and includes reinvested dividends Past performance is not a guarantee of future results Managed using Haugen expected return model & Barra optimizer & risk model nov.96 feb.97 may aug nov feb.98 feb.99 Probability of out-performing the S&P 500 Index since inception (30 Sep 1996) 93.3%

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
0% 5% 10% 15% 20% 25% to -5.0 -5.0 to -4.5 -4.5 to -4.0 -4.0 to -3.5 -3.5 to -3.0 -3.0 to -2.5 -2.5 to -2.0 -2.0 to -1.5 -1.5 to -1.0 -1.0 to -0.5 -0.5 to 0.0 0.0 to 0.5 0.5 to 1.0 1.0 to 1.5 1.5 to 2.0 2.0 to T-statistics for mean out-(under) performance Percent of sample

Part II: Why

Can read Chapters 9 through 12 at your own leisure.

The Great Race (From Ch. 13)

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 (“deductive” models of modern finance).

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)
2 3 4 5 6 7 8 9 10 Decile 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 1 Average Annualized Return

The Capital Asset Pricing Model
Market beta measured over the trailing to 5-year periods). Stocks ranked by beta and formed into deciles monthly.

Decile Returns for CAPM Model
3 4 5 6 7 8 9 10 Decile 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 1 2 Average Annualized Return

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
Annualized 2 3 4 5 6 7 8 9 10 Decile 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 1 Average Return

Overall Results Ad Hoc Expected Return Factor Model
Average Annualized Spread Between Deciles 1 & % Years with Negative Spreads years Models Based on MODERN FINANCE CAPM Average Annualized Spread Between Deciles 1 & % Years with Negative Spreads years APT Average Annualized Spread Between Deciles 1 & % Years with Negative Spreads years

Getting to Heaven and Hell in the Stock Market (From Ch. 14)

Super Stocks Stupid Stocks
The Position of Portfolios in Abnormal Profit Space True Abnormal Profit Efficient Market Line Super Stocks Priced Abnormal Profit Stupid Stocks

Investment Heaven Stupid Stocks
The Position of Portfolios in Abnormal Profit Space True Abnormal Profit Efficient Market Line Investment Heaven Priced Abnormal Profit Stupid Stocks

Investment Heaven Investment Hell
The Position of Portfolios in Abnormal Profit Space True Abnormal Profit Efficient Market Line Investment Heaven Priced Abnormal Profit Investment Hell

Investment Heaven Investment Hell
The Position of Portfolios in Abnormal Profit Space True Abnormal Profit Efficient Market Line Investment Heaven You must go directly to heaven Can’t get to heaven by going around the corner 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 determine desired stock characteristics and estimate expected returns Cannot just screen sequentially (“going around the corner”) for stocks with the desired characteristics Combine this information into optimal portfolios through Markowitz optimization

The Inefficient Market

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