The Inefficient Market Prentice Hall 1999 Visit our web-site at HaugenSystems.com What Pays Off and Why Part 1: What Pays Off

Background l The evolution of academic finance

The Evolution of Academic Finance 1930’s40’s50’s60’s70’s80’s90’sbeyond 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 The Old Finance

1930’s40’s50’s60’s70’s80’s90’sbeyond The Old Finance Modern Finance Bob goes to college Modern Finance Theme:Valuation Based on Rational Economic Behavior Paradigms: Optimization Irrelevance CAPM EMH (Markowitz) ( Modigliani & Miller) (Sharpe, Lintner & Mossen) (Fama) Foundation:Financial Economics The Evolution of Academic Finance

1930’s40’s50’s60’s70’s80’s90’sbeyond The Old Finance Modern Finance The New Finance Bob goes to college 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 The Evolution of Academic Finance

Background l The evolution of academic finance l Estimating expected return with the Asset Pricing Models of Modern Finance –CAPM Strong assumption - strong prediction Strong assumption - strong prediction

Expected Return Risk (Return Variability) Market Index on Efficient Set Market Index A B C Market Beta Expected Return Corresponding Security Market Line x x x x x x x x x x x x x x x x x x x x x x x x

Market Index Expected Return Risk (Return Variability) Market Index Inside Efficient Set Corresponding Security Market Cloud Expected Return Market Beta

Background l The evolution of academic finance l 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 l Estimating the macro-economic betas

Relationship Between Return to General Electric and Changes in Interest Rates -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% Return to G.E. -10%-5%0%5%10% Percentage Change in Yield on Long-term Govt. Bond Line of Best Fit April, 1987

l No-arbitrage condition for asset pricing l If risk-return relationship is non-linear, you can arbitrage The Arbitrage Pricing Theory l Estimating the macro-economic betas

Curved Relationship Between Expected Return and Interest Rate Beta -15% -5% 5% 15% 25% 35% Expected Return -313 Interest Rate Beta A B C D E F

l Two stocks l A: E(r) = 4%; Interest-rate beta = l B: E(r) = 26%; Interest-rate beta = 1.83 l Invest 54.54% in E and 45.46% in A l Portfolio E(r) =.5454 * 26% * 4% = 16% l Portfolio beta =.5454 * * = 0 l With many combinations like this, you can create a risk-free portfolio with a 16% expected return. The Arbitrage Pricing Theory

l Two different stocks l C: E(r) = 15%; Interest-rate beta = l D: E(r) = 25%; Interest-rate beta = 1.00 l Invest 50.00% in E and 50.00% in A l Portfolio E(r) =.5000 * 25% * 15% = 20% l Portfolio beta =.5000 * * = 0 l 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.

l No-arbitrage condition for asset pricing l If risk-return relationship is non-linear, you can arbitrage. l Attempts to arbitrage will force linearity in relationship between risk and return. The Arbitrage Pricing Theory

APT Relationship Between Expected Return and Interest Rate Beta -15% -5% 5% 15% 25% 35% Expected Return -313 Interest Rate Beta A B C D E F

What Pays Off.

Probability Distribution For Returns to a Portfolio Possible Rates of Returns Probability Expected Return Variance of Return

Risk Factor Models l The variance of stock returns can be split into two components: l Variance = systematic risk + diversifiable risk l Systematic risk is computed using the following spreadsheet:

l 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. Risk Factor Models

Relationship Between Return to General Electric and Changes in Interest Rates -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% Return to G.E. -10%-5%0%5%10% Percentage Change in Yield on Long-term Govt. Bond Line of Best Fit April, 1987

Spreadsheet for Computing Systematic Risk Portfolio Beta (Inflation) (Oil Price) Correlation Between Inflation and Oil Price Portfolio Beta (Inflation) (Oil Price) Correlation Between Inflation and Oil Price

l Factor correlations can be estimated over a longer period because they are, presumably, more stable over time. l This may increase the predictive accuracy of factor models relative to more naïve historical estimates. Risk Factor Models

Relationship Between Rate of Inflation and Percentage Change in Price of Oil Monthly Rate of Inflation Monthly Percentage Change in Price of Oil Line of Best Fit

Computing Portfolio Systematic Risk 1.00 Portfolio Beta * Portfolio Beta * 1.00 (Inflation) +Portfolio Beta * Portfolio Beta * Correlation Between (Inflation) (Oil Price) Inflation and Oil Price Portfolio Beta * Portfolio Beta * 1.00 (Oil Price) +Portfolio Beta * Portfolio Beta * Correlation Between (Inflation) (Oil Price) Inflation and Oil Price = Portfolio Systematic Risk

l 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. Risk Factor Models

DiversifiableRisk Decreases with the Number of Stocks in a Portfolio Diversifiable Risk Decreases with the Number of Stocks in a Portfolio Diversifiable Risk Number of Stocks in Portfolio

Study by Fedenia University of Wisconsin l Study covers all NYSE stocks ( ). l Goal is to find lowest volatility portfolio for next 12 months for 100 randomly selected stocks. l The naïve estimate finds the low volatility portfolio over the previous 60 months. l Creates a risk model using, as factors, 5 portfolios that account for the correlations between the 100 stocks. l Finds the lowest volatility portfolio with risk model l Repeats process 270 times for each year.

12.32%. l Average annualized volatility in the next year using the naïve estimate: 12.32% %. l Average annualized volatility in the next year using the risk factor model: 11.93%. Study by Fedenia University of Wisconsin

Expected Return Factor Models l The factors in an expected return model represent the character of the companies. l They might include the history of their stock prices, its size, financial condition, cheapness or dearness of prices in the market, etc. l 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 l Risk l Liquidity l Price level l Growth potential l Price history

Book to Price -100% -50% 0% 50% 100% -1.5 Total Return Relationship Between Total Return and Book to Price Ratio January, 1981 Line of Best Fit

The Most Important Factors l The monthly slopes (payoffs) are averages over the period 1979 through mid l “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/ /07 through 1993/12 FactorMeanConfidenceMeanConfidence One-month excess return -0.97%99%-0.72%99% return Twelve-month excess 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% Trading volume trend -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%

Projecting Expected Return l 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. l Exposures are measured in standard deviations from the cross-sectional mean. l The individual components are then summed to obtain the aggregate expected return for the next period (here a month).

FactorExposurePayoffComponent Book\Price1.5 S.D.x20 B.P.=30 B.P. Short-Term Reversal1.0 S.D.x-10 B.P.= Estimating Expected Stock Returns 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 l The 3000 stocks are ranked by expected return and formed into deciles (decile 10 highest). l The performance of the deciles is observed in the next month. l The expected returns are re-estimated, and the deciles are re-ranked. l The process continues through 1993.

Logarithm of Cumulative Decile Performance

Decile -40% -30% -20% -10% 0% 10% 20% 30% 012 Realized Return Realized Return for 1984 by Decile Realized Return for 1984 by Decile (Y/X = 5.5%) Y X

Extension of Study to Other Periods Nardin Baker l The same family of factors is used on a similar stock population. l Years before and after initial study period are examined to determine slopes and spreads between decile 1 and 10.

1997 0% 10% 20% 30% 40% 50% 60% 70% 80% 90%100% Years 1998 difference slope Slope and Spread

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

Fama-French Three- Factor Model l 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 Market Beta

Sensitivities (Betas) to Relative Performance of Small and Large Stocks Decile Size Beta

Sensitivities (Betas) to Relative Performance of Value and Growth Stocks Performance of Value and Growth Stocks Decile Value/Growth Beta Beta

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

Risk

Decile Risk Characteristics Debt to Equity Stock Volatility Decile 0% Interest Coverage Market Beta Debt to Equity Volatility 41.42% 33.22% 10% 20% 30% 40% 50% Coverage Beta

Liquidity

Size and Liquidity Characteristics $0 $10 $20 $30 $40 $50 $60 $ Decile Stock Price Trading Volume $400 $500 $600 $700 $800 $900 $1,000 $1,100 Size $14.93 $30.21 Price $470 $1011 Size $42.42$60.89

Price History

Technical History Decile -20% -10% 0% 10% 20% 30% Excess Return 2 months -1.80% 1.21% 12 months %30.01% 3 months -6.89%8.83% 6 months %16.60% 1 month 0.09%-0.14%

Profitability

Current Profitability Asset Turnover 115% Return on Equity 15.39% Profit Margin 7.86% Return on Assets 6.50% 90% 100% 110% 120% Asset Turnover Decile 80%-10% 0% 10% 20% 1 Profit Margin Return on Assets Return on Equity Earnings Growth 0.95%

Trends in Profitability

Decile 5 Year Trailing Growth -1.5% -1.0% -0.5% 0.0% Profitability Trends (Growth In) Asset Turnover -0.13% Profit Margin -0.95% Return on Assets -1.11% Return on Equity -1.18%

Cheapness in Stock Price

Price Level Sales-to-Price 214% 207% Cash Flow-to-Price 6% 17% Earnings-to-Price -1.55% 10% Dividend-to-Price 2.19% 3.69% 50% 100% 150% 200% Sales-to-Price Book-to-Price Decile 0% -10% 0% 10% 20% 12 Cash Flow-to-Price Earnings-to-Price Dividend-to-Price Book-to-Price 81% 80%

Simulation of Investment Performance l 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%.

10% 12% 14% 18% 16% 20% 12% Annualized total return 17%18%13%14%15%16% Annualized volatility of return 1000Index G I H L Optimized Portfolios in the Russell 1000 Population

Possible Sources of Bias l Survival bias: –Excluding firms that go inactive during test period. l Look-ahead bias: –Using data that was unavailable when you trade. l 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. l Data snooping: –Using the results of prior studies as a guide and then testing with their data. l Data mining: –Spinning the computer.

Using the Ad Hoc Expected Return Factor Model Internationally l The most important factors across the 5 largest stock markets ( ). l 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 ( ) 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 United States Mean Confidence Level (Different From Zero) -0.32%99% 0.14%99% 0.23%99% 0.18%99% 0.16%99% 0.08%99% -0.01%38% -0.06%96% -0.06%94% -0.08%99% -0.01%31% 0.11%99% Germany Mean Confidence Level (Different From Zero) -0.26%99% 0.16%99% 0.08%99% 0.08%99% 0.04%83% 0.10%99% -0.14%99% -0.06%96% -0.04%83% -0.04%80% -0.02%51% 0.01%31% France France Mean Confidence Level (Different From Zero) -0.33%99% 0.18%99% 0.12%99% 0.15%99% 0.13%99% 0.05%99% -0.08%99% -0.09%99% -0.12%99% -0.09%99% -0.06%94% 0.10%99% UnitedKingdom Mean Confidence Level (Different From Zero) -0.22%99% 0.12%99% 0.21%99% 0.09%99% 0.08%99% 0.05%91% -0.08%99% -0.10%99% -0.01%38% -0.03%77% -0.06%96% 0.04%80% Japan Mean Confidence Level (Different From Zero) -0.39%99% 0.12%99% 0.04%86% 0.05%91% 0.05%94% 0.13%99% -0.26%99% -0.01%31% -0.11%99% 0.00%8% -0.07%98% 0.05%92%

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

Expansion of the 1996 Study Nardin Baker

Performance In Different Countries (September) (September) 0% 5% 10% 15% 20% 25% 30% 12%14%16%18%20%22%24%26%28%30%32% Volatility Return AUSBELCANCHEDEUESPFRA GBRHKGITAJPNNLDSWEUSA

Actual Performance

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. Industrifinans Forvaltning Global Fund % % -20% 0% 20% 40% 60% 80% 100% 120% 140% 160%180% jan.95aprjuloctjan.96aprjuloctjan.97aprjuloctjan.98aprjuloctjan.99apr Cumulative return since inception (31 October 1994 ) Industrifinans World Morgan Stanley World NOK

Industrifinans Forvaltning Probability that the expected return to the Global Fund has been higher than the Morgan Stanley World Index 92.2% 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.94marjunsepdec.95marjunsepdec.96marjunsepdec.97marjunsepdec.98mar Probability of out-performing the Morgan Stanley World Index since inception (31 October 1994)

130.31% 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.96jan.97marmayjulsepnovjan.98marmayjulsepnovjan.99mar Cumulative return since inception (30 Sep 1996) Institutional Composite S&P 500

Analytic Investors Probability that the expected return to the Enhanced Equity Institutional Composite has been higher than the S&P 500 Index 93.3% 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.96feb.97mayaugnovfeb.98mayaugnovfeb.99 Probability of out-performing the S&P 500 Index since inception (30 Sep 1996)

Performance of 413 Mutual Funds 10/96 - 9/98 l “T” stat. on mean monthly out-performance to S&P 500. l 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 to to to to to to to to -1.0 to to to to to to to T-statistics for mean out-(under) performance Percent of sample

Why.

Will return to “why” later on. But first …

A Test of Relative Predictive Power 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 l Risk l Liquidity l Profitability l Price level l Price history l Earnings revision and surprise

Decile Returns for the Ad Hoc Factor Model (1980 through mid 1997) (1980 through mid 1997) Decile 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 1AverageAnnualized Return

The Capital Asset Pricing Model l Market beta measured over the trailing 3 to 5-year periods). l Stocks ranked by beta and formed into deciles monthly.

Decile Returns for CAPM Model Decile 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 12AverageAnnualized Return

The Arbitrage Pricing Theory l 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 l Beta Estimation –Betas re-estimated monthly by regressing stock returns on economic factors over trailing 3-5 years l Payoff Projection –Next month’s payoff is average of trailing 12 months

Average Returns for APT Model Annualized Decile 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 1AverageReturn

Overall Results l Ad Hoc Expected Return Factor Model 46.04% –Average Annualized Spread Between Deciles 1 & % –Years with Negative Spreads 0 years l Models Based on MODERN FINANCE –CAPM -6.94%Average Annualized Spread Between Deciles 1 & % Years with Negative Spreads13 years –APT Average Annualized Spread Between Deciles 1 & % Years with Negative Spreads 6 years

Getting to Heaven and Hell in the Stock Market

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

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

The Position of Portfolios in Abnormal Profit Space Efficient Market Line True Abnormal Profit InvestmentHeaven InvestmentHell Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit Space Efficient Market Line True Abnormal Profit InvestmentHeaven InvestmentHell Priced Abnormal Profit Can’t get to heaven by going around the corner You must go directly to heaven

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