1. The Inefficient Stock Market What Pays Off and Why (Prentice Hall, 1999) Visit our web-site at HaugenSystems.com

2. What

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

4. 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.

5. 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.

6. 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

7. Spreadsheet for Computing Systematic Risk Portfolio Beta (Inflation) (Oil Price) 1.00 1.00 Correlation Between Inflation and Oil Price Portfolio Beta (Inflation) (Oil Price) Correlation Between Inflation and Oil Price 1.00 1.00

8. 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.

9. Relationship Between Rate of Inflation and Percentage Change in Price of Oil -0.500.511.52 Monthly Rate of Inflation -40 -20 0 20 40 60 80 100 120 140 Monthly Percentage Change in Price of Oil Line of Best Fit

10. 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 + 1.00 Portfolio Beta * Portfolio Beta * 1.00 (Oil Price) +Portfolio Beta * Portfolio Beta * Correlation Between (Inflation) (Oil Price) Inflation and Oil Price = Portfolio Systematic Risk

11. 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 (a) the diversifiable risk of each stock and (b) the square of its portfolio weight.

12. DiversifiableRisk Decreases with the Number of Stocks in a Portfolio Diversifiable Risk Decreases with the Number of Stocks in a Portfolio 40 1 4 7 10 13 16 19 22 25 28 31 34 37.00.01.02.03.04.05.06.07.08.09.10 Diversifiable Risk Number of Stocks in Portfolio

13. 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 stks.  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.

14. 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%

15. 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).

16. Five Factor Families  Risk  Liquidity  Price level  Growth potential  Price history

17. -0.50.00.51.01.52.02.53.0 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

18. 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”.

19. Most Important Factors 1979/01 through 1986/06 1986/07 through 1993/12 FactorMeanConfidenceMeanConfidence One-month excess return-0.97%99%-0.72%99% return Twelve-month excess0.52%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 price0.27%99%0.26%99% Return on equity0.24%99%0.13%97% Book to price0.35%99%0.39%99% Trading volume trend-0.10%99%-0.09%99% Six-month excess return0.24%99%0.19%99% Cash flow to price0.13%99%0.26%99%

20. 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)

21. 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.

22. 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. Then expected returns are re- estimated, and the deciles are re-ranked.  The process continues through 1993.

23. Logarithm of Cumulative Decile Performance

24. 345678910 Decile -40% -30% -20% -10% 0% 10% 20% 30% 012 Realized Return Realized Return for 1984 by Decile (Y/X = 5.5%) Y X

25. 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.

26. 1997 0% 10% 20% 30% 40% 50% 60% 70% 80% 90%100%19751977197919811983198519871989199119931995 Years 1998 difference slope Slope and Spread

27. Decile Risk Characteristics The characteristics reflect the character of the deciles over the period 1979-1993.

28. 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.

29. Sensitivities (Betas) to Market Returns 10 Decile 123456789 0.95 1 1.05 1.1 1.15 1.2 1.25 Market Beta

30. Sensitivities (Betas) to Relative Performance of Small and Large Stocks 2345678910 Decile 0 0.1 0.2 0.3 0.4 0.5 1 Size Beta

31. Sensitivities (Betas) to Relative Performance of Value and Growth Stocks Decile 89 10 1234567 -0.2 -0.1 0 0.1 0.2 0.3 Value/Growth Beta

32. Fundamental Characteristics Averaged over all stocks in each decile and over all months (1979-83)

33. Risk

34. Decile Risk Characteristics Debt to Equity 1.030.85 Stock Volatility 123456 7 8910 Decile 0% 0 1 2 3 4 5 6 7 8 Interest Coverage Market Beta Debt to Equity Volatility Volatility41.42%33.22% 10% 20% 30% 40% 50% Coverage Coverage1.76 6.63 Beta1.00 1.21

35. Liquidity

36. Size and Liquidity Characteristics $0 $10 $20 $30 $40 $50 $60 $70 12345678910 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 Trading Volume

37. Price History

38. Technical History 12345678910 Decile -20% -10% 0% 10% 20% 30% Excess Return 2 months -1.80% 1.21% 12 months -15.74%30.01% 3 months -6.89% 8.83% 6 months -12.14%16.60% 1 mon th 0.09%-0.14%

39. Profitability

40. 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 2345678910 Decile 80%-10% 0% 10% 20% 1 Profit Margin Return on Assets Return on Equity Earnings Growth 0.95%

41. Trends in Profitability

42. 12345678910 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%

43. Cheapness in Stock Price

44. 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 345678910 Decile 0%-10% 0% 10% 20% 12 Cash Flow-to-Price Earnings-to-Price Dividend-to-Price Book-to-Price81%80%

45. 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: 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%.

46. 10% 11% 12% 13% 14% 15% 18% 17% 16% 20% 19% 12% Annualized total return 17%18%13%14%15%16% Annualized volatility of return 1000 Index G I H L Optimized Portfolios in the Russell 1000 Population: 1979-1993

47. 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.

48. Using the Ad Hoc Expected Return Factor Model Internationally The most important factors across the 5 largest stock markets (1985-93).

49. 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.

50. Mean Payoffs and Confidence Probabilities for the Twelve Most Important Factors of the World (1985-93) 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%

51. Optimization in France, Germany, U. K., Japan and across the five largest countries. 1985-1994 19.0%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

52. Expansion of the 1996 Study (Nardin Baker)

53. Performance In Different Countries: 1985 - 1998 (Sept.) 0% 5% 10% 15% 20% 25% 30% 12%14%16%18%20%22%24%26%28%30%32% Volatility Return AUSBELCANCHEDEUESPFRA GBRHKGITAJPNNLDSWEUSA

54. Actual Performance

59. 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

60. 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 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