1. A Multi-Factor Residual-Based Trading Strategy Finance 453 Adrian Helfert Terry Moore Kevin Stoll Ben Thomason February 26, 2004

2. Agenda  CAPM Roots  Our Multi-factor Model  Our Trading Strategy  Our Results  Next Steps

3. Is the CAPM Dead?  The CAPM’s beta does not work well for all securities –Fama and French found 3 factors described asset returns better than the basic CAPM

4. An Intuitive Multi-Factor Model  We chose the following risk factors: –CAPM market risk premium –The square of the market risk premium –US dollar returns –GS Commodity Index returns –US long-term govt. bond returns –Change in the term structure

5. Estimating a Better Pricing Model  Dow Jones Industrial: 30 large cap, liquid stocks  In-sample: daily returns 1/1/94-12/31/02  Out-of-sample: 1/1/03-1/31/04  Linear regression for in-sample period –R-squared range from 3% (BS) to 52% (GE) –Significant t-stats –Residuals show negative autocorrelation

6. Screens  Rank residual factors (or expected variance) in ascending order, rebalancing weekly –Ten lowest form Portfolio 1 (long) –Ten highest form Portfolio 3 (short)  Screen 1: sum of last 5 days residuals  Screen 2: sum of last 30 days residuals  Screen 3: 5 day moving avg – 30 day moving avg  Screen 4: 5 day moving avg – 10 day moving avg  Screen 5: expected variance (GARCH)  Screen 6: change in expected variance

7. Screens 1 & 2: Sum Previous Residuals  Low residuals signal underperformance to risk factors –Stock will “catch up” when investors digest news  High residuals signal outperformance to risk factors –Stock should correct downward  Negative autocorrelations in our residuals support this theory

8. Screens 3 & 4: Difference Between Moving Averages of Previous Residuals  Technical reversal –Stocks tend to track longer term trend relative to the market –Profit-taking may cause near-term underperformance –Dip-buying may cause near-term outperformance

9. Screens 5 & 6: Expected Variance (GARCH)  Use residuals to estimate expected variances –Low variance stocks are rewarded by investors –High variance stocks are penalized by investors –Reductions in variance are positive –Increases in variance are negative

10. In-Sample Results  We discarded Screens 2, 4 and 6 - Results were similar, but not as good as 1,3 & 5

11. Scoring System  Screen 1 –Portfolio 1 scores 5, Portfolio 3 scores -4  Screen 3 –Portfolio 1 scores 3, Portfolio 3 scores -3  Screen 5 –Portfolio 1 scores 3, Portfolio 3 scores -2  Add scores for each week, sort and repeat process for next week

12. Out-of-Sample Results  Total scoring screen significantly underperforms in the out-of-sample year: -23.7% return

13. Next Steps  Test different stocks  Estimate a rolling pricing model instead of fixed historical time period  Optimize scoring (weighting) instead of subjective scoring  Factor trading costs and slippage costs explicitly into model  Test a 2-day model instead of 5-day because of autocorrelation results  Test a technical crossover strategy