A Multi-Factor Residual-Based Trading Strategy

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