A Multi-Factor Residual-Based Trading Strategy

Finance 453Adrian HelfertTerry MooreKevin Stoll

Ben Thomason

February 26, 2004

Agenda

CAPM Roots Our Multi-factor Model Our Trading Strategy Our Results Next Steps

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

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

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

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

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

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

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

In-Sample Results

Equally Weighted Value WeightedLong-Short

Return Alpha

Long-Short

Return Alpha5 Day Sum 20.7% 27.9% 22.2% 24.4%

30 Day Sum 20.8% 21.7% 17.0% 15.3%MA5-MA30 12.0% 19.0% 18.0% 17.3%MA5-MA10 3.9% 13.6% 11.3% 14.3%

ExpVar 13.6% 9.7% 7.7% 5.0%ExpVarCh 2.6% 5.0% 4.7% 4.8%

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

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

Equally Weighted Value WeightedLong-Short

Return Alpha

Long-Short

Return Alpha19.7% 24.2% 18.1% 18.9%

In Sample Results

Out-of-Sample Results

13 1994 107.6 102.1 98.7 108.2 104.4 98.8

25 1995 153.2 139.8 117.7 157.1 139.5 121.9

37 1996 144.8 138.6 107.4 147.3 133.6 109.0

49 1997 126.7 116.1 109.8 129.9 129.9 110.8

61 1998 140.9 107.1 98.6 160.4 104.6 113.7

73 1999 144.0 102.2 103.7 126.9 108.4 98.1

85 2000 105.8 101.3 96.0 94.2 109.6 85.5

97 2001 96.5 97.4 100.4 98.8 102.9 90.0

109 2002 93.4 74.5 80.3 83.6 79.3 88.5

Out of Sample 2003 130.6 128.7 153.9 116.5 129.7 148.7

-1- -2- -3- -1- -2- -3-

Portfolios - equal weighted Portfolios - value weighted

Total scoring screen significantly underperforms in the out-of-sample year: -23.7% return

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