Factor modeling and style premia are historically well documented and extensively researched in generating abnormal returns. Despite the large amount of research around factors, there is less clarity around effectively capturing and extracting this alpha from a given universe. In this presentation, Cheng will demonstrate different techniques for combining multiple factors, and the rationale behind maximizing alpha while maintaining scalability.

1. Maximize Alpha
with
Systematic
Factor Testing
By: Cheng Peng

2. Problem:
- Given a basket of Factors, how do we extract the most alpha?
- Concerns: Scalability and consistency
Solution:
- A systematic approach for analyzing and testing factor alpha
- Key Points:
- Universe Factor Tilting
- Alpha Combination Techniques
- Portfolio Diversification
What is this about?

3. Backtesting Conditions
Quantopian Platform
- Universe: 1500 most tradeable US Equities
- Timeframe:
- In Sample: 01/04/2003 - 01/01/2015 (12 Years)
- Out Of Sample: 01/01/2015 - 08/01/2017 (2.5 Years)
- Trading Costs:
- $0.0035 per share (IB Tiered)
- Volume limitations of 2.5% of a minute’s trade volume, with a price impact of 0.1
- Starting balance of $ 1,000,000
- Full rebalance at start of every Month
- Equal weighting with 10% constraint on each stock

4. Picking Factors
Momentum
- 1 Month / 12 Month Price Momentum
Quality
- Return On Equity = Net Income / Shareholder’s Equity
Volatility
- Standard Deviation of Daily Price in last 21 days

5. Picking Factors - Top / Bottom Quintiles
Sharpe Beta Alpha
High Momentum 0.56 1.11 0.02
Low Momentum 0.56 1.34 0.02
High ROE 0.7 1.08 0.04
Low ROE 0.58 1.29 0.02
High Volatility 0.51 1.57 0
Low Volatility 0.83 0.7 0.04
2003 - 2015

6. Picking Factors - Top / Bottom Quintiles
Sharpe Beta Alpha
High Momentum 0.56 1.11 0.02
Low Momentum 0.56 1.34 0.02
High ROE 0.7 1.08 0.04
Low ROE 0.58 1.29 0.02
High Volatility 0.51 1.57 0
Low Volatility 0.83 0.7 0.04
2003 - 2015

7. Combining Winning Factors
Combined Ranking
- Top Quintile of (Momentum Rank + ROE Rank + Low Volatility Rank)
Combined Portfolio
- Top Momentum Quintile + Top ROE Quintile + Bottom Volatility Quintile
Cross Section
- Top Momentum Quintile & Top ROE Quintile & Bottom Volatility Quintile

8. Combining Winning Factors

9. Sharpe Beta Alpha Avg Holdings
Combined Rank 0.64 1.04 0.03 300
Combined Portfolio 0.69 0.99 0.03 700
Cross Section 0.66 0.46 0.03 15
Low Vol 0.83 0.7 0.04
All of these perform WORSE than just the standalone Low Vol factor.
Let’s reinvestigate each factor more carefully.
Combining Winning Factors
2003 - 2015

10. Picking Factors - Top / Bottom Quintiles
Sharpe Beta Alpha
High Momentum 0.56 1.11 0.02
Low Momentum 0.56 1.34 0.02
High ROE 0.7 1.08 0.04
Low ROE 0.58 1.29 0.02
High Volatility 0.51 1.57 0
Low Volatility 0.83 0.7 0.04
2003 - 2015

11. Quintiles Sharpe Beta Alpha
5 0.56 1.11 0.02
4 0.67 1.01 0.03
3 0.69 1.05 0.03
2 0.66 1.11 0.03
1 0.56 1.34 0.02
Momentum - 2003 to 2015

12. Quintiles Sharpe Beta Alpha
5 0.7 1.08 0.04
4 0.68 1.04 0.03
3 0.64 1.08 0.02
2 0.6 1.12 0.02
1 0.58 1.29 0.02
ROE - 2003 to 2015

13. Quintiles Sharpe Beta Alpha
5 0.51 1.57 0
4 0.58 1.29 0.02
3 0.62 1.11 0.02
2 0.74 0.95 0.04
1 0.83 0.7 0.04
Volatility - 2003 to 2015

14. Sharpe Beta Alpha
Mid Momentum 0.69 1.05 0.03
High ROE 0.70 1.08 0.04
Low Vol 0.83 0.7 0.04
Picking Factors - Optimal Quintiles
Repeat process to Combine Portfolios and finding Cross Sections.
However, ranking Mid Momentum cannot be done with the same approach!
2003 - 2015

15. Combining (Actual) Winning Factors
Combined Ranking (with a twist)
- Top Quintile of ((- Momentum2
Rank) + ROE Rank + Low Volatility Rank)
Combined Portfolios
- Mid Momentum Quintile + Top ROE Quintile + Bottom Volatility Quintile
Cross Section
- Mid Momentum Quintile & Top ROE Quintile & Bottom Volatility Quintile

16. Combining (Actual) Winning Factors

17. All of these STILL perform WORSE than just the standalone Low Vol factor.
Try Factor Tilting the Universe!
Sharpe Beta Alpha Avg Holdings
Combine Rank 0.67 1.14 0.04 300
Combine Portfolio 0.73 0.97 0.04 700
Cross Section 0.68 0.72 0.03 20
Low Vol 0.83 0.7 0.04
Combining (Actual) Winning Factors
2003 - 2015

18. Factor Tilting Universes
Original
Universe
Factor 1
Filter
Factor
Universe
Factor 2
Factor 3
Factor
Portfolio

19. Factor Tilting Universes - Example
Q1500US
Momo
Filter
Momo
Universe
ROE
Volatility
Portfolio

20. Universe Tilt Mid Momo High ROE Low ROE High Vol Low Vol
Mid Momo 0.76 0.57 0.49 0.85
High ROE 0.71 0.53 0.85
Low ROE 0.64 0.48 0.76
High Vol 0.61 0.6 0.55
Low Vol 0.74 0.82 0.68
HeatMaps - Sharpe Ratios 2003-2015

21. Universe Tilt Mid Momo High ROE Low ROE High Vol Low Vol
Mid Momo 1.02 1.11 1.42 0.7
High ROE 1 1.46 0.69
Low ROE 1.11 1.65 0.73
High Vol 1.32 1.33 1.48
Low Vol 0.85 0.84 0.89
HeatMaps - Betas 2003-2015

22. Universe Tilt Mid Momo High ROE Low ROE High Vol Low Vol
Mid Momo 0.05 0.01 -0.01 0.05
High ROE 0.04 0.01 0.05
Low ROE 0.03 0 0.04
High Vol 0.03 0.03 0.02
Low Vol 0.04 0.05 0.03
HeatMaps - Alphas 2003-2015

23. Universe Tilt Mid Momo High ROE Low ROE High Vol Low Vol
Mid Momo 0.05 0.01 -0.01 0.05
High ROE 0.04 0.01 0.05
Low ROE 0.03 0 0.04
High Vol 0.03 0.03 0.02
Low Vol 0.04 0.05 0.03
HeatMaps - Best Alphas 2003-2015

24. Factor Tilting Universes - Example
Q1500US
Momo
Filter
Momo
Universe
ROE
Volatility
Portfolio

25. Universe Tilt Mid Momo High ROE Low Vol
Mid Momo 0.05 0.05
High ROE 0.04 0.05
Low ROE 0.03 0.04
Low Vol 0.04 0.05
HeatMaps - Combining Alphas 2003-2015
Now what?
Let’s try this again:
- Combine Rankings
- Combine Portfolios
- Cross Section

26. Sharpe Beta Alpha Holdings
0.77 1.02 0.05 140
0.63 0.89 0.02 140
0.55 0.99 0.01 140
0.8 0.8 0.04 140
Portfolio Construction - Combine Rankings
Based on Factor Tilts:
- Mid Momentum
- (High ROE, Low Volatility)
- High ROE
- (Mid Momentum, Low Volatility)
- Low ROE
- (Mid Momentum, Low Volatility)
- Low Volatility
- (Mid Momentum, High ROE)
2003 - 2015

27. Sharpe Beta Alpha Holdings
0.78 0.87 0.05 260
0.71 0.79 0.03 260
0.65 0.87 0.02 260
0.7 0.8 0.03 260
Portfolio Construction - Combine Portfolios
Based on Factor Tilts:
- Mid Momentum
- (High ROE, Low Volatility)
- High ROE
- (Mid Momentum, Low Volatility)
- Low ROE
- (Mid Momentum, Low Volatility)
- Low Volatility
- (Mid Momentum, High ROE)
2003 - 2015

28. Sharpe Beta Alpha Holdings
0.88 0.69 0.05 30
0.8 0.73 0.04 40
0.82 0.72 0.05 40
0.83 0.82 0.05 30
Portfolio Construction - Cross Section
Based on Factor Tilts:
- Mid Momentum
- (High ROE, Low Volatility)
- High ROE
- (Mid Momentum, Low Volatility)
- Low ROE
- (Mid Momentum, Low Volatility)
- Low Volatility
- (Mid Momentum, High ROE)
2003 - 2015

29. Sharpe Beta Alpha Holdings
0.81 0.81 0.01 30
1.05 0.83 0.04 40
1.33 0.9 0.08 40
0.84 0.91 0.02 30
Portfolio Construction - Out Of Sample
Based on Factor Tilts:
- Mid Momentum
- Cross Section (High ROE, Low Volatility)
- High ROE
- Cross Section (Mid Momentum, Low Volatility)
- Low ROE
- Cross Section (Mid Momentum, Low Volatility)
- Low Volatility
- Cross Section (Mid Momentum, High ROE)
2015 - 2017

30. Sharpe Beta Alpha Holdings
0.81 0.81 0.01 30
1.05 0.83 0.04 40
1.33 0.9 0.08 40
0.84 0.91 0.02 30
Portfolio Construction - Overfitted!
Sharpe Beta Alpha Holdings
0.88 0.69 0.05 30
0.8 0.73 0.04 40
0.82 0.72 0.05 40
0.83 0.82 0.05 30
BEFORE AFTER

31. In Sample - 01/04/2003 - 01/01/2015

32. Out Of Sample - 01/01/2015 - 08/01/2017

33. Several Options (In Sample Results)
- Don’t pick a particular portfolio
- Hold all four portfolios
- Reduce noise in portfolio
- Correlation Rank - Beta Rank
- Mid Momentum
- Cross Section (High ROE, Low Volatility)
- Low Volatility
- Original Factor Bottom Quintile
Sharpe Beta Alpha Holdings
0.85 0.77 0.05 100
0.88 0.75 0.06 30
0.88 0.69 0.05 30
0.83 0.82 0.05 30
Portfolio Construction - Avoid Overfitting
2003 - 2015

34. In Sample - 01/04/2003 - 01/01/2015

35. Out Of Sample - 01/01/2015 - 08/01/2017

36. In Sample - Benchmarked to SPY

37. Out of Sample - Benchmarked to SPY

38. Hedged Version - In Sample

39. Hedged Version - Out Of Sample

40. Takeaways:
- Carefully investigate each factor before drawing conclusions
- Combine factors by ranking factors, mixing them and finding cross sections
- Utilize factor tilting universes to help extract hidden alphas
- Avoid overfitting by holding diversified portfolios
Next Steps:
- Try a different set of factors and rebalance periods
- Try different markets and universes
Conclusion

41. Thank you for your time!
Email: me@chengpeng.ca