Maximize Alphawith

Systematic Factor Testing

By: Cheng Peng

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?

Backtesting ConditionsQuantopian 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

Picking FactorsMomentum

- 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

Picking Factors - Top / Bottom QuintilesSharpe 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

Picking Factors - Top / Bottom QuintilesSharpe 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

Combining Winning FactorsCombined 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

Combining Winning Factors

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

Picking Factors - Top / Bottom QuintilesSharpe 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

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

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

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

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

Combining (Actual) Winning FactorsCombined 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

Combining (Actual) Winning Factors

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

Factor Tilting Universes

Original Universe

Factor 1

Filter

FactorUniverse

Factor 2

Factor 3

FactorPortfolio

Factor Tilting Universes - Example

Q1500USMomo

Filter

MomoUniverse

ROE

Volatility

Portfolio

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

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

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

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

Factor Tilting Universes - Example

Q1500USMomo

Filter

MomoUniverse

ROE

Volatility

Portfolio

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

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 RankingsBased 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

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 PortfoliosBased 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

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 SectionBased 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

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 SampleBased 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

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

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

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

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

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

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

In Sample - Benchmarked to SPY

Out of Sample - Benchmarked to SPY

Hedged Version - In Sample

Hedged Version - Out Of Sample

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

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