1. Active is as Active Does: Active Share vs Tracking Error Melissa Brown Senior Director, Applied Research Axioma, Inc. Joint work with Dieter Vandenbussche and Vishv Jeet

2. Quantitative Management and Active Share
Active Share does not measure how risky or diversified bets are
Many small bets can yield the same Active Share as a few large bets
It does not capture the degree of a manager’s conviction
Alpha characteristics can significantly affect Active Share
It does not adequately measure “activeness” for managers taking factor bets
It is difficult to compare Active Shares of managers with different benchmarks
Copyright © 2016 Axioma

3. Portfolio Diversification and Active Share
Concentrated Portfolio
Diversified Portfolio
Concentrated
Diversified
Active Share
20.00%
Active Risk
3.16%
2.08%
Active Specific Risk
2.61%
1.60%
Active Factor Risk
1.78%
1.34%
Active Share ignores diversification altogether!
Copyright © 2016 Axioma

4. Cross-sectional Alpha Distributions
Some alphas encourage bigger, less diversified active bets, which leads to higher tracking error.
These alphas bump into the tracking error constraint “sooner”.
Fat tailed alpha (higher k) can reduce Active Share.
Fat tailed alpha can also increase the variability of Active Share.
Alpha Distributions
Active Share Histograms
Copyright © 2016 Axioma

5. Fat Tailed Alphas and Active Share
Statistically significant
T-stat (~ -23.0) for the negative slope
Fat tails (higher kurtosis) of cross-sectional alpha distribution reduces Active Share.
Copyright © 2016 Axioma

6. Alphas, Size Bias and the Long-only Constraint
Small cap assets are harder to underweight due to long-only constraint.
Optimized portfolios tend to have a size bias towards small cap, as they have limited ability to underweight small stocks.
To see the effect, we generate random alphas (normally distributed).
On average, alphas have no size bias.
Now we maximize alpha, fully invested with a 3% tracking error bound and long-only.
Copyright © 2016 Axioma

7. The Effect of Alphas With Explicit Size Tilt
Active Share Histograms
Neutral is randomly (normal) generated alphas
Positive puts positive mean on top 100 assets, negative mean on bottom 400
Negative does the opposite.
Negative size tilt in alpha can raise Active Share of quant portfolios and vice-versa
Copyright © 2016 Axioma

8. Higher Correlation of Alpha and Size Leads to Lower Active Share
Copyright © 2016 Axioma

9. Benchmark Selection and Active Share
Broader benchmarks allow for higher Active Share in quant strategies.
Copyright © 2016 Axioma

10. Benchmarks: Active Share Distribution
Active Share Histograms
Cross-sectional distribution of benchmark affect the Active Share of quant portfolios exactly the same way as alpha.
Concentrated benchmarks results in lower Active Share.
Copyright © 2016 Axioma

11. How Does the Tracking Error Constraint Affect Active Share?
Lower Tracking Error limit can drastically reduce Active Share.
Copyright © 2016 Axioma

12. Active Share of a Quant Strategy Through Time
Active Share varies quite a bit thru time for a strategy with fixed Tracking Error target.
During crises, due to raised market volatility and fixed TE targets, Active Share must be compromised.
Copyright © 2016 Axioma

13. Impact of the Long-Only Constraint
Active Share can be improved if shorting is allowed.
Copyright © 2016 Axioma

14. Revisit Fund Classification
Diversified
Stock Pickers
Concentrated
Stock Picks
High
Active Share
Closet
Indexing
Factor
Bets
Low
Pure
Indexing
Low
High
Tracking Error
Copyright © 2016 Axioma

15. Finding the Factor Bettors
Diversified
Stock Pickers
Concentrated
Stock Picks
Closet
Indexing
Factor
Bets
On the left panel Factor bets (with 85% or more systematic variance) are classified as concentrated stock pickers
On the right panel active specific risk correctly identifies them
Copyright © 2016 Axioma

16. Conclusions
Active Share is an interesting measure of portfolio’s activeness that complements other measures of activeness such as Tracking Error and its components.
Active Share is a good auxiliary measure that may help some asset owners and investors interested in aggressive strategies to screen out “closet indexers”.
Many factors impact Active Share of a fund, making it difficult to compare Active Share across funds.
Given that Active Share does not capture the intrinsic variation in volatility across assets and across time, nor the diversification effect, one cannot use Active Share in isolation to categorize funds.
We cannot identify factor betting strategies on the basis of Active Share and Tracking Error. The portion of variance coming from active specific variance may be a better alternative.
Copyright © 2016 Axioma