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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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