Active Share is a popular metric that purports to measure portfolio activity. Though Active Share’s fragility and ease of manipulation are increasingly wellunderstood, there has been no research on its predictive power.
This paper quantifies the predictive power of Active Share and finds that, though Active Share is a statistically significant predictor of the performance difference between portfolio and benchmark, it is a weak one, explaining only approximately 5% of the variation in active management across U.S. equity mutual funds. The predictive power of Active Share is a small fraction of that achieved with robust and predictive equity risk models.
The Breakdown of Active Share
Active Share — the absolute percentage difference between portfolio and benchmark holdings – is a common metric of fund activity. The flaws of this measure are evident from simple examples:

If fund with S&P 500 benchmark buys SPXL (S&P 500 Bull 3x ETF), becoming more similar to the benchmark, its Active Share increases.

If a fund with S&P 500 benchmark indexes Russell 2000, this passive strategy has 100% Active Share.

If a fund F1 differs from the benchmark B in a single 5% position P1 with 20% residual (idiosyncratic, stockspecific) volatility, and F2 differs B in a 10% position P2 with 5% residual volatility F2 has a higher active share, yet is less active.

If a fund holds a secondary listing of a benchmark holding, its Active Share increases.
In light of the above flaws, evidence that Active Share funds that outperform may merely index higherrisk benchmarks is unsurprising.
Measuring Active Management
A common defense is that the above and similar examples are pathological or esoteric, unrepresentative of the actual portfolios. Such defense asserts that Active Share measures active management of realworld portfolios.
Astonishingly, we have not seen a single paper assessing whether Active Share has any effectiveness in doing what it is supposed to do – identify which funds are more and which are less active. This paper provides such an assessment.
We consider two metrics of fund activity: Tracking Error and monthly active returns (measured as Mean Absolute Difference between portfolio and benchmark returns). Both of these metrics measure how different the portfolios are in practice. Whether Active Share has value for measuring fund activity depends on whether it can differentiate among more and less active funds.
The study dataset comprises portfolio histories of approximately three thousand U.S. equity mutual funds that are analyzable from regulatory filings. The funds had 210 years of history. Our study uses the bootstrapping statistical technique – we select 10,000 samples and perform the following steps for each sample:
 Select a random fund F and a random date D.
 Calculate Active Share of F to the S&P 500 ETF (SPY) at D.
 Keep samples with Active Share between 0 and 0.75 indicating that SPY may be an appropriate benchmark. This step excludes small and midcapitalization funds that share no holdings with SPY and would all collapse into a single point with the Active Share of 100, impairing statistical analysis.
 Measure the activity of F for the following 12 months (period D to D + 12 months). We determine how active a fund is relative to a benchmark by quantifying how similarly to the benchmark it performs.
After the above steps, we have 10,000 observations of fund activity as estimated by Active Share and actual subsequent fund activity.
The Predictive Power of Active Share for LargeCap U.S. Equity Mutual Funds
The following results quantify the predictive power of active share for differentiating between more and less active U.S. equity mutual funds. For perspective, we also include results on the predictive power of robust equity risk models. These results illustrate the relative weakness of Active Share as a measure of fund activity. They also indicate that, far from mitigating legal risk by reliance of a best practice, the use of Active Share to detect closet indexing may instead create legal risk.
The Predictive Power of Active Share for Forecasting Future Tracking Error
Active Share is a statistically significant metric of fund activity, but a very weak one, predicting only about 5% of the variation in tracking error across mutual funds:
U.S. Equity Mutual Fund Portfolios: The Predictive Power of Active Share for Forecasting Future Tracking Error
Residual standard error: 1.702 on 9998 degrees of freedom Multiple Rsquared: 0.05163, Adjusted Rsquared: 0.05154 Fstatistic: 544.3 on 1 and 9998 DF, pvalue: < 2.2e16
The Predictive Power of Active Share for Forecasting Future Active Returns
Active Share also predicts only about 5% of the variation in monthly active returns across mutual funds:
U.S. Equity Mutual Fund Portfolios: The Predictive Power of Active Share for Forecasting Future Active Return
Residual standard error: 0.3986 on 9998 degrees of freedom Multiple Rsquared: 0.04999, Adjusted Rsquared: 0.04989 Fstatistic: 526.1 on 1 and 9998 DF, pvalue: < 2.2e16
.
The above results make the generous assumption that all relative returns are due to active management. In fact, much relative performance is attributable to passive differences between a portfolio and a benchmark. This complexity will be captured in our followup research.
The Predictive Power of Robust Equity Risk Models
To put the predictive power of Active Share into perspective, we compare it to the predictive power of tracking error as estimated by robust and predictive equity risk models. Instead of Active Share, we use our default Statistical U.S. Equity Risk Model to forecast tracking error of a fund F at D.
The Predictive Power of Equity Risk Models for Forecasting Future Tracking Error
The equity risk model predicts approximately 38% of the variation in tracking error across mutual funds:
U.S. Equity Mutual Fund Portfolios: The Predictive Power of Robust Equity Risk Models for Forecasting Future Tracking Error
Residual standard error: 1.379 on 9998 degrees of freedom Multiple Rsquared: 0.3776, Adjusted Rsquared: 0.3776 Fstatistic: 6067 on 1 and 9998 DF, pvalue: < 2.2e16
The Predictive Power of Equity Risk Models for Forecasting Future Active Returns
The equity risk model predicts approximately 44% of the variation in monthly active returns across mutual funds:
U.S. Equity Mutual Fund Portfolios: The Predictive Power of Robust Equity Risk Models for Forecasting Future Active Return
Residual standard error: 0.3068 on 9998 degrees of freedom Multiple Rsquared: 0.4375, Adjusted Rsquared: 0.4374 Fstatistic: 7776 on 1 and 9998 DF, pvalue: < 2.2e16
Conclusions

Active Share is a statistically significant metric of active management (there is a relationship between Active Share and how active a fund is relative to a given benchmark), yet the predictive power of Active Share is very weak.

Active Share predicts only about 5% of the variation in tracking error and active returns across U.S. equity mutual funds.

A robust and predictive equity risk model is approximately 7 to 9 times more effective than Active Share, predicting approximately 40% of the variation in tracking error and active returns across U.S. equity mutual funds.

In the following articles, we will put the above predictive statistics into context and quantify how likely Active Share is to identify closet indexers.
The information herein is not represented or warranted to be accurate, correct, complete or timely. Past performance is no guarantee of future results. Copyright © 20122020, Alpha Beta Analytics, LLC. All rights reserved. Content may not be republished without express written consent.