What is Active Share?
Active Share measures the fraction of a portfolio (based on position weights) that differs from the benchmark index.
The Active Share measure was developed by Martijn Cremers and Antti Petajisto, both Yale professors at the time, as a new way to quantify the degree of active management. Active Share measures the fraction of a fund's portfolio (based on position weights) that differs from the benchmark index.
Exhibit 1 provides a very simplistic explanation of how to calculate Active Share. The hypothetical benchmark consists of two equally weighted securities. Active share is calculated by taking the sum of the absolute difference between all of the holdings and weights in the portfolio and those of the benchmark holdings and weights and dividing the result by two.
The sum of the differences is divided by two to avoid double counting and ensures that the Active Share measure falls between zero and 100%. In this example, the fund has an Active Share of 40%. The remaining 60% is considered the passive share representing the portfolio's holdings and weights that directly overlap with the benchmark.
Exhibit 1: Calculating Active Share?
|Sum||100%||100%||80% / 2 =||40%|
With only 40% of the fund's portfolio devoted to active management one might think that this fund is more index-like, and the authors of the study would agree. The authors established that an Active Share of 60% or higher is generally considered active management. An Active Share of 20% to 60% is considered closet indexing, and an Active Share of less than 20% is considered passive (see Exhibit 2).
Exhibit 2: Active Share Levels
Generally, a Fund with an active share of more than 60% is considered actively managed.
Funds with the highest Active Share significantly outperformed their benchmarks, both before and after expenses, and they exhibited strong performance persistence.
After developing the concept of Active Share, Cremers and Petajisto performed a study to see whether Active Share had any bearing on the relative performance of domestic all-equity mutual funds. What they found was that historically "funds with the highest Active Share significantly outperformed their benchmarks, both before and after expenses, and they exhibited strong performance persistence."
As depicted in Exhibit 3, the studies found that the top quintile of funds by Active Share outperformed their benchmarks, net of fees and transaction costs, by 1.4% annualized. The bottom two quintiles underperformed their benchmarks by 1.4%, annualized. The original study covered the period of 1990–2003. Petajisto updated the study in 2010 to capture the significant market decline in 2008. He found that for the period of 2008–2009 the results were consistent with historic findings. During those two years, funds with high Active Share outperformed their benchmark by almost one percent annualized, net of fees, while all other funds underperformed their respective indices. Both studies also found significant persistence in returns for funds with high Active Share. That is those funds with high Active Shares that outperformed in one year were likely to outperform in the next.
Exhibit 3: Benchmark-Adjusted Returns for Active Share Quintiles*
U.S. Equity Funds 1990–2003
*After fees and transaction costs for all-equity mutual funds in 1990-2003.
Source: "How Active is Your Fund Manager? A New Measure That Predicts Performance," by Martijn Cremers and Antti Petajisto of the International Center for Finance at the Yale School of Management, March 2009.
Why Would Active Share be Correlated with Performance?
While greater benchmark differentiation creates the opportunity to outperform, it should also create an equal opportunity to underperform. Following that logic, and considering the added cost of mutual fund fees and transaction costs, it would seem likely that even high Active Share funds would underperform. A number of reasons have been proposed for why this was not the case.
Active Share can be thought of as a measure of the proportion of a fund that is driving performance. A fund with a higher Active Share effectively spreads the work across a greater portion of the portfolio, reducing the overall effort needed to drive higher returns. Conversely, a fund with a higher passive share needs to deliver much higher returns on the active portion to outperform the benchmark. This concept may be better expressed through an example. Exhibit 4 displays two hypothetical funds, one with a high Active Share and one with a lower Active Share. The benchmark has a hypothetical return of 8%. To outperform the benchmark by 2%, the return for the active portion of the portfolio with a 30% Active Share has to be much higher to compensate for the greater allocation toward benchmark holdings.
Exhibit 4: High Active Share/Low Active Share
The highly active manager only needs an excess of 2.2% on the active portion of the portfolio versus 6.7% for the low active share manager to achieve the same return.
It turns out the fees are fairly flat" (regardless of the degree of active share).
The same logic applies to fees. With a fund with low Active Share, a greater proportion of the fees go toward passive management and with a fund with high Active Share, a greater proportion of the fees go toward active management. Yet, one would expect that funds with lower Active Share would have lower fees to prevent them from overcharging investors for the greater passive exposure in the portfolio. The study by Petajisto in 2010 found that high Active Share does not mean higher fees.
A closet indexer charges active management fees on all the assets in the mutual fund, even when some of the assets are simply invested in the benchmark index. If a fund has an Active Share of 33%, this means that fund-level annual expenses of 1.5% amount to 4.5% as a fraction of the active positions of the fund. Since only the active positions of the fund can possibly outperform the benchmark, in the long run it is very difficult for a closet indexer to overcome such fees and beat its index net of all expenses.
Another possible reason for the outperformance displayed by funds with Share is that high Active Share is representative of a high level of conviction. A manager with great conviction would be less concerned with the portfolio relative to the benchmark. A manager with less conviction may introduce benchmark holdings to compensate for uncertainty leading towards a more index-like portfolio. This theory, though, rests on the assumption that conviction in and of itself is suggestive of outperformance which is further explored in the Manager Conviction section that follows.
A surprising take away from the Active Share studies was the clear trend away from higher Active Share (Exhibit 5). The percentage of assets in U.S. equity funds (active and passive) with Active Share less than 60% went from 1.5% in 1980 to 50.2% in 2009. Clearly indexing has had an impact on these results. Yet mutual funds with an Active Share between 20% and 60% (the closet indexers) saw their assets grow from 1.1% in 1980 to 31% in 2009 — as such, closet index funds have seen the greatest proportion of asset growth. Assets in funds managed with a high Active Share, (over 80%), have dropped precipitously from 60% in 1980 to just 19% in 2009. While the 2009 data is likely exaggerated — as Active Share tends to come down in periods of high market volatility —the longer term trend is away from high Active Share.
Exhibit 5: Percent of Assets in U.S. Equity Mutual Funds with Active Share ≥80%
Source: "Active Share and Mutual Fund Performance," by Antti Petajisto of the NYU Stern School of Business, December 2010.
If you have skill, why not apply that skill to your whole portfolio? And if your fund is too large to do that, why not close your portfolio?
Cremers and Petajisto speculate that asset growth may be one of the reasons for the trend toward lower Active Share. They note that the data reveals an inverse relationship between assets in a fund and Active Share. As assets grow, managers may have a tougher time maintaining high Active Share. As the saying goes "nothing fails like success," and quite often asset growth can lead to a more narrow opportunity set due to liquidity constraints that prevent managers from allocating new assets to their best ideas, they then add more liquid benchmark holdings. Cremers states in his study: "If you have skill, why not apply that skill to your whole portfolio? And if your fund is too large to do that, why not close your portfolio?"