The idea that outperformance comes more easily to a fund manager managing portfolios with a larger Active Share is in fact the result of small-capitalisation biases. When such biases are excluded, Active Share has no predictive value for a manager’s performance. The size of a portfolio’s Active Share depends heavily on the composition and structure of the fund's benchmark and a persistently large Active Share may reflect a strong bias to small-cap stocks or an excessive number of non-benchmark assets in a portfolio. We believe Active Share tells investors nothing about the systematic and unsystematic exposures in a portfolio. It should therefore be used in conjunction with other indicators.
“How Active is your Fund Manager? A New Measure That Predicts Performance” is the title of a 2009 paper by K.J. Martijn Cremers and Antti Petajisto. In it, they introduced the concept of a fund’s Active Share, which measures the share of portfolio holdings that differ from the portfolio’s benchmark index. They went on to claim that funds with the highest Active Share significantly outperform their benchmark indices. This claim was reasserted by Antti Petajisto in a more recent paper. According to this latest study, those funds with the highest Active Shares significantly outperform their benchmarks, both before and after expenses. Furthermore, these funds also exhibit persistently strong performance.
Not surprisingly, this research prompted academics and asset managers to devote substantial time and resources to this topic. Nor did the claim go unnoticed by regulators of the financial services industry* - a number of countries have even gone so far as to introduce regulations on Active Share and others are contemplating doing so. So just how important is the Active Share for investors?
What is a fund’s Active Share?
The Active Share measures the extent to which a fund’s holdings deviate from the composition of the index against which the fund is benchmarked. It is calculated as one half of the sum of the absolute value of the stock active weight in a benchmarked long-only portfolio, where active weight is the difference between the weight of a stock in the portfolio and its weight in the benchmark index. An Active Share of 0% means the composition of the portfolio is identical to that of the benchmark. At the other extreme, a portfolio with no holdings in common with those of the benchmark has an Active Share of 100%.
Even though a number of more recent studies corroborate the results of Cremers and Petajisto, their interpretation of these results is now being challenged – the very idea that the Active Share is a measure with a role to play in fund manager selection has been brought into question.
No theory behind the empirical results
Andrea Frazzini, Jacques Friedman and Lukasz Pomorski highlighted an important point in their recent paper: not only is there no theoretical explanation as to why a higher Active Share should lead to more significant outperformance, but it is also not easy to come up with an intuitive economic rationale. So what is going on?
Benchmark market capitalisation and Active Share
As shown by Tim Cohen, Brian Leite, Darby Nielson and Andy Browder in their research note, the distribution of the Active Share is related to the market capitalisation of the fund’s benchmark. Sorting funds by Active Share yields a similar ranking as sorting funds by the market capitalisation of their index. Small-cap funds tend to have a much larger Active Share than large-cap funds – the former in the range of 95%-100% and the latter, on average, just 75%.
Moving the argument along, Frazzini, Friedman and Pomorski showed in their paper that Active Share simply has no predictive power for fund returns after controlling for benchmarks, a conclusion that had already been reached by Todd Schlanger, Christopher Philips and Karin LaBarge in their earlier research note: the so-called high-conviction funds, those with a high Active Share, did not significantly outperform funds with a low Active Share.
Impact of the of the benchmark structure on the Active Share
In their 2013 research note, Steve Sapra and Manny Hunjan had already highlighted the notion that the structure of a benchmark would likely have an impact on the average Active Share one can expect from fund managers. In particular, they demonstrated that a higher Active Share is easier to achieve in global portfolios than in domestic portfolios where benchmark indices typically have fewer stocks. This is because each global portfolio represents a smaller fraction of its benchmark compared to domestic portfolios. Indeed, global portfolios tend to have a larger Active Share than domestic portfolios.
The level of concentration of the benchmark matters. Managers who pick a higher number of stocks from the benchmark and equally weight them in the portfolio will more easily achieve a large Active Share against benchmarks with higher concentration - much of their market capitalisation is concentrated in just a few stocks - than against benchmarks whose market capitalisation is more evenly spread.
These results show that different Active Share levels should be expected for funds benchmarked against different benchmarks. This brings into question the idea that there’s a universal level of desired Active Share that is applicable to all fund managers.
What is behind a large Active Share?
An Active Share of 100% is bad news since it raises the question of whether the manager of such a fund adheres to the investment process stated in the fund’s mandate. For example, a manager benchmarked against a large capitalisation index and investing only in small capitalisation stocks will have a 100% Active Share. But in this case is the chosen benchmark of any use? Asking for a very high Active Share clearly increases the risk that managers will be forced to look beyond the constituents of the benchmark for investments. That defeats the purpose of benchmarking in the first place.
Managers who invest only in the constituents of the benchmark index can still sustain a large Active Share over time by investing only in those stocks with the smallest capitalisations. But this permanent bias towards small caps is not only sub-optimal if large-cap stocks outperform the smaller-cap stocks, it is also a major constraint on stock picking.
Is a large Active Share necessary to generate significant outperformance?
The answer is no. It all depends on a fund manager’s skill. A manager can generate high levels of outperformance with small deviations from the benchmark as long as he or she is skilful enough to overweight/underweight the stocks that deliver the strongest/weakest performance. Frazzini, Friedman and Pomorski give a good example in their paper: a manager benchmarked against the S&P 500 would have outperformed the index by 450bp a year from January 1990 to October 2014 with an Active Share of only 2.2%, provided he or she managed to exclude from the portfolio the five stocks with the poorest performance and held, at market-cap weights, the other 495 stocks.
Relationship between Active Share and tracking error risk
The relationship between Active Share and tracking error risk is not obvious. The reason is that Active Share does not distinguish between systematic and unsystematic risk exposures. Portfolios can run a low or a high level of systematic risk irrespective of the level of their Active Share. The systematic risk decision is independent of the decision on the Active Share.
Active Share versus tracking error risk in quantitative management
Quantitative managers tend to derive excess returns from exposures to systematic risk factors such as value and momentum. Their Active Share will necessarily vary over time if they target constant systematic risk exposures and constant tracking error. As shown in our recent paper “Intertemporal risk parity: a constant volatility framework for factor investing”, targeting a constant tracking error adds value relative to targeting constant Active Share when it comes to systematic risk factor exposures. A variable Active Share over time is what should be expected from the most successful quantitative managers. In particular, one should expect a much smaller Active Share when market volatility and stock correlations are high and a larger Active Share at other times.
Active Share versus tracking error risk in fundamental management
Fundamental managers focused only on bottom-up stock-picking are expected to have low exposure to systematic risk in their tracking error risk. For a manager with exposure only to unsystematic risk, the level of tracking error risk is proportional to the Active Share times the average unsystematic volatility of all stocks in the investment universe and inversely proportional to the square root of the number of stocks in the portfolio, as shown by Sapra and Hunjan in their research note.
While tracking error risk is a function of the average unsystematic volatility of stocks, the Active Share is not. Thus, the Active Share in combination with the tracking error risk and the number of stocks in the portfolio can be informative as to what an active fund manager may be trying to achieve. For example, a fund manager may choose to reduce quite considerably the Active Share to cap the tracking error risk in periods of high volatility. He or she can achieve this by moving the weights of a number of stocks closer to their market capitalisation weight without changing the number of stocks in the portfolio. But the manager may also choose to add stocks to the portfolio to keep the tracking error capped while reducing the Active Share by a smaller amount. Choosing to add stocks or not will depend on the level of confidence the fund manager has in picking additional stocks.
In turn, an active manager who always invests in the same number of stocks and keeps the Active Share high and constant over time will have a much higher tracking error risk in periods of higher market volatility. Such a strategy will generate the largest excess returns in periods of higher market volatility, indicating that the active manager must feel much more confident about his stock selection in such periods. In periods of low market volatility, the excess returns of such a strategy will be considerably lower due to the much lower tracking error risk, indicating much lower confidence in the stock picks during such periods.
Active Share is an intriguing measure of how active your fund manager is. It may well provoke interesting discussions between managers and investors. What’s wrong is the idea that a high Active Share is a prerequisite for outperformance. Data on a fund’s Active Share should be accompanied by more information about how active a fund manager really is. This should include the percentage of Active Share generated from off-benchmark stocks, the level of tracking error risk, the number of stocks in the portfolio and the decomposition of tracking error risk into systematic and unsystematic exposures. All these elements should make it easier to understand the investment process and its consistency over time, and ultimately to explain where performance comes from.* See article "Three Swedish banks accused of 'closet tracking" published 8 June 2015 in the FTfm section of the Financial Times. [starbox id=raul.leotedecarvalho] [starbox id=frederic.surry]