In a 2009 paper, two professors at the Yale School of Management, Martijn Cremers and Antti Petajisto, introduced a new way to evaluate mutual funds/asset managers and the potential for future outperformance. Their metric, called “Active Share”, helped provide another framework to evaluate alpha-generation potential and provided an interesting contribution to the age-old debate within investment management circles concerning “concentrated” vs. “closet indexing” funds and active vs. passive management in general.
What exactly is Active Share? The concept behind the formula they created is incredibly simple. In essence, the formula, which sums the absolute differences in weights between the positions in a portfolio and the positions in the benchmark and divides that number by two, shows the overlap between a portfolio and its benchmark in terms of position weightings. The professors measure active share on a scale between 0% and 100%. A fund/portfolio demonstrating an active share of 90%, for instance, only demonstrates 10% overlap with its relevant benchmark, i.e. the managers of the portfolio have taken a very active approach. An active share of 10% indicates 90% overlap; one would find this level of active share in an index fund, for instance.
Taking the active share formula, the professors identified five categories of managers based upon their level of active share and the level of tracking error, which is basically the “divergence between the price behavior of a portfolio and the price behavior of a benchmark” over time, according to Investopedia. (Specifically, tracking error is the standard deviation of the differences in returns (monthly, quarterly, yearly, but usually monthly) between the fund and benchmark.)
- Diversified/Active Stock Pickers: defined as those with high active share and low tracking error. In other words, there are numerous stocks in the portfolio, which reduces tracking error, but little overlap with a benchmark in terms of holdings/weighting.
- Concentrated Stock Pickers: defined as those with high active share and high tracking error. The concentrated stock pickers have far fewer positions and little overlap with the relevant index.
- Factor Timing: these managers focus more on general market factor bets, such as timing the broader market or making broad bets on sector rotation. They demonstrate low active share but high tracking error. Performance can deviate wildly from an index as they make bigger macro-market directional bets.
- Closet indexers: these funds demonstrate low to middling active share, generally between 40% and 60%, and low tracking error.
- Index funds: essentially an index fund demonstrates nearly zero active share and miniscule tracking error.
Their findings on outperformance and underperformance as it relates to the above are quite interesting. Analyzing a broad database of funds from 1990 to 2003, they found that the high active share funds (exceeding 80%) produced annual outperformance after fees of 1.13% to 1.15%. Funds falling in the lower active share categories underperformed 1.42% to 1.83% per annum when fees are taken into account. Interestingly, the Factor Timing funds, those that tend to take bets on market direction on sector rotation, produced the worst outcomes among the low active share bunch and the worst outcomes overall.
In a follow up paper that added six years to the database, covering the period through the financial crisis, Professor Petajisto provides additional granularity to the outperformance/underperformance debate. The results are very interesting, especially in light of the debate between concentrated and diversified funds. First, overall, high active share funds, concentrated and diversified, again were the winners relative to the other categories when viewed in terms of performance relative to benchmark, net of fees. However, in the follow up study there was only one category of funds that exhibited absolute annual outperformance net of fees: the diversified stock pickers’ category. Diversified stock pickers generated +1.26% annualized performance over time relative to benchmarks. This outperformance occurred within all five quintiles of fund size performance as well. Concentrated funds with a high active share overall produced -0.25% annualized returns relative to benchmarks, though there were differences across fund size quintiles. Concentrated funds in the middle three size quintiles exhibited positive performance net of fees relative to benchmarks; performance was still lower than that of the high active share diversified stock pickers in the middle three quintiles. Funds making factor bets were the worst overall, confirming the data in the original paper; factor bet funds produced annual net relative performance of -1.29%. Similarly, closet indexing funds produced negative net relative performance of -0.92% per annum; basically, the closet indexing firms match the benchmark in gross performance, with nearly all the negative difference attributed to fees.
Going back to the original paper from 2006, there were some interesting findings on the migration of funds from high active share to closet indexing. From 1980 to 2003, the assets under management held in high active share funds decreased from 58% to 28% while assets held in low active share funds increased from 1.5% to 40.7%. In other words, over the past few decades, closet indexing has become much more prevalent in the asset management arena, perhaps an explanation for the disappointment many investors have experienced with mutual funds in recent years.
Like all studies, there is divergence within each category. There are certainly high active share, diversified managers that underperform and factor bet managers that outperform over long periods of time. Another issue that complicates active share analysis is the fact that fund holding and benchmark holding data can be hard to come by for many individuals and professionals.
Nonetheless, the results suggest that investors in general should seek out funds and managers with very high active share (less overlap with the benchmark), who also exhibit lower tracking error. Highly concentrated firms can deliver outperformance, but the results overall don’t appear as consistent overall.
Sources:
Cremers, Martijn, and Antti Petajisto. September 2009. “How active is your fund manager? A new measure that predicts performance.” Review of Financial Studies.
Kidd, Deborah. 2013. “Active Share Adds Value In Search for Alpha.” CFA Institute Investment Risk and Performance Newsletter.
Investopedia.com. February 26, 2009. “Active Share Measures Active Management.” http://www.investopedia.com/articles/mutualfund/07/active-share.asp
Petajisto, Antti. January 15, 2013. “Active Share and Mutual Fund Performance.” Working Paper, New York University Department of Finance. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1685942
