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Assessing the Value of Active Management Defined contribution plans have long included passive and active investments as options in their investment line up. Both investment approaches have their share of adherents and detractors. For plan sponsors, one of the more frequently considered questions about active management, and one of the most inconsistently answered is “Do actively managed funds add enough value to compensate for their fees?” A relatively recent addition to portfolio analytics called active share may provide some clarity on the issue.
Introducing Active Share First introduced by Yale finance professors K. J. Martijn Cremers and Antti Petajisto, active share is a measure of the percentage of stock holdings in a portfolio that differ from the makeup of the benchmark index. The findings from that initial paper concluded that managers with high active share— roughly defined as 80% or higher—generally outperformed their benchmarks.
In a summary of their findings, Cremers and Petajisto state: Active Share predicts fund performance: funds with the highest Active Share significantly outperform their benchmarks, both before and after expenses, and they exhibit strong performance persistence. 1
1 “How Active is Your Fund Manager? A New Measure That Predicts Performance,” by K.J. Martijn Cremers and Antti Petajisto of the International Center for Finance at the Yale School of Management, March 2009.
Active Share Versus Tracking Error
One of the most common means of quantifying how much a portfolio differs from an index is through tracking error, which measures the volatility of a fund’s returns in excess of index’s returns. In concept, if the returns of a given portfolio significantly deviate from the index returns over time, the portfolio makeup must, by extension, differ from that benchmark as well.
However, tracking error is return-based and does not consider specific holdings. Active share, on the other hand, is determined by comparing portfolio holdings against index holdings to quantify the size of active bets. The active share calculation is simple math and is illustrated in Figure 1. In the example, a theoretical portfolio holds four securities and its benchmark index holds three securities. The portfolio and benchmark have just two securities in common, suggesting significant active bets relative to its benchmark.
In the example, Security 1 has a 5% weighting in the portfolio and a 33% weighting in the benchmark. The absolute value of the difference is 28%. To determine the portfolio’s active share, add the absolute differences between the portfolio weights and the benchmark weights and divide by two. Enhanced and closet indexers will likely have lower active share, generally below 60%. Higher active share managers generally will have an active share of 80% or higher.
Figure 1: Calculating Active Share
How Active is Your “Active” Manager?
Considering active share when evaluating managers may help plan sponsors find truly active funds, which the active research indicates is predictive of managers adding value. It may also identify “closet indexers” that hew precipitously close to the benchmark.
Figure 2 segments the active fund management universe based on active share and tracking error. The resulting four broad categories are shown in Figure 3, which provides the average annual alpha each provided from 1990 through 2009. Funds with high active share and tracking error, on average, have seen four times the alpha of any of the other categories.
Despite the significant outperformance of highly active funds, the investment universe has grown increasingly less active. Figure 4 shows the wide range of styles that exists within the boundaries of “active” investing, with the numbers of pure index and closet index managers growing steadily in recent years.
Active share is but one analytical metric among a host of others that investors may consider when evaluating a potential fund manager. It may, however, offer new insight into the long-lingering question of whether an “active” management philosophy is practicing what it preaches and, in the end, whether it is really delivering on its potential for added value.
Figure 2: Types of Active Management
 Source: Petajisto, Antti. “Active Share and Mutual Fund Performance.” Thesis. NYU Stern School of Business, 2010. 15 Dec. 2010. Web. Mar. 2011. www.petajisto.net/research.html
Performance by Active Share Category
1990—2009
Active management has the potential to outperform: Over the period from 1990 to 2009, mutual fund managers with moderate to high active share (stock pickers) outperformed closet indexers and other categories over most time periods. Active share for each category is noted in parentheses.
 *The alpha used in Petajisto’s paper is the Carhart four-factor alpha that controls for exposure to market, size, value or momentum factors.
2 All Funds category represents a sample of 2,740 funds that invested primarily in U.S. stock holdings. Sector funds and funds with less than $10 million in assets were excluded from the calculation.
Past performance does not guarantee future results. Source: Petajisto, Antti. “Active Share and Mutual Fund Performance.” Thesis. NYU Stern School of Business, 2010. 15 Dec. 2010. Web. Mar. 2011. www.petajisto.net/research.html
Figure 3: Evolution of Active Share
1980—2009
Low active share managers—pure and closet indexers—have become increasingly prevalent in the U.S. all-equity fund space over the past nearly 30 years.
 Source: Petajisto, Antti. “Active Share and Mutual Fund Performance.” Thesis. NYU Stern School of Business, 2010. 15 Dec. 2010. Web. Mar. 2011. www.petajisto.net/research.html
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By Martin Coughlan, CFA, CAIA, Calamos Investments LLC