Active management Different types of active and passive management


• Active share represents the fraction of portfolio holdings that differ from the benchmark index, which emphasize stock selection.


• Tracking error is the volatility of fund return in excess of the benchmark, which emphasizes decisions relating to systematic risk.


High


Diversified stock picks


Concentrated stock picks


Low


Pure indexing


0 Low High Tracking error


A new way to measure returns: Active Share Active Share compares the portfolio holdings of a fund to its benchmark index. When a fund overweights a stock relative to the index weight, it has an active long position in that benchmark. When a fund overweights an index stock or does not buy it at all, it implicitly has an active short position in that index stock. We propose the size of this active long-


short portfolio as a new measure of active management, which we label a portfolio’s Active Share. Since funds rarely take actual short positions, their Active Share will nearly always be between zero and 100%. Active Share can thus be easily interpreted as the “fraction of the portfolio that is different from the benchmark index.” We believe that Active Share is useful


to investors for two main reasons. First, it provides information about a fund’s potential for beating its benchmark index – after all, an active manager can only add value relative to the index by deviating from it. Some positive level of Active Share is therefore a necessary (although not sufficient) condition for outperforming the benchmark. Second, while Active Share is a convenient stand-alone measure of active management, it can also be used together with tracking error for a more comprehensive picture of active management. This combination allows us to distinguish between stock selection and factor timing. The main conceptual difference between the measures is that tracking error incorporates the covariance matrix of returns and thus puts significantly


more weight on correlated active stock selection, whereas Active Share puts equal weight on all active selections regardless of diversification. In other words, investors can choose tracking error as a reasonable proxy for factor bets and Active Share as the proxy for stock selection. Using these two proxies, we illustrate the


two dimensions of active management in the chart above. A diversified “stock picker” can be very active despite their low tracking error, because its stock selection within industries can still lead to large deviations from the index portfolio. In contrast, a fund evaluating systemic


factors to make security decisions can generate a large tracking error even without large deviations from index holdings. A concentrated “stock picker” combines the two approaches, thus taking positions in individual stocks as well as in systematic factors, or in a way that is not highly diversified. A “closet indexer” scores low on both dimensions of active management while still claiming to be active. Finally, a pure index fund has almost zero tracking error an Active Share.


Conclusion There has been a rise in the popularity of passive management vehicles such as index funds and exchange-traded funds. The Investment Company Institute estimates that the share of assets invested in equity index funds relative to all equity mutual fund assets has been moving up to 14.5% in 2010.1 We would counter that the rise in indexed assets could also be attributed


1 2011 Investment Company Fact Book, Investment Company Institute


to “closet indexers” and a general tendency of funds to closely mimic the holdings of a benchmark index. In the past, the degree of active


management was quantified along just one dimension: tracking error relative to a benchmark index. Yet this failed to capture the two different dimensions of active management: stock selection and factor timing. Measuring active management in two dimensions by using both Active Share and tracking error permits the empirical identification of the different types of active management. These include diversified stock picks, concentrated stock picks, factor decisions, closet indexing and pure indexing. Active Share helps measure and predict


fund performance relative to the benchmark. Our study found that funds with the highest Active Share outperform their benchmarks both before and after expenses, while funds with the lowest Active Share tend to underperform after expenses. There are merits to both active and


passive portfolio management and many investors incorporate both styles into their overall investment strategy. One of the main advantages of Active Share is that it allows investors to distinguish between different types of active funds and to focus on only those that are truly active.


For a complete copy of Dr. Cremers’ paper, How Active is your Fund Manager? A New Measure that Predicts Performance, please visit http://mba.yale.edu/faculty/ profiles/cremers.shtml


15


Closet indexing


Factor selection


“Active Share can help predict fund performance: funds with the highest Active Share tend to outperform their benchmarks, both before and after expenses, and to exhibit strong performance persistence.”


Active share


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