There are (at least) two distinct ways of measuring the extent to which a manager attempts to create value. One is returns-based (alpha, tracking error, information ratio etc.) and one is holdings-based (the delta between holding weights and index weights). Holdings-based measures can provide a discrete snap-shot of a manager’s “activeness” which seems objective and undeniable. After all, if a manager holds positions in wildly different proportions that those in the index, how can his fund be anything other than highly active?
Unfortunately, things may not be that simple. A manager can pursue a passive strategy using a concentrated, yet representative sample of index names. Thus, security weightings would differ from index weightings, but the fund would perform very much like the market.
Similarly, a fund can have security weightings that are similar to those of the index when the market is rising and different when the market is falling. Catch the fund at the wrong time and it would look passive.
Mustafa Sagun and Scott Leiberton of Principal Global Investors make the case for adding holdings-based analysis to traditional measures of “activeness” in this December 2007 paper (“Alpha Dynamics: Evaluating the Activeness of Equity Portfolios“). Say the duo:
“In assessing the relative attributes of active equity investment strategies, many market participants rely on an incomplete tool kit. Common variability statistics such as tracking error and summary characteristics such as the number of holdings in a portfolio provide incomplete insights on the essence of active exposure.”
“However, the notion that tracking error is a measure of activeness involves some common misperceptions. By definition, tracking error measures the volatility of excess returns (alpha) of a portfolio over time.”
Instead of simply relying on tracking error and information ratio to determine activeness and value-added, Sagun and Leiberton suggest the best approach is to “compare the intersection of the portfolio and benchmark to measure the aggregate overlaps and differences.”
They propose the “coverage ratio” (below) as a measure of this overlap (Wp is the portfolio weight and Wb is the benchmark weight of the same security).
If you’re having a deja vu, it may be because – as the authors point out – this approach to determining activeness was also espoused by Yale researchers Martijn Cremers & Antti Petajisto in an August 2006 paper (see related posting). Sagun and Leiberton say that their long-used coverage ratio is simply the reverse (1-x) of Cremers and Petajisto’s “active share ratio”.
The authors also apply the notion of coverage ratio to 1X0/X0 funds. They suggest that the active share of a 130/30 fund, for example, is equal to the active share of the fund before the addition of the short extension, plus 30%, plus 30% again (since the 30/30 extension is by definition all active). Put another way, this “modified active share” is equal to the gross exposure of the fund (160%) minus the coverage ratio (i.e., minus the passive component of the pre-extension fund).
They show how the coverage ratio can also be used to examine if fee levels are appropriate and warn that the coverage ratios can’t simply be added across managers on a multi-manager platform. Adding a small-cap manager with a coverage ratio of x to a large cap manager with a coverage ratio of y, for example, could lead to a combined portfolio with weightings that are basically equal to the market.
Like Cremers and Petajisto, Sagun and Leiberton conclude that a combination of top-down and bottom-up measures of activeness is best:
“…alpha potential for active stock selection strategies is best measured by the Active Share of the portfolio, while its consistency is determined by tracking error. Using tracking error both for alpha potential and risk in alpha potential would result in ineffective decisions. Thus, the key to delivering high information ratio strategies is to keep the Active Share high and the tracking error low.”