Paper revisits what it means for a manager to be truly “active”

CAPM / Alpha Theory 05 Feb 2008

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.”

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  1. Walt French
    February 6, 2008 at 12:09 am

    These ‘newfangled’ ratios come with all sorts of utterly unsupported assertions that such as “alpha potential… is best measured by the Active Share…”

    This could be true if there were no common sources of alpha in portfolios — an obviously false belief, if you look at how dramatically value or growth strategies differ, or how much similarity there is in performance within industries such as banking, drug stocks, etc. One down.

    It could also be true if managers recognized the many sources of common patterns and completely neutralized all their “tilts” in their portfolios. In fact, many managers try to be more or less roughly sector neutral, but many more methodically over-weight sectors such as tech, where they feel they’ll get more bang for the buck, or shun sleepy sectors such as utilities. And virtually every manager these days has an “approach” to picking names, whether calling it “valuation” or “growth potential,” that tends to favor stocks with the same type of financing structure, recent market success, etc.

    Finally, the stock-specific potential movement — often measured by the individual stock’s tracking error versus its benchmark — would have to be the same for each stock, a notion that’s utter hogwash.

    There are hundreds of firms using sophisticated performance and risk measurement systems from MSCI/Barra, Wilshire, brokers and many independent consultants. I’ll guess that the huge majority of these firms completely ignore the simplistic formulas you describe, mostly because the summary number tells them NOTHING about their portfolio that they don’t have a better measure for.

    Meanwhile, you could count the number of large asset managers who use Active Share and its ilk, to the exclusion of multi-factor systems, on the thumbs of your left foot. I doubt you’d find a single quant or 130/30 PM who even prefers A.S. — none of us see any reason to waste our time on it.

    Several decades after economists fiddled around with the Herfindahl Index and other ad hoc concentration measures, the Finance guys are re-purposing methods that were discarded for lack of insight. I really don’t get it.

  2. Simon
    February 6, 2008 at 10:23 pm

    In my own simplistic words
    The question is still about Graham and Fischer valuation.

    Quants want to find a way to measure active alpha compare to a determined benchmark and that is very positive for the academic knowledge.

    Using stats intuition to compare the intersection of the portfolio and benchmark to measure the aggregate overlaps and differences.

    Minimised the sum of CovaR between benchmark and the equity.

    A beautiful mind for a complex problem.

  3. Simon Jacques
    February 7, 2008 at 11:46 pm

    Remember what MArkowitz said in his 1987 book; (Mean-Variance Analysis in Portfolio Choice and Capital Markets; the riskiness of a portfolio depends on the covariance of its holdings, not on the average riskiness of the separate investments.

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