Active Share: Empirical And Conceptual Issues

by: AllAboutAlpha

In 2009, Martijn Cremers, of the University of Notre Dame, and Antti Petajisto of New York University, introduced a new portfolio measurement they called Active Share, measuring in percentage terms the deviation of a portfolio from its benchmark (deviation in holdings, not in performance). Thus, a portfolio with 100% active share would have no common assets with its benchmark, while one with 0% would be identical to its benchmark.

Cremers and Petajisto argued that their new measure predicted performance among mutual funds; that is, that the greater the deviation, the higher the alpha. The underlying cause-effect claim was that winning portfolios concentrate resources in a small number of nest ideas, and that diffusion amounts to either open or closeted passivity.

There have been a number of critiques of the Cremers-Petajisto thesis over the years, although the Active Share has remained a secure part of the analytical tool kit.

AQR, for example, has argued that Active Share is simply positively related to returns when they're measured against some benchmark indexes, but is negatively related when they are measured against others, and thus that there is no overall relationship.

Antii Petajisto fired back at that, a year and a half ago, contending that Active Shares "is positively related to returns in the indices that are actually used by most of the funds in the sample," the negative counter-weight comes from the S&P 500 Value, which is followed by only 66 funds in a population of about 1,400.

Misspecifications and Inapt Definition

A new paper by two managing directors at Chicago Equity Partners goes deeper, arguing that the evidence on which Cremers and Petajisto relied "is based on groups with benchmark misspecification that do not stand up to logical scrutiny." Even using the same dataset as that employed for the 2009 paper, but "with proper benchmark specification" there is "no consistent long-term relationship between Active Share and outperformance."

They recall, for example, that the original paper employed "factor bets" as part of its classification scheme, but defined "factor bets" in what these authors see as an overly broad fashion. Cremers and Petajisto see a "factor bet" as including any time varying bet on a broad factor portfolio, so that even keeping cash at hand rather than investing it in equity becomes a "factor bet" by stipulation.

The authors of the new paper, "Concentrated vs. Diversified Managers: Challenging What You Thought You Knew About 'High Conviction,'" are Keith E. Gustafson and Patricia A. Halper. They believe that the term "factor bet" should be defined as positions designed to build diversified portfolios, "sampling from a broad set of stocks to remove stock-specific risk," and focusing on exposure.

The point is not a philological one, but involves strategy. Gustafson and Halper are contending that Cremers and Petajisto employed a classification system at odds with achieving consistent factor with relatively low tracking errors.

They are defending, then, the Fundamental Law of Active Management as stated by Richard Grinold in 1989: The productivity of an active asset manner is based both on his skill and the breadth of his choices, that is, how often his skill is put to use.

Who Are They

Gustafson and Halper are each a member of Chicago Equity Partners' quantitative analysis group, responsible for that firm's proprietary model. Mr. Gustafson has his master's degree in financial economics from the University of London. Ms. Halper has her master's degree in financial mathematics from the University of Chicago.

Chicago Equity Partners is a multi-asset class investment platform with roughly $10 billion in AUM.

Gustafson has, more recently, posted another paper on the CEP website with some related themes. Again dealing with the active/passive issue as one looking at a spectrum rather than a dichotomy.

The more recent paper looks at "smart beta" and observes that proponents of that strategy "suggest it is relatively simple to beat a passive index on a risk-adjusted basis over time with simple rules-based factor tilts toward value and small cap." After crunching some numbers, Gustafson concludes that there is truth to this, but that smart beta strategies "have provided the bulk of their historical return in deep value markets and they exhibit a cyclical benchmark-relative return pattern."

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