How Active is Your Fund Manager? A New Measure That Predicts Performance
Aug 22nd, 2006 | Filed under: CAPM / Alpha TheoryBy: Martijn Cremers & Antti Petajisto, Yale School of Management
Published: August 7, 2006
If there is one academic paper you plan to read this year - make this the one! Alpha-philes everywhere will appreciate Cremers and Petajisto’s straighforward, plain-English analysis of alpha and active management.
To begin with, Cremers and Petajisto embrace the notion of what Alpha Male calls an “embedded hedge fund” within a “host fund”:
we can compare 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 it, and when a fund underweights an index stock or does not buy it at all, it implicitly has an active short position in it. In particular, we can decompose any portfolio into a 100% position in its benchmark index plus a zero-net-investment long-short portfolio on top of that. For example, a fund might have 100% in the S&P 500 plus 40% in active long positions and 40% in active short positions.
The authors address a problem the Alpha Male encountered about a year ago when he tried to reconcile the low tracking error of large Canadian mutual funds with the fact that these funds did not seem to hold the same securities as the index. In one case, Alpha Male found that market correlation of a large Canadian equity fund was 0.8 while the only about 20 percent of its holdings actually overlapped with the index holdings. When he shorted the Canadian equity index out of this fund, he was left with an “embedded long/short fund” derived from all the active under- and over-weightings in he fund. There were so many such deviations from index-weightings that the embedded long/short fund has a gross exposure of 80% (40% long and 40%) out of a maximum possible 200% gross exposure (i.e. 100% of fund not in the index means shorting (-100% net) and going long the non-index positions (+100% net)). More…
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[…] We agree, but would extend this reasoning to the world of long-only investing (e.g. mutual funds), where disguising beta as alpha has been the norm for some time (see research on index-hugging by mutual funds). […]
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[…] We were reminded of this study by Martijn Cremers & Antti Petajisto of the Yale School of Management (originally written last summer and covered in these pages but recently updated). Cremers and Petajisto propose a new measure of active management to complement the traditional market correlation measure (a.k.a. “tracking error”). Instead of looking at a fund’s return stream to infer the size of its active and passive components, the new metric actually measures the deviation of each holding from index weights. Cremers & Petajisto suggest this measure be used as a complement to, not a replacement for, tracking error. […]
[…] Maybe I’m working too much. But the more I research alpha, the less I know how to define it. While Andrew Lo asks “Where does alpha come from?”, I’m now back at “What is alpha”?  For example, what might look like alpha over one timeframe is actually “exotic beta” when you shift the window of analysis only a few months. What looks like alpha vs. one benchmark may, of course, be beta when compared to a different benchmark. There’s ”active weight“, “active component“, “active share“, “absolute returns”, “reliance on public information“, “manager value-added” - even ”accidental alpha“. […]