By: 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)). 

“How could such prolific active management yield benchmark-like returns” thought Alpha Male?  Was this fund a closet-indexer because correlation was high, or was this fund truly active because its holdings were different than the index?  Alpha Male even wrote a posting on this topic in July.

It appears Cremers and Petajisto would say this Canadian equity fund has a high “active share”:

 If (an investor) invests in only 50 stocks out of 500 (assuming no size bias), his Active Share will be 90% (i.e. 10% overlap with the index). According to this measure, it is equally active to pick 50 stocks out of a relevant investment universe of 500 or 10 stocks out of 100 .in either case you choose to exclude 90% of the candidate stocks from your portfolio.

Alpha Male would not have agreed with this approach and he eventually lost much sleep over this conundrum.  He concluded that the positions in the large Canadian equity were essentially representative of the overall market.  Alpha Male still believes what William Sharpe said in the early 1990’s when he invented style-analysis - that performance tells most of the story.  In other words, the “proof is in the pudding” - no matter how hard a manager tries, tracking the index is tracking the index.

Still, Cremers and Petajisto come armed with evidence that ”active share” (analogous to the gross exposure of the embedded long/short fund) is somewhat correlated with higher performance.  So security-level deviation from the index must contribute in some way to higher returns.  But while active share does correlate to performance, it only explains a small portion of the variability in performance.  And at the end of the day, active share and tracking error are pretty closely correlated anyway. 

So the jury remains out for Alpha Male.  Just because a manager’s holdings differ from the benchmark, this does not necessarily mean they have made a series of unique bottom-up security selections.  They may have just picked, say, BCE and Royal Bank instead of many smaller telecoms or financials.  

Cremers and Petajisto seem to suggest that individual stocks have no beta:

“In terms of tracking error, the key difference between the two types of active management is that the sector rotators and market timers will bear systematic risk relative to the index, while stock pickers may bear only idiosyncratic risk.”

“A high Active Share can identify a diversified stock picker even when his tracking error is low.”

The authors do not explain why a high active share must be the result of diversification.  It may be possible to replicate Canadian equity markets with only a small handful of stocks  (Alpha Male has not tested this hypothesis, but you get the point).  But even a small number of stocks do not necessarily lead to a reduction in systematic risk.  All stocks have a beta - some more than others.  Buying a single security does not mean a manager has shunned sector betas - on the contrary, their stock pick might actually be a veiled attempt to buy more sector beta.

In any case, here are some of the most interesting excerpts from this fascinating paper:

On Current Mutual Fund Research…

“The current mutual fund literature has done little to investigate active management per se.  Instead, a large volume of research has focused on fund performance directly.”

On Fees…

“…active funds seem to charge similar fees regardless of their Active Share, so the ones that actually tend to hug the benchmark index are most likely doing it without acknowledgement to their investors…”

On the Evolution (Devolution!) of Active Management…

“…the percentage of assets under management with Active Share less than 60% went up from 1.5% in 1980 to 40.7% in 2003. Correspondingly, the percentage of fund assets with Active Share greater than 80% went down from 58% in 1980 to 28% in 2003.  The fraction of index funds before 1990 tends to be less than 1% of funds and of their total assets but grows rapidly after that. Similarly, there are very few non-index funds with Active Share below 60% until about 1987, but since then we see a rapid increase in such funds throughout the 1990s, reaching over 20% of funds and over 30% of their assets in 2000-2001. This suggests that closet indexing has only been an issue since the 1990s . Before that, almost all mutual funds were truly active.”

On Returns…

“…Active Share does help us pick funds. The difference in benchmark-adjusted return between the highest and lowest Active Share quintiles is 2.81% per year (t = 2:90), which further increases to 3.26% (t = 3:66) with the four-factor model. This di¤erence is positive and economically significant within all tracking error quintiles. An investor should clearly avoid the lowest three Active Share quintiles and instead pick from the highest Active Share quintile. Funds in the highest Active Share quintile beat their benchmarks by 1.39% (1.49% with the four-factor model) which is an economically significant point estimate but just falls short of being statistically significant.”

“…funds with low Active Share and high tracking error tend to do worst, both in terms of net and gross returns, which implies that factor bets are not rewarded in the market and actually tend to destroy value for fund investors. Closet indexers (low Active Share, low tracking error) also exhibit no ability and tend to lose money after fees and transaction costs.”

- Alpha Male