Factor Modeling and Benchmarking of Hedge Funds: Can Passive Investment in Hedge Fund Strategies Deliver?

By: Lars Jaeger & Christian Wagner, Partners Group
Published: November 7, 2005 

This article aims to give reference to this academic effort and provide a coherent discussion on the current status of ‘beta versus alpha’ controversy in the hedge fund industry. 

– Jaeger & Wagner 

We admit that we’ve been a little obsessed about the definition of alpha recently. It’s a phase. We’ll grow out of it. But we couldn’t resist the sheer number of Jaeger-isms in this article (i.e. colourful metaphors for alpha).  We even threw in a few of our own.

We have discussed the notion that alpha is simply beta that has not yet been commoditized, that hedge fund alpha is often exotic beta, and that systematic active/passive funds can fill the gap between true alpha and true beta.  This article sheds additional light on these issues. 

A Family Feud 

This extensive white paper was co-written by Lars Jaeger, a leading figure in the alternative investment research field (as many of you are aware). It’s a little long, but remarkably easy to follow. Jaeger and Wagner cover a number of key elements in the alpha/beta hedge fund debate. 

They essentially divide the world into two feuding families [our term, not Jaeger’s]: those that say hedge fund alpha is just a difficult-to-execute beta and those that they call alpha protagonists (Americans, read: the Hatfields and the McCoys). They say the source of this dichotomy is a lack of general agreement on the definition of alpha in the long-only world, let alone in the hedge fund space. 

In attempting to mediate this feud, Jaeger and Wagner propose a sort of continuum from real alpha to alternative beta to traditional beta: 

If the specific return is available only to a handful investors and the scheme of extracting it cannot be simply specified by a systematic process, then it is most likely real alpha. If it can be specified in a systematic way, but it involves non-conventional techniques such as short selling, leverage and the use of derivatives (techniques which are often used to specifically characterize hedge funds), then it is possibly beta, however in an alternative form, which we will refer to as ‘alternative beta’. In the hedge fund industry ‘Alternative beta’ is often sold as alpha, but is not real alpha as we define it. If finally extracting the returns does not require any of these special hedge fund techniques but rather long only investing, then it is ‘traditional beta’. 

Alpha: “Dark Matter” or Left-overs from Dinner?

Building on Fung & Hsieh’s seminal hedge fund factor modeling work, Jaeger & Wagner describe alpha as: 

the dark matter of the hedge fund universe. It can only be measured by separating everything else out and seeing what is left. In other words, alpha is never directly observable, but is measured jointly with beta. It can only be indirectly quantified by separating the beta components out. 

As a result, say the authors, alpha amounts to a garbage bag of inexplicable returns. This bag might contain real alpha or simply just risk factors that have not yet been discovered. (We would submit that two might actually be one in the same). 


Beta in Alpha’s Clothing 

Like many before them, Jaeger and Wagner suggest that beta is actually dressing in alpha’s clothing (Transvestite beta?  Eeeuww!). 

We estimate that up to 80% of the returns from hedge funds originate as the result of beta exposure (i.e. exposure to systematic risk factors) with the balance accounting for manager skill based alpha (or not yet identified risk factors). 

We at AllAboutAlpha.com might remove the or in the parentheses above since we believe that skill-based alpha is the exploitation of not yet identified risk factors. 

Hedge Fund Indices: Alpha or Beta? 

The authors review the commonly cited problems with hedge fund indices (survivorship bias, backfilling etc.). But they depart from the usual griping to define a true test for a hedge fund index: 

The true test of whether a hedge fund index is a valid investment vehicle is whether there is a secondary market for hedge funds, whether one can construct derivatives from it and whether it can be sold short. The possibility of short selling and constructing synthetic positions based on derivatives (in a cost efficient way) creates the prospect of arbitrage opportunities using the hedge fund indices. Ironically such arbitrage opportunities would most likely be exercised by hedge funds, in a sort of Klein bottle of investments that contain themselves. 

Alpha’s Future Career Prospects

The authors run through each major hedge fund sub-index and describe the explanatory power of their model – including the amount of alpha inherent in each strategy. But then they rain on the hedge fund parade: 

There is good reason to believe that generally the average alpha extracted by hedge fund managers is destined to decline. As a matter of fact, we can already today observe that alpha has grown smaller in size over time. 

They go on, like many others, to hypothesize that increasing hedge fund asset flows are ironing out market inefficiencies. Although they do throw the hedge fund industry a bone: 

However, there is no good reason to believe that the global capacity for alpha which is ultimately a function of how many inefficiencies the average global investorwill tolerate actually decreased over time that dramatically. 

An Alternative Explanation 

They propose a second hypothesis to explain low hedge fund returns: that the average quality of manager is decreasing. We like this hypothesis (although many of our best friends are hedge fund managers). Even if net global alpha is zero (which it is), then a sub-set of managers identified as hedge fund managers could, technically, come out on top if they showed some persistence in their positive returns. 

As Jaeger and Wagner suggest, alpha-generating hedge fund managers may, in fact, be taking less obvious cues from the market to make a trade: 

Alpha might depend on market related variables other than prices which are not so easily captured in our risk based models, such as trading volume, open short interest on stocks, insider activity, leverage financing policies of prime brokers, etc. 

And here is where the debate heats up. Are returns generated by the careful analysis of leverage financing policies alpha or beta? Perhaps they used to be alpha. But watch out! As soon as Jaeger and Wagner (and hoards of academics) catch up with you – it morphs into beta.

Alpha, Shmalpha! 

In conclusion, the authors say that our obsession with alpha (returns that can’t be traces to any conceivable risk factor) is misplaced. Rather, orthogonal hedge fund betas (a.k.a. exotic betas, alternative betas) are the primary benefit to be derived from hedge funds. 

the future growth prospects of the hedge fund industry become quite compelling considering that we are far from any limit with respect to beta capacity in the hedge fund industry. While the search of alpha surely remains compelling, we believe it is investment in alternative betas which will be more and more the key to successful hedge fund investing in the future.  

Whither Peak Alpha? 

And this leads us to the most important conclusion in this paper. The authors say that the global tolerance for market inefficiencies is 0.25% of global equity values (US$88 trillion). That’s only about $200 billion of true alpha. They figure that hedge fund managers, as a sub-set of all investment managers, can take about 25% of this alpha pie, or approximately $50 billion. Assuming those returns of $50 billion represented about 15% ROR across all funds, the capacity based on pure alpha alone is about $350 billion – much smaller than the current size of the industry. 

BUT, since the authors have shown us that only 20% of hedge fund returns are true alpha (the rest is made up of various forms of beta), overall hedge fund capacity is 5x larger than this.  They essentially conclude that “peak alpha” will be reached when the hedge fund industry reaches approximately $1.8 trillion. 

At $1 trillion, we’re only about 55% of the way there.  So the only thing Jaeger and Wagner left unsaid was “keep on truckin'”.

Read Full Article 

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  1. Noël Amenc and Lionel Martellini
    May 13, 2013 at 9:06 am

    In the present article, a number of comments are made about a paper we published in the European Financial Management Journal (Amenc, N., L. Martellini, J.-C. Meyfredi and V. Ziemann, 2010, Passive hedge fund replication — Beyond the linear case, European Financial Management Journal, 16, 2, 191-210.) We feel that some of these comments deserve a response, as they might be misleading for the reader who is not overly familiar with the research.

    The contribution of our paper published in the European Financial Management Journal is to extend Hasanhodzic and Lo (2007) by assessing the out-of-sample performance of various non-linear and conditional hedge fund replication models. In a nutshell, our ambition was to improve the performance results in Hasanhodzic and Lo (2007) by considering more sophisticated models and we were quite surprised to find that going beyond the linear case does not necessarily enhance the replication power.

    The article “Hedge Fund Replication: A Re-examination Of Two Key Studies” claims that our paper “includes some very helpful analysis […] but whose conclusions are undermined by selective omission. For instance: Even though there was over two years of live data from replication indices that showed strong results with high correlation through the crisis, the authors neglect to include this and focus instead on re-doing the Lo analysis with the admittedly incomplete five factor set.” We indeed decided not to analyze live performance data from passive replication products, and this for two reasons. First of all, this was not the focus of our paper, which instead was (as mentioned above) to try and improve over linear replication models. Secondly, we did not feel that two years was a sufficiently long sample to allow for any meaningful statistical analysis. It is our belief that showing coherence in the scope of a research project paper, and avoiding meaningless statistical analysis, should be called something other than “selective omission.”

    A second criticism made in the article “Hedge Fund Replication: A Re-examination of Two Key Studies” is that we use a selection of useful factors for each strategy, as opposed to using a large identical set of factors for all strategies. This criticism is phrased as follows: “By starkly reducing the factor set, the authors essentially designed an experiment that was bound to fail.” Unfortunately, we have found that while including more factors improves the performance of replication models in-sample, it tends to hurt the out-of-sample performance of such models. In short, parsimony is a well-known necessary condition for out-of-sample robustness, and we feel it is misleading to claim that one only needs to add an increasingly large number of factors to generate satisfactory hedge fund replication performance.

    Finally, a comment is made that “It is difficult to read this paper without the sense that the authors, who are closely tied to the fund of hedge fund industry (and funded by Newedge), had a predetermined agenda.” We feel that this comment is out of place. EDHEC-Risk has always been known for publishing unbiased academic research and at no point in the research process did Newedge intervene to influence the results in any possible way. In the same way that we consider that professionals have the right to be taken seriously and to be criticized for what they write and not for what they are when they express scientific views, we believe that authors from the academic world deserve the same level of respect. If the only real argument for criticizing a research paper is to disparage the authors’ conduct with no evidence, then we do not think that this criticism is admissible. Just like we think it is logical to display the financial contributions to our research programs that the Institute receives from our sponsors (the authors are not beneficiaries), we also think it is logical for this concern for transparency and the sponsor’s desire to support transparent and independent research to be recognized and not denigrated.

  2. Andrew Beer
    August 15, 2013 at 12:05 pm

    Dear Professors Amenc and Martellini:

    My apologies for the delayed response. Thank you for taking the time to read and provide a critique of my note. I will respond in order:

    1. The reason I highlighted the live performance was that the extant replicators were largely successful at tracking industry returns in 2007-09. As a practitioner and researcher, this is valuable information. It was not a coincidence that the models had similar features — 24 month window length, 5-8 factors across major asset classes, etc. Those parameters were chosen because highly capable researchers at investment banks and asset management firms were conducting similar experiments and reached similar conclusions. Consequently, it seemed to me at the time that there was a lot of other research and live validation that a variant on the Hasandhozic/Lo experiment could work well. This seemed pertinent to me, but perhaps it wasn’t to you.

    2. We’ve found that more factors do in fact improve out of sample results, but up to a limit. Since I don’t have your research, I cannot comment on the specific results you refer to. I fully agree with the concept of parsimony, which we’ve embraced while other firms have added unnecessary factors for appearance of complexity. In addition — and this may simply be a semantic issue — I don’t see how going from 5 or 6 factors to one or two is an “extension” of the study. Instead of working to extend or modify the H/Lo factors, you seemed to scrap them entirely and start again with a much narrower pool — one or two factors for many sub strategies. At the time, I thought it was well established that one or two factor models didn’t work well. I still don’t understand this transition in your paper and it seems to me like you ended up with a very different study (perhaps “Can a two factor model explain hedge fund sub sector returns out of sample?”). As a practitioner, my interpretation of this was that the poor outcome was a foregone conclusion, and hence I questioned why it was included.

    3. I apologize for the insinuation. This was based on a rumor at the time of publication — I don’t remember the source, probably from one of the banks who of course had their own agenda. As a practical matter, though, I would argue that no research is unbiased. As a liberal arts major, I am trained to read into subtext, and my strong impression from reading your papers and the way they were structured was that you had a vested interest in arguing against what you describe as “passive” replication. If I misinterpreted this, then I apologize.

    If you would like to have a live debate on any of these issues, please feel free to contact me directly. And thank you again for taking the time to read and carefully respond to my submission.

    All the best,


  3. Prof Jim Liew
    May 5, 2015 at 11:19 am

    That definitely would be fun to see a live debate! :) Did you guys do it?

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