Newly-released government UFO files aren’t the only controversies pitting skeptics against “believers” these days…

Hedge fund replication is back in the news today with the publication of the results from a survey on the topic conducted last winter by French research institute Edhec Risk and Asset Management Research Centre.  While the results are somewhat dated, they are a good recap of the concept as a lead-up to Edhec’s annual alternative investment conference in London in a couple of weeks (Edhec’s “Alternative Investment Days“).  The bottom line: polarization between those who believe there may be some value in the exercise and those who ridicule it as a hoax.

Regular readers may recall our own poll on this topic (conducted in partnership with conference producer Terrapinn) conducted around the same time (winter 2008).  We were curious to see if our findings lined up with those of Edhec and were encouraged to see that both surveys seemed to have yielded roughly the same results - with a few notable exceptions.  Edhec’s sample was about the same size as ours with slightly more asset managers and fewer end investors.  While we did not ask about geography, Edhec notes that its sample was predominantly European.  As we wrote in the commentary for our recent 130/30 survey, respondents to surveys like this are likely to be skewed toward those with an existing interest in the topic.  As a result, caution should be used in extrapolating the results (of both surveys).

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The Fall issue of the Journal of Alternative Investments contains a great 75 page section on hedge fund replication.  Articles cover the latest developments in the two major techniques used to approximate hedge fund returns (factor and distributional replication), performance characteristics of actual hedge fund replication programs, and practical hurdles to implementing these programs.

These articles have begun to attract interest from the hedge fund and broader financial communities.  One paper by Jean-Francois Bacmann, Ryan Held, Pierre Jeanneret and Stefan Scholz called “The impact of missing factors on replication quality” has caught the eye of AllAboutAlpha.com contributor Pierre Laroche, head of R&D and Innocap, a joint venture between Canada’s National Bank and BNP Paribas (related post).  Below, Laroche examines the delicate balance between adding too many factors and too few factors in a factor-replication model.

Special to AllAboutAlpha.com by: Pierre Laroche, Managing Director, R&D, Innocap Investment Management.

The issue of “missing factors” was raised soon after several major financial institutions launched their HF index replicators last year.  The use of traditional regressions by these products raised some questions about the number of factors required to fully capture the nuances of HF returns.  Specifically, the more factors one adds, the more likely those factors are to be collinear (correlated), thus lowering the regressors’ efficiency. This property of regression-based HF replicators (along with other properties such as their inability to track abrupt changes in weights) pushed financial institutions to look for more appropriate tracking models.  One such model is the “Kalman Filter” (KF).

KFs can contribute greatly to hedge fund replication models for at least two reasons:

• Their tracking algorithm explicitly takes into account that exposure to return-generating factors are dynamic (they vary through time).
• The quality of the estimated weights is impacted much less by the presence of highly correlated factors.

In other words, KFs are influenced less by using a small number of highly correlated factors.  Unfortunately, however, they do not settle the central question of the ideal number of factors to use when trying to “replicate” HF returns.

It is well known that working with too many factors increases the danger of overfit which, ceteris paribus, usually results in a lower in-sample tracking error but a higher out-of-sample tracking error.   To mitigate risk, the “optimal” subset of factors is usually just based on heuristics known as the “information criteria”.  For example, it is often suggested that HF index replication use only 4 to 6 factors - sometimes even less.

However, it is a mistake to select the number of factors solely on these guidelines because:

1. These models completely ignore the results of more than 25 years of sound empirical literature on financial markets.  The arbitrage pricing theory (APT), for Instance, suggests there are some factors that are often totally overlooked.  The interest rate slope is perhaps the best example.  It requires a long-term interest rate factor - a factor that is not generally included in the information criteria.
2. The standard list of factors for HF replication are well suited to linear regression-type replication models.  But it’s still not clear that we can extend their results to KF-based replication models.
3. Working with too few factors also has a fairly important hidden cost: model risk.  This is a lesser known, but still crucial, problem identified by econometric literature.

Let’s focus on the last point here.  To illustrate the problem of model risk (too few factors), imagine a portfolio composed of three factors whose allocations vary randomly around 0.4, 0.4 and 0.2 weightings for a long period of time.

Then imagine that these factor weightings suddenly shift to 0.25, 0.25 and 0.4 following a change in market conditions.  The following figure illustrates such a scenario (with the three factors represented by the green, red and blue lines):

Now let’s use two Kalman Filters to infer the allocations to these factors from the observed monthly returns of the portfolio.

The first filter only uses the first two factors (the ones that would have been chosen by the “information criteria”) and the second filter uses all three assets. The following table contain the out-of sample monthly tracking errors of these two models:

We see that before the market regime change, the two-factor model performs better even if we know that the third asset contributes to the portfolio return.

But after the change in market conditions, the effectiveness of the two-factor model crumbles.  In fact, its monthly out-of-sample tracking error is more than twice as large.  Across the whole period, the three-factor model performs better even if the after-change period is much shorter that the initial period.  Clearly, the third factor adds significantly to our ability to “replicate” this portfolio.

But this is not the end of the story.  As can be seen in the upper panel of the exhibit below, during the pre-change period, the fit of the two-factor model is not only very good, but the two estimated weights are remarkably stable at around 0.5 respectively (which is the anticipated result of the two-factor model since they both have a 0.4 weight in the portfolio).

After the market conditions change, however, the allocations still oscillate around 0.5, but they become extremely volatile, which results in significantly higher trading costs. The estimated weights in the three-factor model do not, however, exhibit such an erratic behaviour.  The estimated weights remain not only accurate, but they are highly stable as well (as can be seen in the lower panel of the exhibit below).

In conclusion, in line with Bacmann et al’s paper in the Journal of Alternative Investments, choosing the right set of factors is a delicate compromise between efficiency (the fewer factors the better) and the cost of discarding a factor in case market environment changes (the more factors the better).

- P. Laroche, November 2008

The opinions expressed in this guest posting are those of the author and not necessarily those of AllAboutAlpha.com.

Day Two of Terrapinn’s annual “Alternative Beta and Hedge Fund Replication” conference in New York kicked-off this morning with an appeal from MIT’s Andrew Lo for hedge fund managers and hedge fund “replicators” to lay down their weapons.   As he wrote in a recent article on the topic:

“…hedge fund beta replication is neither better nor worse than direct investments in hedge funds-it is simply different because replication strategies trade off the full return of hedge funds for improved transparency, liquidity, capacity, and fees.”

Thinking of firing your hedge fund manager for being long Lehman?  No worries, argued Lo.  You can use hedge fund “clones” as a transition tool so you can maintain your exposure to their strategy while you search for another manager.

Have to invest $3 billion in hedge funds quickly and the best hedge funds are all closed to new investments?  Again, no worries.  Lo told the audience this morning that hedge fund replication products are a valid alternative even though they lack the alpha of the world’s elite managers.

In other words, argued Lo, hedge fund replication addresses investors’ extra-economic needs.  While they may not provide true alpha, they remain an elegant solution that just needs to applied to the right problem.

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At a conference on “alternative beta and hedge fund replication” here in New York today, attendees debated questions such as: What is hedge fund beta? What do institutional investors want from hedge funds and has this changed? and Is 2& 20 at risk?

But the elephant in the room was the question of what will happen now that so many short positions - the bread and butter of the hedge fund community - are no longer executable in many parts of the world?  The ban on short-selling seems to be snowballing as various jurisdictions slam the door in an effort to avoid becoming the last place on earth to short financials.  (For a great run-down of the current situation in various countries, see this post at FT Alphaville).  As one attendee here told me today, “This could be spell the end for hedge funds - at least in the short term”.

Will these new constraints on short selling breathe life into the recently anemic “hedge fund replication” business?  If institutional investors begin to steer clear of hedge funds but still want to tap into their unique return distributions and lack of correlation to equities, then we may be on the verge of a renaissance for these funds.

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It used to be that the term “hedge fund clones” referred exclusively to so-called “hedge fund replication” (a.k.a. “alternative beta) strategies.  We noted in December 2006 that the term was already well worn.

But now Man Investments has borrowed the term to describe not just alternative beta strategies, but also other emerging strategies such as 130/30, investible hedge fund indices and “permanent capital” (exchange-listed shares in hedge funds).  What’s the common link?  They amount to what Man calls “hedge fund alternatives” that address the barriers of “high fees and comparatively poor liquidity” that prevent many institutions from investing in hedge fund strategies.

In a report issued this month called, “Attack of the ‘hedge fund’ clones: Investable indices, Alternative beta, 130/30, Permanent capital“, Man ties together these loosely related concepts into one framework that is similar in its intent to this 2007 article, but with a lot more detail.

As a result, this white paper is a great overview of alpha-centric investing that is succinct and easy to read - especially if you like smiley face icons…

This table goes on to list the replicability of all major hedge fund sub-strategies.  Hedge fund replication enthusiasts will recognize much of this data from its various original sources (most of which are available in our Hedge Fund Replication research dossier.  But for the rest of us, this chart is a good summary.

The white paper goes on to list all the major hedge fund replication strategies and tracks the performance since last summer for all strategies whose performance is publicly-available…

Of course, you can’t tell from the above chart which strategy is actually better able to “replicate” hedge funds.  Even displaying these funds as a horse-race highlights the irony in most of their marketing messages.  Are they designed to “replicate” or “perform”?  And if they are truly meant to “replicate” some hedge fund index, then which one?

The paper shows, for example, that at least two major offerings blew away the HFRX Index (a daily-priced, investible index that generally performs quite a bit worse than the non-investible equivalent, see related posting), and just about matched the HFRI Fund-of-Funds Index (which also tends to underperform the main single-manager hedge fund indices due to the presence of the second layer of management fee charged by the fund of funds).

The report also cites research by AllAboutAlpha.com and Terrapinn that investor interest in hedge fund replication is all about liquidity and fees:

The report goes on to say more about investable indices, 130/30 and permanent capital.  But despite all the potential benefits of these “hedge fund alternatives”, nothing beats the real thing:

“FoHF have been and will continue to be an integral part of hedge fund investing. While investors do have alternatives such as direct investing, investable indices, 130/30 or alternative beta replication, FoHF are still the most suitable route for most investors aiming to include hedge funds in their portfolios. This is the case for both private and institutional investors. The long list of casualties in the hedge fund industry has also driven allocators toward the security and diversification provided by a FoHF. On the other hand, as the FoHF industry matures and partially converges with long only asset management, FoHF are having a harder time beating the average return for all hedge fund strategies. Therefore the fees that FoHF charge have to make economic sense. We believe investors should weigh up the fee structure with the value added of the FoHF manager such as fund picking, asset allocation, timing of subscriptions and redemptions, risk management, portfolio construction and continuous monitoring.”