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Despite having its 15 minutes of fame a couple of years ago, so-called “hedge fund replication” still seems to capture the imagination of bargain-hunting institutional investors (see related post). Regular readers and students of this labyrinthine field will recall that there are basically three ways to approximate hedge fund index returns using other means: Factor-based (investing in trade-able versions of off-the-shelf passive exposures), rules-based (using trading algorithms to essentially mimic the trading strategy of various classes of hedge fund) and distributional (re-creating the end result of hedge fund indices – their return distributions – without regard to the timing of returns or correlation with the index being replicated). Distributional replication models have so far been based on the dynamic trading of one particular asset – usually a futures contract – as opposed to the choice of underlying assets.

AllAboutAlpha.com contributor Professor Harry Kat and Helder Palaro formerly of the Cass Business School (at the City University of London) are widely credited with giving life to this approach (see original post). Nicolas Papageorgiou, Bruno Remillard, and Alexandre Hocquard from HEC Business School in Montreal proposed some modifications to this technique in 2007 (see related post).

A forthcoming edition of the Journal of Business Research will feature an article by a pair of academics from the University Tokyo who say they have made a significant improvement to the approach used by both teams of researchers. In their paper “A new hedge fund replication method with the dynamic optimal portfolio” Akihiko Takahashi and Kyo Yamamoto say that the “Kat-Palaro” method of distributional hedge fund replication failed during the credit crisis of 2008 (at least their version of the method – Kat is quick to say that his model is more robust than those of subsequent imitators).

The duo says that the CTA index illustrates the problem most acutely. As the following chart (from the paper) reminds us, CTA kicked butt in 2008…

However, when they ran their distributional model on 2008 data, they found it sadly lacking. The problem, they say is twofold: First, the commonly-used distributional model uses only one asset at a time and dynamically trades it to produce a unique and customizable return distribution; and second, the commonly-used distributional model assumes the position in the reserve asset must be long-only.

By extending the commonly-used model to multiple assets and allowing long and short positions in them, the researchers say they can replicate 2008 – something they argue existing models cannot do.

The table below, based on one in their paper, shows the performance of the commonly-used model (the “single asset” model) excluding 2008. As you can see, the model performs pretty well in replicating the “target” fund (the Eurekahedge CTA Index):

But in 2008, things were markedly different. Return, skew and excess kurtosis turn negative even though those statistics were all positive for the target.

Write the authors:

…(Kat and Palaro) claim that users of this method should choose the replicating tool that has the positive expected return factor uncorrelated to the return of the investor’s portfolio. Then, the long position for is justified. In this case, the choice of a replicating tool is crucial.

This isn’t the first time the choice of the so-called “reserve asset” has been the source of debate. In an exclusive interview with AllAboutAlpha.com back in 2007, Neil Simons of Northwater Capital Management raised the same issue. Their 2007 paper on the topic noted:

The risk-adjusted returns achieved from distributional replication are dependent upon the selection of market factors utilized within the replication process. Alteration of the market factors results in large differences in risk-adjusted performance.

In their original papers Kat and Palaro contend that one asset is enough, but that the choice of asset might still be an open question. As they write in footnote #22 in “Who Needs Hedge Funds?“…

The decision to use Eurodollar futures is primarily based on liquidity considerations. Research into the characteristics of the optimal reserve asset is ongoing, however, and may lead us to change the reserve asset in a later version of this paper.

In addition to the lack of multiple reserve assets, the duo notes that the inability to short the reserve asset was also a culprit in its poor 2008 performance:

Although the replication by single asset with only long position performed well before July 2007, it incurred a large drawdown after this period. This is because the replicating tool substantially declined but the method could not take the short position for the asset.

In response to these lingering questions, Takahashi and Yamamoto propose a “multiple asset” model with shorting. Their model, they say, approximates the target much better in 2008…

Oddly, the proposed “replication” model seems a little lacking when it comes to returns – it beats the target by around 40 bps a month. In any event, when you add in 2008 and look back over the past 8 years (Jan. ‘02 to Oct. ‘09), Takahashi and Yamamoto argue that their “multiple asset” model is a better approximation of CTA returns (see chart and table below).

The paper only addresses the CTA index – the one where the existing distributional replication models seem to have fallen short the most in 2008. Still, Takahashi and Yamamoto’s conclusion is clear. As they write:

Moreover, extension to the multiple assets succeeded in replicating the positive skew and negative excess kurtosis, while single asset did not. It also made the correlation with the investor’s existing portfolio closer to the target. This confirms that the extension of Kat and Palaro (2005) and Papageorgiou et al. (2008) to multiple trading assets with both long and short positions improves the performance of the replication.

Source: A New Approach to Hedge Fund Replication