*Not one to shy away from a debate, Professor Harry Kat responds to last week’s column by Dr. Lars Jaeger on traditional and alternative betas in hedge fund replication. While Kat agrees with several of Jaeger’s arguments, he wonders if the mechanical-trading approach to delivering alternative beta isn’t just too complex.*

**Some Comments on Lars Jaeger’s Hedge Fund Replication and Alternative Beta: Two different ways of looking at replicating hedge funds**

**Special to AllAboutAlpha.com by:** Professor Harry Kat, Cass Business School, London

In a note last week on AllAboutAlpha.com, Lars Jaeger discussed the two most common approaches to hedge fund replication: factor models and mechanical trading rules designed to capture alternative betas. Although I agree with several of the points that he makes, his comments are only part of the hedge fund replication story. In this brief note, I will attempt to fill in the picture. Most of my comments can also be found in some of my earlier writings on the subject. But it doesn’t hurt to repeat them, however, as we need to be clear on the issue.

What is very important when trying to make sense of hedge fund replication products, is to keep an eye on what they actually aim to replicate. Almost without exception they aim to replicate, either explicitly or implicitly, a diversified hedge fund index. So hedge fund replication isn’t really about replicating hedge *funds*. It is about replicating hedge fund *indices*.

Does that matter? Isn’t a hedge fund index just a portfolio of hedge funds? Yes, it is. But therein lays the problem. When combining hedge funds into a portfolio, many typical hedge fund features diversify away. As a result, diversified hedge fund indices have only a few hedge fund-like properties left and are mainly driven by equity and credit risk. This is easily confirmed by calculating their correlation with the S&P 500 for example. The important conclusion from this is that we do not need alternative betas to replicate a diversified hedge fund index. As Jaeger also suggests, it is primarily driven by traditional betas. With precious little alternative beta actually present in a diversified hedge fund index, the main problem when replicating it is traditional beta.

These betas have to be estimated from historical data. And it is here that factor models potentially fall short. Estimating an index’s factor exposures from historical data reveals the average over the time period studied, not necessarily the current factor exposures. Therefore, there is a significant lag between the time when the betas change, and the time when the model finds out about it. Of course, whether this is really a problem depends very much on the speed and extent by which the index betas change over time.

As always, the proof of the pudding is in the eating. So let’s look at the performance of the factor model-based Goldman Sachs ART Index. Bloomberg (ticker: ARTIUSD) provides back-tested data on this product starting in December 1996. We plotted the evolution of the ART Index as well as the HFRI Composite Index and HFRI Fund of Funds Index in Figure 1 below.

*Figure 1: Evolution HFRI Composite, HFRI Fund of Funds and Goldman Sachs ART indices.*

From this chart, we see that the ART Index tracks the HFRI Fund of Funds Index quite well. This is remarkable as over this time period both hedge fund indices’ exposure to the stock market has increased (1996 – 1999), dropped (2000 â€“ 2003), and increased (2004 â€“ 2007) significantly. Although one can always think of different scenarios, this strongly suggests that changes in the factor exposures of diversified hedge fund indices do not necessarily invalidate the factor model approach. In other words, when replicating a diversified hedge fund index the backward-looking nature of factor models might actually be less of a problem than is sometimes suggested.

This brings us to the alternative to factor models: mechanical trading rules. Many hedge fund strategies are well known – especially to their prime brokers – and can easily be captured in a mechanical trading rule. In fact, these mechanical strategies form the foundation of the Alternative Beta revolution, since alternative betas are simply a measure of hedge fund indices’ exposure to the returns generated by these strategies.

How can mechanical strategies be used to replicate a hedge fund index? Well, that’s straightforward: mechanize a large number of different hedge fund strategies and subsequently combine them into a portfolio.

At first sight, one might be inclined to think that such an alternative beta approach to hedge fund index replication should be far superior to a factor model. After all, it relies on deep financial economic reasoning. Upon reflection, however, things are less obvious. When mixing all those different strategies, a lot of their idiosyncratic features get lost in the diversification process. This is similar to what happens when creating a diversified hedge fund index. The result will therefore again heavily depend on equity and credit risk. So is the Alternative Beta approach indeed superior to the factor model approach? Or is it just a very complicated way of doing something very similar?

As I said, the proof is always in the pudding. The chart below contains live data (gross of fees) on the oldest of such mechanical trading rule-based funds – starting in October 2004 â€“ the Partners Group ABS Fund (Bloomberg: PGABS). We plotted the evolution of the ABS fund as well as the HFRI Composite Index and HFRI Fund of Funds Index in Figure 2 below (deducting a fixed 100bps fee – instead of the 1.25% plus 15% with no hurdle that is actually charged by the fund – to make it comparable with some of the other replication products).

*Figure 2: Evolution HFRI Composite, HFRI Fund of Funds and ABS Fund*

In Figure 2 we can see that the mechanically-traded fund has had difficulty keeping up with the HFRI Fund of Funds index recently. In January, for example, the fund was down 5.5%, while the HFRI indices only lost 2.26% and 2.93% respectively. We also see that the mechanically-traded fund is more volatile than both hedge fund indices. Deleveraging the fund to a sample volatility equal to that of both hedge fund indices shows that, over the period in question, the fund has underperformed the HFRI Fund of Funds index (and therefore most factor model-based replication products). One possible reason for this could be that at least some of the strategies included in the fund are among the best known and most popular in the industry and may have reached capacity by now.

Based on the analysis above, it seems the Alternative Beta approach may sound better on paper than it does in practice. It confirms what econometricians have known for a long time: complex models often perform worse than simpler ones. It was for exactly this reason that Albert Einstein (or was it his wife Mileva?) recommended that models should always be kept as simple as possible.

There is no question that thinking about investments and investment portfolios in terms of risk factors, whether traditional or alternative, is very useful. My sense is that rigorous practical implementation of this framework, however, is taking the concept just one step too far. Although we use a lot of the mathematics these days, finance will never be like physics.

*-HMK 20/02/2008*

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

## 3 Comments

February 22, 2008 at 9:44 am## Jason Ruspini