The discussion on alpha versus beta in the breakdown of investment returns is as old as the capital asset pricing model which defined these terms about 40 years ago. The discussion has finally reached the hedge fund industry, an area of investing traditionally associated with ‘pure alpha’ and therefore often referred to as driven by ‘absolute returns’ and the debate on sources of hedge fund returns has started to change the landscape of hedge fund investing. Academic research and investors alike have begun to realise that also for hedge funds the ‘search of alpha’ must begin with the ‘understanding of beta’.

At the same time we have started to realise that hedge fund beta is often very different from traditional beta. While both are the result of exposures to systematic risks in the global capital markets, beta in hedge fund investing can be significantly more complex than traditional beta. We shall therefore refer to this beta as ‘hedge fund beta’, or synonymously ‘alternative beta’. The extraction of the latter requires non-conventional techniques such as short selling, leverage and the use of derivatives, techniques which are often directly used to characterise hedge funds.

Examples of alternative betas extracted by hedge funds include various equity style factors (small cap versus large cap, value versus growth, momentum), event risk premiums, exposure to volatility (Vega risk), commercial hedging demand premiums in the global futures markets, and various types of spread positions such as those employed in FX and interest rate carry strategies.

The increased academic and non-academic effort in modelling and understanding hedge fund return sources has finally reached Wall Street. Several product providers have announced their intention to launch so-called ‘passive hedge fund products’ or, as they have more recently been referred to, ‘hedge fund clones’. The underlying claim is that we can represent hedge fund-like returns at significantly lower fee levels to the investors. In fact, a new buzz term is out: hedge fund replication.

Where did the alpha go?

There is good reason to believe that the average alpha extracted by hedge fund managers is destined to decline. We can already observe today that alpha has decreased in recent years. Figure 2 displays the time-dependent alpha of several hedge fund strategies based on a rolling regression over a 60-month period. Independent of our research, diminishing alpha has been observed elsewhere and *Fung et al* report on this phenomenon in one of their later research papers. Will the alpha in hedge funds disappear? Probably not, but it will become harder to identify and isolate in the growing jungle of hedge funds.

Why hedge fund replication is attractive: The charm of saving fees

The beauty of beta - be it traditional or alternative - is that it can be systematically described, modelled and replicated. And the biggest attraction in replicating hedge fund return profiles is simply described - fees.

If beta (in alternative form) accounts for 80% of hedge fund returns and savings of 2% management fee and 20% performance fee can be achieved on these returns, approximately 2.5- 3.5% pa of total fees can be eliminated compared with a fund of funds. Furthermore, the investor saves an additional ‘fee level’, avoiding asymmetric performance fees charged in a fund of fund’s portfolio. Our estimates for this additional fee layer range from 0.4% to 0.8% per annum.

Financing costs for leverage represent a third, even less transparent, additional fee level that replication strategies avoid by trading futures and options on margin. We can summarise that replication approaches potentially offer significant fee savings of around 350-575 bps/pa, an advantage that conventional managers of broad hedge fund portfolios will find it hard to compete with.

Linear factor models

The basic approach to modelling alternative betas follows along the lines of the various asset pricing models in standard finance. Indeed, a growing amount of academic literature on (linear) systematic risk factors and hedge funds’ exposure to these exists by now. However, the quality of the offered models differs strongly for different hedge fund styles. In other words, the underlying factor models for the different strategy sectors offer a variable degree of explanatory power for hedge fund returns. While long/short equity has been well modelled in academic research, models for strategies such as arbitrage strategies (equity market neutral, convertible arbitrage) display rather limited explanatory power (ie, low R-squared values in linear factor models).

Many of the recently announced efforts on passive hedge fund replication are based in one form or another on these linear factor models. However, such a ‘passive’ hedge fund investing approach has pitfalls and limitations:

o Hedge fund exposure cannot be conclusively described in a stationary linear modelling context. We see plenty of evidence confirming that significant deviations from the linear risk exposures are typical for hedge funds. Where do the non-linear profiles in hedge funds come from?

— Hedge funds contain contingent payout profiles, imposed either explicitly through the inclusion of options into a typical hedge fund portfolio, or implicitly through managers employing conditional rule-based trading strategies.

— The beta exposure of hedge funds is not stationary. Most hedge fund strategies involve active trading in response to opportunities. In other words, hedge fund managers react dynamically to changing market conditions with shifts in the exposure profile.

o Factor models are based on past data only. In contrast, hedge fund managers base their decisions on more recent and current data and developments in the financial markets. Consequently, linear factor models bear a significant time lag in adjusting their risk exposures. Estimating the parameters of the linear regression factors based on past data is similar to driving a car and only looking into the rear mirror.

o A systematic (and even ‘passive’) approach to modelling and investing into individual hedge fund strategies leaves the problem of asset allocation across the different strategy sectors wide open. Quite simply, a ‘passive method’ of creating an optimal hedge fund allocation does not exist because there is no ‘market proxy’ for the global hedge fund industry. The process of asset allocation is one of the key elements of added value of a portfolio manager and is ‘active’ by its very nature.

We are of the opinion that the various passive hedge fund products that have recently emerged should be discussed in light of these points.

Path to full hedge fund replication

How can we overcome the first challenge? By explicitly including the non-linear and contingent return profiles of hedge funds. This sounds simpler than it is in practice - the inclusion of non-linearity in the models results in far greater mathematical intricacies. There are two methods of executing this task: the explicit incorporation of options into the model, and the development of rule-based models of hedge fund strategies which implicitly consider the non-linear exposure.

We prefer the second route as it allows a more flexible adaptation to the dynamic nature of hedge fund strategies. For this we need to establish a set of transparent, rule-based strategies that mimic the hedge fund strategies and their (non-linear) risk exposures. This approach is not new, and the authors claim no intellectual property rights in this regard. To our knowledge, the idea of using strategy replications to model hedge fund returns was first developed in a 2001 academic paper by Fung and Hsieh for Managed Futures strategies, wherein the authors modelled the performance of a generic trend-following strategy using look-back straddle options. Since that date, they and others have applied this type of modelling to a variety of other hedge fund styles including merger arbitrage, fixed income arbitrage, and long/short equity. In most of these studies the employed trading strategies generally reached a good correspondence with the performance of the respective hedge fund strategy sector.

How do we challenge the second point? Instead of relying on and fitting our exposure to past hedge fund return data, we must take a step away from the data and dig into the economic principles of hedge funds’ return generation. In other words, we must directly model the underlying hedge fund risk premiums (alternative betas).

In the world of physics, molecules are described as combinations of individual atoms. Analogously, hedge fund strategies are compositions of individual (alternative) risk premiums. These ‘atoms’ of hedge funds can be described by rule-based risk premium extraction schemes, which we shall refer to as alternative beta strategies (ABS).

Partners Group has created the corresponding rule-based scheme which aims to replicate the numerous individual risk premiums across the global capital markets. The program consists of 19 strategies and has been trading live with a significant volume since October 2004 (current volume is $600m). Each component of the ABS program aims at extracting one single risk premium rather than directly replicating an individual hedge fund strategy. Each model further explicitly integrates the non-linear exposure profiles of the hedge fund by means of rule-based investment approaches.

The third problem refers to the question of asset allocation. Once the various risk premiums are identified and replicated, the next step is to integrate these exposures into an overall asset allocation. This is the decisive step towards the actual replication of hedge funds. We need to match the asset allocation hedge fund strategies with respect to the risk premiums.

Rephrasing this in the context of the above metaphor, we need to construct the molecules of hedge funds out of the risk premium atoms. This occurs on two levels. On the one hand we mimic the asset allocation of a particular hedge fund strategy sector and on the other the level of the asset allocation within the global hedge fund industry. The final goal is to establish an optimal risk/return and correlation profile of the overall portfolio. This constitutes an ‘active element’ and therefore compares to the (in most cases active) asset allocation of a conventional fund of funds.

However, we note that the ABS asset allocation has an important advantage over that of a conventional fund of funds: the atomisation of return sources into single risk premiums provides an additional degree of flexibility in the asset allocation. The portfolio manager has access to a higher granularity of risk exposure profiles, which are better defined and more transparent. The relative attractiveness and value in individual sectors can thus be more accurately defined.

Figure 1 displays the aggregate live performance of Partners Group’s Alternative Beta Strategies program (net of fees, independently calculated and audited daily NAVs) in comparison to an identically composed portfolio of the corresponding HFR investable sub-indices (as HFR does not have an index for Managed Futures strategies, we use MSCI’s Managed Futures index for the CTA sector). We emphasise that this performance is not back-tested, but rather was obtained in a real trading environment.

The out performance is conspicuous; the ABS program comes in ahead by an annualised 4.5%. At the same time, the correlation between the two return curves (based on weekly data) stands at 85%. The latter indicates that ABS captures the essential parts of the hedge fund return generation process. But how can we explain the out performance? The flippant but accurate answer is fees.

Differences between various models

A new hype has started to circulate in the global financial industry - hedge fund replication. A number of providers have already announced their intention of offering a corresponding product which uses the modelling techniques already described, however, attracting investors with back-tested performance numbers.

It appears inevitable that many more will follow. The dam holding back this new wave has finally broken and is bound to change the landscape of hedge fund investing. However, we must convey a clear warning to investors at this point: as attractive as back-tested performance numbers might be, they must by no means be taken at their full face value. Historically, we have seen a number of investment strategies which *a priori* looked great on paper but failed in reality.

Although we believe that most of the approaches currently offered have a solid as well as an intuitive economic basis as outlined above, investors should be prudent when investing in products with no actual track record.

The underlying general economic principles of all these approaches are very similar, namely extracting hedge fund betas. However, the individual approaches can differ substantially in the details. Although extensive comparisons are not possible because only a limited spectrum of different products is currently available, we are already in a position to determine the two poles that are likely to emerge in the landscape of products.

With the term top-down approach we refer to the simple and rather straightforward way of modelling hedge fund returns based on a linear replication of the past returns of a given global hedge fund index.

In contrast, the bottom-up approach to the replication problem consists of two steps. First, considering the level of individual risk premiums, ie, ‘atomising’ the hedge fund return components, and then in a second step reconstructing the allocation of the hedge fund industry to these risk premiums.

The top-down approach takes a given hedge fund index and regresses it against a number of chosen (investable) risk factors. This approach is solely based on fitting past data. As mentioned above, the non-linear risk exposures of hedge funds are left out of the equation here. Further, a global regression approximates only the most prominent risk type hedge funds are exposed to - the equity beta (including small cap beta). The crucial question of asset allocation across strategies and sectors remains with the chosen index provider. This is insofar problematic as the compositions and index construction criteria of the underlying indices still depend more on ‘committee decisions’ than on objectively determined rules.

In contrast, the bottom-up approach starts at the level of risk premiums which are modelled and extracted individually, with the non-linear risk exposures of hedge fund strategies being explicitly considered. As modelling and investing in hedge fund risk premiums (ie, alternative betas) requires alternative investment techniques, simple asset class exposures cannot do the job of extracting them. Instead this task requires the definition and implementation of rule-based trading strategies. We refer to these as alternative beta strategies. It is these rule-based strategies that enable the replicator to get to the atoms of hedge fund returns (ie, the risk premiums or alternative betas). Examples include trend following, spread trading and option strategies. We note that the definition and extraction of alternative beta strategies is not a pure job of mathematical optimisation but also requires sound understanding of hedge funds themselves. A fund of funds perspective can be extremely helpful here.

Once the various rule-based extraction schemes are defined, the second essential part of the bottom-up part of the replication then lies in the asset allocation, meaning the overall exposure scheme in a global portfolio.

We emphasise that there is no unique method or systematic scheme of performing this task. We must therefore refer to this as the ‘active element’ in hedge fund replication. At this point the hedge fund replicator finds himself in a similar position to a fund of funds manager challenged by the task of diversifying his portfolio across the various risk drivers in a hedge fund portfolio. However, guidance for this task is readily available from the traditional portfolio management industry where, over the past 50 years, various tools and methods have emerged and can be (partly) applied to hedge fund portfolio management. In fact, the better understanding of return sources and the clear definition and replication of risk premiums opens the door to applying these tools more directly (such as tracking error minimisation, quantitative portfolio optimisation, Bayesian tools, and so on).

Summary

The academic concept of hedge fund replication has started to show its strengths in a real trading environment. This approach justifies its existence by its significantly lower load of overall fees and therefore its potential to outperform conventional multi-manager hedge fund portfolios. With this, such products will possibly not only attract disgruntled HF investors, but also those who have stayed out of alternatives because of high fees, double fee layer, and low transparency. This development constitutes a further important step in the maturisation and institutionalisation of the hedge fund industry.

However, a simple factor analysis of the broad hedge fund universe based on past data estimation is in our view insufficient to capture the potential of this concept. Early academic work has realised that the integration of non-linearities is essential for properly describing hedge fund returns. Furthermore, replication models should include proper asset allocation across risk factors and strategy sectors. Hedge fund replication is therefore not merely a simple “job for the quants” but requires the understanding of the concept of each strategy,solid quantitative modeling and the fund of funds approach to portfolio management and asset allocation.

The current state of hedge fund research bears analogies to atomic physics at the beginning of the 20th century. We want to understand the ‘atoms’ of hedge fund returns, ie, their breakdown to individual risk premiums. And what we currently observe is the emergence of an underlying fundamental theory, or in analogy to physics, the theory of ‘quantum mechanics for hedge funds’.

The application of this theory to the real world of investing can have effects as revolutionary as applying quantum mechanics did to the world of chemistry and industrial technology. Hedge fund replication has already become the new buzzword in the hedge fund industry. With further product offerings and increased levels of modeling sophistication it is destined to grow above that level and become an entirely new paradigm in hedge fund investing. This might ultimately (as in the traditional investment industry) turn the alternative asset management industry upside down.

## No comments yet