Hedge fund replication has recently garnered attention in some publications and in the market as a possible substitute for hedge fund ‘beta’. In this article, we look at the literature on hedge fund replication and the popular quantitative techniques for building replicators. We also provide a summary of the performance of a replication product that has had an adequate amount of trading history. Our conclusion is that hedge fund replication, while attractive in concept, solves few of the problems that it purports to address and introduces new risks that investors should be aware of.

Why are replicators desirable?
Hedge funds are seen as attractive investments that provide diversification for traditional stock and bond portfolios, but investing in them comes with the acceptance of a lack of transparency, complexity of strategy and implementation, leverage, and restrictions on investing. Also, the industry is characterised by less liquidity, capacity constraints, and higher fees than are generally charged in the traditional (long only) asset management industry. Lastly, many investors are concerned about headline risk arising from the activities of a single manager, be it the failure of the fund itself or, in rare cases, fraud perpetrated by the manager. This has led many investors to seek hedge fund-like returns without the associated complexity and research burden of actually investing in hedge funds.

In response to that desire, hedge fund replicators attempt to mimic the returns of hedge funds and hedge fund indices by strategically allocating among liquid instruments corresponding to common market risks that correlate with past hedge fund performance. Replication products are constructed with liquid ETFs, futures and forwards and charge fees that are consistent with those charged in the long only asset management business, with the end result seeming to address many of the issues associated with hedge fund investing. In theory, if investors could achieve the benefits of this asset class by investing in a rotating basket of ETFs, futures and forwards, they have a legitimate solution to the problems associated with hedge funds. For the firms that sell these products, the result is even better; they now have a scalable offering that can be sold in bulk to an investor community that increasingly demands the return characteristics associated with hedge funds.

Replication techniques
Techniques for replicating hedge funds fall broadly into two categories: linear factor replication and distributional replication. Linear factor replication, a statistical technique based on William Sharpe’s (1992) work in ‘style analysis’ is the simplest and most widely used method. The application to hedge fund replication was first proposed by Fung Hsieh (1997) and receives detailed treatment by Hasanhodzic and Lo (2007). This replication model uses the historical returns of a hedge fund or a hedge fund index to decompose the returns into two components, manager alpha and market beta. Most practitioners use the linear factor replication technique at the hedge fund index level with about two years of historical data and monthly rebalancing.

Distributional replication is a technique that was developed by Harry Kat, Ph.D., of the Cass School of Business in London. Instead of trying to mimic the monthly returns of a hedge fund, this strategy attempts to identify and replicate its long-term statistical properties and match the returns over a period of several years. Properties important to investors such as the expected return of the hedge fund, volatility of the returns, correlation with other investments and the frequency of extreme events are analysed using historical data and replicated using equity, interest-rate, commodity and currency futures contracts. Kat and his colleague, Helder Palaro, have created and licensed a software programme that uses the distributional replication technique to create portfolios of futures contracts that attempt to replicate individual hedge funds and hedge fund indices. At this time a small number of institutional investors have licensed the programme for their own use, but it is too early to elicit feedback.

Distributional replication, like linear factor replication, needs historical data of hedge funds and hedge fund indices to estimate their statistical parameters, but many hedge funds have not been in business long enough to have generated a reasonable amount of data for statistical analysis. Stephen Brown, a statistician at NYU, in a New Yorker article about Kat, is quoted as saying, “On the basis of very limited data, it is a real challenge to construct an accurate and robust model of hedge fund returns.” In addition, because of its complexity and the use of less broadly traded instruments, this technique may suffer from a similar lack of transparency, possible illiquidity and capacity constraints as the hedge funds themselves, rendering thismethod relatively unattractive to investors.

The question of whether hedge fund returns can be replicated successfully using the above techniques should really be posed as ‘how much of a hedge fund’s expected return is due to identifiable market risk factors (beta) versus manager skill (alpha)?’ If it is a significant portion and the relationship can be modelled with some precision, then a passive portfolio with just those risk exposures, created by means of liquid instruments such as ETFs, index futures and forwards and other marketable securities, may be a reasonable alternative to a less liquid and opaque investment in hedge funds. Market factors need to correspond to basic sources of risk and expected return for hedge funds and also must have tradeable equivalents. Generally, risk factors like equities, bonds, currencies, commodities, credit and volatility are used. An important distinction is that replicators explicitly target beta and not alpha. Investors need to be aware of this fact and accept the risks associated with a beta-seeking strategy, which may be at odds with investor assumptions.

Replicating must also deal with rebalancing the exposures and this can present considerable challenges. Replication techniques use historical data to forecast the exposures of hedge funds or hedge fund indices, so the ability to model hedge funds successfully depends on the availability of data, the quality of the data and the ability to access that data in a timely fashion. Historical and ongoing performance for many managers can be obtained from databases such as TASS and HFR. Underlying managers update their performance on a monthly basis, with the process being completed by the middle of the following month under normal market conditions, but volatile months like August 2007 can produce further delays. Most replication strategies rebalance their exposures at the beginning of a given month, but must lag the data that is used to estimate the exposures to account for the delayed data. Delayed data, even by one month, represents a risk because hedge funds usually have very high turnover. While hedge fund turnover has declined during a period of low equity volatility, it is beginning to rise again as market volatility increases, and there is a question of how quickly models can adapt to nimble hedge fund managers who are constantly changing their market exposures. While replication has been in the literature for about ten years, live products were launched only in the last few years during a period of historically low equity volatility which mitigated the effect of the lag. Now that we are entering into a period of normalised volatility, we believe that the lag will represent a bigger issue.

Performance of linear factor analysis models
Northwater (2007) showed that replication produces mixed results. The authors used linear factor replication to replicate the CSFB Tremont, CSFB Long/Short Equity, CSFB Market Neutral and HFRI Composite indices. In an analysis that covered a 10 year period, the replicate for CSFB Tremont was comparable to the index. However, the performance of the replicates for CSFB Market Neutral Equity, CSFB Equity Long/Short and HFRI Composite indices underperformed their indices significantly on a risk adjusted basis. An interesting corollary to the finding is that the replicates were capable of delivering all the risk of the underlying indices while underperforming on an absolute basis.

In the aforementioned paper, Hasanhodzic and Lo used linear factor replication to replicate hedge funds in the TASS database. Using a 24 month rolling window to estimate parameters, the performance of all 1610 funds as well as each of 11 sub-strategies was compared to linear factor replicates. Table 1 summarises the findings of this study. On an absolute basis, the replicates underperformed the funds to varying degrees in the following categories: all funds, convertible arbitrage, emerging markets, event-driven, fixed income arbitrage, long/short equity hedge and multi-strategy. The replicates outperformed the funds on an absolute basis in the following categories: short bias, equity market neutral, global macro, managed futures and funds of funds. On a risk-adjusted basis, almost all of the replicates underperformed or were on par with the funds except in the case of equity market neutral. It should be kept in mind that the funds were examined on a net of fees basis while the replicates were examined gross of fees and with no transaction costs incorporated. With proposed fees of between 0.75% and 1% per annum, this would degrade the performance significantly, as can be seen in column 5 of Table 1 (Annualised Net Mean) where the replicate performance has been adjusted for a 0.75% annual fee. Also, because the hedge fund index returns themselves are reported and modelled net of all underlying hedge fund management and performance fees, investors need to understand that they are inherently paying those fees because they are imbedded in the data that feeds the model.

In the Hasanhodzic and Lo study the equity market neutral replicator exceeded the performance of the funds on an absolute and risk-adjusted basis. This is actually inconsistent with the Northwater study where the replicator for the CSFB Market Neutral Index underperformed its index by a factor of 10 (Sharpe ratio of 0.25 versus 2.5). There are a number of possible explanations for the difference, but the most likely one probably arises from the different time periods that are covered in the two studies and the fact that there is a smaller number of funds in the equity market neutral category (83 funds, below the average of 146).

As a final example, Rydex introduced two replicators at the end of August 2005, the Absolute Return Strategies Fund (ARS) and the Hedged Equity Fund (HE). The ARS fund attempts to replicate the performance of the Dow Jones Hedge Fund Balanced Portfolio Index and HE attempts to replicate the performance of the Dow Jones Equity Long/Short Index. These funds utilise Linear Factor Analysis at the hedge fund index level (not with individual managers) and monthly rebalancing to achieve the target weightings of the market risk factors that have been identified to be relevant by their models. Performance of both replicators has been poor relative to their benchmarks. Table 2 shows a summary of the performance from inception during September 2005 to the end of November 2007.

The performance of the Rydex replicators underscores some of the difficulties encountered when attempting to bypass a direct investment in hedge funds through replication. The absolute return fund has underperformed its benchmark by over 4% per year with higher volatility while the hedged equity fund has underperformed by almost 10% per year with almost the same volatility. This result is consistent with the conclusions reached by the Northwater study that showed replication studies over long periods of time underperforming their targets but achieving the same level of risk.

A number of investment banks and brokerages have also recently launched replication products based on the linear factor replication method to replicate indexes like the HFR Composite Index and the CSFB/Tremont Hedge Fund Index. It is too early to provide a balanced view of the performance, but Ivy is monitoring the space closely and will provide a view when sufficient evidence has been gathered.

Conclusion
Hedge fund replication presents a seemingly attractive alternative to investors who want exposure to this asset class but do not want exposure to some of the characteristics that are deemed to be undesirable such as illiquidity, premiumfees and opacity. A review of the existing literature and performance of products that have already been launched leads us to a conclusion that some hedge fund beta can be replicated but with mixed success. In terms of fees, replication does nothing to address this issue as the models are attempting to mimic index data that is based on net-of-fee hedge fund performance. Investors are implicitly paying the fees.

Replication works best on broadly diversified strategies with significant exposure and correlation to common market risks, where those exposures change slowly over time. Replication works poorly with specialised strategies that bear idiosyncratic risks (liquidity, credit), where manager alpha is significant and where exposures are tactical and change rapidly over time. The inherent risk here is that replication products, by definition, will have significant correlations to market indices, especially equities and credit.

This leads us to conclude that while hedge fund replication is an attractive concept, it is very much a work in progress in terms of achieving its stated goals in implementation. Investors who desire this exposure need to be aware of the risks inherent in the strategy and understand that in the end one set of risks is simply being traded for another.

ABOUT THE AUTHOR

Ann H Tucker, PhD is Director, Investment Strategies Group, Ivy Asset Management

REFERENCES

Hasanhodzic, J and Lo, A (2007). “Can Hedge Fund Returns Be Replicated?: The Linear Case.” Journal of Investment Management 5, 5-45.

Northwater Capital Management, Northwater Capital Management’s Thoughts on Hedge Fund Replication (May 2007).