hedge fund replication, alternative beta and benchmarking

Russell Investments // Hedge fund replication, alternative beta and benchmarking

By: Barry Feldman, Senior Research Analyst, Russell Indexes JULY, 2009 Mary Fjelstad, Senior Research Analyst, Russell Indexes Daniel Murray, Director, Alternative Investment Strategy

Hedge fund replication, alternative beta and benchmarking Industry overview and the case of equity market-neutral

1. Introduction

Hedge fund replication is an active area of research and product development. A wide body of research demonstrates that systematic risk exposures are an important component of hedge fund returns.1 This work has set the stage for replication products designed to provide systematic exposures at lower cost and with greater transparency. In this Russell Research Report, we explore the potential for replication in the context of the evolution of the hedge fund industry and the investment industry as a whole. Our key theme is the importance of alternative beta indexes, both for replication and as benchmarks for the hedge fund industry. With the term alternative beta, we refer to systematic factors beyond those that can today be traded at low cost in liquid markets. We call easily tradable factors conventional beta. Alternative beta includes broad systematic factors such as value, volatility and momentum.2 We distinguish two levels of alternative beta: tradable and non-tradable. Equity style indexes — value and growth — have been available for more than 20 years, are broadly 1 See, for example, Asness, Krail and Lieu (2001), Fung and Hsieh (2004, 2007), Jaeger and Wagner (2005), and Foerster (2006). 2 Momentum was first studied by Jagadeesh and Titman (1993) and was recently reviewed by Figelman (2007). Alternative beta also includes more complex hedge fund strategy–level factors, such as the insurance premia earned by merger arbitrage and volatility strategies and the liquidity premia earned by convertible arbitrage strategies.

Russell Investments // Hedge fund replication, alternative beta and benchmarking / p 2

accepted and are tradable. Equity volatility is also tradable through derivative contracts. We isolate one non-tradable alternative beta factor: equity momentum. The performance characteristics of this non-tradable factor are based upon a rules-based security trading strategy. The key methodological innovation in our work is that we use separate large and small cap momentum factors.

Many current hedge fund replication techniques make use of conventional beta in an approach we call top-down replication. This approach uses statistical analysis of peer group hedge fund indexes to infer changing beta exposures to various factors. Investments in derivatives such as futures, options and Exchange Traded Funds (ETFs) are then used to replicate these exposures and, hopefully, the properties of the target hedge fund index as well.

In our discussion, we shed some light on the importance of including alternative beta factors in top-down replication. We find that adding alternative beta improves modeling and performance for all hedge fund styles. The impact is most profound for the equity market–neutral hedge fund style, where the inclusion of our rules-based non-tradable momentum factors results in significant modeling and performance improvements. We refer to the creation of rules-based alternative beta factors as strategy or rules-based replication.

Like many others, we believe that investable benchmark indexes are central to the long-term growth of the hedge fund industry.3 Investable benchmarks have obviously been one of the keys to success in traditional long-only asset management. Non-investable benchmark indexes are inherently not credible, given that they provide no passive-investment alternative to the active products, while investable indexes that are not representative are not benchmarks. All current commercial hedge fund indexes are peer-group universes. Today’s replication products are investable, but they have not to date been accepted as representative, particularly not of individual strategies. Strategy replication holds out the possibility of providing both investability and representativeness.

Section 2 reviews the development of the hedge fund industry and existing hedge fund indexes and replication products. We look at the rapid recent growth of the industry, and, crucially, investor experience with investable hedge fund indexes, which have considerably underperformed non-investable indexes: replication strategies appear as a natural alternative. Section 3 presents factor analyses of the Hedge Fund Research (HFR) hedge fund indexes as a framework for understanding the relationship between hedge fund performance and conventional beta exposures. Section 4 focuses specifically on the equity market–neutral strategy, and explores the significance of time-varying exposures. Section 5 looks at the ability of alternative beta indexes to improve risk analysis. The conclusion provides a synthesis of our results and our larger perspective.

2. Historical background

2.1 GROWTH OF THE HEDGE FUND INDUSTRY The hedge fund industry experienced tremendous growth during the past two decades, as shown in Figure 1. Assets under management (AUM) expanded at a compounded annual growth rate of over 25%, with nearly $1 trillion in cumulative inflows from 1990 through June 2008; AUM was just under $2 trillion at the start of 2008, according to data from HFR (see Figure 1). Over the same time period, the number of hedge funds grew from about 600 to over 10,000, including nearly 2,500 funds of hedge funds.

3 See, for example, Martellini, Vaissie and Goltz (2004).


Most of the growth in AUM occurred from 2000 through mid-2008. In the early 2000s, when the TMT4 equity bubble burst, hedge funds appeared very attractive to investors as a source of diversification and potential returns. Between the end of 1999 and the end of 2002, the MSCI World Equity Index (with net dividends reinvested) lost a cumulative 42% in U.S. dollar terms, compared with a return of +8% for the HFRI Fund Weighted Composite Index. As the bottom was falling out of technology stocks, many of the world’s central banks aggressively reduced interest rates. Not only did this diminish the attractiveness of cash as an asset class, but it also meant that leverage was cheap, a factor that hedge funds were much better able to exploit than their long-only cousins.

Figure 1 / Hedge fund assets under management

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Investors poured money into hedge funds, buying into the beliefs, actively promoted by many within the industry, that hedge fund managers were more skilled than their long-only counterparts in delivering positive returns in any market environment; that hedge funds delivered “absolute returns” with attractive asymmetry (decreased downside risk) based on option-like strategies unavailable to long-only managers; that hedge funds provided greater diversification benefits relative to traditional investment asset classes; and that freeing managers from leverage and shorting restrictions would increase performance.

Recent events have illustrated all too well, however, that investing in hedge funds is not without risk and that it has certain drawbacks compared with investing in traditional products. These include but are not limited to: limited regulatory oversight, limited transparency, liquidity restrictions, high levels of manager idiosyncratic operational risk, difficulty in selecting and effectively monitoring good managers, capacity constraints and high fees. The lack of reliable market and performance benchmarks adds to the opaqueness of hedge fund investments.

4 Technology, Media and Telecommunications


This last point has increasing relevance as the use of hedge funds becomes more widespread for institutional mandates.5 High-net-worth individuals — the investors who traditionally contribute the bulk of hedge fund assets — are typically concerned with simple absolute returns (unadjusted for risk) and are therefore benchmark-agnostic. Institutional clients, in contrast, are usually more sensitive to the underlying risk/return characteristics of the assets in which they are investing. Their interest in knowing how their own assets are performing relative to some representative measure is spurred at least in part by the needs of consultants and by pension fund trustees’ mandates to fulfill their fiduciary duties.

2.2 PEER GROUP HEDGE FUND INDEXES Credible benchmarks are essential to an industry where conventional wisdom holds that alpha performance fees should not be paid for beta exposures.6 Available commercial hedge fund indexes are not widely accepted as manager performance benchmarks. These indexes are essentially peer group universe performance averages. Studies have revealed multiple problems with these indexes that disqualify them as credible benchmarks, starting from the difficulty of reliable categorization into peer groups. Most index providers use the manager’s self-reported classification. Significant survivorship and backfill (instant history) biases, which inflate performance, have been identified.7 Reporting self-selection bias is hard to quantify, but hedge fund managers decide whether they want to disclose their returns and where and when they want to report. Finally, hedge funds that report to an index may be closed to investment. Peer group hedge fund indexes thus are not representative or investable.

Despite their drawbacks, peer group hedge fund indexes are commonly used as proxies for the overall hedge fund market as well as for specific styles/strategies in terms of performance and risk characteristics. Their popularity has been bolstered by the lack of any credible alternative. A number of organizations — including Hedge Fund Research, Inc. (HFR), CSFB/Tremont, the Center for International and Derivatives Markets (CISDM), Hennessee and EurekaHedge — provide peer group–based indexes. However, there is no consistency among the different providers in terms of how these indexes are constructed. In fact, one could argue that the providers are motivated to adopt alternative methods of construction in order to differentiate their index family from those of their competitors. Variations between different providers include entry criteria, number of funds, longevity, reporting requirements and fund classification.

These differences tend to be less important at the aggregate index level than at the substyle level. There are no standard definitions of hedge fund substyles. Different providers have different ways of subdividing their universes. Even in situations where hedge fund providers maintain superficially similar indexes, it is possible for a given fund to be assigned to different strategies across index providers.

2.3 INVESTABLE HEDGE FUND INDEXES A desirable property of a valid investment benchmark is investability.8 For example, for a traditional long-only equity index such as the Russell 1000®, it would be possible to buy the underlying securities in the correct weights to re-create the index, notwithstanding trading 5 See, for example, the 2008 Greenwich Capital / Global Custodian study that estimates that U.S. institutions’ investments in hedge funds increased from $113 billion in 2005 to $140 billion in 2006 to $195 billion in 2007. The same study estimates that hedge fund allocations “represent 2.6% of institutional assets as of 2007 – up from 2.2% in 2006 and 1.9% in 2005.” 6 Seigel and Waring (2006). 7 See, for example, Brown, Goetzman and Ibbotsen (1999); Liang (2000); Posthuma, Nolke & Sluis (2003). 8 See, for example, Richards (2001).


costs and frictions. The analogue for peer group hedge fund indexes requires knowledge of what funds are in a particular index and their associated weights. In theory it would be possible to re-create the peer group index by buying the underlying hedge funds in the correct proportions. In practice there are a number of hurdles that prevent this from happening.

Access to managers, specialist investment knowledge and minimum investment size are three such hurdles that make it difficult to re-create a peer group hedge fund index. A further complication arises from the fact that many hedge fund managers have limited capacity — they close their books to new investors when their AUM reaches a particular level. This is often because the manager believes that the returns from the investment strategy will be adversely affected if too much capital flows in. It may also be related to the liquidity conditions prevalent in the underlying markets. Thus, even if a manager is represented in an index, this does not mean that it is possible to invest with that manager. To circumvent this, some index providers now construct ‘investable’ indexes that are comprised solely of managers that are open to new investors. Investable indexes have experienced disappointing returns relative to the non-investable indexes, however, as shown in the chart below.

Figure 2 / Cumulative performance of the HFRI Fund Weighted Composite and its investable equivalent.

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Source: HFR Industry Reports, © HFR, Inc. 2008, www.hedgefundresearch.com. Data is historical and not indicative of future results. Indexes are unmanaged and cannot be invested in directly.

Some hedge fund index providers also manage fund of hedge funds products that seek to track investable peer group indexes. The main advantage of these products is that they permit a type of passive hedge fund investing. Given the poor performance of investable hedge fund indexes relative to the full indexes, it is not surprising that these passive hedge fund vehicles have failed to attract significant inflows.

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2.4 HEDGE FUND REPLICATION Aside from performance difficulties, passive peer group hedge fund products also suffer from a lack of transparency. While the underlying managers may be known, it can be difficult to ascertain what securities the managers themselves own. An alternative approach is top-down hedge fund replication. This takes its cue from the high levels of conventional beta exposures found in hedge fund indexes and focuses on producing a hedge fund-like performance profile by use of inexpensive index derivatives such as futures, ETFs, swaps and options. Strategy replication uses baseline trading strategies to gain exposure to a specific alternative beta factor.9

2.4.1 TOP-DOWN HEDGE FUND REPLICATION Top-down replication is typically based on quantitative analysis of past returns. Regression analysis is used to identify a combination of factors that track the performance of a target hedge fund universe or strategy.10 Rolling windows of a predetermined size may be employed to utilize only more recent performance information. Investment may then be made in a basket of liquid derivatives according to the weights specified in the results of the regression analysis. The main advantages of this procedure are that it is transparent and relatively quick and easy to implement, and that the product offers a high degree of liquidity. If basket components are restricted to the most liquid factors, the performance drag from transactions costs can be minimized; transactions costs for alternative beta are much higher.

The chief limitation of a statistical modeling process is that it is intrinsically backward-looking: past index returns are used to determine future factor weightings. A shift in investment strategy by the underlying managers would therefore take some time to be reflected in the regression results. A further drawback of this approach is that its construction results in linear exposures to the underlying factors. Any asymmetric response to markets must result from changes in factor exposures and cannot derive from true optionality in strategies.11

It is worth noting that equity long/short managers account for the bulk of hedge fund AUM. HFR estimates that as of the end of the third quarter of 2008, hedge funds focusing on equity long/short strategies comprised 43% of all hedge funds, and 30% of hedge fund AUM. As the descriptor suggests, managers operating in this space have short as well as long equity exposures, although they are typically long-biased. Consequently, aggregate hedge fund index replication products tend to have high equity factor exposure because of the high weighting of equity long/short managers. This can result in these products being more highly correlated with equity markets than may be desirable.

Newer factor-based hedge fund replication products have been distinguished by modifying the target universe through proprietary screening or algorithms. Examples include sorting the universe into performance buckets and targeting the top-performing quartile or quintile, 9 There is also a third methodology, known as “distribution replication.” Rather than attempting to replicate returns from month to month, this approach attempts to replicate the distribution of returns over a period of time by constantly updating positions in liquid futures contracts. Kat and Palaro (2005) developed this technique. While this is an interesting and original approach, it struggled to attract investor interest well before the cascade of recent events. This is principally because of the strategy’s dependence on managing futures positions according to complex relationships from theoretical finance. It is also not clear how much time it will take for the return distribution to be replicated. 10 More technically: the analysis is usually performed under the constraint that the factor weightings sum to one. This is a form of what is sometimes called ”style analysis,” as in Sharpe (1992). However, style analysis usually also constrains the factor betas to be greater than zero, whereas this approach when applied to hedge funds does not make this assumption, thus opening up the possibility of having short exposure to one or more of the factors. 11 It may be possible to impart some asymmetry by using factors that are themselves nonlinearly correlated to equity markets.


or sorting to eliminate the more directional, beta-oriented funds. The claim is that this will improve performance, reducing equity beta exposure while increasing asymmetry and diversification. Whether this does improve performance remains to be seen, but a downside is that it reduces transparency.

2.4.2 RULES-BASED STRATEGY REPLICATION Experience and observation suggest that hedge funds operating within selected hedge fund styles or substyles share certain aspects of their investment approaches. There is a degree of commonality, even when there is large variance in individual hedge funds’ performance within a given strategy, due to such factors as timing, costs, implementation, periodicity, manager skill and leverage.

Rules-based strategy replication attempts to exploit these similarities. The developers of these products create a set of passive trading rules that attempt to mimic the core processes of specific hedge fund styles. One approach involves defining trading rules that are designed to capture the essence of trend-following strategies. Alternatively, the rules may specify situations in which relationships between various fixed income spreads are exploited. Diversification can be achieved by grouping a number of these different processes, thereby reducing the risks associated with any one particular trading rule. The aggregation of these different passive processes could be used to proxy individual hedge fund styles or to mimic generic hedge fund returns.

A point of debate with regard to these products is just where the line between passive and active management lies. Indeed there is a similarity between the sorts of rules-based strategies described above and some of the systematic strategies employed by members of the hedge fund community. Simple rules have the advantage of being easy to understand and implement, but their very simplicity lessens the probability that they are rules worth using. At the other end of the scale, a more complex set of rules may produce results that are successful in generating the desired return profile, but their complexity may result in reduced transparency and increased implementation costs. It is not clear at which point a set of trading rules stops being a passive indexation/replication product and becomes a full-blown investment strategy in its own right.

Hedge funds by their nature often utilize a variety of different investment techniques that change over time. Capturing this dynamism in index form is hard to do. Nevertheless, it is possible to create investable passive alternatives to some hedge fund strategies by use of this rules-based trading approach. Depending on the risk/return characteristics of a specific strategy, a passive index may offer the desirable asymmetrical return and diversification benefits associated with actively managed funds. To the extent that it mimics the behavior of a given hedge fund strategy, a rules-based trading strategy can be used as a type of performance benchmark or baseline return hurdle for active managers.

3. Analysis of hedge fund index performance using a hybrid approach The discussion above describes two separate approaches to replication: regression-like techniques using tradable factors applied to historical data, and rules-based trading strategies designed to try to capture alternative beta factors. In this section we examine the potential contribution to benchmarking and replication of adding both tradable and rules-based alternative beta factors to standard factor models. Here we study a broad selection of hedge fund strategies and aggregate indexes preparatory to focusing on equity market–neutral in Section 4.


3.1 DATA DESCRIPTION Here we analyze selected HFR hedge fund indexes. They are widely used and have a long history. Our analysis is based on data from January 1990 to September 2008. All analysis is based on excess returns relative to yields on the 30 day T-Bill. We examine a broad selection of HFR’s peer group indexes, as well as the specific equity strategies: equity market–neutral, short selling, equity non-hedge and merger arbitrage. Descriptive statistics for these indexes are provided in Table A1 in the Appendix.

We develop three sets of factors suitable for analysis and replication. These factors are selected, most importantly, for the examination of equity market–neutral strategies; however, they are intended to be informative for other strategies as well. These factors are presented in Table 1. Descriptive statistics and correlations for all factors are presented in Tables A2 and A3 in the Appendix. The basic factor set is meant to represent conventional and tradable asset exposures; it includes proxies for U.S. large cap equity, U.S. small cap premium, emerging markets performance, corporate credit and interest rates. These exposures are represented by, respectively, the Russell 1000; the difference between the Russell 2000® and the Russell 1000; the MSCI Emerging Markets Index; the return on the Merrill Lynch High Yield Master II Index (H0A0); and the return on the 10-year treasury, as represented by the Merrill Lynch GA10 Constant Maturity Index. All these factors are either directly investable or have investable equivalents. To keep the total number of factors manageable, we do not include some commonly used proxies, such as the MSCI EAFE and Barclays Aggregate indexes.

Table 1 / Factors

Initial factor set Factor Market Index Return Abbreviation Basic LC Equity Russell 1000 R1000 Basic Equity SC Premium Russell 1000 – Russell 2000 R2 – R1 Basic Emerging Markets MSCI Emerging Markets Index MSCI EM Basic Corporate Credit Merrill Lynch High Yield Master II Index (H0A0) HY Basic Interest Rates Merrill Lynch GA10 Constant Maturity Index T10 Augmented Volatility VIX VIX Augmented Large cap style premium Russell 1000® Value – Russell 1000® Growth R1V – R1G Augmented Small cap style premium Russell 2000® Value – Russell 2000® Growth R2V – R2G Complete Large cap style premium Russell 1000® High Momentum –

Russell 1000® Low Momentum LCM

Complete Small cap style premium Russell 2000® High Momentum – Russell 2000® Low Momentum

SCM

Source: Merrill Lynch, MSCI and S&P.

We create an augmented factor set by adding tradable alternative beta volatility and equity-style exposures to the conventional exposures of the first factor set. Volatility is represented by the return on the CBOE VIX index of S&P 500 option volatility. Large and small cap style exposures are represented by the difference between the Russell 1000 Value and Growth indexes and the Russell 2000 Value and Growth indexes, respectively. All these factors are investable, although the liquidity of their trading instruments does not compare to that for the conventional tradable factors.12

12 These include CBOE VIX futures, variance swaps, and Russell 1000 Growth and Value ETFs and futures contracts.


Finally, we add proxies for U.S. large cap and small cap momentum to form the complete factor set. These indexes — our examples of non-parametric trading strategies — are based on the Russell 1000 and Russell 2000 indexes. The standard research definition of “momentum” for a security (Carhart 1997) is used: the cumulative return over the period t-12 months to t-1 month. Securities are sorted by momentum, and the top and bottom quintiles by market cap, define high- and low-momentum indexes for a universe. The indexes are rebuilt on a quarterly basis. Momentum returns are defined as the return difference between the corresponding high- and low-momentum indexes. Momentum is not a tradable factor; it is, however, a rules-based strategy that can be implemented at low operational cost. These momentum indexes refine the standard Carhart (1997) momentum index widely used in the research literature by identifying small and large cap momentum, rather than by aggregating them.13

3.2 STATIC ANALYSIS Our first perspective on the systematic exposures to the hedge fund strategies represented by the HFR indexes is based on static factor modeling. Models were constructed using the basic, augmented and complete factor sets. Figure 3 presents R-squared values for all models across all strategies. We observe that the basic factors are reasonably successful at explaining the variability in historical time series returns for some hedge fund substyles, but relatively unsuccessful for others.

13 We note that the use of commercial equity indexes and equity universes, as opposed to CRSP market indexes and Fama-French factors, is consistent with the work of Cremers, Petajisto and Zitzewitz (2008), who find that the Fama-French factors create performance attribution biases.


Figure 3 / Static analysis R-squared values for all models and indexes14

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The regression that generates the highest R2 is equity non-hedge; at the other end of the scale, the basic factors R2 for the equity market–neutral regression are very low. The basic factors R2 for the HFRI Fund Weighted Composite Index is 80%.

Much of the variability in aggregate hedge fund returns can be well explained by a static factor analysis using conventional beta factors. An implication is that the diversification benefits of investing in a hedge fund or group of hedge funds with properties similar to the aggregate factor set may be overplayed.

The results of the analysis also indicate that in every single case, the intercept term — the static model alpha — is positive and statistically significant at the 99% level. A naïve interpretation would be that hedge funds generate alpha across all investment styles. A more skeptical assessment would be that important factors are missing from the model.

The effect of including alternative beta factors can also be observed in Figure 3. For most strategies, the augmented and complete factors sets have a modest effect on model explanatory power. The most notable exception is equity market–neutral, where the R2

jumps from 8.5% using the basic factors to 35.1% using the complete factor set. Momentum factors dramatically increase the factor model explanatory power of the equity market–neutral strategy. The two other strategies that have more visible increases in explanatory power for the expanded factor sets are equity hedge, short selling and, perhaps

14 HFR has recently reorganized its hedge fund indexes. The correspondence between the indexes used in this study and the new index system may be seen in “New HFRI Indices Classifications” at https://www.hedgefundresearch.com.


surprisingly, the fund-of-funds composite. F-tests, not reported, show that the incremental explanatory power of the expanded factor sets is statistically significant in almost all cases.

Figure 4 / Static model alphas (intercepts) and index excess returns (index returns minus cash)

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Source: HFR Industry Reports, © HFR, Inc. 2008, www.hedgefundresearch.com, Merrill Lynch, MSCI and S&P. This example is for illustrative purposes only and is not intended to reflect the return of any actual investment.

A different perspective on the performance of static models is provided by examining the model alpha (the constant, or intercept), which measures the hedge fund strategy index performance that cannot be explained by the model factor exposures. The greater the value of the intercept, the higher the implied alpha of the hedge fund strategies. Figure 4 shows strategy excess returns (the index return less the cash return) and model alphas (intercepts) for the basic and complete factor sets. How much of the return over cash is due to factor exposures? The equity market–neutral model alpha for the basic factor set is nearly equal to the average excess return of the strategy (28 vs. 32 bp), implying that only 4 bp of average excess return is due to factor exposures and that the rest is alpha. However, the model alpha for the complete factor set is reduced to 21 bp: the additional factors in a static model explain 11 bp, or about a third of the average excess return of the strategy. Momentum factors contribute 10 bp.

Among other strategies, emerging markets stands out for having model alphas that are considerably smaller than the average excess returns. The emerging markets’ complete model alpha is 35 bp, compared to the average 86 bp excess return for the strategy, implying that approximately 60% of the excess return could be obtained from fixed exposures to conventional and alternative betas. In the case of equity non-hedge, 50% of


the excess return could be obtained from fixed exposures to the basic factors. Note that equity non-hedge model alpha increases when moving to the complete factor set. This also happens to a lesser degree for event-driven. Adding more factors does not automatically increase model alpha. Short selling results indicate that the slightly negative average excess return was more than 40 bp over the return to be expected from the passive conventional asset exposures.

Table 2A / Static complete model regression results

Equity Market–Neutral

Convertible Arbitrage Macro

Relative-Value

Arbitrage Merger

Arbitrage Market Timing

Fixed Income Distressed

Intercept 0.205 *** 0.213 ** 0.537 *** 0.437 *** 0.290 *** 0.513 *** 0.220 *** 0.497 ***

R1000 0.074 *** –0.038 0.051 0.008 0.117 *** 0.247 *** 0.004 0.035 R2 – R1 0.039 ** –0.048 0.084 * 0.020 0.076 *** 0.090 ** 0.025 0.108 ***

MSCI EM –0.011 0.025 0.137 *** 0.025 ** 0.012 0.088 *** 0.042 *** 0.056 ***

HY 0.022 0.348 *** 0.088 0.206 *** 0.143 *** –0.143 ** 0.290 *** 0.414 ***

T10 0.008 –0.027 0.373 *** –0.052 * –0.017 0.097 * –0.024 –0.091 ** VIX –0.001 –0.011 ** 0.003 –0.011 *** –0.005 0.012 –0.003 –0.005 R1V – R1G 0.044 0.052 0.089 0.078 ** 0.058 0.032 0.014 0.066 R2V – R2G 0.043 –0.037 –0.056 –0.021 0.022 –0.102 0.012 0.032 LCM 0.068 *** 0.021 0.067 * 0.012 0.006 0.025 0.009 0.045 ** SCM 0.022 0.014 0.011 0.015 0.015 0.016 0.020 0.011


Table 2B / Static complete model regression results

Equity Hedge

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Composite Intercept 0.599 *** 0.371 ** 0.481 *** 0.352 ** 0.502 *** 0.441 *** 0.246 *** R1000 0.300 *** –0.926 *** 0.173 *** 0.078 0.604 *** 0.179 *** 0.008 R2 – R1 0.178 *** –0.557 *** 0.140 *** 0.046 0.397 *** 0.126 *** –0.001 MSCI EM 0.054 *** 0.000 0.036 ** 0.502 *** 0.080 *** 0.099 *** 0.114 *** HY 0.093 * 0.140 0.325 *** 0.141 * 0.115 ** 0.148 *** 0.084 * T10 0.009 –0.056 –0.043 0.055 0.039 0.019 0.021 VIX 0.003 –0.029 ** –0.005 0.007 0.014 ** 0.001 –0.006 R1V – R1G 0.115 ** 0.076 0.132 *** 0.037 0.029 0.071 ** 0.103 ** R2V – R2G –0.206 *** 0.422 *** –0.079 ** 0.037 –0.228 *** –0.114 *** –0.123 *** LCM 0.088 *** –0.058 0.044 ** 0.127 *** 0.064 *** 0.062 *** 0.094 *** SCM 0.006 0.009 –0.018 –0.020 –0.046 ** –0.003 –0.010


Further insight can be obtained from the factor model for the complete factor set presented in Tables 2A and 2B. Statistical significance is indicated by asterisks to the right of the coefficients. A single asterisk indicates a two-tail 90% significance level (t = 1.65); two asterisks, 95% (t = 1.96); and three asterisks, 99% (t = 2.58). Except for the long bond, the conventional factors are highly statistically significant for a variety of hedge fund strategies. Note that the basic equity factors are all highly significant for equity hedge and equity non-


hedge. Large cap and small cap styles are important in characterizing equity hedge, event-driven and the composites. Volatility shows up as significant for convertible and relative-value arbitrage, short selling and equity non-hedge. Large cap momentum is important for characterizing equity market–neutral and several other strategies, including the composites. Small cap momentum appears statistically significant only for characterizing equity non-hedge.

3.3 DYNAMIC ANALYSIS In this subsection we present a direct comparison between static and dynamic models, reporting both overall model performance and the market performance of the factor exposures. In Section 4 we look more carefully at the dynamic exposures of the equity market–neutral strategy.

Static factor model analysis of hedge fund index performance is helpful in assessing net factor exposures over a given time period; however, it is of limited value in benchmarking. Factor exposures are averaged over a long time period and are of limited value in assessing replication strategies due to the inherent look-ahead bias, because the regression produces a single estimation of factor exposures based on the entire sample. The average static factor exposures can be determined only with performance information available at the end of the period under study: static model alphas are based on future information.

The rolling-window approach is a simple dynamic method that substantially eliminates this problem by estimating factor exposures for a time period on the basis of a trailing history of fixed length. Although most replication products use rolling-window factor models, most academic research is based on static models. The model alpha obtained from the dynamic model is not exactly equal to the implied replication return, but the average difference was found to be less than 2 bp/mo.15 We report the average dynamic alpha to facilitate comparison with the static model results.

The dynamic results are generated using a 36-month rolling window. Factor exposures at time t are based on data for months t-1 to t-36. A factor model is built for each month with sufficient prior history. Observations in the moving window are weighted with a 1%/month decay rate, so that more recent months are more heavily weighted. The reported R2 is the average over all rolling-window months. The reported dynamic model alpha is the model alpha averaged over all available months.

Table 3 reports the same static model R2s as shown in Figure 3, together with average dynamic R2 values. The dynamic R2 values are in all cases greater than the static R2s. This suggests that the ability to vary factor positions more than compensates for the inability to look ahead. However, the magnitude of this difference varies greatly among strategies. Dynamic modeling is of the most benefit to equity market–neutral, where the improvement ranges from five times for the basic factor set to almost double for the complete factor set. The improvement is only about 4% for equity non-hedge. In general, strategies with lower R2 have greater absolute and proportional gain.

15 The replication return is computed as the product of factor returns in the current month multiplied by the factor exposures estimated in the trailing month model.


Table 3 / Static and dynamic model R-squared

Static Model R-Squared Dynamic Model R-Squared

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Factors Equity Market–Neutral 8% 9% 35% 38% 48% 67% Convertible Arbitrage 33% 35% 36% 44% 49% 52% Macro 39% 39% 42% 54% 60% 63% Relative-Value Arbitrage 38% 41% 43% 55% 61% 63% Merger Arbitrage 39% 42% 43% 53% 60% 62% Market Timing 46% 50% 51% 69% 74% 76% Fixed Income 54% 54% 56% 60% 65% 68% Distressed 55% 56% 59% 60% 66% 70% Equity Hedge 69% 74% 78% 84% 87% 88% Short Selling 72% 81% 81% 82% 88% 89% Event-Driven 73% 75% 75% 75% 80% 81% Emerging Market 77% 77% 79% 84% 86% 89% Equity Non Hedge 89% 92% 92% 93% 95% 96% Weighted Composite 80% 83% 85% 88% 90% 92% Fund of Funds Composite 46% 50% 58% 69% 73% 78%


Table 4 / Monthly static and dynamic model alphas

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Equity Market–Neutral 0.32% 0.28% 0.29% 0.21% 0.26% 0.23% 0.20% 0.15% Convertible Arbitrage 0.31% 0.19% 0.25% 0.21% 0.28% 0.32% 0.32% 0.32% Macro 0.81% 0.58% 0.61% 0.54% 0.65% 0.44% 0.46% 0.44% Relative-Value Arbitrage 0.52% 0.43% 0.47% 0.44% 0.45% 0.42% 0.42% 0.44% Merger Arbitrage 0.69% 0.31% 0.32% 0.29% 0.45% 0.39% 0.39% 0.39% Market Timing 0.42% 0.54% 0.56% 0.51% 0.69% 0.30% 0.36% 0.32% Fixed Income 0.36% 0.24% 0.26% 0.22% 0.26% 0.31% 0.28% 0.29% Distressed 0.71% 0.54% 0.55% 0.50% 0.60% 0.50% 0.47% 0.47% Equity Hedge 0.83% 0.59% 0.68% 0.60% 0.72% 0.57% 0.60% 0.61% Short Selling –0.01% 0.47% 0.34% 0.37% –0.06% 0.63% 0.41% 0.38% Event-Driven 0.68% 0.46% 0.49% 0.48% 0.66% 0.52% 0.50% 0.52% Emerging Market 0.86% 0.44% 0.42% 0.35% 0.79% 0.56% 0.45% 0.51% Equity Non-Hedge 0.86% 0.44% 0.48% 0.50% 0.78% 0.37% 0.46% 0.52% Weighted Composite 0.66% 0.44% 0.49% 0.44% 0.59% 0.44% 0.45% 0.47% Fund of Funds Composite 0.37% 0.23% 0.31% 0.25% 0.31% 0.20% 0.18% 0.19%


Table 4 reports static and dynamic model alphas. Static model alphas should be compared to average excess returns, which are presented in the first column. Note that these average excess returns cover the entire study period. The static model alphas are the same as those partially reported in Figure 4. To the left of the dynamic model alphas are the average


excess returns over the rolling-window period from January 1993 to September 2008. Excess returns over this period are the appropriate comparison for the dynamic model alphas.

The single most important observation to be drawn from Table 4 is that high model R2 is not predictive of low model alpha, regardless of the type of model or the factors used. Adding factors will always increase model R2, but may not consistently reduce model alpha. There are a number of potential explanations for this result. One statistical explanation is that additional factors can increase model multicollinearity, which will tend to increase the standard deviation of model alphas. Another possibility is that some of the exposure provided by an added factor is “more efficiently” provided by an existing factor. For example, a style factor might sometimes be relatively highly correlated with the size factor that mimics the style exposure, but with better return.

Comparing static and dynamic replication returns in Table 4 makes evident that static model alphas can be lower than dynamic model alphas for the same hedge fund strategy index and factor set. This is the case for all factor sets with convertible arbitrage, merger arbitrage and emerging markets. In these cases, the value of knowledge of future market performance outweighs the opportunity to implement a dynamic strategy. The implication is that the factor exposures in these strategies are less predictable than the others.

Equity market–neutral dynamic model alphas are always lower than the static model alphas. This implies the presence of slowly varying and hence predictable dynamic factor tilts in equity market–neutral strategies. Equity market–neutral model performance also always improves with the addition of new factors. One possible explanation for this result is that equity market–neutral strategies are believed to have a stronger quantitative influence. As a result, equity market–neutral factor exposures may change more predictably and smoothly.

The short-selling results are notable because the model alphas are much larger than the average excess returns. This indicates that short sellers generate considerable alpha that offsets their factor exposures.

3.4 SUMMARY Static and dynamic analyses of hedge fund indexes demonstrate the importance of tradable and non-tradable alternative beta factors. These factors are statistically significant for many strategies, and they generally increase replication return, both in the hypothetical static case and in the more realistic dynamic rolling-window method. Alternative beta factors are seen to be particularly important for the modeling of the equity market–neutral strategy and for its replication performance. We turn next to further analysis of the equity market–neutral strategy.

4. Equity market–neutral This section focuses on the equity market–neutral strategy. Our principal goal is to determine the contributions tradable and non-tradable alternative beta factors make to the characterization of this strategy and the replication of its performance. Foerster (2006) demonstrated the value of momentum factors in helping to explain equity market–neutral returns. Our analysis adds to the knowledge base by splitting momentum into small and large cap exposures. Furthermore, we investigate the dynamic properties associated with our factor analysis. This then forms the basis for assessing out-of-sample performance.

4.1 COMPLETE ANALYTIC RESULTS Table 5 presents complete equity market–neutral static regression results for all three factor sets. The R2 and model alpha estimates have already been discussed. The large cap beta


almost doubles to about 7% in the complete factor model, and the statistical significance increases considerably as well. This change in the exposure of a basic model factor with the addition of alternative factors appears to be an example of omitted variable bias in the basic model results. The estimated average small cap exposure is smaller, at about 4%, but is still statistically significant.

An interesting aspect of the use of sequential factor sets is the apparently significant long bond exposures in the basic and augmented models. This estimated exposure declines greatly in magnitude and loses statistical significance in the complete model. The implication is that when relevant alternative beta exposure is missing, conventional beta may serve as a “proxy factor.” Note, however, that Table A3 in the appendix shows no obviously important correlations between the momentum factors and the 10-year bond.

Finally, large cap momentum is the most important factor in the complete model when judged by statistical significance. More importantly, large and small cap momentum together approximately quadruple model explanatory power. This is an important result, which suggests that momentum is by far the most important of all model factors.16 Considering the still-low R-square for the complete model, however, it appears that there may be other similarly important factors that have not been considered.

Table 5 / Complete regression results for the equity market–neutral strategy

Factor Set I II III Coefficient ‘t’ Stat Coefficient ‘t’ Stat Coefficient ‘t’ Stat Intercept 0.285 4.92 0.293 15.02 0.205 3.81 R1000 0.044 2.18 0.039 3.60 0.074 3.32 R2 – R1 0.053 2.80 0.049 1.57 0.039 2.01 MSCI EM –0.004 –0.34 –0.005 –0.18 –0.011 –1.02 HY –0.001 –0.03 –0.002 –0.50 0.022 0.70 T10 0.069 2.25 0.070 2.40 0.008 0.31 VIX –0.002 –0.07 –0.001 –0.27 R1V – R1G 0.017 1.21 0.044 1.52 R2V – R2G –0.011 –0.73 0.043 1.41 LCM 0.068 4.77 SCM 0.022 1.48 R2 6.38% 8.70% 35.05%


4.2 TIME-VARYING FACTORS We have seen so far how we have been able to improve our understanding of hedge funds by moving from a relatively simple set of factors to a broader set. In particular, this made an important difference to the equity market–neutral substyle. The index analysis was performed by use of returns data from January 1990 to September 2008. One issue to

16 It is in principle possible that other factors would show similar marginal performance contributions. Variance decomposition analysis confirms that momentum (particularly, large cap momentum) dominates model performance. Proportional marginal variance decomposition (Feldman, 2006) of the complete model allocates 24% of variance to large cap momentum, 4% to the market, 3% to large cap style, 2% to the size premium and 1% to small cap momentum and emerging markets.


investigate is just how stable the relationships are between substyle returns and the factors over time. Stable relationships would suggest that manager behavior within a substyle is reasonably time-invariant, so that no matter what the market conditions, one might expect the investment strategy to remain broadly unchanged.

The analysis was performed by use of rolling regressions with 36-month windows of data. Figure 5 displays results for small and large cap momentum, large cap equity and the equity size spread. It is apparent that the coefficients for all factors vary independently over time. Exposures for all four factors appear compressed between 2003 and 2006. Note the steep drop in large cap exposure found in late 2008. We tested for factor significance to ensure that we were not just picking up noise in the data; rolling t-statistics validate that many of these factor exposures are significant in sub-periods, most notably for large cap momentum in the first half of the sample, and for small cap momentum beginning in 2003.

Figure 5 / Factor exposures over time

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This example is for illustrative purposes only and is not intended to reflect the return of any actual investment.


Figure 6 / Style exposures over time

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Style exposures over time are shown in Figure 6. Large and small cap styles appear to move in opposite directions. Large cap value exposure reaches a peak in 1997, and large cap growth reaches a peak during the internet bubble in 2000. Small cap growth shows a different pattern, with value peaking in 1996 and 2000 (and with a smaller increase in 1998). The decay of the small cap value peak after the bubble collapse is much slower than the decay of the large cap growth peak.

These results suggest the possibility of multicollinearity leading to polarized large and small cap style loadings. Yet investigation suggests that this is not the case. Test statistics, both F- and t-tests, indicate that style factor exposures for large exposures are generally statistically significant. Essential dynamic features also remain when one index is removed. These results suggest that equity market–neutral managers have relatively sophisticated factor strategies and indicate the value of examining factor interactions in understanding equity market–neutral manager behavior.

4.3 REPLICATION The dynamic factor model used to generate Table 4 can also be used to generate crude replication returns. We report here such results for the equity market–neutral strategy. The replication return for a month (month t) is based on factor returns for month t, and factor exposures are estimated in month t-1 or t-2. Month t-1 might seem to be adequate, but because of the delay between month-end and the release of that month’s performance for a hedge fund index, t-2 is more realistic from an operational perspective. Comparing results using exposures inferred from t-1 and t-2 windows gives some idea of the seriousness of the resulting information decay.


Figure 7 / EQMN replication using the complete factor set

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Source: HFR Industry Reports, © HFR, Inc. 2008, www.hedgefundresearch.com, Merrill Lynch, MSCCI and S&P. This example is for illustrative purposes only and is not intended to reflect the return of any actual investment.

When using month t-1 estimated exposures, we obtain average replication returns over cash of 4 bp/mo, 8 bp/mo and 16 bp/mo for the basic, augmented and complete factor sets, respectively. Using t-2 exposures, the corresponding returns are 2 bp/mo, 6 bp/mo and 12 bp/mo. These results compare to average equity market–neutral index returns of 15 bp/mo and are for the period January 1992 to September 2008 for t-1 exposures, and from February 1992 to September 2008 for t-2 exposures. These results do not include transaction costs, which could impact realized performance of these products.

It appears that the information decay from using t-2 exposures is not great in replicating the equity market–neutral strategy. This suggests that factor exposures do not change very rapidly over time. Nonetheless, it appears there would be value in adjusting exposures as quickly as possible once updated performance history is obtained.

Factor exposures are determined using unconstrained regressions. Factor exposures could be constrained to add up to one or not to exceed one, which implies that all derivative exposures are fully collateralized. The average gross exposure for the complete factor set is 68%. The maximum exposure is 143% (which occurs, not surprisingly, at the time of the April 2000 NASDAQ crash. There are 23 months with exposures greater than 100%.

Monthly t-1 replication returns have a correlation coefficient of 53% with the equity market–neutral index. Annualized replication geometric excess returns over cash are 3.64% compared to the 3.17% return on the equity market–neutral index. Annualized standard deviations are 2.67% compared to 3.10%.


Figure 8 / Monthly t-1 replication return minus HFR EMN return over time.

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Source: Merrill Lynch, MSCCI and S&P. Indexes are unmanaged and cannot be invested in directly. This example is for illustrative purposes only and is not intended to reflect the return of any actual investment.

Figure 7 shows a scatter plot of replication returns against equity market–neutral index returns. It can be seen that there is substantial deviation of the equity market–neutral return from the index return. Figure 8 shows the excess replication return over the return of the index. It appears that the replication return exceeded the index return in the period from 2002 on. The average replication excess return is 11 bp/mo in this period, compared to 6 bp/mo for the index. The replication excess return is statistically significant (p = <0.05), whereas the index return is not. The difference between the two, however, is not statistically significant.

These results demonstrate the relevance of alternative beta indexes for characterizing the performance of equity market–neutral strategies, and indicate replication potential.

5. Risk analysis Alternative beta indexes can contribute to our understanding and forecasting of hedge fund risk as well as return. Standard measures of risk — such as volatility, skew, kurtosis and Sharp and Sortino ratios — are readily supplied in hedge fund marketing literature. But these measures are all absolute in nature; they do not indicate sources of risk, nor how risk has evolved relative to a benchmark. Moreover, they are often based on relatively short time frames, and thus do not necessarily capture the true risk profile associated with a particular fund or strategy.

Using an alternative beta approach permits more detailed risk analysis of hedge funds. We examine one standard risk measure and one example of scenario analysis to illustrate how alternative beta indexes aid in the identification of factor risk and investigations into how hedge fund strategies and individual managers might perform under different market conditions.

January 31, 1993 – September 30, 2008


5.1 VaR A commonly used metric for assessing potential downside is the value-at-risk (VaR) measure.17 VaR seeks to answer this question: “With xx% confidence (usually 95% or 99%), what is the maximum likely loss over a given time period?” The potential loss can be calculated in a number of ways. One could use the average return and the standard deviation to infer one-tail downside risk, or one could take the historical time-series of returns to ascertain the point below which only (1-X) % of observations lie. In the analysis below, we illustrate VaR by use of the former methodology.18 We estimate factor exposures on the basis of a rolling regression, as in Section 3.3; however, all observations are equally weighted. VaR estimates assume a normal distribution and a 24-month trailing window for measurement of means and standard deviations.19 We measure at the 95% confidence level.

Figure 9 shows four different estimates of VaR for the equity market–neutral strategy using a rolling 24-month analysis — estimates derived from returns associated with each of the three factor sets and with the HFR Equity Market Neutral Index returns. The VaR measures derived from our factor sets get progressively closer to the VaR derived from the HFR returns as the factor set grows. The complete data set adds momentum indexes, and it appears that momentum contributes considerably to improving the factor-based VaR portrait. The trends of the factor set VaRs closely follow the same trends displayed by the HFR VaR. We note that for much of the time there has been only a small gap between the factor set VaRs and the actual VaR.

17 VaR has been much criticized as a stand-alone risk measure. With regard to hedge funds, problems arise due to the underlying assumption of a symmetric normal distribution; the limited measure of risk at one point in the left tail; and VaR’s dependence upon recent history. We utilize a simple measure of VaR here for illustration purposes, as one of many risk measures applied to hedge funds. See, for example, Liang and Park (2007). There are many other more sophisticated methods of calculating VaR that address some of these problems. See Neftci (2000). 18 The VaRs were calculated using MPI Stylus, a commercially available software package. 19 Source: Markov Processes MPI Stylus documentation.


Figure 9 / Value at risk metrics, 24-month rolling window

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Source: HFR Industry Reports, © HFR, Inc. 2008, www.hedgefundresearch.com, Merrill Lynch, MSCI and S&P. This example is for illustrative purposes only and is not intended to represent any actual investment. Created with MPI Stylus™

By itself, this analysis does not tell us anything new about risk in the aggregate. We have access to actual HFR Equity Market Neutral Index data over the time period in question and so are able to calculate and observe the risk characteristics associated with it. However, the rolling factor–based approach provides a good approximation of the risk profile of the actual index. We conclude that the factor-based analysis deepens our understanding of the sources of risk within the portfolio.

5.2 SCENARIO ANALYSIS A further advantage of the factor-based approach is that it allows us to explore what characteristics a hedge fund index might have exhibited in time periods not covered by the actual index. It is possible to see how a factor-based index performed during previous periods of market stress or what might happen in hypothetical situations. Because the risk profile of the factor-based return index is similar to that generated by the actual HFR index, this gives us confidence that the simulated results will provide meaningful information.


Figure 10 / Scenario analysis comparison of projected performance of select HFRI Indexes during October 1987, based on exposures to all factors

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Source: HFR Industry Reports, © HFR, Inc. 2008, www.hedgefundresearch.com, Merrill Lynch, MSCI and S&P. This example is for illustrative purposes only and is not intended to represent any actual investment.

We use the stock market crash of October 1987 as an example and apply conditions back then to our factor model for the HFRI Equity Market Neutral Index.20 Although a handful of hedge funds have performance data going back to October 1987 or earlier, none of the major hedge fund indexes provide data going back that far. An analyst may nonetheless be interested in finding out how hedge funds would have performed in those difficult market conditions, and our factor-based approach would provide some insight. The results are shown in Figure 10. The results are not surprising, except perhaps for the decline of the fund-of-funds composite (which many nevertheless expected).

An analyst may also be interested in investigating how hedge fund styles would perform under various hypothetical market situations. There are numerous ways one could perform such scenario analyses. For example, an analyst may have specific views on how the factors will behave and use these as inputs. Alternatively, the analyst may be interested in stress-testing the strategy to see under what conditions returns are most vulnerable.

In Figure 11 we consider two dimensions for a scenario analysis of the HFRI Equity Market Neutral Index. The first dimension is the range of possible returns for each of the factor inputs. The second dimension is the range of factor coefficients over time. For each factor, we established the maximum and minimum values over the entire set of available data. We then applied these values to the factor coefficients to create best-case and worst-case scenarios for each set of coefficients over time.

20 See for example Hsieh (2004) for a discussion of this approach.


Figure 11 / Scenario analysis with rolling best- and worst-case outcomes for HFRI Equity Market Neutral Index21

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Source: HFR Industry Reports, © HFR, Inc. 2008, www.hedgefundresearch.com, Merrill Lynch, MSCI and S&P. This example is for illustrative purposes only and is not intended to represent any actual investment.

The results of this analysis are illustrated above. In this example, the best-case and worst-case scenarios are approximate mirror images of one another. In practice an analyst may legitimately be more interested in understanding the potential for negative returns, in which case it would be easy to adjust the model inputs accordingly. For example, one could test to see how bad returns might be if each of the factors moved away from its mean by five standard deviations. In all cases the potential downside is much greater than what might be inferred from a VaR analysis. This is because the technique assumes that extreme factor moves occur concurrently. In reality it is unlikely that the “perfect storm” of factors would be experienced at the same time, but as an exercise in investigating the potential properties of the index, there is some merit to the technique.

The general point with this type of analysis is that peer group indexes do not tell us much about how different hedge fund styles might be expected to perform under different market conditions. Our factor-based approach is much more flexible in this regard, permitting as it does stress testing, performance simulation and risk investigation for user-generated situations.

21 1) Calculate the maximum and minimum values for each of the factors over the entire sample. 2) Perform rolling regressions using 24 months of data, capturing exposures (coefficients) at each time point. 3) Worst case: for each time point, we multiply the negative coefficients by the maximum value associated with each factor; then sum across all time points. 4) Best case: for each set of time points, we multiply the negative coefficients by the minimum values associated with each factor over the entire sample and the positive coefficients by the maximum values associated with each factor; then sum across all time points.


5.3 FOURTH-QUARTER 2008 December 2008 was a challenging time for the investment industry as a whole, including hedge funds. The industry itself had been repeatedly rocked — in 2007 by the collapse of the subprime mortgage market and in 2008 by broad deleveraging, the bankruptcy of Lehman Brothers and the ensuing global credit crisis. Hedge funds are still experiencing a continuing flow of redemption requests. According to data from HFR, the hedge fund industry experienced net outflows of $183 billion in 2008. Morgan Stanley has estimated that industry assets may shrink from a peak of around $2 trillion at the end of 2007 to $0.9 trillion at the end of 2009.

Some of these withdrawals are undoubtedly due to the poor performance of hedge funds during 2008. For the calendar year 2008, the HFRI Fund Weighted Composite Index was down by 19% and the HFRX Global Hedge Index was down by 23.3%. Investor disappointment likely stems from the expectation that hedge fund managers should have delivered positive returns in any market environment, an expectation actively promoted by many within the industry. Still, according to the HFR indexes, during 2008, hedge funds outperformed equity markets quite considerably22 and so have provided a degree of diversification and protection.

Hedge funds performed well in the last equity bear market; consequently, it might have been hoped — and in many cases expected — that they would perform well in the current market crisis. The factor-based approach provides a useful perspective on recent hedge fund performance. In particular, it is possible to examine how much hedge fund performance is directly driven by factor exposures. Beyond direct factor exposures, for example, timing strategies, leverage constraints or redemption demand could create losses that are only indirectly factor-driven.

October 2008 was notable in many respects, not least because of the extreme market movements that were experienced over the month. The Russell 1000 index was down 17.6% in October and the Merrill Lynch High Yield Master II Index fell by 16.3%. The HFRI Fund Weighted Composite Index was down 5.4%, although returns varied enormously by style. At one end of the spectrum we have the HFRI Convertible Arbitrage Index, which fell by 19.2% over the month, and at the other end the HFRI Macro Index, which was up by 3.8%. Apart from the Macro Style Index, all other HFRI indexes produced negative returns in October. The next-best-performing HFRI substyle was the Equity Market–Neutral Index, returning –0.6%.

During the period of market stress in August 2007, equity market–neutral managers struggled, with the HFRI Equity Market–Neutral index down by 1.3%. October 2008 was a much more difficult month than August 2007 in terms of market action, so equity market–neutral managers might have been expected to perform rather poorly. Yet a return of –0.6% is very respectable in the circumstances. As we have previously noted, there are a number of problems associated with peer group indexes, including self-reporting. A skeptical observer might then wonder if equity market–neutral managers to some degree “massaged” the reported returns they provided to hedge fund databases.

22 For 2008 the Russell 1000 U.S. Equity index experienced a decline of 37.6% and the Russell Global Index (in U.S. dollars) a decline of 42.8% while over the same period the HFRI Fund Weighted Composite Index lost 19%.


Table 6 / Expected versus actual performance of the HFR EQMN Index in October 2008

R1000 R2- R1

MSCI EM HY T10

Change in VIX

R1V-R1G

R2V-R2G LCM SCM TOTAL

Factor Returns –17.46 –3.34 –27.38 –16.30 –0.84 52.04 0.30 1.72 3.49 4.56 Factor Coefficients –0.18 –0.03 0.07 0.10 –0.12 –0.01 –0.05 –0.08 –0.01 0.06 Factor Contribution 3.11 0.10 –1.96 –1.57 0.10 –0.69 –0.02 –0.13 –0.04 0.28 –0.81

Source: HFR Industry Reports, © HFR, Inc. 2008, www.hedgefundresearch.com, Merrill Lynch, MSCI and S&P. Indexes are unmanaged and cannot be invested in directly. Historical returns are not indicative of future performance. Forecasting represents predictions of market process and/or volume patterns utilizing varying analytical data.

Our factor model allows us to investigate this possibility. Summary results using a 24-month rolling window are shown in Table 6. The model explains returns satisfactorily, which gives greater assurance that reported returns are accurate. The model suggests that, based on the factor returns over the month, we would have expected equity market–neutral managers as a group to have returned –0.8%, very close to the reported –0.6%. The most important exposures over the month seem to have been overall short exposure to the Russell 1000 offset by long EM and HY positions. This may be a proxy for something else, such as sector return differences or domestic versus international business exposure. The increase in the VIX also seems to have detracted from returns. The small cap momentum term appears to have made a small positive contribution to returns, but the large cap momentum term does not seem to have had a meaningful impact.


Figure 12 / Actual, explained and out-of-sample HFRI Equity Market–Neutral returns

-4

-3

-2

-1

0

1

2

Aug-07

Sep-07

Oct-07

Nov-07

Dec-07

Jan-0

8

Feb-08

Mar-08

Apr-08

May-08

Jun-0

8Ju

l-08

Aug-08

Sep-08

Oct-08

Nov-08

Dec-08

Mon

thly

Per

cent

age

Ret

urn

Explained HFRI EMN Returns Actual HFRI EMN Returns

T+1 Forecast HFRI EMN Returns

Source: HFR Industry Reports, © HFR, Inc. 2008, www.hedgefundresearch.com, Merrill Lynch, MSCI and S&P. Indexes are unmanaged and cannot be invested in directly. Historical returns are not indicative of future performance. Forecasting represents predictions of market process and/or volume patterns utilizing varying analytical data.

In fact, the model has performed well in terms of explaining returns over the whole of the past year, a period notable for its unusual volatility and extreme market moves. Figure 12 shows actual HFRI Equity Market–Neutral returns, explained (in sample) model returns and out-of-sample (one period ahead) model returns. It is clear that in terms of size and direction, the in-sample model explains well the actual return series. The out-of-sample model also does well most of the time, correctly matching the sign of the return on the actual index in 12 out of 15 months with an average forecast error over this period of –0.4%. The notable exception is in September 2008, when the HFRI Equity Market–Neutral index returned –3.1% and the out-of-sample model returned +1.6%. The major components of the out-of-sample model returns were large positive contributions from the small cap value minus growth term, the high-yield-bond term (short position) and the change in VIX (long position), offset somewhat by large detractions from long positions in the Russell 1000 and MSCI Emerging Markets and the small cap momentum quintile difference.

6. Concluding remarks For hedge fund indexes to gain broad acceptance, we posit that it is essential to understand more about the key drivers of hedge fund returns. A large body of literature on this topic already exists. Here we illustrate the potential benefits of adding currently non-tradable alternative beta factors, specifically large cap and small cap momentum, to those tradable beta factors previously identified. We show that such indexes have particular value in extending our understanding of the process by which returns are generated for equity market–neutral managers.


More generally, our results indicate the value of non-tradable alternative beta exposures in understanding a broad range of hedge fund style returns. Today these exposures must be obtained with rules-based trading strategies built from individual securities. Over time, currently non-tradable betas may become directly tradable in derivative form and function as alternative beta indexes. An advantage is that this would then facilitate the construction of conglomerate indexes comprised of both traditional and non-traditional betas. If constructed in an appropriate way, these conglomerate indexes could then form the basis for investable hedge fund indexes. Such a product would fulfill the basic criteria required for a hedge fund benchmark: it would be transparent, investable, well-defined, prespecified and (contingent on its construction) representative.

Such a benchmark could then be used in much the same manner as traditional long-only benchmarks in the measurement and attribution of both performance and risk. It should be possible, for example, to form expectations for how various hedge fund strategies would perform under particular factor scenarios and, further, to compare the performance of individual managers against these passive measures. The acceptance of alternative beta-based benchmarks and attribution methods would likely, in turn, increase the credibility of and demand for replication products. Similarly, the success of alternative beta-based replication products would foster greater acceptance of benchmarking. We have demonstrated the value in applying dynamic modeling techniques in this regard.

Such benchmarks hold out the possibility of devising effective measures for selecting and timing alpha, and thus provide a realistic basis on which to heed the injunction not to pay alpha fees for beta exposures. Existing peer group–based hedge fund indexes have not succeeded as benchmarks for obvious reasons, such as the difficulty of identifying managers using similar strategies and survivorship and backfill bias. Alternative beta-based benchmarks hold the promise of a clear, transparent and objective methodology.

The vision advanced here, then, is that alternative beta indexes have the potential to re-create for hedge fund management an essential aspect of long-only investment architecture: indexes that serve as the basis for both benchmarks and passive investment products. Such an architecture would greatly increase the credibility and value of replication products. Similarly, benchmarks tied to replication products would have greater credibility.


Appendix

Table A1 / Descriptive statistics for HFR hedge fund indexes23

Monthly percentage returns net of fees

Equity Market–Neutral

Convertible Arbitrage Macro

Relative-Value

ArbitrageMerger

ArbitrageMarket Timing

Fixed Income Distressed

Avg. excess return 0.32 0.31 0.81 0.52 0.42 0.69 0.36 0.71 Standard deviation 0.88 1.37 2.29 1.09 1.22 2.09 1.11 1.75 Skew –0.19 –4.15 0.38 –1.27 –2.54 0.11 –1.48 –0.68 Excess kurtosis 1.38 33.27 0.75 10.26 11.14 –0.16 8.92 4.98 Minimum –3.22 –12.44 –6.65 –6.23 –7.11 –4.76 –6.63 –8.93 Maximum 3.20 2.98 7.61 5.37 2.78 6.25 4.76 6.71

Monthly percentage returns net of fees

Equity Hedge

Short Selling

Event -Driven

Emerging Market

Equity Non-

Hedge Weighted

Composite

Fund of Funds

Composite Avg. excess return 0.83 –0.01 0.68 0.86 0.86 0.66 0.37 Standard deviation 2.54 5.65 1.91 4.15 3.90 1.97 1.66 Skew –0.04 0.11 –1.28 –0.86 –0.49 –0.68 –0.54 Excess kurtosis 1.55 2.15 4.25 3.82 0.70 2.60 3.71 Minimum –8.08 –21.68 –9.33 –21.45 –13.77 –9.13 –7.90 Maximum 10.43 22.34 4.74 14.35 10.29 7.20 6.40

Source: Merrill Lynch, MSCI and S&P

Table A2 / Descriptive statistics for factors

Monthly percentage returns R1000 R2 – R1 MSCI EM HY T10 Avg. excess return 0.46 0.07 0.66 0.31 0.20 Standard deviation 4.06 3.24 6.65 2.06 1.96 Skew –0.55 0.17 –0.74 –0.72 –0.25 Excess kurtosis 0.91 4.65 1.48 3.90 0.62 Minimum –15.38 –15.71 –29.34 –8.45 –7.17 Maximum 11.04 16.78 16.26 8.15 5.52

Monthly percentage returns VIX R1V – R1G R2V – R2G LCM SCM Avg. excess return 1.82 0.12 0.29 0.60 0.88 Standard deviation 18.12 3.18 3.89 6.10 6.26 Skew 1.32 0.14 0.04 0.02 –0.03 Excess kurtosis 3.37 4.15 4.05 4.38 6.61 Minimum –32.67 –12.32 –17.15 –24.32 –30.02 Maximum 90.75 14.20 16.12 28.96 33.34


23 HFR has recently reorganized its hedge fund indexes. The correspondence between the indexes used in this study and the new index system may be seen in “New HFRI Indices Classifications” at https://www.hedgefundresearch.com.


Table A3 / Factor correlations

R1000 R2 – R1 MSCI EM HY T10 R1000 100% R2 – R1 1% 100% MSCI EM 65% 24% 100% HY 55% 24% 52% 100% T10 1% –17% –17% 7% 100% VIX return –65% –15% –47% –43% 4% R1V – R1G –37% –10% –25% –15% 4% R2V – R2G –49% –37% –43% –25% 13% LCM 1% 17% 7% –1% 13% SCM –3% 18% 0% –9% 12%

VIX return R1V – R1G R2V – R2G LCM SCM R1000 R2 – R1 MSCI EM HY T10 VIX return 100% R1V – R1G 21% 100% R2V – R2G 29% 80% 100% LCM –1% –37% –36% 100% SCM –1% –37% –46% 80% 100%



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Asness, C., R. Krail and J. Liew. “Do Hedge Funds Hedge?” Journal of Portfolio Management, 2001, 28(1), pp. 6–19.

Capocci, D. “Neutrality of Market Neutral Funds.” Global Finance Journal, December 2008, 17:2, pp. 309–333.

Carhart, M. “On Persistence in Mutual Fund Performance.” Journal of Finance, 1997, 52, pp. 57–82.

Cremers, M., A. Petajisto and E. Zitzewitz. “Should Benchmark Indices Have Alpha? Revisiting Performance Evaluation.” 2008, Yale School of Management Working Paper.

Feldman, B. “Using Proportional Marginal Variance Decomposition to Understand Hedge Fund Performance Drivers.” Chapter 7 in Portfolio Analysis: Advanced Topics in Performance Measurement, Risk and Attribution (T.P. Ryan, ed.). 2006, Risk Books, London.

Figelman, I. “Interaction of Stock Return Momentum with Earnings Measures.” Financial Analysts Journal, 2007, Vol. 63, No. 3, pp. 71–78.

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Fung, W., and D. Hsieh. “Will Hedge Funds Regress Towards Index-Like Products?” Journal of Investment Management, 2007, Vol. 5, No. 2.

Hasanhodzic, J., and A. Lo. “Can Hedge-Fund Returns Be Replicated? The Linear Case.” 2006, MIT Laboratory for Financial Engineering Working Paper.

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Disclosures

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Nothing contained in this material is intended to constitute legal, tax, securities, or investment advice, nor an opinion regarding the appropriateness of any investment, nor a solicitation of any type. The general information contained in this publication should not be acted upon without obtaining specific legal, tax, and investment advice from a licensed professional.

Russell Investments and Standard and Poor’s corporation are the owner of the trademarks, service marks and copyrights related to their respective indexes.

Indexes are unmanaged and cannot be invested in directly.

In general, alternative investments involve a high degree of risk, including potential loss of principal; can be highly illiquid and can charge higher fees than other investments. Hedge strategies are not subject to the same regulator requirements as registered investment products. Hedge strategies often engage in leveraging and other speculative investment practices that may increase the risk of investment loss.

Russell 1000 Index – Measures the performance of the large-cap segment of the U.S. equity universe. It is a subset of the Russell 3000® Index and includes approximately 1000 of the largest securities based on a combination of their market cap and current index membership. The Russell 1000 represents approximately 92% of the U.S. market.

Russell 1000 Growth Index – Measures the performance of the large-cap growth segment of the U.S. equity universe. It includes those Russell 1000 companies with higher price-to-book ratios and higher forecasted growth values.

Russell 1000 Value Index – Measures the performance of the large-cap value segment of the U.S. equity universe. It includes those Russell 1000 companies with lower price-to-book ratios and lower expected growth values.

Russell 2000 Index – Measures the performance of the small-cap segment of the U.S. equity universe. The Russell 2000 Index is a subset of the Russell 3000® Index representing approximately 8% of the total market capitalization of that index. It includes approximately 2000 of the smallest securities based on a combination of their market cap and current index membership.

Russell 2000 Growth Index – Measures the performance of the small-cap growth segment of the U.S. equity universe. It includes those Russell 2000 companies with higher price-to-value ratios and higher forecasted growth values.

Russell 2000 Value Index – Measures the performance of small-cap value segment of the U.S. equity universe. It includes those Russell 2000 companies with lower price-to-book ratios and lower forecasted growth values.

Russell Momentum Indexes – The Russell Momentum Indexes used in this paper are indexes currently under development by the Russell Indexes Research Group. They identify the securities in a reference Russell Equity Index with the highest or lowest momentum. Momentum is defined as the total return of a security over the period from one year before the current date to one month before the current date. High momentum indexes include the securities with highest momentum that comprise 20% of the market capitalization of the reference index. Low momentum indexes include the securities with the lowest momentum that comprise 20% of the market capitalization of the reference index. The reference equity indexes used in this study are the Russell 1000 Large Cap Index and the Russell 2000 Small Cap Index.


Source for MSCI data: MSCI. The MSCI information may only be used for your internal use, may not be reproduced or redisseminated in any form and may not be used to create any financial instruments or products or any indices. The MSCI information is provided on an "as is" basis and the user of this information assumes the entire risk of any use made of this information. MSCI, each of its affiliates and each other person involved in or related to compiling, computing or creating any MSCI information (collectively, the MSCI Parties.) expressly disclaims all warranties (including, without limitation, any warranties of originality, accuracy, completeness, timeliness, non-infringement, merchantability and fitness for a particular purpose) with respect to this information. Without limiting any of the foregoing, in no event shall any MSCI Party have any liability for any direct, indirect, special, incidental, punitive, consequential (including, without limitation, lost profits) or any other damages.

MSCI World Equity Index – A free float-adjusted market capitalization weighted index that is designed to measure the equity market performance of developed markets.

MSCI Emerging Markets Index – A free float-adjusted market capitalization index that is designed to measure equity market performance of emerging markets.

Source: Merrill Lynch, used with permission. Merrill Lynch is licensing the Merrill Lynch Indices "as is", makes no warranties regarding same, does not guarantee the quality, accuracy, and/or completeness of the Merrill Lynch Indices or any data included therein or derived there from, and assumes no liability in connection with their use.

Merrill Lynch US High Yield Master II Index (H0A0) – Tracks the performance of below investment grade, but not in default, U.S. dollar-denominated corporate bonds publicly issued in the U.S. domestic market, and includes issues with a credit rating of BBB or below, as rated by Moody’s and Standard & Poor’s.

Merrill Lynch GA10 Constant Maturity Index – The monthly return derived from the average yield on United States Treasury securities adjusted to a constant maturity of 10 years.

HFRI Fund Weighted Composite Index – A benchmark designed to reflect hedge fund industry performance by constructing equally weighted composites of constituent funds, as reported by the hedge fund managers listed within HFR Database.

HFRX Global Hedge Index – A benchmark designed to be representative of the overall composition of the hedge fund universe.

CBOE Volatility Index (VIX) – A key measure of market expectations of near-term volatility conveyed by S&P 500 stock index option prices.

S&P 500 Index – An index of 500 stocks representative of leading companies in the U.S. large cap securities market.

Unless otherwise noted, source for the data in this document is Russell Investments.

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Copyright © Russell Investments 2009. All rights reserved.

First use: July 2009.

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