Hedge Fund Risk Modeling Version 1.2

Transcription

1 Version 1.2 April 2007 Miguel Alvarez Mike Levinson 2007 MSCI Barra. All rights reserved. 1 of 27

2 Contents 1. Introduction A Brief Overview of Hedge Funds Sources of Hedge Fund Return and Risk Modeling Hedge Fund Returns Factor Selection Estimating Exposures Out-of-Sample Model Evaluation The Barra Hedge Fund Exposure Generator Modeling Hedge Fund Risk Important Considerations Modeling Common Factor Behavior Why Use Common Factors Instead of Hedge Fund Indices? Comparing Estimation Approaches Conclusion...16 References...17 Appendix 1: Hedge Fund Peer Group Descriptions and Corresponding Factors MSCI Barra. All rights reserved. 2 of 27

3 1. Introduction Interest in hedge funds has mushroomed over the past several years. Today, the hedge fund industry manages more than USD 1 trillion, having more than doubled in size over the past five years. In addition, hedge fund investment no longer is limited to high net worth individuals. Pension funds and other institutional investors, located both within the US and abroad, are increasing their allocations to hedge funds. The precipitous decline in stock prices following March 2000 spurred many investors to search for alternative investments less correlated with traditional markets. Hedge funds appear to fit the bill, especially since many hedge fund managers promise positive absolute returns independent of market direction. Against this backdrop of explosive growth, investors are now faced with analyzing the role of hedge funds within their investment processes. Naturally, they are concerned about how an investment in hedge funds may affect the risk of their portfolios. Do hedge funds provide investment diversification with some alpha, or do they exaggerate some of the bets already placed within the portfolio? Do they add new risks that manifest themselves at just the wrong times, such as periods of great market stress? To answer such questions, we need to understand what drives hedge fund returns. At first glance, it would seem that an investor could use standard factor models to analyze hedge fund risk. However, there are two main reasons why this is not so easy. First, these models require portfolio holdings and many hedge fund managers are reluctant to disclose their positions for fear of compromising their strategies. Even large institutional investors currently have difficulty obtaining this information. Second, some of the risks inherent in hedge funds arise from the strategies they employ, not just from those assets in which they invest. These strategy risks are not captured by conventional factor models. In this paper, we introduce the Barra Hedge Fund Model, which is designed to overcome these challenges. This model provides a forecast of the risk of a hedge fund, or a portfolio of funds, using the fund return series and information regarding its peer group membership. Towards this goal, the model identifies two major sources of hedge fund risk: (i) the factors that drive traditional securities markets and (ii) the strategies characteristic of certain hedge fund styles. Each fund s exposure to these risks is calculated using a returns-based analysis that we discuss throughout the rest of the paper. In section 1.1 of this paper, we provide a brief overview of hedge funds and introduce our data sources. Section 2 reviews the two primary sources of hedge fund risk and provides examples of each. We introduce the Barra Hedge Fund Attribution Model in section 3, which outlines a framework to capture the different sources of hedge fund risk. In section 3.1, we outline the procedure used to select the best factors to model a single hedge fund. Section 3.2 provides a description of exposure estimation procedures used by the Barra Hedge Fund Exposure Generator. Section 3.3 describes our approach to out-of-sample model evaluation and return replication. In section 4, we place the previous discussions into perspective with a high-level overview of the Barra Hedge Fund Exposure Generator. Section 5 builds upon our previous discourse to generate a hedge fund portfolio risk forecast. Essentially, this involves aggregating factor exposures, factor covariance and idiosyncratic risk into a single risk forecast. In section 6, we illustrate typical hedge fund style peer group common factor behavior, explain the drawbacks of using hedge fund style 2007 MSCI Barra. All rights reserved. 3 of 27

4 indices to model risk, and compare estimation approaches used by the Barra Hedge Fund Exposure Generator. We then provide a few concluding comments in section A Brief Overview of Hedge Funds Hedge funds are a diverse lot. This is not surprising given that even most definitions of a hedge fund reveal little about their investment process. Connor and Woo (2003) describe a hedge fund as an actively managed, pooled investment vehicle that is open to only a limited group of investors and whose performance is measured in absolute units of return. The term hedge suggests that these funds reduce their volatility by taking positions that offset their exposures to various risk factors. The degree of hedging that actually occurs varies widely among these funds. To further investors understanding of hedge funds, data providers have classified them into more homogeneous categories or styles. The funds within each category serve as a peer group for the style. Hedge fund classifications differ in both definition and granularity. Table 1 depicts the classification schemes of two different databases used in our analysis. We mapped the more refined MSCI categories to the broader TASS styles. The last column shows the number of nonduplicate 1 funds in the two databases for which at least 24 months of data was available as of September Table 1: Hedge Fund Classification TASS Style Name MSCI HFI Process Name Number of Funds* Long/Short Equity Long Bias 1,046 Variable Bias Short Bias Equity Market Neutral No Bias 153 Statistical Arbitrage Convertible Arbitrage Arbitrage-Convertibles 111 Merger Arbitrage+ Merger Arbitrage 45 Fixed Income Arbitrage Arbitrage-Fixed Income 119 Long/Short Credit Distressed Securities+ Distressed Securities 135 Managed Futures (CTAs) Systematic Trading 255 Global Macro Tactical Allocation Discretionary Trading 233 * Non-duplicate funds from MSCI HFI + TASS databases as of September TASS fund counts were estimated for these style peer groups. 1 We identified duplicate funds using a correlation analysis and then verified the names across those that showed abnormally high correlations (95% and above). Duplicate funds identified in this manner were eliminated from our analysis MSCI Barra. All rights reserved. 4 of 27

5 2. Sources of Hedge Fund Return and Risk The risk of a hedge fund is shaped both by broad, systematic factors, those that potentially influence many funds, as well as the idiosyncratic behavior of the fund. There are two major sources of systematic risk, the first of which comes from the markets themselves. Most hedge funds invest in traditional asset classes such as equities, bonds, currencies and commodities or derivatives written on them. Extensive research has identified factors that drive the returns to securities within each of these asset classes. What may be surprising to some investors is that many hedge fund managers do not fully hedge their exposure to these factors. Long/short equity funds, for example, usually are biased toward following the direction of the market. Also, fixed income arbitrage funds often bet on the convergence of credit or interest rate spreads between instruments with different risk profiles. Thus, a portion of hedge fund risk is due to exposures to familiar factors that underlie conventional investments. Strategy is the second systematic source of hedge fund risk. Strategy captures additional risks that are not already explained by asset class factors. These risks arise from the manner in which a portfolio is managed. For example, one strategy of merger arbitrage funds is to buy shares of announced takeover targets at a discount to the acquisition price while shorting the shares of the acquirers. The risk of any individual deal breaking may be diversified by investing in several takeover targets. The systematic risk, one affecting many merger arbitrage funds, is that many deals may break at the same time, which tends to occur during periods when the market plummets. This risk is not apparent when examining the merger arbitrage fund s holdings under the lens of a standard factor model. Other researchers, including Mitchell and Pulvino (2001) and Anson and Ho (2003), demonstrated the need for an additional factor to explain the returns to merger arbitrage funds. Similarly, other hedge fund styles including convertible arbitrage and managed futures also exhibit strategy risk. Strategy risk also may arise from a fund s trading behavior or its use of derivatives to create desired payoff profiles. In their seminal work, Fung and Hsieh (2001) showed that the risk of managed futures funds is due more to their trend-following behavior than to the commodities and currencies in which these funds are invested. The risk that does not stem from systematic sources is fund specific. It reflects the idiosyncratic investments, strategies or processes of the fund. This component of risk tends to diversify by spreading investments across funds MSCI Barra. All rights reserved. 5 of 27

6 3. Modeling Hedge Fund Returns To quantify the risk of a hedge fund, we first model the sources of its return. The common factor, or systematic, portion of a hedge fund s return comes from its exposure to traditional asset classes and from its strategy. We identify factors that capture both types of systematic influences for each fund (see 3.1 Factor Selection) and attribute a fund s return using the following model: r = α + X f + ε and (1) t k,t k,t t k where: r t = Return to the hedge fund at time t. α = Return net of contribution from factors. X k,t = Exposure of the hedge fund to factor k at time t. f k,t = Return to factor k at time t. ε = Hedge fund specific return at time t. t This model decomposes return into three components. One portion of the return, X f k k,t k,t, is attributable to a fund s exposures to the common factors. This return also is known as the common factor return and is not diversifiable within the hedge fund universe. Another part of the return, ε t, represents the specific, or idiosyncratic, portion of a fund s return. The final component is the fund s alpha, a measure of its performance relative to the factors. In the sections that follow, we provide an overview of the factor selection process and the different exposure estimation techniques that we use to model individual hedge funds. We then introduce the out-of-sample methodology used for both the factor selection and exposure estimation processes. 3.1 Factor Selection The Barra factor selection process identifies a relevant set of factors for each hedge fund separately. This approach requires a return history and hedge fund peer group membership. This peer group membership information is mapped onto an initial, pre-defined set of common factors. We summarize these factors for each peer group in Appendix 1. These factors explain the systematic behavior of the funds in the corresponding peer group. However, as we will show later in Table 2, the heterogeneity of hedge funds within their peer groups generally is quite high. Therefore, we cannot expect every fund to have a significant exposure to each pre-defined factor used to model its peer group(s). The inclusion of extraneous factors within a returns-based model risks the introduction of spurious results. Consequently, a subset of these factors is selected using in-sample and out-of-sample statistical analyses based on stepwise regression. This methodology is used to eliminate potentially extraneous factors. As a result, we use only the final subset of factors selected by the algorithm for a given hedge fund to model its returns. MSCI Barra classifies hedge fund common factors into two groups: traditional and alternative. Traditional factors are selected to capture those sources of a hedge fund s return due to known or conventional risk factors. The exposure to these factors sometimes is referred to as traditional 2007 MSCI Barra. All rights reserved. 6 of 27

7 beta. Examples of traditional factors are equity or fixed income portfolios, as well as Barra equity or fixed income risk model factors. Alternative factors capture the systematic portion of a hedge fund s return which cannot be explained by traditional factors. As such, these factors are necessary to capture the nontraditional portion of systematic risks within a hedge fund peer group stemming from strategy, illiquidity or nonlinearities. Alternative factors are especially useful in modeling hedge funds within peer groups such as merger arbitrage, distressed securities and convertible arbitrage. This is because the funds within these peer groups tend to follow similar, unconventional strategies and manage a relatively homogeneous set of investments. This behavior generates commonality across the funds within each of these peer groups that does not arise from passive investing in liquid asset classes (see Alvarez, Levinson 2006). MSCI Barra determines alternative factors first by assembling hedge funds that are representative of a particular peer group. Next, that portion of the hedge funds returns which is attributable to traditional common factors is removed from the individual hedge fund returns. Statistical techniques then are applied to the remaining portion of the hedge fund returns to identify alternative factors. Additional information on alternative factors and their construction is available in Appendix Estimating Exposures After having established a set of factors that are well suited to modeling the returns of a particular fund we then can attempt to estimate this fund s exposures, or betas, with respect to these factors. While a variety of exposure estimation techniques exist, it is critical that we adopt the most appropriate modeling approach. In this section, we describe notable attributes of a few methods used by the Barra Hedge Fund Exposure Generator to estimate common factor exposures. An obvious and popular technique used to estimate model parameters, such as exposures, is ordinary least squares (OLS) multivariate regression. This technique is used frequently because its implementation is straightforward and it is easy to understand. However, a critical assumption necessary to obtain robust exposures from regression estimation is that they remain constant over the estimation period. Consequently, it will be difficult to capture a hedge fund s typically diverse and dynamic behavior using a model based solely on regression estimation. Indeed, it would be naive to assume that hedge fund managers do not change their factor exposures over the life of their fund. A lack of rigid investment restrictions provides hedge fund managers with the flexibility to make rapid and significant changes in their style, sector or market bets according to their future expectations. As a result, hedge fund managers can be much more dynamic in their investment approach than traditional managers. A method used frequently within the regression framework to account for the dynamic behavior of hedge funds is the moving window regression. This method involves using a shorter and more recent data window to estimate the regression parameters. Discarding past data in this manner will allow the model to capture recent changes in the exposures more rapidly. However, this comes at a cost of statistical accuracy since the estimation is performed using a smaller data sample. In addition, this method will not capture exposure changes over the shorter window MSCI Barra. All rights reserved. 7 of 27

8 Another drawback is that the estimation window usually is chosen in an ad-hoc manner and may not be optimal for every fund. This may result in the exclusion of critical data from the exposure estimation process, regardless of the individual fund s dynamics. Consequently, the use of a shorter data window may produce noisy estimates and inferior forecasts. When a fund s exposures vary over an estimation window, the use of a more general model can improve the parameter estimates. The state space model (Hamilton 1994) is similar to a regression model, but does not assume that the exposures are constant over the estimation window. Instead, it introduces a stochastic element which allows the exposures to vary over the estimation period. The new model of return using this framework is: where: r = α+ X f + ε, where t k,t k,t t k X = X + ω and t k,t k,t 1 k,t 2 ( ε) t ( Σω) ε ~IN 0, σ, ω ~IN 0,. (2) r t = Excess return to hedge fund at time t. α = Average return net of contribution from factors. X k,t = Exposure of the hedge fund to factor k at time t. X k,t-1 = Exposure of the hedge fund to factor k at time t-1. f k,t = Return to factor k at time t. ε t = Hedge fund specific return at time t. ω = Vector of exposure disturbances at time t. t In this model, calculation of the exposure estimates for every point in time involves using the Kalman filter 2. The disturbances ε t and ω t are time-independent Gaussian noise processes 3. The exposures, the variance of ε t, and the variance-covariance matrix of ω t usually are estimated using a maximum likelihood technique 2. In addition, the state space framework and Kalman filter allow for the computation of contemporaneous, predicted and smoothed values of the exposures. In principle, this model may seem superior due to its ability to capture dynamic hedge fund exposures. However, this additional flexibility sometimes has a drawback. When the model specification is inaccurate, or when there are too few return data points available, this approach inadvertently will fit excess noise. As was the case with the regression approach, the state space model also can suffer from outdated data if there is a significant shift in a hedge fund s risk profile. However, the dynamic quality of the state space model allows it to be more adaptive, and therefore more robust than the constant exposure modeling assumption used in regression analysis. 2 See chapter 13 of Hamilton (1994). 3 The interpretation of ε t remains the same as in equation (1). In equation (2), the state space version of our hedge fund return attribution model, we allow the exposure to factor k, X k,t, to vary over time. The amount by which Xk,t has changed since the prior period, time t-1, is represented by ω k,t MSCI Barra. All rights reserved. 8 of 27

9 The automated exposure estimation approach used by the Barra Hedge Fund Exposure Generator can vary by hedge fund. This flexibility is necessary in order to capture the dynamic behavior of a fund s exposures with respect to the common factor returns. As a result, the exposure estimation methodology can vary over time and across hedge funds, or even for a particular hedge fund. For example, OLS multivariate regression might be the best choice for a hedge fund whose exposures vary little over time. Conversely, a state space model might be selected as the superior estimation approach for a hedge fund during a period when its common factor exposures have been very volatile. The Barra Hedge Fund Exposure Generator conducts an out-of-sample statistical analysis to select the best estimation method Out-of-Sample Model Evaluation As stated in sections 3.1 and 3.2, both the factor selection and the exposure estimation processes use in-sample and out-of-sample statistical analysis. In broad terms, the in-sample analysis is used to reveal the significant relationships between the fund and the factors. The outof-sample analysis is used to verify these relationships and reduce spurious results. These techniques are combined to specify the attribution model in (1) with the most robust risk forecasting ability. When evaluating a model on an out-of-sample basis, we begin by analyzing the predictability of the exposure estimates. This is accomplished by first calculating a series of out-of-sample returns in the following manner. At the beginning of each month, we estimate the fund exposures to a set of factors using data available through the end of the previous month. These exposures are combined with the factor returns observed over the current month to compute the common factor return that can be replicated by the model over the month. In particular, for month t, the replicated return is ˆX k k,t-1 fk,t, where the Xˆ kt, 1 s are the fund s exposures estimated using data through the end of the previous month, t 1, and the f k, t s are returns to the factors over the month. There is a variety of analyses that can be performed on these replicated common factor returns to measure particular aspects of the model s out-of-sample performance 4. We conduct a series of statistical analyses on a combination of the replicated and realized fund returns to gauge the out-of-sample accuracy of the model. 4 A commonly used measure in this framework is the R² of the regression of the realized returns versus the replicated returns. With respect to the hedge fund model outlined in (1), we note that this R² is only a measure of the ratio of the out-of-sample return variation captured by the factors to the hedge fund s total return variation. The variation of return unexplained by the factors is due to the idiosyncratic risk of the fund. In this context, R² is not a measure of the model s total risk forecasting ability. Unfortunately, it sometimes is subject to misinterpretation MSCI Barra. All rights reserved. 9 of 27

10 4. The Barra Hedge Fund Exposure Generator The Barra Hedge Fund Exposure Generator calculates factor exposures and risk forecasts for a set of hedge funds. All that is required to perform these calculations are the hedge funds return history and their corresponding style classifications over time. Regional investment information also is considered on a limited basis. The Barra Hedge Fund Exposure Generator models each hedge fund holding in a manner consistent with, and which represents an extension of, Barra s traditional risk modeling approach, as applied to equity and fixed income assets. Initially, it will perform a number of quality assurance tests. Any fund with insufficient data will be dropped from further consideration. Exposures are estimated for each remaining hedge fund separately. The exposure estimation algorithm of the update is complex due its use of returnsbased estimation in order to accommodate the dynamic nature of hedge funds. Its modeling approach is cognizant of the fact that a hedge fund may be exposed to multiple investment styles concurrently, and it adapts to style changes over time. Towards this end, it uses a returns-based model represented in equation (1), and a different set of factors for each style peer group, as described in Appendix 1. Standard returns-based estimation techniques described in section 3.2 are used for this purpose. In addition, this process classifies a set of factors as the best using thorough in-sample and out-of-sample statistical analyses, as described in sections 3.1 and 3.3. This approach identifies the best set of factors for each hedge fund and estimates the fund s exposures to these factors. Some of the factors initially selected may not be relevant in modeling a particular hedge fund. Such extraneous factors will introduce noise into the model and could have undesirable effects on the risk forecast. The factors identified by the process are those that are significant in explaining the fund returns across time. The exposures to this best set of hedge fund factors can be mapped directly to the Barra Integrated Model (BIM) factors. Consequently, the results generated by this process facilitate the integration of hedge fund risk forecasts across portfolios containing a wide variety of asset classes by users of various risk modeling applications. 5. Modeling Hedge Fund Risk A hedge fund s risk forecast is based upon its return attribution model. One widely-accepted measure of the risk of a fund is the standard deviation of its return. To forecast risk for a hedge fund or a portfolio of hedge funds, we need a covariance matrix of the factor returns. From our model provided in equation (1), it follows that the variance of a hedge fund can be written as: where: σ ( σ ) 1 = x Fx + (3) 2 2 f f f ε σ f x f F σ 2 ε = Total risk of the hedge fund. = Vector of exposures of the hedge fund to the factors. = Covariance matrix of factor returns. = Variance of the specific return of the hedge fund MSCI Barra. All rights reserved. 10 of 27

11 2 We calculate the variance forecast of the fund s specific return, σ ε, as the variance of the residuals obtained from the exposure estimation process. In addition, we compute different estimates of the variance of these residuals using a variety of exponentially weighted moving average weighting schemes. For each of these calculations, we use a different and relatively short half-life to capture the most recent changes in specific risk. We then use an out-of-sample analysis to select the method that provides the best residual variance estimate. We can expand equation (3) to represent a portfolio of hedge fund holdings. In addition, we can further generalize this portfolio total risk calculation to include other holdings whose representation extends across different asset classes and regions. To do so, we use the Barra Integrated Model (BIM) factor covariance matrix 5. The BIM covariance matrix factors provide comprehensive asset class coverage. Consequently, it can be used to attribute risk for a portfolio whose holdings cut across a wide swath, including equity, fixed income, currency and commodity markets. Among the multiplicity of factors incorporated into the BIM covariance matrix are those used in our hedge fund modeling process. In particular, we can compute the risk of a portfolio of hedge funds, or a portfolio represented by a variety of asset classes including hedge funds, as follows: where: h σ ( ) 1 2 σ = hxf Xh +hdh (4) p p p B I M p p p p p p = Vector of portfolio holding weights. p = Total risk of the portfolio. X p = Matrix of exposures of the portfolio holdings to the factors. F BIM = Barra Integrated Model (BIM) covariance matrix of factor returns. D = Diagonal matrix of the portfolio holdings specific return variances. p This factor return model is useful in assessing other aspects of risk. For example, it may be used to better understand how a fund s return might respond to severe downturns in the world equity market. Scenario analyses or simulations can be performed to investigate this issue by shocking a certain factor or a set of factors, such as the equity market return, and observing the resulting impact on the fund s replicated return. 6. Important Considerations In this section, we expand upon a few concepts that are important to this modeling approach. For example, when modeling hedge fund returns, one goal is to accurately model a hedge fund s common factor risk. Even when a common factor risk forecast is highly accurate, it still is 5 See The Barra Integrated Model, Stefek (2002), at MSCI Barra. All rights reserved. 11 of 27

12 possible for it to represent a relatively small portion of a hedge fund s total risk. Under this scenario, we would expect a very low R² value to accompany our results. How can this be? A model goodness of fit statistic, such as R², is only a measure of how much common factor return variation, or risk, is captured. It is not indicative of the accuracy of the model s risk forecasts. In order to investigate this concept further, section 6.1 discusses the systematic behavior of hedge funds within various peer groups. In addition, section 6.2 explains why common factors provide a better representation of the systematic portion of a hedge fund s return and risk than broad hedge fund indices. Finally, in section 6.3, we demonstrate the behavior of different exposure estimation approaches that were described in section 3.2 above Modeling Common Factor Behavior When modeling fund risk, the first step is to understand and measure that portion of risk which is systematic across other funds. This systematic or common factor risk is not diversifiable. As a result, it becomes the dominant component of risk in a well-diversified portfolio of funds. In contrast, specific, or idiosyncratic, returns are independent and uncorrelated across funds. Therefore, specific risk should be diversified away as more funds are added to the portfolio. It is important to note that the factors are designed to capture only that portion of return which is common or systematic across the funds in a peer group. These factors are not designed to explain the specific or idiosyncratic return of any particular fund. Therefore, the explanatory power of the factors depends on the proportion of common or systematic return shared by the funds in the peer group 6. One method to gauge the degree of systematic behavior within a hedge fund style peer group is to compute the correlation between historical returns for every pair of funds within that style. As indicated above, the returns to a group of funds that exhibit greater common factor risk and less idiosyncratic risk can be expected to be more homogeneous and will exhibit a higher correlation. Conversely, these returns can be expected to be more heterogeneous and display a lower correlation if less common factor risk and more idiosyncratic risk were present. Table 2 displays the median, the upper and the lower quartiles of the distribution of pairwise correlation coefficients between each pair of funds within each hedge fund style peer group. The correlations were computed across non-duplicate funds with at least 24 monthly returns over the period spanning January 1994 to August Results are sorted in descending order by the 50 th percentile correlation coefficient. At the top of this table are the same correlation calculations for roughly 1000 US equity mutual funds from the Lipper database. This group of mutual funds includes a representative sample of large, medium and small capitalization funds, in addition to funds of various styles within each of these size categories. Notice that the level of heterogeneity within the hedge fund universe generally was much higher than that of equity mutual funds. This is manifest by the consistently lower correlation coefficients 6 Ideally, we would like to identify a set of factors that could fully explain the return to a fund. In practice, this is not possible without detailed knowledge of a fund s strategy MSCI Barra. All rights reserved. 12 of 27

13 at each percentile for all hedge fund styles compared to those calculated for the equity mutual funds. Also, note that fixed income arbitrage and equity market neutral funds were especially heterogeneous. We should not expect to capture much common factor return in the more heterogeneous funds and observe that this is indeed the case. This was probably because these funds neutralized most of their systematic bets and applied dissimilar strategies over the observed period. Consequently, it is very likely that the most salient portion of the monthly returns generated by the more heterogeneous strategies will be specific. Table 2: Measuring Hedge Fund Heterogeneity Fund Pairwise Correlation Percentiles Hedge Fund Style 25 th Pctl 50 th Pctl 75 th Pctl US Equity Mutual Funds Event Driven Convertible Arbitrage Long/Short Equity Managed Futures Global Macro Fixed Income Arbitrage Equity Market Neutral Hedge fund pairwise correlations were computed using non-duplicate monthly hedge fund returns from the MSCI HFI + TASS database that had at least 24 data points across January 1994 to August Mutual fund pairwise correlations were computed using large, medium and small cap funds from the Lipper database. + Includes Distressed Securities and Merger Arbitrage styles Why Use Common Factors Instead of Hedge Fund Indices? The choice of factors is critical to the success of the model. A natural approach is to define these factors to be hedge fund style indices. Each style index is designed to reflect the average behavior of the funds within a style peer group. A hedge fund s exposure to a style index is a measure of the sensitivity of its returns to those of the corresponding style peer group. Since funds may invest according to more than one style, their returns also may be responsive to the behavior of multiple style peer groups. To the extent that such style peer groups have a meaningful impact on the performance of a hedge fund, hedge fund indices can be useful in accounting for their returns. Using this methodology, L Habitant (March 2001) showed that the Tremont hedge fund indices help explain the return of funds within the TASS hedge fund database on an in-sample basis. Though appealing in its simplicity, the use of broad hedge fund indices in a risk model has two shortcomings. First, many of these indices do not account for the substantial variation in the returns of funds within their style category. Consequently, for several styles, the average behavior does not adequately represent that of individual funds. An example of one such hedge fund style index is one that measures the performance of US long/short equity funds. Though 2007 MSCI Barra. All rights reserved. 13 of 27

14 many of these funds demonstrate a positive exposure to the equity market, they differ according to the individual bets they place. Some tilt toward momentum, others focus on value or growth, while still others concentrate on select industries. Similarly, convertible arbitrage funds differ significantly in their exposures to a variety of risk factors including interest rates, credit, gamma and the equity markets. A second problem is that hedge fund indices offer little transparency. Investors frequently analyze the risk of a portfolio by assessing its sensitivity to interest rates, industries, equity styles and other measures which may be derived from fundamental accounting data. A hedge fund risk model should highlight a fund s exposure to these traditional factors as well as to any arising from hedge fund strategies. This would help enhance the manager s understanding of a hedge fund s risk profile in terms with which he is familiar. Unfortunately, indices do not provide this degree of resolution. For example, knowing that a fund has an exposure to the US long/short equity index provides little insight into the particular bets the fund is taking. As an attempt to remedy these shortcomings, we use a more granular set of factors. These more granular sources of return provide greater transparency and explanatory power than broad style indices. The benefits of using more granular factors were demonstrated in a previous paper (Alvarez, et al 2004) by modeling long/short equity and convertible arbitrage fund returns Comparing Estimation Approaches To exemplify the behavior of the different estimation techniques described in section 3.2, we estimated exposures of the Tremont Long/Short Equity Index to the Russell 3000 Index and to four factors from the Barra US Equity Risk Model: Size, Size Nonlinearity, Momentum and Earnings Variability 7. Figure 1 illustrates the evolution of the market exposure over time that was estimated using three different approaches: an expanding window regression, a 36-month moving window regression and the Kalman filter model in (2). As one can see, the resulting exposure estimates are quite different depending upon the estimation method used. The expanding window regression model estimates the exposures at each point in time using the entire range of past data. For example, the market exposure shown in the figure for January 2000 was estimated via OLS regression using data ranging from January 1994 to January Note that, as time unfolds, this model uses a larger data window to estimate the exposures. This has the effect of anchoring the exposure estimates firmly to past return behavior. As a result, the model is restricted from capturing rapid or sudden changes in return behavior and expressing these changes as revisions to the estimated exposures. Indeed, failing to capture these changes could have a significant negative impact on our risk forecasts. The exposure estimated using the more flexible Kalman filter model looks quite different and provides interesting historical insights into typical long/short equity fund behavior. The Kalman filter exposure estimates indicate that long/short equity funds ramped up their exposure to the US equity market precipitously during late 1999, as the technology valuation bubble of the late 7 A thorough description of these factors can be found at (login required) MSCI Barra. All rights reserved. 14 of 27

15 twentieth century moved towards a crescendo. Subsequently, the managers seemed to lower their sensitivity to the market as the contemporaneous technology bubble burst and the market plunged headlong into the bear market starting in Finally, after the bear market ended in the beginning of 2003, the funds are shown to have increased their exposure to the market. In this example, we used the methodology outlined in section 3.3 to conclude that the Kalman filter model outperformed the regression model on an out-of-sample basis. This result would lead us to accept the Kalman filter model as the better model to capture the return behavioral dynamics of this particular index. Also note that the 36-month moving window model estimates are playing catch-up to the more responsive Kalman filter estimates and actually do worse than the regression model when analyzed out-of-sample. This is because the 36-month moving window model adds more noise to the estimates and does not react quickly enough to capture the changing dynamics in the index. Figure 1: Three Methods for Estimating Exposures 8 Brunnermeier and Nagel (2004) made a similar observation using 53 hedge fund managers stock holdings obtained from the CDA/Spectrum database. They concluded that the hedge funds within their sample were over-weighted in technology stocks throughout their study period, from March 31, 1998 through December 31, Initially, this high active portfolio weighting in technology stocks rose and peaked along with the level of the Nasdaq during March Subsequently, hedge fund managers reduced their technology and overall equity exposure by December The CDA/Spectrum database is maintained by Thomson Financial and is based upon the use of 13F filings with the US Securities Exchange Commission MSCI Barra. All rights reserved. 15 of 27

16 7. Conclusion We have developed a flexible hedge fund risk modeling process based upon a multi-factor return attribution model. The Barra Hedge Fund Model captures the systematic sources of hedge fund risk using a combination of traditional and alternative risk factors. Traditional factors capture conventional sources of risk arising from hedge fund asset holdings. Alternative factors are designed to capture the systematic portions of risk not explained by traditional factors. These alternative risks can arise from a fund s strategy, illiquid investments or nonlinear return behavior. In addition, the modeling process uses a sophisticated factor selection algorithm to screen out spurious or extraneous factors when modeling a fund. This process identifies that subset of factors which provides the most robust model of a fund s systematic risk. The exposures to these factors are estimated using an algorithm which accounts for the dynamic behavior of the fund with respect to the factors. This hedge fund risk modeling process provides a robust model that can be used to forecast the risk of a hedge fund or a portfolio of hedge funds. It also can gauge other aspects of risk. For example, it can be used to perform stress testing and scenario analysis. In addition, investors may use the model to analyze hedge fund holdings in conjunction with other investments in traditional asset classes MSCI Barra. All rights reserved. 16 of 27

17 References Aggrawal, V. and N Naik. Characterize the Risk and Return of Equity Hedge Funds. Working Paper, Georgia State University and London Business School (2001). Alvarez, Miguel, Mike Levinson and Dan Stefek. Hedge Fund Risk Modeling. Version 1.1., MSCI Barra, Inc. (November 2004), Alvarez Miguel, and Mike Levinson. Hedge Funds and Common Factors. MSCI Barra, Inc. (Fall Research Presentation 2006) Asness, Clifford, Robert Krail and John Liew. Do Hedge Funds Hedge? The Journal of Alternative Investments, (Fall 2001). Anson, Mark and Ho, Ho. Short Volatility Strategies: Identification, Measurement and Risk Management. The Journal of Investment Management, Vol 1, No. 2 (2003), pp R.A. Brealey and E. Kaplanis. Changes in the Factor Exposures of Hedge Funds. Working Paper, London Business School, (January 2001). Brown, Stephen J. and William N. Goetzmann. Hedge Funds With Style. Yale International Center for Finance, Working Paper No (February 2001). Brunnermeier, Markus K. and Stefan Nagel. Hedge Funds and the Technology Bubble. The Journal of Finance: Vol. LIX, No. 5, pp (October 2004). Connor, Gregory and Mason Woo. An Introduction to Hedge Funds. London School of Economics (September 2003). Fung, W. and D.A. Hsieh. Asset-Based Style Factors for Hedge Funds. Financial Analysts Journal, Vol. 58, No. 5 (September/October 2002a). Fung, William and David A. Hsieh. Risk in Fixed-Income Hedge Fund Styles. The Journal of Fixed Income (September 2002b). Fung, William K.H. and David A. Hsieh. The Risk in Hedge Fund Strategies: Alternative Alphas and Alternative Betas. Center for Hedge Fund Research and Education, London business School, U.K. and Fuqua School of business, Duke University, USA (2004). Fung, William and David A Hsieh. The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers. The Review of Financial Studies, Vol. 14, No. 2, pp (Summer 2001). Hamilton James D. (1994), Time Series Analysis, Princeton, N.J.: Princeton University Press. L Habitant Francios-Serge. Assessing Market Risk for Hedge Funds and Hedge Fund Portfolios. Union Bancaire Privee and Thunderbird, the American Graduate School of International Management, Research Paper No. 24 (March 2001). Mark Mitchell and Todd Pulvino. Characteristics of Risk and Return in Risk Arbitrage. The Journal of Finance: Vol. LVI, No. 6, pp (December 2001). Shumway and Stoffer (2000), Time Series Analysis and its Applications, Springer-Verlag New York, Inc. Stefek, Dan. Barra Integrated Model. Barra Research Insights (2002) MSCI Barra. All rights reserved. 17 of 27

18 Appendix 1: Hedge Fund Peer Group Descriptions and Corresponding Factors 9 This appendix provides a brief description of the salient hedge fund style categories and their corresponding systematic factors, as are used within the Barra Hedge Fund Model. Factors were identified for a particular style only if they were useful in accounting for a broad cross section of returns to funds within their category. Consequently, the Barra Hedge Fund Model maximizes the amount of information captured from a hedge fund s returns and minimizes the amount of unwelcome noise. MSCI Barra maps each peer group to a separate, pre-defined set of traditional and alternative factors. These factors are used to model returns for hedge funds in an associated peer group. Consequently, factors are selected to capture both the asset class and the strategy systematic return available within the peer group. For example, in modeling equity market neutral funds, we use market neutral style factors, such as size and volatility, as well as strategy factors, such as momentum and reversal. Each factor is designed to capture a separate portion of a hedge fund s overall common factor return. When combined in the model, they provide a greater degree of flexibility, transparency and explanatory power than broad based indexes (see Alvarez, et al 2004). Long/Short Equity Description: Long/Short equity hedge funds usually hold a combination of long and short positions in equities, while maintaining an overall long or short bias with respect to the market. These hedge funds often have a regional focus. They also tend to concentrate their positions to a greater extent than conventional funds across either preferred sectors or equity market fundamentals (e.g. value, growth, size and momentum). The positions held by these hedge funds can be extremely dynamic, since their managers often are provided much flexibility. Consequently, their market and factor exposures can vary substantially depending upon the manager s outlook and strategy. For example, a typical US hedge fund may have been concentrated in technology stocks with a momentum tilt during the recent technology valuation bubble period. During the subsequent technology bust, this hedge fund may have switched holdings to value or large-cap stocks. Funds within this category sometimes employ equity derivatives such as options and futures to hedge out certain market or asset risks. Factors: We use an equity market factor and a set of fundamental risk factors to model long/short equity funds. These fundamental risk factors have been selected from Barra equity models to capture behavioral tilts or equity style bets. Russell 3000 Index: The return to this index is used as the US equity market factor. We use it to capture the systematic return of a fund resulting from its overall market exposure. 9 The classification and style descriptions are consistent with those used in the MSCI HFI + TASS databases MSCI Barra. All rights reserved. 18 of 27

19 Barra US Equity Model Risk Factors 10 : Each risk factor is tested for in-sample fit and out-ofsample performance against each fund before it is included into the factor-set of that fund. In general, we have found the following equity risk factors to be useful for modeling long/short equity funds within our database: momentum, size, volatility, growth and value. Additional Barra equity model risk factors are sometimes used as well: dividend yield, earnings yield, earnings variability, leverage and liquidity. The styles represented by these additional risk factors are not encountered frequently within the long/short equity fund category of our database. However, each such factor is tested and occasionally incorporated to improve the model s performance. These conventional equity factors capture a significant portion of the long/short equity hedge fund return which is systematic, or is shared across those funds in our database of this category. A fund s industry preferences are seldom known in advance by MSCI Barra when we model its risk. However, during those rare circumstances when industry preferences are available, we can include a set of corresponding industry factors from the Barra equity model. For funds that invest in equity markets outside of the US, we use equivalent market indices and risk factors that target the corresponding region(s) of investment. For example, in order to model a European long/short equity fund, we would use the standard MSCI Europe Index and risk factors (e.g., momentum, size, value, etc.) obtained from the Barra European equity model. Equity Market Neutral Description: These funds hold offsetting long and short positions in equity market instruments. They generally neutralize their overall net market exposure by controlling for beta risk. More sophisticated hedging techniques involve neutralizing across sectors, industries and other fundamental characteristics. This is done while exploiting perceived equity market inefficiencies manifest by identifiable mispricing opportunities. Many widely practiced equity market neutral strategies rely upon technical or fundamental signals, or some combination thereof. Residual reversal and relative strength are two popular technical strategies that are based upon the application of reversal and momentum signals. Also, a popular value-based fundamental strategy employs signals derived from variations of the dividend discount model. Factors: We utilize a combination of factors from the Barra Alphabuilder 11 suite and Barra equity risk models to model equity market neutral funds. In addition, we use two hedge fund factors to capture any remaining systematic behavior within the funds. US Residual Reversal Factor: This factor is the return to a beta-controlled strategy based on the Alphabuilder US Reversal signal. This signal accounts for the fact that stocks which 10 For a detailed description of these factors see the Barra US Equity Model Handbook, available at (login required). 11 For a detailed description of these factors see the Barra Alphabuilder Model Handbook, available at (login required) MSCI Barra. All rights reserved. 19 of 27

20 outperform (underperform) on a beta-adjusted basis subsequently tend to underperform (outperform) on that same basis. US Dividend Discount Model Factor: This factor is the beta-controlled return to the Alphabuilder US Dividend Discount Model signal. These signals were calculated for each stock using a 3-stage dividend discount valuation model. Barra US Equity Model Risk Factors: Those US Equity model risk factors most widely utilized to capture return within the equity market neutral category of our database are momentum, volatility, liquidity, value, earnings yield, earnings variance and dividend yield. These risk factors are controlled for industry effects. Equity Market Neutral Alternative Factors: These factors are used sparingly to capture the remaining systematic return of funds within our database of the equity market neutral category. We use a retruns-based analysis together with a statistical procedure similar to principal component analysis (PCA) to construct these factors. This is done to identify that portion of each equity market neutral fund return which could not be explained by conventional equity factors described above. For those equity market neutral funds that invest outside of the US market, the determination of factors is limited to the Barra equity model risk factors corresponding to the particular markets in which the fund invests. Convertible Arbitrage Description: These funds manage positions in convertible instruments and their issuers underlying equity to create portfolios that tend to be equity market neutral. The plain vanilla convertible arbitrage strategy involves taking a long position in a convertible bond and shorting the issuer s stock. One goal of this strategy is neutralize the equity sensitivity inherent in the option that is embedded within this bond. Some convertible arbitrage funds also trade credit default swaps. These swaps are used to mitigate that portion of the bond s inherent credit risk which was not hedged out of the portfolio by shorting the stock. This variety of hedge sometimes is managed dynamically 12. Dynamic management often presents the fund manager with additional opportunities to capture profit. Consequently, this management style can add additional complexity to the monthly return profile. Such opportunities frequently arise from large fluctuations in the price of an issuer s underlying equity. Factors: These funds can be modeled using a high yield bond portfolio, a pure convertible arbitrage factor and Barra credit model spread factors. High Yield Bond Portfolios: The Barra Hedge Fund Model utilizes three representative high yield portfolios. These portfolios are constructed using returns to bonds within the Barra 12 This is a common practice when a bond has an imbedded option whose strike price is close to the price of the underlying security (i.e., it is near-the-money) and has a high gamma exposure MSCI Barra. All rights reserved. 20 of 27