Investing in Hedge Funds: Adding Value through Active Style Allocation Decisions

Significant value can be added in a hedge fund portfolio through the systematic implementation of active style allocation decisions, both at the strategic and tactical levels.

Given the low allocation typically made to alternative investment strategies (i.e., generally 5% to 15% of the global allocation), investors must try to maximise the benefits of their hedge fund portfolios. This can be done by customising an optimal hedge fund portfolio and by taking into account the investor’s original allocation to stocks and bonds.

One of the by-products of the bull market of the 90’s has been the consolidation of hedge funds as an important segment of financial markets. It was recently announced that the value of the hedge fund industry worldwide had passed the $1 trillion mark for the first time, with approximately 7,000 hedge funds in the world, around 1,000 of which were launched in 2003.

One of the key reasons behind the success of hedge funds in institutional money management is that such alternative investment strategies seem to provide diversification benefits with respect to other existing investment possibilities. In an attempt to fully capitalize on such beta benefits in a top-down approach, investors or (funds of hedge funds) managers must be able to rely on robust techniques for optimization of portfolios including hedge funds. Standard mean-variance portfolio selection techniques are known to suffer from a number of shortcomings, and the problems are exacerbated in the presence of hedge funds. Most importantly it can be argued that the following two aspects require specific care. First, because hedge fund returns are not normally distributed, a mean-variance optimization would be severely ill-adapted. Secondly, the problem of parameter uncertainty needs to be carefully addressed, as the lack of a long history and the non-availability of high frequency data imply that parameter estimation is a real challenge in the case of hedge fund returns.

While both problems (non-trivial preferences about higher moments of asset return distribution and the presence of parameter uncertainty) have been studied independently, what is still missing for active style allocation in the hedge fund universe is a model that would take into account both of these two aspects. Our contribution is precisely to introduce an optimal allocation model that incorporates an answer to both challenges within a unified framework. To this end, we introduce a suitable extension of the Black-Litterman Bayesian approach to portfolio construction that allows for the incorporation of active views about hedge fund strategy performance in the presence of non-trivial preferences about higher moments of hedge fund return distributions.

In a nutshell, we suggest the following approach. We first generate “neutral” views on expected hedge fund returns based on the desire to match a benchmark portfolio composition, where the benchmark is designed based on minimizing the portfolio Value-at-Risk. For this purpose, we use an asset pricing model that incorporates investors’ preferences not only on expected return and volatility, but also on higher moments of hedge fund return distributions. Next, we present a simple factor analysis that allows us to obtain a bullish, a bearish or a neutral view concerning the expected return. The next step involves blending such active views with the neutral views, applying a Bayesian statistical approach similar to that introduced by Black-Litterman. Finally, we generate optimal allocations to hedge funds that are consistent with this mixture of neutral and active views.

We also present a numerical application illustrating how investors can use a multi-factor approach to generate such active views and dynamically adjust their allocation to various hedge fund strategies while staying coherent with a long-term strategic allocation benchmark. We were able to show that the active style selection process, combined with the Black-Litterman portfolio selection method, allows for significant outperformance without a large increase in tracking error. In particular, the implementation of the process led to a 100 basis points excess return over the period January 1997 to December 2004 for a small tracking error (0.86%), leading to a 1.17 information ratio. A more aggressive portfolio version, based on an increase in the parameter defining the relationship between neutral and active views, led to outperformance of almost 200 basis points for a 1.37 tracking error, leading to a 1.41 information ratio. We also show that the optimal design of a hedge fund portfolio based on active allocation decisions to various alternative strategies leads to a significant improvement in the Omega function, a relevant risk-adjusted measure of performance.

The bulk of the message conveyed in this paper is straightforward and has important potential implications for the hedge fund industry: it is only by taking into account the exact nature and composition of an investor’s existing portfolio, as opposed to regarding hedge fund investing from a stand-alone approach, that institutional investors can truly customize and maximize the benefits they can expect from investing in these modern forms of alternative investment strategies. Overall the results in this paper strongly suggest that significant value can be added in a hedge fund portfolio through the systematic implementation of active style allocation decisions, both at the strategic and tactical levels. While this fact has long been recognized by market participants, the lack of reliable asset allocation tools has not facilitated the implementation of effective top-down approaches to investment in hedge funds. In this study, we argue that such techniques are actually already available and we show that a suitable extension to the Black-Litterman model can be used to implement active views on hedge fund style performance in a meaningful and consistent approach that avoids the pitfalls of standard optimization procedures.

The "Investing in Hedge Funds: Adding Value through Active Style Allocation Decisions" study was supported by SG Asset Management.

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Portfolio Optimization and Hedge Fund Style Allocation Decisions

This paper attempts to evaluate the out-of-sample performance of an improved estimator of the covariance structure of hedge fund index returns, focusing on its use for optimal portfolio selection. Using data from CSFB-Tremont hedge fund indices, we find that ex-post volatility of minimum variance portfolios generated using implicit factor based estimation techniques is between 1.5 and 6 times lower than that of a value-weighted benchmark, such differences being both economically and statistically significant. This strongly indicates that optimal inclusion of hedge funds in an investor portfolio can potentially generate a dramatic decrease in the portfolio volatility on an out-of-sample basis. Differences in mean returns, on the other hand, are not statistically significant, suggesting that the improvement in terms of risk control does not necessarily come at the cost of lower expected returns.

A dramatic change has occurred in recent years in the attitude of institutional investors, banks and the traditional fund houses towards alternative investment in general, and hedge funds in particular. Interest is undoubtedly gathering pace, and the consequences of this potentially significant shift in investment behavior are far-reaching, as can be seen from the conclusion of a recent research survey about the future role of hedge funds in institutional asset management (Gollin/Harris Ludgate survey {2001}): "Last year it was evident (...) that hedge funds were on the brink of moving into the mainstream. A year on, it is safe to argue that they have arrived". According to this survey, 64% of European institutions for which data was collected currently invest, or were intending to invest, in hedge funds (this Exhibit is up from 56% in 2000). Interest is also growing in Asia, and of course in the United States, where the hedge fund industry was originated by Alfred Jones back in 1949. As a result, the value of the hedge fund industry is now estimated at more than 500 billion US dollars, with more than 5,000 funds worldwide (Frank Russell - Goldman Sachs survey {1999}), and new hedge funds are being launched every day to meet the surging demand.

Among the reasons that explain the growing institutional interest in hedge funds, there is first an immediate and perhaps superficial one: hedge funds always gain in popularity when equity market bull runs end, as long-only investors seek protection on the downside. This certainly explains in part the rising demand for hedge funds in late 2000 and early 2001. A more profound reason behind the growing acceptance of hedge funds is the recognition that they can offer a more sophisticated approach to investing through the use of derivatives and shortselling, which results in low correlations with traditional asset classes. Furthermore, while it has been documented that international diversification fails when it is most needed, i.e., in periods of crisis (see for example Longin and Solnik {1995}), there is some evidence that conditional correlations of at least some hedge strategies with respect to stock and bond market indexes tend to be stable across various market conditions (Schneeweis and Spurgin {1999}).ⁱ

A classic way to analyze and formalize the benefits of investing in hedge funds is to note the improvement in the risk-return trade-off they allow when included in a traditional long-only stock and bond portfolio. Since seminal work by Markowitz {1952}, it is well-known that this trade-off can be expressed in terms of mean-variance analysis under suitable assumptions on investor preferences (quadratic preferences) or asset return distribution (normal returns).ⁱⁱ In the academic and practitioner literature on the benefits of alternative investment strategies, examples of enhancement of long-only efficient frontiers through optimal investments in hedge fund portfolios abound (see for example Schneeweis and Spurgin {1999} or Karavas {2000}).

One problem is that, to the best of our knowledge, all these papers only focus on in-sample diversification results of standard sample estimates of covariance matrix. In sharp contrast with the large amount of literature on asset return covariance matrix estimation in the traditional investment area, there has actually been very little scientific evidence evaluating the performance of different portfolio optimization methods in the context of alternative investment strategies. This is perhaps surprising given that the benefits promised by portfolio optimization critically depend on how accurately the first and second moments of hedge fund return distribution can be estimated. This paper attempts to fill in this gap by evaluating the out-of-sample performance of an improved estimator of the covariance structure of hedge fund index returns, focusing on its use for optimal portfolio selection.

It has since long been recognized that the sample covariance matrix of historical returns is likely to generate high sampling error in the presence of many assets, and several methods have been introduced to improve asset return covariance matrix estimation. One solution is to impose some structure on the covariance matrix to reduce the number of parameters to be estimated. Several models fall within that category, including the constant correlation approach (Elton and Gruber {1973}), the single factor forecast (Sharpe {1963}) and the multi-factor forecast (e.g., Chan, Karceski and Lakonishok {1999}). In these approaches, sampling error is reduced at the cost of some specification error. Several authors have studied the optimal tradeoff between sampling risk and model risk in the context of optimal shrinkage theory. This includes optimal shrinkage towards the grand mean (Jorion {1985, 1986}), optimal shrinkage towards the single-factor model (Ledoit {1999}). Also related is a recent paper by Jagannathan and Ma {2000} who show that imposing weight constraints is actually equivalent to shrinking the extreme covariance estimates to the average estimates. In this paper, we consider an implicit factor model in an attempt to mitigate model risk and impose endogenous structure. The advantage of that option is that it involves low specification error (because of the "let the data talk" type of approach) and low sampling error (because some structure is imposed). Implicit multi-factor forecasts of asset return covariance matrix can be further improved by noise dressing techniques and optimal selection of the relevant number of factors (see section 1).

We choose to focus on the issue of estimating the covariances of hedge fund returns, rather than expected returns, for a variety of reasons. First, there is a general consensus that expected returns are difficult to obtain with a reasonable estimation error. What makes the problem worse is that optimization techniques are very sensitive to differences in expected returns, so that portfolio optimizers typically allocate the largest fraction of capital to the asset class for which estimation error in the expected returns is the largest. On the other hand, there is a common impression that return variances and covariances are much easier to estimate from historical data. Since early work by Merton {1980} or Jorion {1985, 1986}, it has been argued that the optimal estimator of the expected return is noisy with a finite sample size, while the estimator of the variance converges to the true value as the data sampling frequency is increased. As a result, we approach the question of optimal strategic asset allocation in the alternative investment universe in a pragmatic manner. Because of the presence of large estimation risk in the estimated expected returns, we evaluate the performance of an improved estimator for the covariance structure of hedge fund returns, focusing on its use for selecting the one portfolio on the efficient frontier for which no information on expected returns is required, the minimum variance portfolio.ⁱⁱⁱ

In particular, we consider a portfolio invested only in hedge funds and an equity-oriented portfolio invested in traditional equity indices and equity-related alternative indices. Our methodology for testing minimum variance portfolios is similar to the one used in Chan et al. {1999} and Jagannathan and Ma {2000}: we estimate sample covariances over one period and then generate out-of-sample estimates. Using data from CSFB-Tremont hedge fund indices, we find that ex-post volatility of minimum variance portfolios generated using implicit factor based estimation techniques is between 1.5 and 6 times lower than that of a value-weighted benchmark (the S&P 500), such differences being both economically and statistically significant. This strongly indicates that optimal inclusion of hedge funds in an investor portfolio can potentially generate a dramatic decrease in the portfolio volatility on an out-of-sample basis. Differences in mean returns, on the other hand, are not statistically significant, suggesting that the improvement in terms of risk control does not necessarily come at the cost of lower expected returns.

The rest of the paper is organized as follows. In Section 1, we introduce the implicit factor approach to asset return covariance estimation. In Section 2, we present the data, the methodology and the results. Section 3 extends the analysis to an investment universe mixing alternative and traditional investment strategies. Section 4 concludes.

An article based on this paper appeared in the Fall 2002 edition of the Journal of Alternative Investments.

Footnotes:

1. In a follow up paper, Schneeweis and Spurgin {2000} find that different strategies exhibit different patterns. They make a distinction between good, bad and stable correlation depending whether correlation is higher (respectively lower, stable) in periods of market up moves compared to periods of market down moves. Agarwal and Narayan {2001} also report evidence of higher correlation between some hedge fund returns and equity market returns when conditioning upon equity market down moves as opposed to conditioning upon up moves.

2. There is clear evidence that hedge fund returns may not be normally distributed (see for example Amin and Kat {2001} or Lo {2001}). Hedge funds typically exhibit non-linear option-like exposures to standard asset classes (Fung and Hsieh {1997a, 2000}, Agarwal and Naik {2000}) because they can use derivatives, follow all kinds of dynamic trading strategies, and also because of the explicit sharing of the upside profits (post-fee returns have option-like element even if pre-fee returns do not). As a result, hedge fund returns may not be normally distributed even if traditional asset returns were. Fung and Hsieh {1997b} argue, however, that mean-variance analysis may still be applicable to hedge funds as a second-order approximation as it essentially preserves the ranking of preferences in standard utility functions. An alternative is mean-VaR analysis (see for example Favre et Galinao {2000} or Amenc and Martellini {2002}).

3. Alternatively, one motivation in focusing on the minimum variance portfolio is to note that it is the efficient portfolio obtained under the null hypothesis of no informative content in the cross-section of expected returns.