**Introduction**

Hedge fund portfolio managers and consultants make extensive use of historical data for the purposes of manager selection and portfolio construction. The conventional use of historical hedge fund data along with portfolio optimisation techniques will frequently result in portfolios that in practice maximise risk and illiquidity.

Most methods of quantitative analysis assume that managers’ distributions of returns and correlation coefficients versus other managers are stationary. The latter is “fairly” true, but the former is almost never true. While historical returns can be useful for characterising risk and return, this is usually true only when sufficient data is available to permit a measure of a manager’s performance through a broad range of market conditions. Unfortunately, the length of historical track records of hedge fund managers is rarely sufficient.

Since the vast majority of hedge fund track records are too short to fully characterise a manager’s behaviour, we have developed a new method for evaluating a manager’s return characteristics. This method is less dependent on the length of historical returns and provides greater insight into a manager’s behaviour over a broad range of market conditions. We refer to this method as “Generic Model Decomposition” (GMD).

GMD consists of a non-parametric factor analysis of a manager’s returns. GMD models can be used to estimate a manager’s behaviour in market conditions not exhibited during the manager’s historical track record and to extract insights into the sources of return.

The past decade has witnessed a substantial increase in the number, asset size and importance of hedge funds. Correspondingly, there has been an attempt to analyse these new investment vehicles by extending or modifying the factor analysis that was successfully employed by Sharpe (Sharpe 1992) to analyse the performance of mutual funds. Examples of this research include Schneeweis and Spurgin (Schneeweis 1998), Liang (Liang 1999) and Fung and Hsieh (Fung 1997).

Fung and Hsieh extended Sharpe’s factor analysis to include factors that captured stylistic differences of alternative managers. They identify five hedge fund style categories (distressed, global macro, systems, opportunistic and value) that are shown to explain somewhat more of hedge fund return variation than Sharpe’s original factors. The primary result of Fung and Hsieh’s research, however, was to categorise hedge fund styles without using factor analysis to identify the specific factors that explain hedge fund returns. When Fung and Hsieh used the same factors as Sharpe to explain hedge fund returns, they found that 48% of the hedge funds had R^{2} below 25%, compared to half of mutual funds having an R^{2} above 75%. Even when the new factors are included in Sharpe’s original set, Fung and Hsieh found that they could produce reasonably high R^{2} for no more than 40% of the hedge funds they studied.

Schneeweis and Spurgin (Schneeweis 1998) modelled hedge fund returns using four factors: 1) the natural return of an asset class, 2) the ability to go long and short, 3) intra-month volatility, and 4) temporary price trends. They used this common set of factors to explain the returns of hedge funds, mutual funds and commodity trading advisors. This research was performed to draw very general conclusions about the factors that determine hedge fund performance. However, they note in their paper, as did Fung and Hsieh, that the heterogeneous nature of hedge fund styles may require detailed examination of individual hedge funds in order to understand their specific return generating processes.

This paper presents a methodology for identifying the return generating processes of individual hedge funds to a much greater degree than that achieved in previous research. Ultimately, we are attempting to model hedge fund returns based on empirical data. When performing empirical research, it is important to analyse both the returns and the process by which those returns are generated. The authors are fortunate to have many years of experience in both managing hedge funds and analysing hedge funds managed by others. We will rely upon this experience to select candidate factors that are likely to explain the returns for various hedge funds.

The objective of this methodology is to combine the insights gained through experienced qualitative due diligence with quantitative modelling techniques to model manager returns and estimate behaviour in market conditions not exhibited during a manager’s performance history. Additionally, these models can be used to extract insights into the sources of return and risk for specific managers.

Unlike previous methodology, GMD seeks to construct non-parametric factor models of managers’ returns using factors (and/or proxies of factors, herein referred to solely as factors) that explain the unique characteristics of specific hedge fund strategies. Additionally, we review individual manager’s trading methodologies and historical records (as part of the due diligence process) to select candidate factors that we believe explain manager performance. This represents a significant departure from previous research because we do not attempt to draw broad conclusions about hedge funds in general. Rather, models are developed for individual managers in recognition of the uniqueness of many hedge fund strategies and managers.

**GMD: A Method for Characterising the Returns of Alternative Investments**

GMD quantitatively models a manager’s returns as a linear combination of factors that produce reasonable estimates of the manager’s behaviour.

GMD is conducted in two steps. First we identify a universe of candidate factors that are related to the manager’s sources of risk and return. This is done as part of a qualitative due diligence study. Second, we perform an optimisation to weight the factors to best “fit” our model to the manager’s returns.

We can define the GMD returns model as:

Where is the estimate for the manager’s actual returns, r(t). Our job is to select the universe of candidate factors, {s_{i}(t)} and weights {a_{i}(t)} that results in an that best replicates r(t) in the sense that:

Where we attempt to minimise C, a cost (objective) function that represents the goodness of fit over time between manager’s returns r(t) and the returns of the associated GMD model .

To pick the universe of candidate factors, a qualitative due diligence analysis of the manager’s portfolio and trading strategy is required. The candidate factors consist of various time series such as equity and bond indices, their associated option contracts, and returns resulting from simplistic dynamic trading techniques. As shown later in two examples, we employ option contract time series (as suggested by Fung (1997) and Glosten (1994)) to serve as a proxy for dynamic trading strategies and to represent the option-like behaviour of certain securities held by hedge funds.

The objective function used to derive a GMD was designed to allow us to define the most important characteristics of a manager’s returns. To accomplish this we use a non-parametric, non-linear objective function that attempts to match large winning and losing months rather than just fitting in a mean-square sense:

Assume:

= The selected manager’s net asset value (NAV) for period i.

= The Generic investment strategy’s NAV for period i. Assumes a common starting date and equity amount as the selected manager.

= Number of periods in the performance history.

= The difference between the ranks assigned to % (selected manager’s percent return for period i) and %(Generic investment strategy’s percent return for period i) for a given set of paired data.

{(% ,%); }

The numerator of the equation represents the root mean squared error of the differences in the equity curves^{1}. By ensuring that the two performance series have similar absolute rates of return, the derived GMD investment strategy will be forced to reflect an appropriate degree of leverage.

The denominator is a non-parametric measure of correlation known as Spearman’s Rank Correlation. This correlation statistic tends to force the factor weights, , in the GMD to appropriately describe the sources of risk and return inherent in the manager’s strategy by aligning the various inflection points in the two equity curves. Additionally, the use of a non-parametric measure of association makes the resulting factor weights less likely to be the product of optimising to a singularity.

By minimising the above objective function, a specific factor weighting is derived that will estimate, as closely as possible, the manager’s reported returns. The factor weightings, which include leverage, represent allocations to the underlying factors that best characterises a manager’s return series.

We must acknowledge that the Generic investment strategy derived in this manner is subject to criticism. Simply put, there is an “identification” issue; we can never be certain that the derived factor weights in any sense fully describe the manager’s behaviour. This is essentially a “guerrilla statistic” designed to be used in an environment of highly imperfect information. Unfortunately, given the constraints associated with accuracy and transparency in the hedge fund world, it may not be appropriate to attempt to extract too “optimal” a result.

The full article follows up by presenting two sample GMDs analysis of Manager A and Manager B. The data employed in the two examples cover the period from the inception of trading for each manager up to August 1998. With the exception of the final month, the time span was a reasonably trouble-free period in the history of hedge fund investing. Much of the “reported” volatility in the hedge fund world occurred directly following the analysed period. Through this period of analysis, the authors demonstrate the value of GMD with respect to the evaluation of out-of-sample risk.

*For the full version of the research article, please visit *http://www.stonebrook.ws/research.html or *http://www.stonebrook.ws/research_papers/dangers.pdf.*

**Footnote**

^{1} An equity curve is a graphical or numerical representation of the value of (typically) a $1,000 investment, over time, as a function of the manager’s periodic (usually monthly) performance.

**References**

Alexander, Sharpe, and Bailey: Fundamentals of Investments (Englewood Cliffs, NJ: Prentice Hall, 1993)

Edwards (1988) Edwards, Ma: “Commodity Fund Performance: Is the Information Contained in Fund Prospectuses Useful?” Journal of Futures Markets, Vol 8, No 5, 1988

Elton (1995) Elton, Gruber, Blake: “Fundamental Economic Variables, Expected Returns, and Bond Fund Performance” The Journal of Finance Vol L, No 4, September 1995

Fung (1997) Fung, Hsieh: “Empirical Characteristics of Dynamic Trading Strategies: The Case of Hedge Funds” The Review of Financial Studies Vol 10, No 2 Summer 1997

Glosten (1994) Glosten, Jagannathan: “A Contingent Claim Approach to Performance Evaluation” Journal of Empirical Finance, 1, 133-160.

Liang (1999) Liang: “On the Performance of Hedge Funds” Association for Investment Management and Research, July/August 1999

McCarthy (1997) McCarthy, Schneeweis, Sprugin: “Informational Content in Historical CTA Performance” Journal of Futures Markets, June 1997.

McCarthy (1998) McCarthy, Spurgin: “A Review of Hedge Fund Performance Benchmarks” Journal of Alternative Investments, Summer 1998

Schneeweis (1998) Schneeweis, Spurgin: “Multifactor Analysis of Hedge Fund, Managed Futures, and Mutual Fund Return and Risk Characteristics” Journal of Alternative Investments, Fall 1998

Sharpe (1992) Sharpe: “Asset Allocation: Management Style and Performance Measurement” Journal of Portfolio Management, Vol 18, No 2, 1992

Silber (1994) Silber: “Technical Trading: When It Works and When It Doesn’t” The Journal of Derivatives”, Spring 1994

Weisman (1998) Weisman: Conservation of Volatility and the Interpretation of Hedge Fund Data” Alternative Investment Management Association, June/July 1998

*Andrew Weisman is the chief investment officer of Nikko Securities International, where he is primarily responsible for managing the firm’s efforts in the area of alternative investments. Jerome Abernathy is managing partner of Stonebrook Structured Products LLC, a financial engineering and asset management firm. The authors thank Mark Anson of the California Public Employee Retirement System for his invaluable input.*