Research suggests better way to measure true alpha performance of hedge fund return profiles

An accurate measure of alpha is difficult. Defining hedge fund risk exposures can be particularly tricky due to the large varieties of strategies and the specific nature of hedge fund return profiles.

A number of institutional investors now allocate a sizeable portion of their portfolios to hedge funds. This interest in hedge funds can be explained by the poor performance exhibited by traditional asset management.

For some years now, numerous studies have shown that the vast majority of active asset managers do not outperform ­passive ­investment.

Some authors find that the outperformance generated by active management just covers the costs generated by the strategy (Grossman and Stiglitz 1980; Ippolito 1989), while others conclude that the after-fee performance of active management is lower than that of passive management (Jensen 1968; Grinblatt and Titman 1992; Hendricks, Patel and Zechauser 1993; Elton, Gruber, Das and Hlavka 1993; Kahn and Rudd 1995; Malkiel 1995; Elton, Gruber and Blake 1996; Gruber 1996; Carhart 1997, Cuthbertson, Nitzche and O’Sullivan 2008; French 2008; Fama and French 2010, among many others).

All of these studies, conducted to propose improvement in terms of performance measurement, underline the difficulty of evaluating a portfolio’s true alpha.

Within such a context of disappointing performance, hedge funds were seen as a way of improving portfolio performance. Evaluating hedge fund returns requires specific attention because hedge funds invest in a heterogeneous range of asset classes and cover a wide range of dynamic strategies that have different risk and return ­profiles.

Hedge funds also include options and derivative products, which are not part of traditional management. The widely used performance measures, which were developed based on modern portfolio theory, were specifically designed for traditional investment and particularly for equity investment, even if some authors have included factors to suit other asset classes such as bonds (Sharpe 1992; Elton, Gruber, Das and Hlavka 1993).

When risk exposures of traditional asset class returns can be represented with linear models, hedge fund returns present nonlinear exposures to traditional asset classes, mimicking an option pay-off. This aspect has to be taken into account when evaluating their ­performance.

When it comes to performance measurement, it appears that asset managers are not fully using the techniques proposed by the literature. This was highlighted by Amenc, Goltz and Lioui (2011). They reported the results of a 2008 survey on traditional asset management. Respondents to the survey were European asset managers.

It appears from this survey that the vast majority of respondents do not use sophisticated approaches for portfolio performance measurement. There is still a wide gap between practices and ­academic models.

The Sharpe ratio (80% of the respondents) and the information ratio (80% of the respondents) appear to be the most widely used measures to evaluate the performance of asset management.

When evaluating the relative performance of a portfolio, 33% of the respondents compare their returns with those of a simple index. However, it has been largely demonstrated that such a comparison does not make it possible to take into account the differences in risk exposures between the portfolio and the index, consequently making it impossible to accurately measure the asset manager’s value added.

Finally, if many professionals look at their alpha, the methodology used appears to be critical for most of them, since about 62% of the respondents evaluate alpha with regard to a peer group. This approach has been largely criticised (see Myners’ report (2001)), as the risk characteristics of the portfolio do not usually appear to be accurately reflected by the peer group. Only 23% used multifactor models to evaluate alpha.

Measuring true alpha
Measuring the true alpha of a portfolio is the only way to identify skilful managers who may be able to repeat their performance in the future. An accurate measure of alpha can only be obtained after isolating the specific performance (due to manager skill) from the risk premiums that reward the various risk factors to which the portfolio is exposed.

The problem of performance measurement robustness has been well documented for traditional portfolio management. It has been shown that the result of performance measurement may change depending on the index chosen as market factor (see Roll 1977) due to the inefficiency of the proxies and to a poor description of portfolio risk exposures.

As a result the ranking of portfolios may be affected by the choice of the reference index. This is especially true for alpha measured with a single-index model as well as for ratios referring to a benchmark, such as the information ratio.

The use of multifactor models does not completely solve this problem as these models are not necessarily able to include all risk factors supported by the portfolios. Using a mis-specified model can lead to the conclusion that a manager has produced alpha, although this alpha is in fact the return premium rewarding a forgotten risk factor. As a result investors may be misled in their investment choice. This problem of robustness is exacerbated as soon as hedge funds are concerned.

Defining hedge fund risk exposures can be particularly tricky due to the large varieties of strategies and the specific nature of hedge fund return profiles (option-like pay-offs). A small change in risk can produce a large change in returns in option-like strategies, as opposed to the linear exposures encountered in ­traditional ­investment.

The results of hedge fund performance evaluation can then be largely modified if the model used is mis-specified.

Robustness is key when assessing the performance of hedge funds. The possibility of using a model that takes it into account is crucial. Traditional ratios involving mean returns and volatility or even more sophisticated ratios accounting for downside risk are not sufficient to rank funds.

Peer benchmarking also has its limits. Measuring performance through alpha after adjusting the returns for risk exposures to several factors delivers a more precise basis for comparing funds.

Given the wide diversity of hedge fund strategies, equity, fixed income, credit, commodity or currency risks are included together with returns on option strategies built on these primitive factors. A main drawback of the current approach is linearly relating hedge fund returns to such risk factors.

Capturing exposures
Recent research, supported by Newedge as part of the advanced modelling for alternative investments research chair at Edhec-Risk Institute1, proposes a new method that captures the non-linear exposures of a hedge fund strategy to several risk factors. The model accommodates many non-linear functions of returns for the risk factors, hence the term non-parametric, over and above the usual option pay-off patterns.

The risk-adjustment non-linear functions are easily obtained by solving a portfolio problem in which the investors set their own risk tolerance. A hedge fund that exhibits a consistent alpha under all levels of risk tolerance delivers robust performance.

The research elaborates how this approach overcomes the limitations of the existing methods to evaluate the performance of hedge funds.

Performance ratios are the simplest measures since they involve statistics that can be computed directly from returns series of any hedge fund. Some involve the first two moments of the return distribution (Sharpe, Treynor or information ratios) while some others aim to capture the downside risk associated with the fund (Sortino, gain-loss or omega ratios). The main drawback of this approach is that it does not account for the very different strategies used by hedge funds.

One solution involves using peer benchmarks. The idea is to form homogenous groups of managers based on qualitative analysis and/or statistical techniques so as to alleviate the concern over hetero­geneity of hedge fund strategies.

The managers’ performance is assessed in terms of their ability to outperform the average performance of comparable managers within their peer group. While intuitively attractive, this approach suffers from two major shortcomings.

First, it is impossible to form entirely homogenous groups of managers in the absence of information regarding the hedge funds’ holdings and strategies. It is often observed that the best performing managers within a given peer group are those who deviate the most from the average factor exposure in their peer group.

Such factor tilts can emanate from active views of the managers and should be regarded as skill but they can also emanate from a simple misclassification of the manager.

A second, arguably more severe, shortcoming is that the investors have no way of knowing whether or not the average manager within the peer group generates any value.

To address the challenge of risk-adjusted performance assessment for hedge funds, a natural approach involves using an asset-pricing model, which by construction allows investors to measure what the fair reward should be given the risk exposures of the hedge fund manager. Researchers have used models with a single factor, most often an equity index representing the market or with multiple factors, adding such risks as international equity, fixed income, equity volatility, commodities or currencies, and other factors such as book-to-market, size, momentum or default.

The alpha of a fund is then obtained from the difference between the fund’s actual performance and what the normal return should have been on the basis of the estimated factor model.

While representing clear progress with respect to the previous approaches, traditional multi-factor models only capture linear exposures to the various risk factors, while it has been shown that hedge fund returns exhibit non-linear exposures to traditional asset classes.

These non-linearities arise because hedge fund managers can use derivatives and follow dynamic trading strategies as well as because of the explicit sharing of the upside profits. The fee structure of hedge funds is more complex than that of ­traditional funds.

In addition to the usual management fees, which are based on the amount of assets under management, hedge fund managers receive an incentive remuneration related to the performance of the funds. Hence, post-fee returns exhibit option-like features even if pre-fee returns do not.

This phenomenon has significant consequences on performance measurement and requires the development of specific methodologies that take into account the non-linear structure of hedge fund returns.

Some authors (Foster and Young 2008) observe that these incentive schemes do not make it possible to distinguish between skilled managers who consistently deliver performance and unskilled managers who alternate between profit and loss periods. This is an additional argument for carefully considering the choice of the approach to measure hedge fund returns.

Therefore, recent literature has added returns on buy-and-hold or dynamic positions in derivatives to the set of traditional risk factors in a linear regression setting.

However, even if we could introduce the most complete set of option returns, nothing can guarantee that the chosen underlying assets and levels of ‘moneyness’ accurately represent the true state-dependent factor exposure of hedge fund managers.

A statistical approach exists to estimate the level of ‘moneyness’ of the options that best characterise the returns of a particular fund but in practice it is limited by the relatively short samples of hedge fund returns.

Studies have therefore focused on identifying positions in put or call options or straddle one risk factor at a time. It appears impractical to extend the method to several risk factors and to more complex option strategies such as spreads.

Improving the toolkit
Our research proposes to further improve the toolkit for hedge fund risk-adjusted performance evaluation and aims to overcome the main limitations in previous approaches.

First, it allows one to analyse the non-linear exposure of any hedge fund or hedge fund strategy to several risk factors.

Second, it is not limited to shapes resembling standard option pay-off patterns and can accommodate more exotic pay-offs. Being nonparametric, it produces a factor model that captures many nonlinear functions of returns for the assets chosen as risk factors, overcoming the aforementioned problem of limited data availability.

Moreover, it can add non-linearities to option risk factors such as the straddle strategies used in Fung and Hsieh (2001).

The main idea is to risk-adjust hedge fund pay-offs in a way that accounts for the asymmetry or tail risk exposures created by the dynamic strategies pursued by the hedge funds. Abnormal performance is measured by the expected product of a portfolio’s returns and a risk-adjustment function called stochastic discount factor in asset-pricing theory. The evaluation process can be extended to make risk-adjusted performance assessment conditional upon a set of lagged financial ­instruments.

Intuitively, the methodology is based on seeking to identify, in a nonparametric way, the proper risk-adjustment function to be used in hedge fund performance assessment by requiring that it prices the basis assets selected as factors as accurately as possible. The methodology will assign a zero alpha to any pay-off that is trivially related to available factors so that the measure of abnormal performance for hedge fund returns will only capture the fraction of the hedge fund return that is attributable to the manager’s active skills.

Our analysis explicitly accounts for higher moments of returns induced by option-like strategies and can capture more complex non-linearities since options portfolios can be included as ­factors themselves.

As a result of this process, the risk-adjusted performance measure will not only be based on means and volatilities of hedge fund returns, which are not sufficient statistics given the strong deviations from normality that hedge fund returns exhibit. The risk-adjusted performance measure takes into account higher order moments and the whole distribution of hedge fund returns.

One additional advantage of this approach is that it shows how reference assets chosen as risk factors should be weighted within the risk-adjustment function that will be used for analysing hedge fund performance. Therefore, it indicates which risk factors are really important for the performance of hedge funds under analysis and allows one to discard spurious factors that only have a marginal influence in explaining the performance of hedge fund managers.

Finally, this approach can be used to evaluate the performance of hedge fund managers conditionally to specific macroeconomic environments such as high or low interest rate states, large or limited economic uncertainty, bull or bear markets, or liquid or illiquid markets, thus making the performance measurement more transparent to general economic conditions.

Prior studies have used conditioning information to evaluate the performance of managed portfolios but they limit themselves to conditional measures of performance that only involve conditional means and variances of portfolio returns. We extend the literature on conditional performance measurement by producing conditional measures that take into account all conditional moments of the risk-adjustment functions.

To establish the relevance of our approach from an empirical standpoint, we evaluate the performance of various hedge fund indices, considering a set of risk factors including equities, bonds, credit, currencies and commodities, as well as several straddle strategies. We compare the measured alphas to the more traditional linear or option based performance measures obtained by the usual simple regression analysis.

The first striking empirical finding is that alpha valuations obtained with the implied non-linear risk-adjustment measures are in general much lower than the performances exhibited when introducing option factors linearly.

We also show the robustness of performance to variations in the risk aversion parameter (illustrated by chart 1). Moving from right to left (decreasing risk tolerance), the alpha decreases significantly for some categories (emerging markets), while remaining fairly unchanged for others (equity hedge and macro). In the latter case, we will conclude that the performance is robust.

The research from which this article was drawn was produced with the support of Newedge as part of the advanced modelling for alternative investments research chair at Edhec-Risk Institute.

René Garcia, professor of finance at Edhec Business School, and Caio Almeida, assistant professor, graduate school of economics, Getulio Vargas Foundation2, wrote this article.

Footnotes
1 Garcia, R and Almeida, C (July 2012). Robust Assessment of Hedge Fund Performance through Nonparametric Discounting. Edhec-Risk Publication produced with the support of Newedge.
2 The authors would like to thank Lionel Martellini and Véronique Le Sourd for their assistance in preparing this article.

References
Amenc, N; Goltz, F and Lioui, A (2011). Practitioner Portfolio Construction and Performance Measurement: Evidence from Europe. Financial Analysts Journal 67, 3, 39-50.
Carhart MM (1997). On Persistence in Mutual Fund Performance. Journal of Finance, 52, 1, 57-82.
Cressie, N and Read, TRC (1984). Multinomial Goodness-of-Fit Tests. Journal of the Royal Statistics Society Series B, 46, 440-464.
Cuthbertson, K; Nitzche, D and O’Sullivan, N (2008). UK Mutual Fund Performance: Skill or Luck? Journal of Empirical Finance 15, 4, 613-634.
Elton, EJ; Gruber, MJ and Blake, CR (1996). The Persistence of Risk-adjusted Mutual Fund Performance. Journal of Business 69, 2, 133-157.
Elton, E; Gruber, M; Das S. and Hlavka, M (1993). Efficiency with Costly Information: a Reinterpretation of Evidence from Managed Portfolios. Review of Financial Studies 6, 1, 1-22.
Foster, D and Young, P (2008). The Hedge Fund Game: Incentives, Excess Returns, and Piggy-backing. Working paper
French, KR (2008). The Cost of Active Investing. Journal of Finance 63, 4, 1537-1573.
Fung, W. and D.A. Hsieh (2001). The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers. Review of Financial Studies, 14, 2, 313-341.
Garcia, R and Almeida, C (July 2012). Robust Assessment of Hedge Fund Performance through Nonparametric Discounting. Edhec-Risk Publication produced with the support of Newedge.
Grinblatt, M and Titman, S (1992). Performance Persistence in Mutual Funds. Journal of Finance 47, 5, 1977-1984.
Grossman, SJ and Stiglitz, J (1980). On the Impossibility of Informationally Efficient Markets. American Economic Review 70, 3, 393-408.
Gruber, MJ (1996). Another Puzzle: the Growth of Actively Managed Mutual Funds. Journal of Finance 51, 3, 783: 810.
Hendricks, D; Patel, J and Zechauser, R (1993). Hot Hands in Mutual Funds: Short-run Persistence of Relative Performance. Journal of Finance 48, 1, 93-130.
Ippolito, R (1989). Efficiency with Costly Information: a Study of Mutual Fund Performance. 1965-84. Quarterly Journal of Economics 104, 1-23.
Jensen, MC (1968). The Performance of Mutual Funds in the Period 1945-1964. Journal of Finance 23, 2, 389-416.
Kahn, R and Rudd. A (1995). Does Historical Performance Predict Future Performance? Financial Analysts Journal 51, 6, 43-52.
Malkiel, BG (1995). Returns from Investing in Equity Mutual Funds: 1971-1991. Journal of Finance 50, 2, 549-572.
Roll, R (1977). A Critique of the Asset Pricing Theory’s Tests. Journal of Financial Economics, 4, 2, 129-176.
Sharpe, W (1992). Asset Allocation: Management Style and Performance Measurement. Journal of Portfolio Management 18, 2, 7-19.