The past decade has seen a dramatic increase in the attention paid to hedge funds as investment vehicles. The assets under management have compounded at an explosive growth rate unmatched by any other part of the active fund management industry (see Fig.1). Even more impressive is the significant shift in the asset base from high net worth individuals to institutional clients as they come to realise the potential value adding features of hedge funds. This growth pattern has naturally caught the attention of regulators, the media and academics alike as they strive to provide a stable framework to the industry.

Academic research into the return generating process of hedge funds has had a profound impact on investment decision making. Participants have not only gained a much deeper understanding of the industry and its operations but have also witnessed the rise of systematic replicators that aim to mimic the strategies followed by hedge funds by providing similar statistical properties. While these do not capture the dynamic nature of hedge fund strategies, they do prove to be cheaper alternatives. This internal evolution coupled with the recent financial turmoil has put fees back into the limelight amongst investors. Moreover, the practical implications of academic research into the fees debate have been somewhat limited. Currently, managers are paid on average 2% management fees and 20% of profits above a high water mark provision. The asymmetric nature of the fees in the absence of claw back clauses results in limited downside for the manager as investors bear the losses. One pertinent question crops up: are the fees charged justified given the returns generated?

My aim in this article is to draw some provisional conclusions about this by discussing one particular aspect of this question: the systematic sources of hedge fund returns and their subsequent adjustments. The importance of this discussion has never been greater and is of clear interest to existing and potential new investors, either looking to assess allocations to managers or begin making a process of gaining exposure to hedge funds.

Factor exposures and beta adjustment
Prior to discussing the concept of beta adjustment, both hedge fund analysts and investors alike must first reach a consensus on the scope of hedge funds. For instance, long/short is an investment technique but often assumed to be a strategy. The subsequent choice of sector (value/growth, small-cap/large-cap) and method of implementation (long value/short growth) is what constitutes the strategy. Essentially, hedge funds are structured to provide investors with absolute returns irrespective of wider market conditions. To achieve this, managers make use of a combination of short selling, leverage and derivative instruments which increases the scope of investment decision making not enjoyed by traditional counterparts such as mutual funds. As a result, hedge funds are better placed on the efficient frontier when considering standard mean variance analysis.

Since these vehicles function within the same financial markets as other investment companies, alpha generation is not esoteric but rather surfaces as a result of the investment style, experience and skill of the individual manager. Therefore, the distinguishing feature of hedge funds is their relative flexibility in investment management. It should be noted that alpha here does not mean the intercept term as estimated from a standard regression model but rather the excess value generated over an appropriate benchmark. While a debate on the constituents of alpha may require an article in itself, the above working definition should suffice for our purposes.

Measuring managerial ability
The argument made above suggests that a hedge fund manager must be judged on his ability to make efficient use of the tools available to him. To appropriately measure this, a model that captures the essence of managerial ability needs to be constructed. Below I use standard modelling techniques to provide a first glimpse at how this could be done.

Consider a hedge fund (i) whose historical return distribution (Rit) can be broken down into the following fundamental parts.

The above multi-factor model attempts to highlight the various return sources of the underlying hedge fund distribution. The intercept (ai) is a residual factor that captures the unexplained part of the return series and the coefficient values β,λ are factor loadings to passive market and alternative sources of risk respectively. A key question to consider is the choice of the systematic factor F. While standard econometrics assumes this to be indices such as the S&P500 or a member of the Russell family as proxies for the market portfolio, it is also possible to use an active reference portfolio. While this is confusing at first given β is the sensitivity to a passive risk factor, the justification is logical. Hedge funds are active managers who strive to generate absolute returns. Moreover, the aim is to isolate linear passive exposures maintained by the hedge fund in order to analyse what remains. Mutual funds on the other hand are relative return generators and track the index. Therefore, it is appropriate to assume that an active reference portfolio of this type can be a proxy for an optimal long-only strategy and thus serve as our systematic factor F.

By doing so, we would be able to take the mutual fund out of the hedge fund and analyse what remains. Moreover, it is this part of the return that should attract performance fees as we would directly be rewarding the manager for making efficient use of the tools available to him and thus demonstrating true skill.

The above methodology can also be useful when considering the Sharpe Ratio as a performance assessment mechanism. While the standard formula has been shown to be adequate when considering the ranking of hedge funds (see Eling and Schumacher (2007) for an empirical justification), the ratio is sensitive to macroeconomic conditions. A low interest rate environment automatically leads to an upward bias in the ratio. Furthermore, hedge funds usually have a hurdle rate over which fees start to accrue. This rate is usually equal to LIBOR or the US T-Bill. Since hedge funds can only get paid any performance fee over a high water mark provision which in most cases will be greater than the hurdle rate the use of this reference rate is rendered inadequate to assess performance. As a result, modifying the benchmark to be a reference portfolio such as an active mutual fund in this example would reflect risk-adjusted performance more accurately.

To complete the case for the development of an active reference portfolio such as an active mutual fund, a note on consistency and reliability is appropriate here. In particular, I intend to answer the following questions:

Choice of F given the significant level of heterogeneity within the hedge fund industry?
While the hedge fund industry does possess a significant level of distinctiveness both at an inter-strategy and intra-strategy level, it is possible to broadly group hedge funds based on their strategy andstyle. This grouping would allow us to narrow the universe of active reference portfolios such as mutual funds that can serve as appropriate benchmarks. For instance, a long/short equity hedge fund would find a mutual fund with a focus on public equities largely appropriate while a multi-strategy outlet would possibly demand a hybrid mutual fund that invests in stocks, bonds and convertibles. Slight modifications at an individual fund level such as choosing a growth focus instead of value might be required in order to make the benchmark more in line with the hedge fund.

The mutual fund portfolio as an active reference benchmark may work well for relatively liquid strategies; what about illiquid ones?
Another common feature of hedge funds is their ability to hold illiquid securities that possess a higher expected premium as compensation for the added risk. While, mutual funds do not directly chase this illiquidity premium, there is evidence of concentration as well as a bias towards small cap securities in mutual fund portfolios which could serve as a partial proxy for illiquidity. A thorough analysis of the hedge fund/strategy under question would have to be carried out before an appropriate active benchmark can be chosen.

Exotic strategies where such a benchmark is difficult to implement?
The application of an active mutual fund will prove to be the least straightforward under this category of hedge fund strategies. Based on the nature of the strategy, the construction of a portfolio that aims to mimic the strategy but with the added no short sales constraint may be required.

Case study
To summarise the above arguments, I present a short empirical study on monthly data between December 1993 and June 2011 using the variables shown in Table 1. Given the correlation between mutual funds and market indices is very high, the latter is used for ease.

Fig.2 shows the evolution of $100 invested for the indicated time period for various portfolios. The Hedge Fund Index portrays the most impressive growth rate particularly post the pricking of the 2000 equity market bubble. However, this accumulation of assets is met by significant redemptions following the 2008 financial crisis.

We have discussed that the broader mandate of hedge funds allows them to exploit multiple risk premia across markets and sectors. In order to analyse hedge fund performance after adjustment for linear passive exposures, I used the work of Fung and Hsieh (2004) and run the following model on a 24-month rolling basis in order to capture time variation in factor loadings.

The beta coefficient is then used to hedge out the passive market exposures and a second model is created that attempts to analyse returns generated from alternative sources of risk.

Fig.3 plots the time varying factor loadings to the size and value spread maintained by long/short equity hedge funds during the period 1996-2010. We are now able to analyse the returns generated by these funds net of passive exposures.

Value/Growth: A clear picture emerges as we find that hedge funds were pro-growth stocks pre 2000 and were successful in exploiting the technology bubble by switching to value post 2001 – a trend that was maintained all the way through the equity bull market until 2006 where funds switched back to growth amidst the financial crisis. It is interesting to note that it is this outperformance of hedge funds that led to a dramatic increase in AUM as shown in Fig.1.

Size: A predominant feature of most funds falling under the equity hedgebracket is being able to capitalise on the premium earned on small capitalisation under-researched stocks as reflected by the positive factor loading. However, post 2006 a reversal of trend is observed which exposed hedge funds to among other things the large systematic risk build-up within the markets.

Conclusion
Hedge funds as investment vehicles are fast becoming an integral part of the investment management landscape providing excellent diversification benefits to institutional and high net worth individual portfolios alike. As hedge funds become more mainstream, performance measurement and subsequent fees have taken centre stage. In turn, this has fuelled demand for the development of tools that can accurately capture the risk-adjusted performance of hedge funds.

It is critical for investors to fully understand the scope of their investment as well as the scope of the manager himself. Keeping in mind the investment mandate of the fund, investors need to refocus their attention on the ways in which managers build portfolios and structure their strategies. As we have seen, after controlling for passive market exposures, the time varying factor loadings to alternative return drivers such as size and value maintained by hedge funds help explain a major part of the return series.

Moreover, successful bets such as the technology bubble trade can justify the level of fees generated. At an individual fund level, it is this efficient use of the available techniques and dynamic exposure management that either preserves capital or produces a profit. It is this activity by the manager that is being compensated for.