Alternative Investment Management Association
Key Asset Management (UK) Ltd.
Hedge fund performance track records have the ability to hide a multitude of sins where risk analysis and potential worst-case losses are concerned. In this article, we consider the use of factor-based models to provide a more realistic understanding of potential risks.
In contrast to long-only fund management, where investment strategies are often tethered to benchmarks and usually employ linear trading strategies, hedge funds can invest in a vast range of opportunity sets through a wide array of instruments, often employing complex non-linear or levered trading strategies, or potentially illiquid positions. Furthermore, these investment themes and niche opportunities are often turned over on a much more frequent basis, and hence the historic return profile will inevitably lag the changing dynamics of the investment basis.
Accounting for all of the above, it is evident that, relative to long-only strategies, the presence of these additional degrees of freedom in alternative strategies invariably means that traditional, return-analysis based, risk measurement techniques will fail to adequately capture a true sense of fund risk. Compounding matters, this discrepancy is widely understood to be of greatest significance in the extreme downside tail of the prevailing risk profile.
In short, a reliance on the historic return profile of a hedge fund will ultimately lead to significant underestimation of potential worst-case losses.
The multi-factor approach
A more appropriate framework for hedge fund risk analysis is the multi-factor based approach. A number of authors have successfully applied both factor-based and style-based techniques to hedge fund returns from a fund classification perspective, most notably Fung and Hsieh (1997), as well as Agarwal and Narayan (2000). In addition to taxonomical benefits, this approach can also be employed to generate factor-based implied risk profiles, Goodworth and Jones (2004). However, before discussing the benefits of these implied risk profiles, it is worthwhile considering the construction of the factor universe itself.
As a rule of thumb, a factor universe should be broad enough to cover the full range of potential investment themes, employing, where possible, factors that will give the widest scope for inclusion. This will avoid micro-descriptivity which can lead to over-specification of a given fund, as well as factor, or more explicitly theme, repetition at the universe level. In addition to the breadth of factors, importance is placed on the quality of the data. Outliers are not screened (such events are often catalysts for barrier-type strategies) and the data is employed in its empirical form rather than a reduction to a normalised profile, as structural alpha resulting from intra-factor asymmetries should not be confused with the classic definition of alpha resulting from manager skill. This necessarily preserves implicit higher moments within the dataset.
At present, our working factor universe extends to over 100 factors, covering major themes including: equity, debt, credit, volatility, commodities, currency, as well as corporate event data. Within each of these broad themes, both factor and geographical subsets provide additional layers of granularity, for example: convertibles, high yield, sovereign debt, asset-backed and CBO/CDO factors along with yield curve, interest rate and issuance data form a core component of the debt theme.
Clearly, given the complexity and wealth of opportunity sets across the wide range of different hedge fund strategies, the use of just a single factor (CAPM) approach is inappropriate, as is the use of the entire universe through an over-specification argument. The multi-factor approach requires distillation of the universe to a discrete basis set of between four and eight factors, balancing an ever present trade-off between more factors (higher descriptivity) and fewer factors (improved statistical significance).
From a purely quantitative perspective, the scarcity of data resulting from monthly, or at best, weekly pricing drives a bias towards fewer factors to maintain as many degrees of freedom within the ensuing system. Use of stepwise regression in conjunction with scree tests can easily provide a quantitative subset solution.
However it is also essential to adopt a qualitative selection framework, augmenting the quantitative basis set through Bayesian adjustment. The immediate benefit to hedge fund-of-funds of working in a factor-based space, such as the one described above, is that all strategies, where previously quantitatively isolated, are now subject to a common basis set. This facilitates cross-strategy as well as intra-strategy analysis, which has important consequences for the overall diversification properties of the aggregate portfolio.
A typical implied risk profile generated under the factor-based approach is shown in Figure 1. For comparative purposes, the equivalent risk profile resulting from a traditional historic return analysis under the assumption of a normal distribution has been superimposed.
The discrepancy between the historic risk profile and the factor-based implied risk profile is relatively small in the central bulk region of the risk distribution, which contains ‘everyday’ high probability returns. However, this discrepancy becomes significantly more pronounced as one moves out towards the tails where the large magnitude returns, or extreme events, reside. The negative skew implicit to the majority of hedge fund strategies means this underestimation of risk is often far more apparent in the downside tail, as is clearly illustrated in the case of Figure 1.
Figure 1: How risk is underestimated in the downside ‘tail’
Typical implied risk profile (bars), superimposed with the historic return profile (line), clearly illustrates the underestimation of downside tail risk.
Unlike historic return profiles, which are generally very slow to respond to the dynamic risk profile of a hedge fund, the factor-based implied risk profiles respond significantly faster to changes in both strategic allocation and the absolute level of portfolio risk, as the profile is driven by the underlying factors rather than the ex-post returns. Within such a framework, style drift can therefore be monitored proactively rather than simply responding to realised returns, thereby enabling the fund-of-funds manager to act more promptly over the evolution of the portfolio.
Control of style drift is of primary importance within a fund-of-funds portfolio, as constituent funds have the potential to rapidly converge on ‘hot’ themes with a herd mentality which, left unchecked, could seriously unbalance a previously diversified portfolio. Perhaps more importantly though, the implied risk profile provides a robust technique for investigating and quantifying potential return scenarios outside the scope of the realised historic return profile, thus yielding a better understanding of the current positioning of the fund rather than relying on past returns that need not have any bearing on the current stance of the portfolio.
A simple example to illustrate the point is an historically aggressive fund rebalancing to a more conservative stance. The future return stream delivered by the new, less risky, portfolio will appear unattractive when taken in the context of the previous return profile, simply because the risk profile has not yet responded to the dynamic factor set, a process that would require months of data under traditional techniques.
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Similarly, a strategy that writes leveraged naked out-of-the-money call options might traditionally appear attractive simply because the historic return profile has not yet taken into account the potentially catastrophic non-linear pay-out encountered, in this instance, from a rapidly rising market. These two simple examples also clearly highlight the unequivocal need for a firm qualitative understanding of the investment strategy upon which quantitative risk analysis can build supporting evidence.
In summary, it has been proposed that factor-based implied risk profiles provide a more appropriate framework for evaluating the risk profile of hedge funds compared with traditional techniques, which rely on historic return analysis alone. It has also been concluded that the implied risk profiles provide a more responsive tool for portfolio managers within the context of hedge fund-of-fund investment.
Agarwal V., and Narayan Y., J. Asset Management, 1.1 32-64 (2000)
Fung W., and Hsieh D., Review of Financial Studies, 10 275-302 (1997)
Goodworth T., and Jones C., Research Papers in Man. Studies, Cambridge WP08 (2004)