In the same vein, backfill bias or instant history bias, which occurs when the historical performance of a successful fund is suddenly and retroactively added (backfilled) into the database, also distorts the performance of the hedge fund industry (up to 435 basis points, as shown by Posthuma and van der Sluis [2004]). These biases are not negligible and tend primarily to inflate the returns posted by non-investable hedge fund indices; hence the recent development of investable hedge fund indices that can help investors mitigate the effects, which are never done away with entirely, of these biases.

By definition, however, investable indices cannot include all existing funds. The number of underlying funds is often twenty times less than that of non-investable indices. It goes without saying that, in these conditions, investable indices are less representative than non-investable indices.

For one, they logically attempt to avoid poorly performing funds through thorough due diligence: at first glance, this restriction could, in theory, make their returns superior to those of their non-investable counterparts, but this superiority has yet to be demonstrated.

For another, they must invest in hedge funds that offer full transparency, especially to avoid fraud and mitigate extreme risk resulting from operational problems. It is for this reason that they favour managed accounts. Such funds must also offer enough capacity for new investments while meeting minimum liquidity requirements: conversely, this second restriction may have a detrimental effect on the performance of investable indices since it inherently excludes many top performers from their portfolio (for example, hard-closed funds, small-size funds implementing niche strategies, funds imposing lock-up periods and/ or long notice periods, and so on). Such constraints usually result in a selection bias to the detriment of investable indices. Consequently, it is hardly surprising that investable indices tend torecursively underperform their non-investable versions.

That being said, in light of recent events, we can wonder whether the liquidity crisis that occurred in the wake of the Lehman collapse and had a significant impact on the performance of hedge fund strategies (more particularly on the strategies that are exposed to credit risk) has increased this excess return or not. In this respect, it would be interesting to compare the excess returns of non-investable indices and those of their investable counterparts before and after 2008.

From this perspective, excess returns have been computed over two distinct periods using the HFRI and HFRX indices: from December 2005 to December 2007, on the one hand, and from January 2008 to January 2010 on the other.

Table 1 shows the results obtained for strategies proxied by the HFR indices (HFRI returns minus HFRX returns). The least we can say is that these results are mixed. First, there was a striking contrast between liquid and illiquid strategies. For the latter, the significant increase in the excess returns of the non-investable indices during the second period perfectly coincided with the global credit crunch.

The lower the liquidity of underlying assets, the higher the excess return, as evidenced by the annualised excess return differential posted by distressed securities and convertible arbitrage (+20.7% and +13.43% respectively). Such a differential is beyond belief, but it is corroborated by the figures posted by other index providers (e.g., CSFB: convertible arbitrage annualised excess return from December 2005 to December 2007 = 3.44% versus 15.73% from January 2008 to January 2010, that is, a return differential of 12.29% between the two periods). By contrast, the most liquid strategies saw the excess returns of the non-investable indices decrease over the second period. This decrease was typically the case of long/short equity and equity market neutral funds. By comparison with the upward trend characterising illiquid strategies, however, this downward trend is negligible.

It is for this reason that the performance of multi-strategy indices whose portfolios included illiquid (or less liquid) strategies was extraordinarily overstated after mid-2008. For example, the annualised performance of the HFRI EWS index was flat from January 2008 to January 2010 even though that of the investable index was down 635 basis points! Consequently, the annualised excess return of the non-investable index had more than doubled over the second period (from 2.75% to 6.24%). In these conditions and despite their larger universe, it is more and more difficult to justify the use of non-investable composite indices as benchmarks unless we can suggest a practical and easy-to-implement solution that could substantially reduce the biases that overstate their performance, especially in periods of market stress.

The rationale behind our approach to providing such a solution is first to compare the monthly returns of the EDHEC composite indices, known as the most representative (non-investable) benchmarks in the alternative universe, and the average monthly returns of a set of investable indices for each underlying strategy (HFRX – CSFB – LYXOR). The average return of the investable indices (independent variable) is then used to model the excess return of each strategy.

The model is a cubic polynomial that makes it possible to improve the fit of the data with respect to linear models. In this respect, it would be problematic to apply linear models here, as the relationship between the dependent variable and the independent variable tends not to be linear. More precisely, the cubic polynomial consists of regressing the returns of the non-investable EDHEC-Risk Alternative Index not only on the returns of the corresponding investable indices but also on the squared and cubed returns of these indices. Intuitively, this can be interpreted as an attempt to take into accountthe impact of second- and third order moments (which can be related to volatility and skewness).

Over a 38-month period (from December 2005 to January 2009), which has the advantage of including extreme events (but the drawback of being short— very little data on investable indices was available before 2006), the fraction of variance explained by the non-linear models (coefficient of determination or R²) varies from 43% (event-driven multi-strategy funds) to 82% (global macro).

To loop the loop, the R² obtained with the funds of hedge funds is 71%.

Unsurprisingly, all these models point to the fact that the highest excess returns always correspond to the poorest returns posted by the investable indices, regardless of underlying strategy. On the face of it, the evidence argues that the survivorship and selection biases peak just as the underlying strategies experience the worst market conditions (sharp change in stock volatility, historical widening of credit spreads in particular). Conversely, we can see in Fig.1 that the excess returns of the EDHEC fund of funds composite index are concentrated along the x-axis when the investable indices exhibit positive returns (i.e., in relatively calm markets). In other words, despite their additional fees, the investable indices would rival the non-investable indices in performance when market conditions are more favourable with sustainable trends, as shown below over the bullish period ranging from December 2005 to mid-2007.

Although we do not have an abundance of data over the out-of-sample period (even if, unlike the in-sample period, it includes the Lyxor investable indices), which is characterised by a strong rally, the first results tend to corroborate the above-mentioned assumption: the cumulative excess return is highest at the end of the bear market and then stabilizes as from the trend reversal. In other words, the excess return is all the lower as the market environment is favourable.

Thus it is interesting to note that the annualised excess return observed over the out-of-sample period is comparable to that computed from December 2005 to July 2007, which is also a period characterised by little market turbulence.

That said, we must bear in mind that little performance data on investable indices is available over the analysis period. In addition, the series of monthly returns are too short to allow us to assert that the results obtained are robust enough. In this respect, the coming months will certainly provide us with interesting occurrences to test and improve our adjustment models.

**Felix Goltz**, PhD, is Head of Applied Research at EDHEC-Risk Institute. He conducts research in empirical finance, asset allocation, and performance analysis, with a focus on indexing strategies.

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