Survivorship bias is one of the biggest causes of grossly overstated hedge fund index performance. Considering the returns of surviving funds alone leads to a strong upward bias.

The biases that inflate the performance of hedge funds have been well documented in the financial literature. Survivorship bias, which results from the ex post exclusion of unsuccessful funds from databases, is clearly one of the greatest causes of grossly overstated performance.

Considering the returns of surviving funds alone leads to a strong upward bias, according to recent studies (up to 442 basis points (bp) as demonstrated by Malkiel and Saha [2005]).

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 435bp 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 indexes. This has led to the recent development of investable hedge fund indexes that can help investors mitigate the effects, which are never done away with entirely, of these biases.

By definition, however, investable indexes cannot include all existing funds. The number of underlying funds is often 20 times less than that of non-investable indexes. In these conditions, investable indexes are less representative than non-investable indexes.

In such circumstances they logically attempt to avoid poorly performing funds through thorough due diligence. In theory this restriction could make their returns superior to those of their non-investable counterparts but this superiority has yet to be demonstrated.

They must invest in hedge funds that offer full transparency, especially to avoid fraud and mitigate extreme risk resulting from operational problems. For this reason they favour managed accounts. Such funds need to offer enough capacity for new investments while meeting minimum liquidity requirements.

Conversely, this may have a detrimental effect on the performance of investable indexes since it inherently excludes many top performers from the 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 indexes.

Consequently, it is hardly surprising that investable indexes tend to recursively 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 indexes 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 indexes: from December 2005 to December 2007 and from January 2008 to January 2010. Table 1 shows the results obtained for strategies proxied by the HFR indexes (HFRI returns minus HFRX returns).

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 indexes 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 unbelievable but it is corroborated by the figures posted by other index providers (for example, 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 indexes 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.

For this reason the performance of multi-strategy indexes, 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 635bp. 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 difficult to justify the use of non-investable composite indexes as benchmarks unless a practical and easy-to-implement solution can be suggested that could substantially reduce the biases that overstate the performance, especially in periods of market stress.

The rationale behind our approach to providing such a solution is to compare the monthly returns of the Edhec composite indexes, known as the most representative (non-investable) benchmarks in the alternative universe, and the average monthly returns of a set of investable indexes for each underlying strategy (HFRX, CSFB, Lyxor). The average return of the investable indexes (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.

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 indexes but also on the squared and cubed returns of these indexes. Intuitively this can be interpreted as an attempt to take into account the 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 indexes was available before 2006), the fraction of variance explained by the non-linear models (co-efficient of determination or R²) varies from 43% (event-driven multi-strategy funds) to 82% (global macro).

To complete the set, 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 indexes, regardless of underlying strategy. The evidence argues 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, graph 1 shows that the excess returns of the Edhec fund of funds composite index are concentrated along the x-axis when the investable indexes exhibit positive returns (for example, in relatively calm markets).

Despite their additional fees the investable indexes would rival the non-investable indexes in performance when market conditions are more favourable with sustainable trends, as shown below over the bullish period 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 indexes), which is characterised by a strong rally, the first results tend to corroborate the abovementioned assumption: the cumulative excess return is highest at the end of the bear market and then stabilises as from the trend reversal. The excess return is all the lower as the market environment is favourable.

So 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.

Little performance data on investable indexes 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.

This article was written by Philippe Malaise, professor of finance, Edhec Business School, and Felix Goltz, head of applied research, Edhec-Risk Institute

References
Malkiel, B G and Saha, A. 2005. Hedge funds: Risk and return. Financial Analysts Journal 61 (6): 80-88.
Posthuma, N and van der Sluis, PJ. 2004. A reality check on hedge fund returns. In Hedge Fund Intelligent Investing, ed Barry Schachter. RiskBooks.