Since institutional investors use relative returns in their investment process, there is a requirement for index construction in the hedge fund industry, like in the traditional universe. However, the construction of hedge fund indexes is complex. This is due to the uncertainty on the size of the hedge fund universe, the biases that affect the data, the strategy classification of the hedge funds and the need for investable indexes.

The uncertainty on the size of the hedge fund universe is related to the fact that hedge funds are not required to report their performance to the index providers. The author illustrates this uncertainty through the previously observed low proportion of funds in common between the TASS and HFR indexes. This problem is strengthened by a high attrition rate in the hedge fund industry, engendering a turnover to which the indexes have to be adapted.

Biases associated with hedge fund data introduce the risk of overestimating the performance in the hedge fund indexes. The author cites the survivorship bias, the selection bias, the backfill bias and the liquidation bias, which are upward biases. Estimations of these biases have been carried out in various previous studies. Survivorship bias is estimated to be between 2.6 and 3.7%, while the sole estimation of the selection bias is 1.9%, and of the liquidation bias is 0.7%. Instant history bias is estimated to be between 0.4 and 1.4%. These estimations show the importance of taking such biases into consideration.

The classification of hedge funds by strategy is specific to each hedge fund index provider. This classification is rendered more difficult by several features of the hedge fund universe. Firstly, some hedge funds follow strategies that are not clearly explained in their offering documents. This can lead to erroneous classification or an exclusion of the fund from the database. Secondly, style drift can make the initial correct classification of the database obsolete.

Index investability assumes that the underlying funds are always investable. This is not the case for hedge funds, which are generally closed after reaching a determined level of assets under management. This illustrates the incompatibility between completeness and investability.

Ten hedge fund indexes are studied, namely EACM, MAR, HFR, Zurich Capital, CSFB/Tremont, Van Hedge, Hennessee Group, Tuna Indices, MSCI and S&P. All these indexes calculate the performance net of fees. However, while the incentive fees are calculated quarterly or annually, the index providers have to estimate the incentive fees to calculate the net of fees performance each month, introducing a potential source of error.

Examination of the performance of the 10 indexes reveals that they exhibit very different risk/return profiles. This confirms the problem of the representativeness of these indexes. Annual returns are comprised between 7.62 and 16.35%, while standard deviations are between 3 and 14%. Focusing on the long/short sub-indexes of the same providers, a similar dispersion in the risk/return profiles is observed. The correlation across hedge fund indexes is also variable. In most cases, the coefficients are comprised between 0.8 and 0.9. The author compares it to a coefficient of 0.999 between two traditional indexes, the Russell 1000 and the S&P 500.

To construct indexes, funds can be either asset-weighted or equal-weighted. Only two of the 10 indexes, namely CSFB and MSCI, are asset-weighted. According to the author, the index providers privilege equal weighting in order to "reflect fully all strategies". Conversely, asset-weighting permits the market impact of each fund to be taken into account. Moreover, traditional indexes such as the S&P 500 are asset-weighted. Consequently, to compare the alternative universe to the traditional universe, it is better to be based on the same weighting process.

The size of an index, i.e. the number of funds on which it is based, is related to the notion of idiosyncratic risk diversification. While size among indexes ranges from 60 to 2000, previous studies found that 20 funds are sufficient to diversify the idiosyncratic risk. On the other hand, to follow a coherent index-based approach, sufficient correlation between the investment program and the index is required. According to Lhabitant and Learned (2002), an investment in 20 hedge funds allows 80 to 90% of the correlation to be captured.