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In traditional equity investment, indices play a central and unambiguous role.
They are widely accepted as representative, and products such as futures and ETFs provide investable access to them in most developed markets.
However hedge funds are illiquid, heterogeneous and ephemeral, which makes it hard to construct a satisfactory index.
Non-investable indices are representative, but, due to various biases, their quoted returns may not be available in practice.
Investable indices achieve liquidity at the expense of limited representativeness.
Clone indices seek to replicate some statistical properties of hedge funds but are not directly based on them.
None of these approaches is wholly satisfactory.

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