A hedge-fund index is not an index in the sense that a stock index is one. It is an average of the funds that chose to report to a database and were still reporting at the time the average was struck. Three separate distortions follow, they point in different directions, and they can be measured separately and reconciled.
How are the three biases measured?
Survivorship bias is the gap between the funds still alive and everybody who ever existed. In a universe of 1,240 live funds averaging 9.80% and 860 dead funds averaging 3.10%, the attrition rate is 40.95% and the all-fund mean is 7.0562%. Reporting only the survivors overstates the return by 2.7438 points.
Backfill bias comes from the moment a fund joins a database. It arrives with a track record, and the track record is the reason it joined; a fund with two bad years does not apply. If 22% of the live funds' observations are backfilled and those months averaged 13.40% against 8.10% for the post-listing months, the mixed reported average is 9.266% and the backfill bias is 1.166 points.
Self-reporting bias runs the other way. A fund closed to new money has nothing to gain from reporting and often stops. Add 180 such funds averaging 12.10% and the full-universe mean rises to 7.4544%, so this bias is -0.3982 points as a component of the overstatement.
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How do the three biases reconcile?
The three reconcile exactly. The headline number, live funds with the backfill included, is 10.966%. The full universe is 7.4544%. The gap is 3.5116 points, and 2.7438 + 1.166 - 0.3982 = 3.5116 to twelve decimal places. Run that gap for ten years and the difference is not a rounding matter: 1.10966^10 = 2.8307 against 1.074544^10 = 2.0523, so a dollar compounds to a claimed 2.83 against a real 2.05, and $77.84 of every $100 invested is phantom terminal wealth.
Two corollaries an allocator should hold. Any comparison of a fund against a hedge-fund index compares a real fund against a number that has never been available to buy. And private-equity benchmark universes carry the same three problems in a slower form: funds that stop reporting are usually the funds that stopped working.