Survivorship bias: why your fund data is 20 points too good

Simulate 500 funds. Give every one of them the same expected return: zero. Fifteen percent annual volatility. Ten years. One rule: a fund closes when its net asset value falls below 0.60.

Nothing else happens. No skill, no manager alpha, no market timing. The funds are indistinguishable by construction.

The result

• Funds simulated: 500.
• Closed early: 160.
• Survived ten years: 340.
• Mean ten-year return, all 500 funds: -3.70%.
• Mean ten-year return, survivors only: +16.27%.
• Gap: 19.97 percentage points.

The 160 funds that closed averaged about -46%. Remove them from the sample and the average jumps by almost twenty points, on a population whose true expected return was zero.

That is the entire mechanism. Survivorship bias does not require anyone to lie. It requires a database that drops dead funds, which is what databases do.

Why the full-sample mean is negative

Two things push the all-fund mean below zero. Volatility drag makes the typical compounded path fall even when the arithmetic mean return is zero. The closure rule then realises a loss at 0.60 instead of letting the fund recover. Neither is a property of the market; both are properties of compounding and of the stop.

The survivors escape both. They are, by definition, the funds whose paths did not get stopped. Their average is not a return premium. It is the average of a sample selected on the outcome.

Where it shows up outside fund databases

• Crypto backtests on today’s top 100 coins. The list is a survivor list. Coins that went to zero are not in it.
• Stock screens on current index members. Every company removed for failure is missing from the history you tested.
• Strategy marketplaces. Failing strategies get delisted, so the average listed strategy looks better than the average strategy ever launched.
• Prop-firm payout statistics. Firms publish payouts; they do not publish the traders who stopped paying fees. The 9-in-10 figure is the honest version of that distribution.
• Your own trade journal. You remember the system that worked and quietly stop running the one that did not.

The check: point-in-time universe

Rebuild the universe as it existed on each date. If you are testing 2016, use the assets that were tradable in 2016, including the ones that later failed, and include their final, realised return. That is the only sample that answers the question you are actually asking: what would I have earned picking from what was available then?

This is expensive. It is also the difference between a 20-point overstatement and an honest number. If point-in-time membership is unavailable, the next best thing is to state the bias explicitly and treat the result as an upper bound.

For fund data, that means the full CRSP-style universe with delisting returns, not the subset that still reports. For crypto, it means every pair that was listed and liquid on the date, including the ones that were later removed. For equities, it means the index membership file as of the test date, not today’s.

The second-order effect

Survivorship bias does not just inflate the mean. It compresses the variance. The worst outcomes are gone, so the drawdown distribution looks tame, so the strategy looks safer than the population it was drawn from. Two errors for the price of one, and the second one is the dangerous one because it changes position sizing.

A backtest that understates drawdown invites leverage. The leverage is sized to a distribution that never contained the failures, and the first real failure is larger than anything the model prepared for.

What it does to a decision

If you buy on the survivors’ +16.27%, you are pricing an asset at the average of a sample selected on the outcome. The population expectation was -3.70%. The difference is not a return premium; it is a deleted sample.

This is also why vault leaderboards flatter their winners. The vaults that blew up stop reporting, and the ones that remain are ranked against each other rather than against the population they came from.

The rule

Any dataset that only contains things that still exist is a dataset about survival, not about returns.

Ask one question of every historical sample: what had to go right for this row to be here? If the answer is “it had to not fail”, the sample is biased by construction, and the audit has already found its first defect.

How these numbers were produced

Seeded simulation: Mulberry32(7), 500 funds, ten years, 15% annual volatility, zero expected return, closure below NAV 0.60. The closed funds average about -46%, which is where the 19.97-point gap comes from. Re-running with that generator reproduces these figures exactly.

Questions

What is survivorship bias?

Building a sample only from things that survived. Closed funds, delisted stocks and failed strategies drop out of the data, so the remaining sample looks better than the population it came from.

How large is the survivorship bias effect?

In a simulation of 500 zero-edge funds over ten years, 160 closed and 340 survived. The survivors averaged +16.27% while the full population averaged -3.70% — a gap of 19.97 points created only by deleting the dead.

Why does survivorship bias make strategies look safer?

Because the worst outcomes are missing. Removing failed funds truncates the left tail, so the observed drawdown distribution is narrower than the one you would actually have lived through.

How do I remove survivorship bias from a backtest?

Use point-in-time universe membership: the assets that were tradable on each date, including the ones that later failed, with their final realised returns. If that data is unavailable, state the bias and treat the result as an upper bound.

Does survivorship bias affect trader statistics too?

Yes. Prop firms publish payouts, not the traders who stopped paying fees, and marketplaces delist failing strategies. The published average is a survivor average.