How does survivorship bias inflate the average return in a table of funds that still exist today?

## The shape of the mistake Survivorship bias is a form of **selection bias** in which the rule that decides whether a unit appears in your data is correlated with the outcome you are measuring. It is not sampling noise, it is not a data-quality problem, and it does not shrink as you add rows. A table of "all funds available today" is assembled by asking a live database which funds currently exist. That question silently applies a filter: *did this fund survive to today?* Funds are closed or merged for a reason, and the dominant reason is bad performance — assets flow out, fees no longer cover costs, and the sponsor folds the fund into a healthier one. The record that leaves is systematically worse than the records that stay. ## What the average is actually estimating Write `S` for the event that a fund survived to the end of the observation window and `R` for its annualised return. The number you compute from the surviving-only table is an estimate of the conditional mean `E[R | S = 1]` while the number an investor cares about — what could I have expected from a fund chosen at the start? — is the unconditional mean over the whole starting cohort `E[R] = P(S=1) * E[R | S=1] + P(S=0) * E[R | S=0]` Because `E[R | S=0] < E[R | S=1]` (the dead funds did worse), the surviving-only average sits above the cohort average. The gap grows with the death rate: the longer the window, the more of the starting cohort disappears, and the more flattering the survivors look. Ten-year and twenty-year "track records" are the worst offenders precisely because they require ten or twenty years of survival. ## It is not only the mean The same filter truncates the **left tail** of the return distribution. Consequences that candidates often miss: - **Variance and standard deviation are understated.** The catastrophic outcomes were deleted, so the strategy looks less volatile than it was. - **Downside risk measures collapse.** Maximum drawdown, worst-year return and the frequency of large losses are all computed on a population from which the worst cases have been removed. - **Win rates are inflated.** "Eight of the last ten years beat the benchmark" is trivially easier to satisfy if the funds that failed to do so were removed from the list. - **Apparent skill appears out of nowhere.** If a sponsor launches many small funds, quietly closes the ones that stumble and markets the ones that do well, a pure-luck process manufactures an impressive-looking track record. This is sometimes called incubation bias, and it is survivorship applied at the fund-launch stage. ## Diagnosing it The diagnostic question is always the same: **what had to be true for a row to appear in this table?** If the answer includes anything downstream of the outcome — the fund still trades, the company still exists, the customer is still subscribed, the machine came back — you are looking at survivors. To quantify the bias, you need a database that keeps dead entities: freeze the roster at the start of the window, follow every member forward, and record a terminal outcome for the ones that vanish. Comparing the cohort mean with the survivor-only mean gives the size of the bias directly. If no such data exists, the honest move is to state the direction of the bias (upward, for returns) and treat the survivor figure as an upper bound rather than an estimate. ## The same pattern outside finance - A table of successful startups showing that founders dropped out of university tells you nothing without the failed founders who also dropped out. You are reading `P(dropped out | succeeded)` and treating it as `P(succeeded | dropped out)`. - "Buildings from 300 years ago were better made" — the badly made ones are not standing to be inspected. - Employee-engagement scores computed on people who are still at the company omit precisely those who were unhappy enough to leave. ## What a good answer contains Name the filter, say which direction it pushes the estimate, and describe the fix in terms of the *cohort*: define membership at the start of the period and follow everyone, dead or alive. If a candidate says the bias would go away with more funds, they have confused bias with variance — adding more surviving funds gives a tighter estimate of the wrong quantity.