Plain record › Study 33

Does trimming extreme values restore a bootstrap test's false-alarm rate on heavy-tailed returns?

Study 33 · Changed a rule or plan · recorded 2 October 2026 · answer: Partly · full paper with figures

The question

On returns with very heavy tails, the bootstrap test we fall back on raised false alarms at about twice its 5% target. We remove a fixed share of the most extreme values, from 0.5% to 5%, and ask whether a trim of 2% or less brings the false-alarm rate back to target.

Rules fixed before the result

We fixed in advance five trims (none, 0.5%, 1%, 2% and 5% of values removed), two sample sizes and the pass rule: the test holds when the 95% interval of its false-alarm rate in each tail contains 2.5%. A pool recovers if the test holds at both sample sizes at a trim of 2% or less and at every larger trim. If only the less heavy-tailed pool recovered, the test would be kept only where its own check passes.

Data and method

This is a methods study on simulated samples, not on real events: each is drawn from one of two pools of five-day returns with a true mean of zero, so every rejection is a false alarm. For each trim and for samples of 221 and 548 values, we drew 10,000 samples and counted how often the test rejected in each tail, against the 2.5% each tail should give.

The answer

On the less heavy-tailed of the two pools, removing the most extreme 2% of values brought the test's false-alarm rate in each tail back to its 2.5% target at both sample sizes, a larger trim than the 1% we expected. On the heavier-tailed pool it took 5%, beyond the 2% limit set in advance, so the test is no longer used on returns with tails that heavy.

What it changes

It changed a planning rule. The bootstrap test is now used for planning only on pools of returns whose own false-alarm check passes, as the less heavy-tailed pool's does; on tails as heavy as the other pool's it is withdrawn, and a later study on such returns must choose another test after its own false-alarm check.

What remains uncertain

Two pools and one five-day horizon only, and the samples are simulated, not real events. A trim changes what is measured to a trimmed mean, so a test that holds after trimming says nothing about the untrimmed mean. The trim is applied to the whole pool, not to each sample, so it shows what lighter tails would do rather than how a per-sample trimming rule would work, and only five trims and two sample sizes were tried.

How it was made

Run took 43 minutes; independent code review: approve.

Exploratory work on development data; not a performance claim.