Methodology — Bootstrap Uncertainty Ranges

Transparency is a feature. This page explains what the quiet ranges beside the risk tiles are and why we show them — in plain terms. The precise formulas and numeric conventions are documented in our internal methodology; the summary here is deliberate, not an omission.

Every estimated number on the Risk tab — volatility, the diversification ratio, the effective-bets count — is computed from one finite window of history. A different but equally plausible sample of the same market would have produced a somewhat different number. The ranges show how different: they are the spread of each statistic when we recompute it many times on resampled versions of your book's own return window.

How the resampling works

We rebuild the window from blocks of consecutive days rather than single days, so the short-run momentum and clustering that real return series carry survives the resampling. Block lengths average about the cube root of the window length (roughly two trading weeks on a five-year window) and the payload discloses the exact value.
All names are resampled together: one sequence of days is drawn, and every holding re-reads those same days. That preserves how your names co-move — the very thing portfolio risk is about. Resampling each name separately would destroy it.
The whole procedure is deterministic: the random draws are seeded by the request itself, so the same book over the same window always shows the same ranges — they are reproducible facts about your window, not a lottery.
Typically about 500 resamples; each range is the central 95% of the recomputed values.

What you'll see

Quiet ranges beside annualized volatility, the diversification ratio, and the minimum-torsion effective-bets count (the bets range is coarse, like the number itself). A range appears only when the point estimate itself passes its own gates — a range never outlives its number.
A rank-stability chip on the risk decomposition: "top risk contributor is the same name in NN% of resamples." Per-row error bars on the Euler table would all overlap in a 10–40 name book; whether the #1 risk seat survives resampling is the question that actually matters.
CVaR ranges only on long windows (three or more years of daily data), always with this label: sampling variability only; the point estimate is downward-biased for heavy tails. Resampling your own window can show its sampling noise — it cannot see tail events your window never contained.
A regime note or badge: we compare how much your window's rolling half-year volatility ranged against how much it ranges across the stationary resamples of the same days. A rolling estimate wanders even when nothing changed, so the bar is calibrated from the resamples themselves — never a fixed rule of thumb. The badge describes this window; it is not a forecast.

What the ranges are not

They are not confidence in the future, not a guarantee, and not model-error bars: a range computed under a given covariance estimator describes that estimator's sampling noise on this window. Anything we could not compute honestly is shown as missing with the reason spelled out, never guessed.