+1 d
Median return +0.21%Completed observations: 4
- Middle 50%
- -0.31% … +0.36%
- Positive returns
- 75%
Stellar · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
Stellar's latest move against its own history.
What happened afterwards
All history-qualified moves of at least 2.5σ. Results after the event are descriptive statistics, not trading instructions.
+7 d
Median return -6.28%Completed observations: 4
- Middle 50%
- -9.18% … -1.60%
- Positive returns
- 25%
+30 d
Median return -1.12%Completed observations: 4
- Middle 50%
- -13.17% … +8.58%
- Positive returns
- 50%
Every rare move, in context
Instrument: binance:spot:XLMUSDT
| Date | σ | Move | Observed rarity | +1 d | +7 d | +30 d |
|---|---|---|---|---|---|---|
| 4 Nov 2022 | +2.64σ | +6.25% | About once every 37 days34 comparable moves / 1,252 observations | -1.73% | -17.56% | -24.13% |
| 22 Sep 2022 | +2.55σ | +11.31% | About once every 34 days36 comparable moves / 1,209 observations | +0.16% | -6.18% | -9.51% |
| 13 Sep 2022 | -2.66σ | -8.25% | About once every 36 days33 comparable moves / 1,200 observations | +0.67% | +12.15% | +7.27% |
| 9 Sep 2022 | +3.22σ | +9.58% | About once every 63 days19 comparable moves / 1,196 observations | +0.26% | -6.38% | +12.50% |
The number has a method behind it
Sigma measures the size of a log return relative to volatility estimated before the period. Rarity is counted from actual historical standardized moves, not inferred from a normal distribution.
σt = ln(Ct / Ct−1) / vtvt ← t−1, t−2, …
Volatility adapts to the market regime with EWMA (λ = 0.94 for daily and weekly observations). Current-period returns are excluded. Each historical σ uses its own prior volatility.
Both directions count toward rarity. Reference history spans up to five years. A period with no prior exceedances is labelled unprecedented in the observed sample; it is never given an invented recurrence interval.
Stock observations use split-adjusted price returns, without dividend reinvestment. Commodities are explicitly labelled ETF price proxies; they do not represent spot commodity prices.
Questions behind the sigma
What does a 3σ move mean?
The period log return is three times the volatility estimated from earlier periods. Sigma is signed: negative for declines and positive for rises.
Why not calculate rarity from a normal distribution?
Market returns have heavy tails and changing volatility. We count actual past absolute sigma exceedances for the same instrument and period.
Does “once every 200 days” predict the next event?
No. It is the number of historical observed periods divided by comparable moves. Events can cluster and the market regime can change.
How much history is required?
At least three years of valid standardized observations, after a one-year volatility warm-up. This normally requires approximately four years of source history.
Are all instruments directly comparable?
The engine is shared, but each instrument has its own prices, calendar, volatility and reference sample. Commodity cards use explicitly labelled ETF proxies.
What happens on quiet days?
The page shows the largest covered standardized move, the complete rarity scale and recent records. Missing data is reported separately from market calm.
For information only. Historical observations are not investment advice and do not predict future moves. A rare move can be followed by another rare move.