+1 sessions
Median return +0.10%Completed observations: 27
- Middle 50%
- -0.41% … +0.69%
- Positive returns
- 63%
US 30 (Dow Jones) · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
US 30 (Dow Jones)'s latest move against its own history.
DJI Rare
+1.89%
+2.94σ
About once every 74 trading sessions
17 comparable moves / 1,255 observations
What happened afterwards
All history-qualified moves of at least 2.5σ. Results after the event are descriptive statistics, not trading instructions.
+7 sessions
Median return +1.24%Completed observations: 27
- Middle 50%
- -0.85% … +2.82%
- Positive returns
- 56%
+30 sessions
Median return +3.35%Completed observations: 27
- Middle 50%
- +0.65% … +5.23%
- Positive returns
- 78%
Every rare move, in context
Instrument: ^DJI (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 22 Aug 2025 | +2.94σ | +1.89% | About once every 74 trading sessions17 comparable moves / 1,255 observations | -0.77% | -0.79% | +2.33% |
| 9 Apr 2025 | +4.18σ | +7.87% | 4 times in 5 years4 comparable moves / 1,256 observations | -2.50% | -6.00% | +3.08% |
| 4 Apr 2025 | -4.22σ | -5.50% | 3 times in 5 years3 comparable moves / 1,256 observations | -0.91% | +5.36% | +11.69% |
| 3 Apr 2025 | -4.37σ | -3.98% | 2 times in 5 years2 comparable moves / 1,256 observations | -5.50% | -0.05% | +5.20% |
| 21 Feb 2025 | -2.58σ | -1.69% | About once every 45 trading sessions28 comparable moves / 1,257 observations | +0.08% | -2.09% | -11.77% |
| 18 Dec 2024 | -4.07σ | -2.58% | 3 times in 5 years3 comparable moves / 1,258 observations | +0.04% | +0.58% | +5.27% |
| 6 Nov 2024 | +5.28σ | +3.57% | Not previously observed in 5 years0 comparable moves / 1,258 observations | -0.00% | -0.65% | -3.17% |
| 5 Aug 2024 | -3.12σ | -2.60% | About once every 90 trading sessions14 comparable moves / 1,258 observations | +0.76% | +3.37% | +7.50% |
| 16 Jul 2024 | +3.59σ | +1.85% | 4 times in 5 years4 comparable moves / 1,258 observations | +0.59% | -2.49% | +0.72% |
| 23 May 2024 | -2.57σ | -1.53% | About once every 45 trading sessions28 comparable moves / 1,259 observations | +0.01% | -0.91% | +0.58% |
| 13 Feb 2024 | -2.64σ | -1.35% | About once every 48 trading sessions26 comparable moves / 1,258 observations | +0.40% | +2.24% | +3.89% |
| 2 Jun 2023 | +3.05σ | +2.12% | About once every 60 trading sessions21 comparable moves / 1,258 observations | -0.59% | +1.33% | +3.52% |
| 21 Feb 2023 | -2.62σ | -2.06% | About once every 45 trading sessions28 comparable moves / 1,258 observations | -0.26% | -0.38% | +0.82% |
| 10 Nov 2022 | +2.61σ | +3.70% | About once every 36 trading sessions35 comparable moves / 1,258 observations | +0.10% | -0.04% | -1.52% |
| 13 Sep 2022 | -3.73σ | -3.94% | About once every 178 trading sessions7 comparable moves / 1,243 observations | +0.10% | -3.31% | +2.35% |
| 26 Aug 2022 | -3.15σ | -3.03% | About once every 82 trading sessions15 comparable moves / 1,232 observations | -0.57% | -2.17% | -9.54% |
| 18 May 2022 | -2.57σ | -3.57% | About once every 34 trading sessions34 comparable moves / 1,163 observations | -0.75% | +5.47% | -1.25% |
| 22 Apr 2022 | -3.07σ | -2.82% | About once every 57 trading sessions20 comparable moves / 1,145 observations | +0.70% | -2.02% | -2.65% |
| 26 Nov 2021 | -4.85σ | -2.53% | 3 times in 4 years3 comparable moves / 1,044 observations | +0.68% | +2.35% | +3.35% |
| 20 Sep 2021 | -3.12σ | -1.78% | About once every 66 trading sessions15 comparable moves / 996 observations | -0.15% | +1.24% | +5.72% |
| 19 Jul 2021 | -3.22σ | -2.09% | About once every 73 trading sessions13 comparable moves / 952 observations | +1.62% | +2.85% | +4.23% |
| 21 Jun 2021 | +2.62σ | +1.76% | About once every 33 trading sessions28 comparable moves / 933 observations | +0.20% | +1.85% | +3.66% |
| 18 Jun 2021 | -2.85σ | -1.58% | About once every 37 trading sessions25 comparable moves / 932 observations | +1.76% | +3.01% | +4.65% |
| 12 May 2021 | -2.87σ | -1.99% | About once every 38 trading sessions24 comparable moves / 906 observations | +1.29% | +1.85% | +1.81% |
| 29 Jan 2021 | -2.54σ | -2.03% | About once every 26 trading sessions32 comparable moves / 835 observations | +0.76% | +4.65% | +9.91% |
| 27 Jan 2021 | -3.28σ | -2.05% | About once every 76 trading sessions11 comparable moves / 833 observations | +0.99% | +2.79% | +7.20% |
| 28 Oct 2020 | -3.27σ | -3.43% | About once every 70 trading sessions11 comparable moves / 772 observations | +0.52% | +6.80% | +13.12% |
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.