+1 sessions
Median return +0.40%Completed observations: 19
- Middle 50%
- -0.44% … +0.88%
- Positive returns
- 68%
Germany 40 (DAX) · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
Germany 40 (DAX)'s latest move against its own history.
DAX Rare
+2.16%
+2.68σ
About once every 40 trading sessions
32 comparable moves / 1,267 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 +1.54%Completed observations: 19
- Middle 50%
- +0.44% … +2.97%
- Positive returns
- 79%
+30 sessions
Median return +4.46%Completed observations: 19
- Middle 50%
- -0.19% … +5.93%
- Positive returns
- 74%
Every rare move, in context
Instrument: ^GDAXI (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 2 Feb 2023 | +2.68σ | +2.16% | About once every 40 trading sessions32 comparable moves / 1,267 observations | -0.21% | -0.72% | -3.50% |
| 15 Dec 2022 | -3.82σ | -3.28% | About once every 181 trading sessions7 comparable moves / 1,265 observations | -0.67% | +0.06% | +8.32% |
| 10 Nov 2022 | +3.04σ | +3.51% | About once every 70 trading sessions18 comparable moves / 1,265 observations | +0.56% | +1.65% | -1.64% |
| 4 Oct 2022 | +2.84σ | +3.78% | About once every 53 trading sessions24 comparable moves / 1,262 observations | -1.21% | -2.49% | +13.48% |
| 2 Sep 2022 | +2.72σ | +3.33% | About once every 46 trading sessions27 comparable moves / 1,241 observations | -2.22% | +1.06% | -4.69% |
| 9 Mar 2022 | +3.68σ | +7.92% | About once every 112 trading sessions10 comparable moves / 1,116 observations | -2.93% | +4.08% | +2.12% |
| 24 Feb 2022 | -3.18σ | -3.96% | About once every 69 trading sessions16 comparable moves / 1,107 observations | +3.67% | -8.66% | +0.19% |
| 24 Jan 2022 | -3.79σ | -3.80% | About once every 155 trading sessions7 comparable moves / 1,084 observations | +0.75% | +4.01% | -14.50% |
| 26 Nov 2021 | -7.38σ | -4.15% | Not previously observed in 4 years0 comparable moves / 1,045 observations | +0.16% | +3.65% | +4.49% |
| 20 Sep 2021 | -3.68σ | -2.31% | About once every 142 trading sessions7 comparable moves / 996 observations | +1.43% | +1.54% | +4.46% |
| 8 Sep 2021 | -2.53σ | -1.47% | About once every 31 trading sessions32 comparable moves / 988 observations | +0.08% | -0.77% | -0.56% |
| 19 Jul 2021 | -3.06σ | -2.62% | About once every 68 trading sessions14 comparable moves / 951 observations | +0.55% | +2.89% | +4.98% |
| 18 Jun 2021 | -2.60σ | -1.78% | About once every 33 trading sessions28 comparable moves / 930 observations | +1.00% | +1.57% | +0.62% |
| 4 May 2021 | -3.61σ | -2.49% | About once every 112 trading sessions8 comparable moves / 898 observations | +2.12% | +2.31% | +5.75% |
| 8 Mar 2021 | +3.88σ | +3.31% | About once every 172 trading sessions5 comparable moves / 859 observations | +0.40% | +1.50% | +5.67% |
| 21 Dec 2020 | -2.67σ | -2.82% | About once every 37 trading sessions22 comparable moves / 808 observations | +1.30% | +3.06% | +6.12% |
| 9 Nov 2020 | +2.80σ | +4.94% | About once every 46 trading sessions17 comparable moves / 778 observations | +0.51% | +0.81% | +1.15% |
| 28 Oct 2020 | -2.92σ | -4.17% | About once every 55 trading sessions14 comparable moves / 770 observations | +0.32% | +7.95% | +15.40% |
| 26 Oct 2020 | -3.14σ | -3.71% | About once every 70 trading sessions11 comparable moves / 768 observations | -0.93% | +1.21% | +8.98% |
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.