+1 sessions
Median return +0.53%Completed observations: 35
- Middle 50%
- -0.43% … +1.18%
- Positive returns
- 69%
Euro Stoxx 50 · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
Euro Stoxx 50's latest move against its own history.
SX5E Rare
-4.55%
-2.68σ
About once every 39 trading sessions
32 comparable moves / 1,260 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 +1.63%Completed observations: 35
- Middle 50%
- +0.26% … +2.65%
- Positive returns
- 74%
+30 sessions
Median return +5.86%Completed observations: 35
- Middle 50%
- +1.58% … +7.71%
- Positive returns
- 80%
Every rare move, in context
Instrument: ^STOXX50E (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 7 Apr 2025 | -2.68σ | -4.55% | About once every 39 trading sessions32 comparable moves / 1,260 observations | +2.52% | +6.66% | +16.49% |
| 4 Apr 2025 | -3.50σ | -4.60% | About once every 140 trading sessions9 comparable moves / 1,260 observations | -4.55% | +1.89% | +11.81% |
| 3 Apr 2025 | -3.55σ | -3.59% | About once every 158 trading sessions8 comparable moves / 1,260 observations | -4.60% | -3.95% | +6.68% |
| 4 Mar 2025 | -3.30σ | -2.77% | About once every 97 trading sessions13 comparable moves / 1,260 observations | +1.89% | -1.09% | -7.74% |
| 6 Jan 2025 | +3.22σ | +2.36% | About once every 74 trading sessions17 comparable moves / 1,261 observations | +0.50% | +0.92% | +10.69% |
| 2 Aug 2024 | -5.43σ | -4.81% | 1 times in 5 years1 comparable moves / 1,261 observations | -1.45% | +1.21% | +4.43% |
| 22 Feb 2024 | +2.65σ | +1.68% | About once every 33 trading sessions38 comparable moves / 1,260 observations | +0.35% | +1.19% | +3.93% |
| 24 Jan 2024 | +3.48σ | +2.20% | About once every 90 trading sessions14 comparable moves / 1,260 observations | +0.40% | +1.98% | +7.70% |
| 3 Jan 2024 | -3.24σ | -1.63% | About once every 74 trading sessions17 comparable moves / 1,260 observations | +0.58% | +0.72% | +5.87% |
| 10 Oct 2023 | +2.88σ | +2.25% | About once every 48 trading sessions26 comparable moves / 1,258 observations | -0.11% | -2.73% | +3.01% |
| 2 Aug 2023 | -3.29σ | -3.02% | About once every 74 trading sessions17 comparable moves / 1,258 observations | -0.73% | -0.35% | -2.61% |
| 27 Jul 2023 | +2.77σ | +2.33% | About once every 43 trading sessions29 comparable moves / 1,258 observations | +0.43% | -3.57% | -4.73% |
| 6 Jul 2023 | -4.12σ | -2.93% | About once every 180 trading sessions7 comparable moves / 1,258 observations | +0.32% | +3.17% | -0.24% |
| 15 Mar 2023 | -2.88σ | -3.46% | About once every 50 trading sessions25 comparable moves / 1,258 observations | +2.03% | +2.37% | +8.04% |
| 13 Mar 2023 | -3.64σ | -3.14% | About once every 105 trading sessions12 comparable moves / 1,258 observations | +2.02% | +2.42% | +6.13% |
| 15 Dec 2022 | -4.14σ | -3.51% | About once every 209 trading sessions6 comparable moves / 1,256 observations | -0.83% | -0.07% | +8.42% |
| 10 Nov 2022 | +2.73σ | +3.18% | About once every 43 trading sessions29 comparable moves / 1,256 observations | +0.57% | +1.63% | -0.60% |
| 4 Oct 2022 | +3.44σ | +4.26% | About once every 105 trading sessions12 comparable moves / 1,256 observations | -1.05% | -3.50% | +12.36% |
| 9 Mar 2022 | +3.36σ | +7.44% | About once every 93 trading sessions12 comparable moves / 1,113 observations | -3.04% | +3.62% | +1.96% |
| 4 Mar 2022 | -2.64σ | -4.96% | About once every 33 trading sessions34 comparable moves / 1,110 observations | -1.23% | +5.12% | +7.73% |
| 24 Feb 2022 | -2.85σ | -3.63% | About once every 48 trading sessions23 comparable moves / 1,104 observations | +3.69% | -8.28% | -0.71% |
| 24 Jan 2022 | -3.96σ | -4.14% | About once every 135 trading sessions8 comparable moves / 1,081 observations | +0.59% | +4.14% | -13.37% |
| 26 Nov 2021 | -7.60σ | -4.74% | Not previously observed in 4 years0 comparable moves / 1,042 observations | +0.49% | +4.56% | +4.69% |
| 28 Sep 2021 | -2.90σ | -2.56% | About once every 53 trading sessions19 comparable moves / 999 observations | +0.53% | +0.97% | +7.04% |
| 20 Sep 2021 | -3.09σ | -2.11% | About once every 83 trading sessions12 comparable moves / 993 observations | +1.33% | +0.90% | +5.86% |
| 19 Jul 2021 | -3.02σ | -2.66% | About once every 68 trading sessions14 comparable moves / 948 observations | +0.71% | +4.44% | +6.88% |
| 8 Jul 2021 | -2.95σ | -2.13% | About once every 59 trading sessions16 comparable moves / 941 observations | +1.91% | -1.58% | +3.33% |
| 18 Jun 2021 | -2.70σ | -1.80% | About once every 40 trading sessions23 comparable moves / 927 observations | +0.71% | +0.59% | +0.15% |
| 4 May 2021 | -2.73σ | -1.89% | About once every 43 trading sessions21 comparable moves / 896 observations | +1.99% | +2.36% | +5.95% |
| 20 Apr 2021 | -3.07σ | -1.98% | About once every 74 trading sessions12 comparable moves / 886 observations | +0.91% | +1.43% | +3.52% |
| 8 Mar 2021 | +2.88σ | +2.55% | About once every 57 trading sessions15 comparable moves / 857 observations | +0.61% | +2.30% | +5.66% |
| 21 Dec 2020 | -2.71σ | -2.74% | About once every 42 trading sessions19 comparable moves / 806 observations | +1.42% | +2.88% | +6.00% |
| 9 Nov 2020 | +3.96σ | +6.36% | About once every 129 trading sessions6 comparable moves / 776 observations | +1.02% | +2.18% | +1.20% |
| 28 Oct 2020 | -2.75σ | -3.49% | About once every 45 trading sessions17 comparable moves / 768 observations | -0.12% | +8.12% | +19.08% |
| 26 Oct 2020 | -2.67σ | -2.93% | About once every 43 trading sessions18 comparable moves / 766 observations | -1.12% | +1.80% | +13.68% |
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.