+1 sessions
Median return +0.49%Completed observations: 32
- Middle 50%
- -0.55% … +0.76%
- Positive returns
- 66%
France 40 (CAC) · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
France 40 (CAC)'s latest move against its own history.
CAC Very rare
-4.26%
-3.64σ
About once every 214 trading sessions
6 comparable moves / 1,282 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 +0.95%Completed observations: 32
- Middle 50%
- -0.06% … +3.04%
- Positive returns
- 72%
+30 sessions
Median return +3.43%Completed observations: 32
- Middle 50%
- +0.15% … +6.65%
- Positive returns
- 78%
Every rare move, in context
Instrument: ^FCHI (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 4 Apr 2025 | -3.64σ | -4.26% | About once every 214 trading sessions6 comparable moves / 1,282 observations | -4.78% | +0.83% | +8.74% |
| 3 Apr 2025 | -3.75σ | -3.31% | About once every 256 trading sessions5 comparable moves / 1,282 observations | -4.26% | -4.29% | +4.52% |
| 16 Jan 2025 | +2.60σ | +2.14% | About once every 38 trading sessions34 comparable moves / 1,283 observations | +0.98% | +3.56% | +6.13% |
| 6 Jan 2025 | +2.86σ | +2.24% | About once every 53 trading sessions24 comparable moves / 1,283 observations | +0.59% | +0.39% | +9.98% |
| 12 Nov 2024 | -3.23σ | -2.69% | About once every 75 trading sessions17 comparable moves / 1,282 observations | -0.14% | -0.19% | +0.77% |
| 26 Sep 2024 | +2.53σ | +2.33% | About once every 38 trading sessions34 comparable moves / 1,282 observations | +0.64% | -2.15% | -4.09% |
| 19 Sep 2024 | +3.19σ | +2.29% | About once every 61 trading sessions21 comparable moves / 1,282 observations | -1.51% | +0.27% | -3.48% |
| 14 Jun 2024 | -3.02σ | -2.66% | About once every 56 trading sessions23 comparable moves / 1,282 observations | +0.91% | +2.12% | +0.19% |
| 13 Jun 2024 | -2.63σ | -1.99% | About once every 38 trading sessions34 comparable moves / 1,282 observations | -2.66% | -0.01% | -3.65% |
| 29 May 2024 | -2.67σ | -1.52% | About once every 40 trading sessions32 comparable moves / 1,282 observations | +0.55% | +0.84% | -4.56% |
| 16 Apr 2024 | -2.69σ | -1.40% | About once every 41 trading sessions31 comparable moves / 1,280 observations | +0.62% | +1.06% | +0.03% |
| 26 Jan 2024 | +3.53σ | +2.28% | About once every 85 trading sessions15 comparable moves / 1,281 observations | +0.09% | +0.06% | +5.16% |
| 3 Jan 2024 | -3.21σ | -1.58% | About once every 67 trading sessions19 comparable moves / 1,281 observations | +0.52% | +0.72% | +3.58% |
| 10 Oct 2023 | +2.69σ | +2.01% | About once every 41 trading sessions31 comparable moves / 1,281 observations | -0.44% | -3.37% | +0.94% |
| 6 Jul 2023 | -4.22σ | -3.13% | About once every 183 trading sessions7 comparable moves / 1,281 observations | +0.42% | +2.96% | +1.55% |
| 15 Mar 2023 | -3.23σ | -3.58% | About once every 75 trading sessions17 comparable moves / 1,281 observations | +2.03% | +1.88% | +8.80% |
| 13 Mar 2023 | -3.61σ | -2.90% | About once every 107 trading sessions12 comparable moves / 1,281 observations | +1.86% | +1.71% | +6.49% |
| 15 Dec 2022 | -4.06σ | -3.09% | About once every 183 trading sessions7 comparable moves / 1,279 observations | -1.08% | +0.43% | +8.81% |
| 4 Oct 2022 | +3.54σ | +4.24% | About once every 98 trading sessions13 comparable moves / 1,279 observations | -0.90% | -2.66% | +9.97% |
| 9 Mar 2022 | +3.27σ | +7.13% | About once every 81 trading sessions14 comparable moves / 1,137 observations | -2.83% | +3.64% | +3.03% |
| 4 Mar 2022 | -2.70σ | -4.97% | About once every 38 trading sessions30 comparable moves / 1,134 observations | -1.31% | +4.84% | +7.81% |
| 24 Feb 2022 | -3.21σ | -3.83% | About once every 81 trading sessions14 comparable moves / 1,128 observations | +3.55% | -8.26% | -0.91% |
| 24 Jan 2022 | -3.95σ | -3.97% | About once every 123 trading sessions9 comparable moves / 1,105 observations | +0.74% | +4.82% | -11.87% |
| 26 Nov 2021 | -8.47σ | -4.75% | Not previously observed in 4 years0 comparable moves / 1,064 observations | +0.54% | +4.83% | +7.12% |
| 19 Aug 2021 | -3.19σ | -2.43% | About once every 83 trading sessions12 comparable moves / 993 observations | +0.31% | +1.23% | -1.30% |
| 19 Jul 2021 | -3.02σ | -2.54% | About once every 61 trading sessions16 comparable moves / 970 observations | +0.81% | +4.98% | +6.22% |
| 9 Jul 2021 | +2.52σ | +2.07% | About once every 29 trading sessions33 comparable moves / 964 observations | +0.46% | -2.80% | +1.48% |
| 8 Jul 2021 | -3.04σ | -2.01% | About once every 64 trading sessions15 comparable moves / 963 observations | +2.07% | -1.58% | +3.27% |
| 11 May 2021 | -2.68σ | -1.86% | About once every 37 trading sessions25 comparable moves / 921 observations | +0.19% | +1.22% | +5.49% |
| 20 Apr 2021 | -3.47σ | -2.09% | About once every 82 trading sessions11 comparable moves / 906 observations | +0.74% | +2.23% | +5.26% |
| 9 Nov 2020 | +4.82σ | +7.57% | 3 times in 3 years3 comparable moves / 794 observations | +1.55% | +3.28% | +1.07% |
| 28 Oct 2020 | -2.79σ | -3.37% | About once every 46 trading sessions17 comparable moves / 786 observations | -0.03% | +8.53% | +21.34% |
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.