+1 sessions
Median return +0.00%Completed observations: 45
- Middle 50%
- -0.48% … +0.34%
- Positive returns
- 51%
U.S. Dollar / Japanese Yen · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
U.S. Dollar / Japanese Yen's latest move against its own history.
USDJPY Exceptional
-1.91%
-7.64σ
Not previously observed in 5 years
0 comparable moves / 1,295 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 +0.16%Completed observations: 45
- Middle 50%
- -0.67% … +0.74%
- Positive returns
- 58%
+30 sessions
Median return +0.22%Completed observations: 45
- Middle 50%
- -1.38% … +2.10%
- Positive returns
- 56%
Every rare move, in context
Instrument: USDJPY=X (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 31 Jul 2026 | -7.64σ | -1.91% | Not previously observed in 5 years0 comparable moves / 1,295 observations | -1.62% | -0.64% | -3.56% |
| 3 Jul 2026 | -2.83σ | -0.67% | About once every 46 trading sessions28 comparable moves / 1,295 observations | +0.00% | +0.61% | -1.25% |
| 1 May 2026 | -5.78σ | -2.00% | 1 times in 5 years1 comparable moves / 1,295 observations | -0.08% | +0.16% | +2.01% |
| 26 Jan 2026 | -5.07σ | -2.10% | 1 times in 5 years1 comparable moves / 1,295 observations | -0.53% | +0.41% | +2.10% |
| 22 Dec 2025 | +3.37σ | +1.34% | About once every 130 trading sessions10 comparable moves / 1,299 observations | -0.51% | -0.67% | -0.57% |
| 6 Oct 2025 | +3.45σ | +1.67% | About once every 130 trading sessions10 comparable moves / 1,299 observations | +0.48% | +1.42% | +3.33% |
| 4 Aug 2025 | -4.13σ | -2.27% | About once every 217 trading sessions6 comparable moves / 1,299 observations | -0.37% | +0.28% | +0.22% |
| 11 Apr 2025 | -3.15σ | -2.48% | About once every 93 trading sessions14 comparable moves / 1,302 observations | -0.04% | -0.60% | +0.30% |
| 8 Apr 2025 | +2.54σ | +1.62% | About once every 35 trading sessions37 comparable moves / 1,302 observations | -1.32% | -3.97% | -2.66% |
| 20 Dec 2024 | +3.31σ | +1.92% | About once every 100 trading sessions13 comparable moves / 1,305 observations | -0.70% | -0.41% | -1.50% |
| 7 Nov 2024 | +3.05σ | +1.91% | About once every 69 trading sessions19 comparable moves / 1,305 observations | -0.74% | +0.22% | +0.23% |
| 3 Oct 2024 | +2.59σ | +1.98% | About once every 33 trading sessions39 comparable moves / 1,305 observations | +0.18% | +1.88% | +6.04% |
| 5 Aug 2024 | -3.13σ | -2.42% | About once every 73 trading sessions18 comparable moves / 1,305 observations | +0.14% | +0.95% | -3.29% |
| 1 Aug 2024 | -2.89σ | -1.92% | About once every 47 trading sessions28 comparable moves / 1,305 observations | -0.36% | -1.80% | -4.78% |
| 18 Jul 2024 | -2.95σ | -1.68% | About once every 52 trading sessions25 comparable moves / 1,305 observations | +0.94% | -0.99% | -7.23% |
| 12 Jul 2024 | -5.90σ | -2.11% | Not previously observed in 5 years0 comparable moves / 1,305 observations | +0.07% | -0.83% | -7.58% |
| 3 May 2024 | -2.57σ | -1.71% | About once every 33 trading sessions40 comparable moves / 1,303 observations | +0.34% | +2.08% | +2.67% |
| 29 Apr 2024 | +5.02σ | +1.69% | 1 times in 5 years1 comparable moves / 1,303 observations | -1.21% | -2.20% | -0.88% |
| 20 Mar 2024 | +2.86σ | +1.27% | About once every 45 trading sessions29 comparable moves / 1,303 observations | -0.18% | +0.27% | +4.43% |
| 5 Feb 2024 | +2.83σ | +1.40% | About once every 45 trading sessions29 comparable moves / 1,302 observations | +0.09% | +1.50% | +0.31% |
| 8 Dec 2023 | -3.60σ | -1.97% | About once every 163 trading sessions8 comparable moves / 1,302 observations | +0.49% | -1.08% | +2.67% |
| 1 Nov 2023 | +4.74σ | +1.46% | 1 times in 5 years1 comparable moves / 1,302 observations | -0.48% | +0.04% | -3.98% |
| 10 Jul 2023 | -2.61σ | -1.21% | About once every 36 trading sessions36 comparable moves / 1,302 observations | -0.64% | -2.24% | +2.18% |
| 1 May 2023 | +3.47σ | +1.93% | About once every 145 trading sessions9 comparable moves / 1,302 observations | +0.83% | -0.81% | +2.19% |
| 6 Feb 2023 | +3.15σ | +2.53% | About once every 77 trading sessions17 comparable moves / 1,302 observations | +0.47% | +0.74% | +0.21% |
| 21 Dec 2022 | -4.15σ | -3.72% | 4 times in 5 years4 comparable moves / 1,302 observations | +0.36% | +0.78% | -1.35% |
| 11 Nov 2022 | -4.53σ | -3.06% | 2 times in 5 years2 comparable moves / 1,300 observations | -1.54% | +0.26% | -6.62% |
| 24 Oct 2022 | -2.88σ | -1.57% | About once every 50 trading sessions26 comparable moves / 1,300 observations | +0.72% | +0.06% | -9.03% |
| 7 Sep 2022 | +2.90σ | +1.94% | About once every 52 trading sessions25 comparable moves / 1,288 observations | +0.68% | +0.15% | +4.23% |
| 20 Jun 2022 | +2.95σ | +2.16% | About once every 54 trading sessions23 comparable moves / 1,231 observations | -0.14% | +0.57% | -1.38% |
| 29 Apr 2022 | +2.82σ | +1.88% | About once every 46 trading sessions26 comparable moves / 1,195 observations | -0.61% | -0.33% | +2.76% |
| 20 Apr 2022 | +3.29σ | +1.76% | About once every 99 trading sessions12 comparable moves / 1,188 observations | -1.02% | +1.14% | -0.46% |
| 23 Mar 2022 | +3.35σ | +1.46% | About once every 117 trading sessions10 comparable moves / 1,168 observations | -0.18% | +0.34% | +7.23% |
| 14 Mar 2022 | +3.49σ | +1.16% | About once every 166 trading sessions7 comparable moves / 1,161 observations | +0.59% | +3.24% | +9.42% |
| 27 Jan 2022 | +2.59σ | +0.74% | About once every 39 trading sessions29 comparable moves / 1,129 observations | +0.55% | +0.44% | +1.04% |
| 5 Jan 2022 | +2.60σ | +0.73% | About once every 40 trading sessions28 comparable moves / 1,113 observations | -0.04% | -1.77% | -0.46% |
| 29 Nov 2021 | -3.18σ | -1.17% | About once every 99 trading sessions11 comparable moves / 1,086 observations | +0.07% | -0.17% | +1.67% |
| 11 Nov 2021 | +2.74σ | +0.88% | About once every 49 trading sessions22 comparable moves / 1,074 observations | +0.12% | +0.20% | +0.19% |
| 12 Oct 2021 | +2.86σ | +1.00% | About once every 53 trading sessions20 comparable moves / 1,052 observations | +0.12% | +0.88% | +1.24% |
| 13 May 2021 | +3.02σ | +0.87% | About once every 67 trading sessions14 comparable moves / 944 observations | -0.13% | -0.68% | +1.23% |
| 5 Mar 2021 | +2.54σ | +0.84% | About once every 36 trading sessions25 comparable moves / 895 observations | +0.43% | +1.09% | +0.68% |
| 8 Jan 2021 | +2.64σ | +0.74% | About once every 39 trading sessions22 comparable moves / 855 observations | +0.29% | -0.08% | +1.79% |
| 10 Nov 2020 | +5.65σ | +1.82% | Not previously observed in 3 years0 comparable moves / 812 observations | +0.12% | -1.18% | -1.71% |
| 6 Nov 2020 | -3.10σ | -0.80% | About once every 68 trading sessions12 comparable moves / 810 observations | -0.34% | +0.91% | -0.46% |
| 22 Oct 2020 | -2.99σ | -0.76% | About once every 61 trading sessions13 comparable moves / 799 observations | +0.23% | -0.09% | -0.21% |
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.