+1 sessions
Median return +0.06%Completed observations: 43
- Middle 50%
- -0.47% … +0.48%
- Positive returns
- 51%
Australian Dollar / Japanese Yen · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
Australian Dollar / Japanese Yen's latest move against its own history.
AUDJPY Below threshold
+0.39%
+0.84σ
Common move: this size or larger in 36% of observations
471 comparable moves / 1,296 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 +0.13%Completed observations: 43
- Middle 50%
- -0.94% … +1.27%
- Positive returns
- 51%
+30 sessions
Median return +1.60%Completed observations: 42
- Middle 50%
- -0.82% … +2.65%
- Positive returns
- 62%
Every rare move, in context
Instrument: AUDJPY=X (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 4 Sep 2026 | -3.88σ | -1.53% | About once every 259 trading sessions5 comparable moves / 1,295 observations | +0.41% | -1.71% | — |
| 3 Aug 2026 | -3.07σ | -1.33% | About once every 108 trading sessions12 comparable moves / 1,295 observations | -0.71% | +1.34% | -1.16% |
| 31 Jul 2026 | -2.67σ | -0.99% | About once every 54 trading sessions24 comparable moves / 1,295 observations | -1.33% | -0.20% | -1.75% |
| 24 Jun 2026 | -2.90σ | -1.15% | About once every 68 trading sessions19 comparable moves / 1,295 observations | -0.10% | -0.05% | -0.52% |
| 8 Apr 2026 | +3.22σ | +1.69% | About once every 162 trading sessions8 comparable moves / 1,295 observations | -0.57% | +1.47% | +0.60% |
| 9 Feb 2026 | +2.97σ | +2.00% | About once every 65 trading sessions20 comparable moves / 1,295 observations | -0.00% | -1.93% | +0.89% |
| 23 Jan 2026 | +2.61σ | +1.30% | About once every 48 trading sessions27 comparable moves / 1,295 observations | -1.04% | -0.27% | +1.89% |
| 22 Dec 2025 | +2.81σ | +1.29% | About once every 62 trading sessions21 comparable moves / 1,299 observations | +0.19% | +0.88% | +4.04% |
| 13 Oct 2025 | -2.98σ | -1.54% | About once every 62 trading sessions21 comparable moves / 1,299 observations | +0.45% | -0.21% | +2.48% |
| 6 Oct 2025 | +4.65σ | +1.61% | 3 times in 5 years3 comparable moves / 1,299 observations | +0.84% | -0.14% | +2.38% |
| 4 Aug 2025 | -3.49σ | -1.67% | About once every 260 trading sessions5 comparable moves / 1,299 observations | -0.29% | +1.22% | +3.00% |
| 7 Apr 2025 | -7.76σ | -5.84% | Not previously observed in 5 years0 comparable moves / 1,302 observations | +1.81% | +4.17% | +6.22% |
| 20 Dec 2024 | +3.07σ | +2.34% | About once every 93 trading sessions14 comparable moves / 1,305 observations | -0.37% | -0.62% | -1.72% |
| 4 Sep 2024 | -2.57σ | -2.01% | About once every 42 trading sessions31 comparable moves / 1,305 observations | -1.37% | -2.46% | +2.10% |
| 5 Aug 2024 | -2.65σ | -2.39% | About once every 47 trading sessions28 comparable moves / 1,305 observations | +0.43% | +3.13% | -0.07% |
| 18 Jul 2024 | -3.05σ | -1.71% | About once every 65 trading sessions20 comparable moves / 1,305 observations | +0.57% | -3.59% | -6.50% |
| 12 Jul 2024 | -4.77σ | -1.89% | 3 times in 5 years3 comparable moves / 1,305 observations | +0.13% | -2.68% | -8.38% |
| 5 Jun 2024 | -2.68σ | -1.26% | About once every 52 trading sessions25 comparable moves / 1,305 observations | +0.63% | +1.09% | +3.40% |
| 29 Apr 2024 | +3.93σ | +1.97% | 4 times in 5 years4 comparable moves / 1,305 observations | -0.91% | -1.48% | -0.25% |
| 25 Mar 2024 | -2.52σ | -1.06% | About once every 42 trading sessions31 comparable moves / 1,305 observations | +0.39% | +0.13% | +2.95% |
| 20 Dec 2023 | +3.11σ | +1.68% | About once every 93 trading sessions14 comparable moves / 1,304 observations | -0.59% | -0.76% | -0.10% |
| 8 Dec 2023 | -2.52σ | -1.34% | About once every 43 trading sessions30 comparable moves / 1,304 observations | +0.27% | +0.57% | +2.45% |
| 1 Aug 2023 | +2.69σ | +1.96% | About once every 52 trading sessions25 comparable moves / 1,304 observations | -1.03% | -1.74% | -1.33% |
| 28 Jul 2023 | -3.01σ | -1.78% | About once every 69 trading sessions19 comparable moves / 1,304 observations | +0.60% | +0.51% | +0.82% |
| 16 Mar 2023 | -3.07σ | -2.14% | About once every 82 trading sessions16 comparable moves / 1,304 observations | +1.02% | -1.29% | +0.26% |
| 21 Dec 2022 | -6.77σ | -3.96% | Not previously observed in 5 years0 comparable moves / 1,304 observations | +0.72% | +1.96% | +4.01% |
| 29 Nov 2022 | -2.74σ | -1.33% | About once every 54 trading sessions24 comparable moves / 1,304 observations | +0.50% | -0.57% | -1.36% |
| 20 Apr 2022 | +3.17σ | +2.26% | About once every 92 trading sessions13 comparable moves / 1,192 observations | -0.34% | -2.78% | -3.31% |
| 23 Mar 2022 | +3.20σ | +2.37% | About once every 117 trading sessions10 comparable moves / 1,172 observations | +0.32% | +0.72% | +2.07% |
| 17 Mar 2022 | +3.19σ | +1.85% | About once every 106 trading sessions11 comparable moves / 1,168 observations | +0.94% | +6.08% | +5.59% |
| 29 Nov 2021 | -2.74σ | -1.60% | About once every 52 trading sessions21 comparable moves / 1,090 observations | +0.12% | -0.45% | +2.18% |
| 12 Oct 2021 | +3.46σ | +1.74% | About once every 211 trading sessions5 comparable moves / 1,056 observations | -0.07% | +3.17% | -0.43% |
| 24 Sep 2021 | +2.58σ | +1.35% | About once every 39 trading sessions27 comparable moves / 1,044 observations | -0.06% | +0.48% | +4.76% |
| 20 Aug 2021 | -2.54σ | -1.24% | About once every 35 trading sessions29 comparable moves / 1,019 observations | -0.08% | +2.18% | +2.71% |
| 9 Jul 2021 | -3.06σ | -1.42% | About once every 82 trading sessions12 comparable moves / 989 observations | +1.13% | -1.50% | -3.89% |
| 18 Jun 2021 | -3.42σ | -1.15% | About once every 195 trading sessions5 comparable moves / 974 observations | -0.85% | +0.40% | -2.94% |
| 24 Mar 2021 | -3.67σ | -2.05% | 4 times in 4 years4 comparable moves / 912 observations | +0.06% | +2.09% | +2.19% |
| 25 Feb 2021 | +2.62σ | +1.37% | About once every 41 trading sessions22 comparable moves / 893 observations | -0.84% | -0.99% | -0.92% |
| 22 Feb 2021 | +3.20σ | +1.42% | About once every 127 trading sessions7 comparable moves / 890 observations | -0.16% | +0.37% | +1.32% |
| 4 Jan 2021 | +3.06σ | +1.57% | About once every 107 trading sessions8 comparable moves / 855 observations | -0.67% | +1.33% | +2.46% |
| 1 Jan 2021 | -2.64σ | -1.14% | About once every 47 trading sessions18 comparable moves / 854 observations | +1.57% | +2.40% | +3.58% |
| 10 Nov 2020 | +2.64σ | +1.73% | About once every 48 trading sessions17 comparable moves / 816 observations | +0.15% | -0.88% | +2.29% |
| 4 Nov 2020 | +3.29σ | +1.85% | About once every 162 trading sessions5 comparable moves / 812 observations | -0.33% | +1.13% | +4.07% |
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.