+1 sessions
Median return -0.02%Completed observations: 35
- Middle 50%
- -0.33% … +0.29%
- Positive returns
- 43%
U.S. Dollar / Canadian Dollar · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
U.S. Dollar / Canadian Dollar's latest move against its own history.
USDCAD Below threshold
-0.36%
-1.59σ
About once every 9 trading sessions
148 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 +0.24%Completed observations: 35
- Middle 50%
- -0.62% … +0.81%
- Positive returns
- 51%
+30 sessions
Median return +0.01%Completed observations: 35
- Middle 50%
- -1.00% … +1.60%
- Positive returns
- 51%
Every rare move, in context
Instrument: USDCAD=X (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 20 Aug 2026 | -2.66σ | -0.63% | About once every 54 trading sessions24 comparable moves / 1,295 observations | -0.21% | +0.64% | +3.08% |
| 15 Jul 2026 | -3.49σ | -0.69% | About once every 259 trading sessions5 comparable moves / 1,295 observations | -0.10% | +0.24% | -1.53% |
| 18 Jun 2026 | +3.65σ | +0.74% | 3 times in 5 years3 comparable moves / 1,295 observations | +0.29% | +0.64% | -0.45% |
| 2 Feb 2026 | +3.10σ | +1.07% | About once every 108 trading sessions12 comparable moves / 1,295 observations | +0.28% | -0.61% | +0.56% |
| 28 Jan 2026 | -3.28σ | -0.88% | About once every 162 trading sessions8 comparable moves / 1,295 observations | -0.39% | +0.89% | -0.06% |
| 8 Dec 2025 | -3.75σ | -0.90% | 3 times in 5 years3 comparable moves / 1,299 observations | +0.10% | -0.57% | -0.37% |
| 4 Feb 2025 | -3.78σ | -2.03% | 3 times in 5 years3 comparable moves / 1,303 observations | -0.58% | -0.81% | -0.85% |
| 3 Feb 2025 | +3.79σ | +1.55% | 2 times in 5 years2 comparable moves / 1,303 observations | -2.03% | -2.93% | -2.36% |
| 21 Jan 2025 | -3.27σ | -1.19% | About once every 163 trading sessions8 comparable moves / 1,303 observations | +0.28% | +0.67% | +1.31% |
| 19 Dec 2024 | +2.79σ | +1.06% | About once every 69 trading sessions19 comparable moves / 1,305 observations | -0.40% | -0.40% | +1.77% |
| 26 Nov 2024 | +3.64σ | +1.19% | 2 times in 5 years2 comparable moves / 1,305 observations | -0.32% | -0.18% | +1.98% |
| 7 Nov 2024 | +3.40σ | +0.83% | About once every 261 trading sessions5 comparable moves / 1,305 observations | -0.58% | +0.99% | +3.68% |
| 25 Sep 2024 | -3.45σ | -0.80% | 4 times in 5 years4 comparable moves / 1,305 observations | +0.46% | +0.95% | +3.07% |
| 26 Aug 2024 | -2.96σ | -0.70% | About once every 131 trading sessions10 comparable moves / 1,305 observations | -0.19% | +0.26% | +0.53% |
| 1 May 2024 | +2.60σ | +0.81% | About once every 57 trading sessions23 comparable moves / 1,303 observations | -0.39% | -0.72% | -0.16% |
| 11 Apr 2024 | +2.72σ | +0.84% | About once every 72 trading sessions18 comparable moves / 1,303 observations | -0.00% | +0.38% | +0.01% |
| 21 Mar 2024 | -2.58σ | -0.75% | About once every 52 trading sessions25 comparable moves / 1,303 observations | +0.41% | +0.37% | +1.86% |
| 14 Feb 2024 | +2.65σ | +0.82% | About once every 65 trading sessions20 comparable moves / 1,302 observations | -0.20% | -0.62% | +0.11% |
| 3 Oct 2023 | +2.53σ | +0.76% | About once every 48 trading sessions27 comparable moves / 1,302 observations | +0.24% | -0.60% | +0.92% |
| 8 May 2023 | -2.81σ | -1.06% | About once every 69 trading sessions19 comparable moves / 1,302 observations | -0.06% | +0.73% | -1.36% |
| 8 Mar 2023 | +2.59σ | +0.97% | About once every 45 trading sessions29 comparable moves / 1,302 observations | +0.37% | -0.21% | -2.60% |
| 5 Jan 2023 | -2.84σ | -1.38% | About once every 69 trading sessions19 comparable moves / 1,302 observations | +0.55% | -0.66% | -0.70% |
| 7 Nov 2022 | -3.17σ | -1.67% | About once every 100 trading sessions13 comparable moves / 1,300 observations | -0.14% | -1.77% | +1.30% |
| 14 Sep 2022 | +3.23σ | +1.41% | About once every 108 trading sessions12 comparable moves / 1,293 observations | -0.02% | +2.34% | +3.45% |
| 6 Jul 2022 | +3.30σ | +1.38% | About once every 124 trading sessions10 comparable moves / 1,243 observations | -0.01% | +0.56% | -1.45% |
| 10 Jun 2022 | +2.91σ | +1.20% | About once every 77 trading sessions16 comparable moves / 1,225 observations | +0.75% | +2.20% | +1.38% |
| 21 Apr 2022 | -2.83σ | -0.93% | About once every 70 trading sessions17 comparable moves / 1,189 observations | +0.82% | +2.94% | +1.43% |
| 8 Dec 2021 | -2.92σ | -0.91% | About once every 73 trading sessions15 comparable moves / 1,093 observations | +0.05% | +1.06% | -1.17% |
| 12 Nov 2021 | +2.60σ | +0.82% | About once every 45 trading sessions24 comparable moves / 1,075 observations | -0.34% | +0.90% | +1.87% |
| 24 Aug 2021 | -2.81σ | -1.36% | About once every 64 trading sessions16 comparable moves / 1,017 observations | -0.43% | -0.23% | -0.48% |
| 20 Aug 2021 | +3.31σ | +1.33% | About once every 113 trading sessions9 comparable moves / 1,015 observations | -0.04% | -1.73% | -1.15% |
| 4 Jan 2021 | +3.48σ | +3.01% | About once every 122 trading sessions7 comparable moves / 851 observations | +0.46% | -0.11% | -0.27% |
| 1 Jan 2021 | -9.15σ | -3.14% | Not previously observed in 3 years0 comparable moves / 850 observations | +3.01% | +3.41% | +2.84% |
| 3 Nov 2020 | -2.81σ | -1.10% | About once every 62 trading sessions13 comparable moves / 807 observations | -0.90% | -1.23% | -3.48% |
| 29 Oct 2020 | +2.53σ | +0.90% | About once every 42 trading sessions19 comparable moves / 804 observations | +0.04% | -2.17% | -3.65% |
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.