+1 sessions
Median return +2.32%Completed observations: 6
- Middle 50%
- +0.98% … +3.20%
- Positive returns
- 100%
Crude Oil WTI · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
Crude Oil WTI's latest move against its own history.
USOIL Rare
+5.57%
+2.77σ
About once every 54 trading sessions
18 comparable moves / 977 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 +4.06%Completed observations: 6
- Middle 50%
- +2.97% … +6.22%
- Positive returns
- 83%
+30 sessions
Median return +6.25%Completed observations: 6
- Middle 50%
- +1.59% … +15.72%
- Positive returns
- 83%
Every rare move, in context
Instrument: USO ETF proxy (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 23 Aug 2021 | +2.77σ | +5.57% | About once every 54 trading sessions18 comparable moves / 977 observations | +3.32% | +4.54% | +21.33% |
| 19 Jul 2021 | -4.67σ | -6.72% | 2 times in 4 years2 comparable moves / 952 observations | +1.46% | +8.46% | +5.58% |
| 18 Mar 2021 | -4.34σ | -7.64% | 2 times in 3 years2 comparable moves / 868 observations | +3.21% | +3.58% | +6.92% |
| 4 Mar 2021 | +2.56σ | +4.69% | About once every 41 trading sessions21 comparable moves / 858 observations | +3.18% | +2.76% | +0.26% |
| 22 Feb 2021 | +2.67σ | +4.03% | About once every 50 trading sessions17 comparable moves / 850 observations | +0.82% | -0.34% | -1.41% |
| 5 Jan 2021 | +3.01σ | +4.82% | About once every 68 trading sessions12 comparable moves / 818 observations | +0.50% | +6.78% | +18.65% |
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.