+1 sessions
Median return +0.48%Completed observations: 23
- Middle 50%
- -0.49% … +2.47%
- Positive returns
- 65%
Bank of America · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
Bank of America's latest move against its own history.
BAC Rare
+3.51%
+2.68σ
About once every 43 trading sessions
29 comparable moves / 1,258 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 +2.48%Completed observations: 23
- Middle 50%
- -1.65% … +5.42%
- Positive returns
- 65%
+30 sessions
Median return +3.71%Completed observations: 23
- Middle 50%
- -0.52% … +8.74%
- Positive returns
- 74%
Every rare move, in context
Instrument: BAC (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 30 Jan 2024 | +2.68σ | +3.51% | About once every 43 trading sessions29 comparable moves / 1,258 observations | -2.24% | -4.80% | +3.71% |
| 14 Dec 2023 | +3.36σ | +5.93% | About once every 140 trading sessions9 comparable moves / 1,258 observations | -1.00% | -0.24% | +2.50% |
| 13 Dec 2023 | +2.91σ | +4.23% | About once every 50 trading sessions25 comparable moves / 1,258 observations | +5.93% | +4.34% | +4.90% |
| 14 Nov 2023 | +3.00σ | +5.49% | About once every 57 trading sessions22 comparable moves / 1,257 observations | +1.37% | +1.75% | +15.95% |
| 2 Nov 2023 | +2.58σ | +4.62% | About once every 38 trading sessions33 comparable moves / 1,257 observations | +2.90% | +0.29% | +21.65% |
| 18 Jul 2023 | +3.11σ | +4.42% | About once every 84 trading sessions15 comparable moves / 1,257 observations | +2.70% | +4.07% | -4.98% |
| 13 Mar 2023 | -3.00σ | -5.81% | About once every 50 trading sessions25 comparable moves / 1,258 observations | +0.88% | -3.05% | +1.16% |
| 9 Mar 2023 | -4.72σ | -6.20% | 2 times in 5 years2 comparable moves / 1,258 observations | -0.88% | -9.14% | -2.19% |
| 7 Mar 2023 | -2.86σ | -3.20% | About once every 43 trading sessions29 comparable moves / 1,258 observations | -1.33% | -12.21% | -8.91% |
| 17 Oct 2022 | +2.50σ | +6.06% | About once every 29 trading sessions43 comparable moves / 1,258 observations | +3.75% | +6.19% | +10.05% |
| 13 Oct 2022 | +2.98σ | +6.13% | About once every 45 trading sessions28 comparable moves / 1,258 observations | +0.03% | +10.67% | +18.96% |
| 15 Jul 2022 | +3.81σ | +7.04% | About once every 172 trading sessions7 comparable moves / 1,202 observations | +0.03% | +2.48% | +5.52% |
| 23 May 2022 | +2.71σ | +5.94% | About once every 38 trading sessions31 comparable moves / 1,166 observations | -0.61% | +2.31% | -11.18% |
| 7 Mar 2022 | -3.09σ | -6.37% | About once every 62 trading sessions18 comparable moves / 1,112 observations | +0.65% | +11.63% | +3.21% |
| 4 Feb 2022 | +2.56σ | +3.98% | About once every 30 trading sessions37 comparable moves / 1,092 observations | +0.48% | -1.01% | -11.27% |
| 3 Jan 2022 | +2.66σ | +3.80% | About once every 36 trading sessions30 comparable moves / 1,069 observations | +3.92% | +5.80% | +3.49% |
| 26 Nov 2021 | -2.88σ | -3.93% | About once every 37 trading sessions28 comparable moves / 1,044 observations | -0.37% | -2.29% | +6.93% |
| 14 Oct 2021 | +3.04σ | +4.47% | About once every 48 trading sessions21 comparable moves / 1,014 observations | +2.88% | +5.41% | +1.53% |
| 20 Sep 2021 | -2.66σ | -3.43% | About once every 36 trading sessions28 comparable moves / 996 observations | +0.05% | +10.13% | +22.35% |
| 17 Jun 2021 | -4.36σ | -4.37% | 3 times in 4 years3 comparable moves / 931 observations | -2.56% | +4.42% | -3.62% |
| 6 Jan 2021 | +3.22σ | +6.25% | About once every 68 trading sessions12 comparable moves / 819 observations | +2.21% | +2.67% | +7.43% |
| 9 Nov 2020 | +5.89σ | +14.19% | Not previously observed in 3 years0 comparable moves / 780 observations | -0.36% | -2.81% | +5.22% |
| 14 Oct 2020 | -3.12σ | -5.33% | About once every 54 trading sessions14 comparable moves / 762 observations | +2.24% | +5.42% | +22.90% |
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.