+1 sessions
Median return -0.05%Completed observations: 22
- Middle 50%
- -1.37% … +0.93%
- Positive returns
- 45%
Apple · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
Apple's latest move against its own history.
AAPL Very rare
+4.33%
+3.51σ
About once every 126 trading sessions
10 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 -0.79%Completed observations: 22
- Middle 50%
- -3.41% … +1.43%
- Positive returns
- 36%
+30 sessions
Median return -0.89%Completed observations: 22
- Middle 50%
- -4.53% … +5.02%
- Positive returns
- 41%
Every rare move, in context
Instrument: AAPL (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 11 Apr 2024 | +3.51σ | +4.33% | About once every 126 trading sessions10 comparable moves / 1,258 observations | +0.86% | -5.26% | +6.76% |
| 21 Mar 2024 | -3.65σ | -4.09% | About once every 157 trading sessions8 comparable moves / 1,259 observations | +0.53% | -1.48% | +7.01% |
| 5 Mar 2024 | -2.64σ | -2.84% | About once every 45 trading sessions28 comparable moves / 1,259 observations | -0.59% | +1.69% | -1.25% |
| 4 Mar 2024 | -2.79σ | -2.54% | About once every 63 trading sessions20 comparable moves / 1,259 observations | -2.84% | -2.27% | -3.27% |
| 18 Jan 2024 | +2.88σ | +3.26% | About once every 70 trading sessions18 comparable moves / 1,257 observations | +1.55% | +1.64% | -4.76% |
| 2 Jan 2024 | -4.33σ | -3.58% | 3 times in 5 years3 comparable moves / 1,258 observations | -0.75% | -0.03% | -0.80% |
| 6 Sep 2023 | -2.70σ | -3.58% | About once every 52 trading sessions24 comparable moves / 1,257 observations | -2.92% | -4.32% | -3.87% |
| 4 Aug 2023 | -5.45σ | -4.80% | Not previously observed in 5 years0 comparable moves / 1,257 observations | -1.73% | -2.49% | -2.21% |
| 5 May 2023 | +3.83σ | +4.69% | About once every 210 trading sessions6 comparable moves / 1,258 observations | -0.04% | -0.86% | +6.59% |
| 13 Apr 2023 | +2.69σ | +3.41% | About once every 52 trading sessions24 comparable moves / 1,258 observations | -0.21% | -0.14% | +4.49% |
| 10 Nov 2022 | +3.19σ | +8.90% | About once every 84 trading sessions15 comparable moves / 1,258 observations | +1.93% | +0.78% | -10.22% |
| 28 Oct 2022 | +3.32σ | +7.56% | About once every 97 trading sessions13 comparable moves / 1,258 observations | -1.54% | -10.43% | -7.22% |
| 29 Sep 2022 | -2.64σ | -4.91% | About once every 45 trading sessions28 comparable moves / 1,255 observations | -3.00% | -1.45% | +3.08% |
| 13 Sep 2022 | -3.36σ | -5.87% | About once every 104 trading sessions12 comparable moves / 1,243 observations | +0.96% | -0.72% | -0.98% |
| 5 May 2022 | -2.52σ | -5.57% | About once every 34 trading sessions34 comparable moves / 1,154 observations | +0.33% | -7.16% | -16.08% |
| 28 Jan 2022 | +4.66σ | +6.98% | 2 times in 4 years2 comparable moves / 1,087 observations | +2.61% | +2.64% | -11.57% |
| 26 Nov 2021 | -2.70σ | -3.17% | About once every 50 trading sessions21 comparable moves / 1,044 observations | +2.19% | +9.16% | +9.81% |
| 18 Nov 2021 | +2.55σ | +2.85% | About once every 35 trading sessions30 comparable moves / 1,039 observations | +1.70% | +4.71% | +15.29% |
| 10 Sep 2021 | -2.90σ | -3.31% | About once every 58 trading sessions17 comparable moves / 990 observations | +0.39% | -3.72% | -0.19% |
| 30 Aug 2021 | +2.76σ | +3.04% | About once every 55 trading sessions18 comparable moves / 982 observations | -0.84% | +0.62% | -7.58% |
| 1 Mar 2021 | +2.90σ | +5.39% | About once every 53 trading sessions16 comparable moves / 855 observations | -2.09% | -6.11% | +5.20% |
| 15 Dec 2020 | +2.76σ | +5.01% | About once every 47 trading sessions17 comparable moves / 805 observations | -0.05% | +3.20% | +3.19% |
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.