+1 sessions
Median return +0.06%Completed observations: 38
- Middle 50%
- -0.56% … +0.97%
- Positive returns
- 55%
Hong Kong 50 (Hang Seng) · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
Hong Kong 50 (Hang Seng)'s latest move against its own history.
HSI Below threshold
-1.43%
-1.50σ
About once every 8 trading sessions
162 comparable moves / 1,227 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 +0.89%Completed observations: 37
- Middle 50%
- -2.87% … +3.74%
- Positive returns
- 54%
+30 sessions
Median return +0.79%Completed observations: 37
- Middle 50%
- -5.84% … +5.05%
- Positive returns
- 54%
Every rare move, in context
Instrument: ^HSI (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 2 Oct 2026 | -3.32σ | -2.60% | About once every 205 trading sessions6 comparable moves / 1,227 observations | +0.28% | — | — |
| 8 Jul 2026 | +2.50σ | +2.99% | About once every 38 trading sessions32 comparable moves / 1,226 observations | -0.70% | +1.50% | +5.35% |
| 23 Mar 2026 | -2.77σ | -3.54% | About once every 53 trading sessions23 comparable moves / 1,227 observations | +2.79% | +3.74% | +8.25% |
| 28 Jan 2026 | +2.77σ | +2.58% | About once every 53 trading sessions23 comparable moves / 1,228 observations | +0.51% | -4.55% | -7.16% |
| 2 Jan 2026 | +2.83σ | +2.76% | About once every 58 trading sessions21 comparable moves / 1,228 observations | +0.03% | +1.94% | +0.87% |
| 13 Aug 2025 | +2.73σ | +2.58% | About once every 51 trading sessions24 comparable moves / 1,228 observations | -0.37% | -1.07% | +3.53% |
| 7 Apr 2025 | -9.21σ | -13.22% | Not previously observed in 5 years0 comparable moves / 1,227 observations | +1.51% | +6.20% | +19.03% |
| 21 Feb 2025 | +2.59σ | +3.99% | About once every 41 trading sessions30 comparable moves / 1,229 observations | -0.58% | -2.28% | -15.54% |
| 14 Feb 2025 | +2.65σ | +3.69% | About once every 46 trading sessions27 comparable moves / 1,229 observations | -0.02% | +1.83% | +3.56% |
| 8 Oct 2024 | -4.31σ | -9.41% | Not previously observed in 5 years0 comparable moves / 1,231 observations | -1.38% | -0.59% | -5.84% |
| 2 Oct 2024 | +3.20σ | +6.20% | About once every 123 trading sessions10 comparable moves / 1,230 observations | -1.47% | -6.02% | -13.40% |
| 26 Sep 2024 | +2.92σ | +4.16% | About once every 72 trading sessions17 comparable moves / 1,230 observations | +3.55% | +5.03% | +2.52% |
| 24 Sep 2024 | +3.81σ | +4.13% | 1 times in 5 years1 comparable moves / 1,230 observations | +0.68% | +19.66% | +10.28% |
| 19 Jun 2024 | +2.55σ | +2.87% | About once every 35 trading sessions35 comparable moves / 1,232 observations | -0.52% | -3.86% | -6.11% |
| 17 Jan 2024 | -2.97σ | -3.71% | About once every 77 trading sessions16 comparable moves / 1,230 observations | +0.75% | +4.42% | +8.59% |
| 15 Nov 2023 | +2.86σ | +3.92% | About once every 62 trading sessions20 comparable moves / 1,230 observations | -1.36% | -2.87% | -5.71% |
| 25 Jul 2023 | +2.81σ | +4.10% | About once every 47 trading sessions26 comparable moves / 1,231 observations | -0.36% | -0.07% | -5.07% |
| 2 Jun 2023 | +3.11σ | +4.02% | About once every 82 trading sessions15 comparable moves / 1,231 observations | +0.84% | +3.02% | +0.35% |
| 1 Mar 2023 | +3.18σ | +4.21% | About once every 112 trading sessions11 comparable moves / 1,231 observations | -0.92% | -6.30% | +0.79% |
| 11 Nov 2022 | +2.89σ | +7.74% | About once every 68 trading sessions18 comparable moves / 1,232 observations | +1.70% | +0.57% | +13.09% |
| 24 Oct 2022 | -3.65σ | -6.36% | About once every 205 trading sessions6 comparable moves / 1,232 observations | -0.10% | +4.26% | +28.57% |
| 5 Oct 2022 | +4.06σ | +5.90% | 1 times in 5 years1 comparable moves / 1,224 observations | -0.42% | -8.29% | +0.93% |
| 28 Sep 2022 | -2.65σ | -3.41% | About once every 42 trading sessions29 comparable moves / 1,220 observations | -0.49% | -0.20% | -6.78% |
| 25 Aug 2022 | +2.83σ | +3.63% | About once every 57 trading sessions21 comparable moves / 1,197 observations | +1.01% | -3.72% | -13.78% |
| 16 Mar 2022 | +3.54σ | +9.08% | About once every 218 trading sessions5 comparable moves / 1,088 observations | +7.04% | +6.56% | +5.05% |
| 15 Mar 2022 | -2.87σ | -5.72% | About once every 72 trading sessions15 comparable moves / 1,087 observations | +9.08% | +19.17% | +14.52% |
| 14 Mar 2022 | -3.04σ | -4.97% | About once every 91 trading sessions12 comparable moves / 1,086 observations | -5.72% | +13.43% | +3.81% |
| 7 Mar 2022 | -2.58σ | -3.87% | About once every 36 trading sessions30 comparable moves / 1,081 observations | -1.39% | -4.61% | -1.78% |
| 20 Jan 2022 | +3.15σ | +3.42% | About once every 117 trading sessions9 comparable moves / 1,052 observations | +0.05% | -4.61% | -16.78% |
| 12 Jan 2022 | +2.62σ | +2.79% | About once every 39 trading sessions27 comparable moves / 1,046 observations | +0.11% | +2.31% | -6.92% |
| 26 Nov 2021 | -2.85σ | -2.67% | About once every 68 trading sessions15 comparable moves / 1,014 observations | -0.95% | -0.40% | -1.39% |
| 27 Jul 2021 | -2.84σ | -4.22% | About once every 62 trading sessions15 comparable moves / 930 observations | +1.54% | +4.46% | +5.05% |
| 26 Jul 2021 | -3.68σ | -4.13% | 3 times in 4 years3 comparable moves / 929 observations | -4.22% | +0.89% | -0.11% |
| 8 Jul 2021 | -3.29σ | -2.89% | About once every 153 trading sessions6 comparable moves / 917 observations | +0.70% | +1.24% | -6.76% |
| 26 Feb 2021 | -2.64σ | -3.64% | About once every 41 trading sessions20 comparable moves / 829 observations | +1.63% | -0.71% | -0.27% |
| 19 Jan 2021 | +3.13σ | +2.70% | About once every 115 trading sessions7 comparable moves / 803 observations | +1.08% | -3.68% | -1.37% |
| 30 Dec 2020 | +2.68σ | +2.18% | About once every 44 trading sessions18 comparable moves / 790 observations | +0.31% | +2.80% | +11.15% |
| 5 Nov 2020 | +2.93σ | +3.25% | About once every 94 trading sessions8 comparable moves / 752 observations | +0.07% | +2.67% | +3.82% |
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.