+1 sessions
Median return -0.47%Completed observations: 24
- Middle 50%
- -1.57% … +0.96%
- Positive returns
- 38%
Goldman Sachs · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
Goldman Sachs's latest move against its own history.
GS Exceptional
+4.35%
+4.20σ
2 times in 5 years
2 comparable moves / 1,259 observations
Small historical sample 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 +1.19%Completed observations: 24
- Middle 50%
- -1.82% … +3.28%
- Positive returns
- 58%
+30 sessions
Median return +7.17%Completed observations: 24
- Middle 50%
- -0.09% … +10.73%
- Positive returns
- 75%
Every rare move, in context
Instrument: GS (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 21 Mar 2024 | +4.20σ | +4.35% | 2 times in 5 years2 comparable moves / 1,259 observations | -1.67% | -0.86% | +5.91% |
| 13 Feb 2024 | -3.22σ | -3.54% | About once every 157 trading sessions8 comparable moves / 1,258 observations | -0.19% | +3.25% | +9.64% |
| 14 Dec 2023 | +3.87σ | +5.72% | 4 times in 5 years4 comparable moves / 1,258 observations | -0.77% | -0.49% | +0.89% |
| 3 Nov 2023 | +2.80σ | +4.42% | About once every 63 trading sessions20 comparable moves / 1,257 observations | -1.13% | +3.39% | +14.89% |
| 30 Oct 2023 | +2.85σ | +3.77% | About once every 70 trading sessions18 comparable moves / 1,257 observations | +0.92% | +7.89% | +17.21% |
| 3 Oct 2023 | -3.29σ | -3.89% | About once every 157 trading sessions8 comparable moves / 1,257 observations | +0.81% | +1.22% | +10.65% |
| 10 Mar 2023 | -2.59σ | -4.22% | About once every 39 trading sessions32 comparable moves / 1,258 observations | -3.71% | -3.17% | +4.97% |
| 28 Feb 2023 | -3.06σ | -3.80% | About once every 79 trading sessions16 comparable moves / 1,258 observations | -1.54% | -2.72% | -6.09% |
| 17 Jan 2023 | -5.08σ | -6.44% | Not previously observed in 5 years0 comparable moves / 1,258 observations | -0.24% | +1.44% | -1.05% |
| 10 Nov 2022 | +2.53σ | +4.51% | About once every 31 trading sessions40 comparable moves / 1,258 observations | +1.81% | +0.50% | -8.67% |
| 4 Oct 2022 | +2.73σ | +5.25% | About once every 43 trading sessions29 comparable moves / 1,258 observations | -1.86% | -2.48% | +21.60% |
| 13 Sep 2022 | -3.03σ | -4.14% | About once every 78 trading sessions16 comparable moves / 1,243 observations | -0.34% | -4.71% | +1.22% |
| 19 Jul 2022 | +2.52σ | +5.57% | About once every 32 trading sessions38 comparable moves / 1,204 observations | +1.07% | +3.48% | +4.90% |
| 24 Jun 2022 | +2.77σ | +5.79% | About once every 52 trading sessions23 comparable moves / 1,188 observations | -0.65% | -2.97% | +10.55% |
| 10 Jun 2022 | -3.11σ | -5.65% | About once every 79 trading sessions15 comparable moves / 1,179 observations | -1.29% | -0.86% | +10.99% |
| 22 Apr 2022 | -2.79σ | -4.35% | About once every 55 trading sessions21 comparable moves / 1,145 observations | +0.52% | -1.60% | +0.23% |
| 18 Jan 2022 | -4.03σ | -6.97% | 3 times in 4 years3 comparable moves / 1,079 observations | -2.00% | -3.77% | -5.08% |
| 17 Dec 2021 | -2.56σ | -3.92% | About once every 34 trading sessions31 comparable moves / 1,059 observations | -2.67% | +1.15% | -4.65% |
| 15 Oct 2021 | +2.54σ | +3.80% | About once every 32 trading sessions32 comparable moves / 1,015 observations | +1.88% | +2.84% | -4.81% |
| 20 Sep 2021 | -2.94σ | -3.41% | About once every 66 trading sessions15 comparable moves / 996 observations | -0.61% | +1.79% | +10.20% |
| 18 Jun 2021 | -2.51σ | -3.50% | About once every 30 trading sessions31 comparable moves / 932 observations | +2.50% | +6.82% | +8.42% |
| 6 Jan 2021 | +2.74σ | +5.40% | About once every 41 trading sessions20 comparable moves / 819 observations | +2.14% | +5.41% | +10.53% |
| 21 Dec 2020 | +3.70σ | +6.13% | 4 times in 3 years4 comparable moves / 809 observations | -2.68% | +2.62% | +14.31% |
| 9 Nov 2020 | +3.56σ | +6.79% | About once every 156 trading sessions5 comparable moves / 780 observations | +1.18% | +4.36% | +16.36% |
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.