+1 sessions
Median return +0.15%Completed observations: 37
- Middle 50%
- -0.57% … +1.11%
- Positive returns
- 59%
Merck · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
Merck's latest move against its own history.
MRK Rare
-4.44%
-2.80σ
About once every 46 trading sessions
27 comparable moves / 1,255 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 -0.43%Completed observations: 37
- Middle 50%
- -1.68% … +3.06%
- Positive returns
- 49%
+30 sessions
Median return +0.13%Completed observations: 37
- Middle 50%
- -1.58% … +6.00%
- Positive returns
- 51%
Every rare move, in context
Instrument: MRK (price return)
| Date | σ | Move | Observed rarity | +1 sessions | +7 sessions | +30 sessions |
|---|---|---|---|---|---|---|
| 31 Jul 2025 | -2.80σ | -4.44% | About once every 46 trading sessions27 comparable moves / 1,255 observations | +1.50% | +2.44% | +6.00% |
| 12 May 2025 | +2.61σ | +5.87% | About once every 35 trading sessions36 comparable moves / 1,256 observations | -4.72% | -4.29% | -0.94% |
| 4 Apr 2025 | -3.43σ | -5.70% | About once every 84 trading sessions15 comparable moves / 1,256 observations | -0.36% | -3.78% | -5.20% |
| 25 Mar 2025 | -3.40σ | -4.81% | About once every 79 trading sessions16 comparable moves / 1,256 observations | +0.27% | -1.68% | -9.96% |
| 4 Feb 2025 | -7.73σ | -9.07% | 2 times in 5 years2 comparable moves / 1,257 observations | -1.18% | -6.96% | +3.61% |
| 30 Jul 2024 | -7.87σ | -9.81% | 1 times in 5 years1 comparable moves / 1,258 observations | -1.84% | -1.15% | -0.47% |
| 28 Jun 2024 | -4.51σ | -4.64% | About once every 180 trading sessions7 comparable moves / 1,258 observations | +3.31% | +2.83% | -8.34% |
| 28 May 2024 | -2.80σ | -2.63% | About once every 42 trading sessions30 comparable moves / 1,259 observations | -0.15% | +3.51% | +2.28% |
| 25 Apr 2024 | +3.06σ | +2.93% | About once every 52 trading sessions24 comparable moves / 1,259 observations | +0.37% | -2.41% | -0.04% |
| 27 Mar 2024 | +5.65σ | +4.96% | 2 times in 5 years2 comparable moves / 1,259 observations | +0.15% | -3.94% | -1.15% |
| 4 Mar 2024 | -2.61σ | -2.29% | About once every 34 trading sessions37 comparable moves / 1,259 observations | -0.98% | -1.52% | +0.81% |
| 1 Feb 2024 | +5.06σ | +4.64% | 4 times in 5 years4 comparable moves / 1,258 observations | +0.02% | -0.82% | -3.85% |
| 2 Jan 2024 | +3.94σ | +3.87% | About once every 140 trading sessions9 comparable moves / 1,258 observations | +1.35% | +4.58% | +11.11% |
| 13 Dec 2023 | +2.74σ | +2.64% | About once every 38 trading sessions33 comparable moves / 1,258 observations | -1.15% | +0.55% | +13.23% |
| 18 Oct 2023 | -2.65σ | -2.09% | About once every 36 trading sessions35 comparable moves / 1,257 observations | -1.53% | +0.81% | +0.48% |
| 23 Aug 2023 | +3.40σ | +3.80% | About once every 90 trading sessions14 comparable moves / 1,257 observations | -1.66% | -1.31% | -6.92% |
| 6 Jun 2023 | -2.71σ | -2.74% | About once every 37 trading sessions34 comparable moves / 1,258 observations | -1.27% | -0.55% | -1.41% |
| 6 Mar 2023 | +3.03σ | +3.95% | About once every 52 trading sessions24 comparable moves / 1,258 observations | +0.15% | -3.12% | +3.36% |
| 2 Feb 2023 | -2.92σ | -3.29% | About once every 48 trading sessions26 comparable moves / 1,258 observations | -0.50% | +5.89% | +0.62% |
| 9 Jan 2023 | -3.97σ | -3.88% | About once every 157 trading sessions8 comparable moves / 1,258 observations | +0.39% | -0.43% | -1.11% |
| 11 Nov 2022 | -3.35σ | -3.86% | About once every 79 trading sessions16 comparable moves / 1,258 observations | +2.44% | +9.13% | +14.45% |
| 10 Oct 2022 | +2.79σ | +3.29% | About once every 41 trading sessions31 comparable moves / 1,258 observations | +0.63% | +3.07% | +16.72% |
| 22 Sep 2022 | +3.01σ | +3.53% | About once every 50 trading sessions25 comparable moves / 1,250 observations | -0.83% | +0.05% | +12.84% |
| 21 Jun 2022 | +3.46σ | +4.03% | About once every 74 trading sessions16 comparable moves / 1,185 observations | +1.28% | +3.57% | -0.47% |
| 28 Apr 2022 | +4.62σ | +4.94% | About once every 164 trading sessions7 comparable moves / 1,149 observations | +0.12% | -1.06% | -1.58% |
| 25 Feb 2022 | +2.82σ | +3.82% | About once every 44 trading sessions25 comparable moves / 1,106 observations | +0.34% | +0.83% | +14.88% |
| 24 Feb 2022 | -2.78σ | -3.07% | About once every 39 trading sessions28 comparable moves / 1,105 observations | +3.82% | +5.74% | +18.08% |
| 3 Feb 2022 | -3.24σ | -3.66% | About once every 61 trading sessions18 comparable moves / 1,091 observations | -0.57% | -3.21% | +0.13% |
| 5 Nov 2021 | -5.24σ | -9.86% | 4 times in 4 years4 comparable moves / 1,030 observations | +1.31% | +3.06% | -6.37% |
| 28 Oct 2021 | +3.63σ | +6.14% | About once every 102 trading sessions10 comparable moves / 1,024 observations | +1.73% | -4.47% | -16.09% |
| 1 Oct 2021 | +8.18σ | +8.37% | 1 times in 4 years1 comparable moves / 1,005 observations | +2.09% | -2.22% | +3.19% |
| 29 Sep 2021 | +2.79σ | +2.41% | About once every 46 trading sessions22 comparable moves / 1,003 observations | +0.03% | +7.38% | +11.88% |
| 29 Apr 2021 | -5.21σ | -4.42% | 3 times in 4 years3 comparable moves / 897 observations | +1.11% | +6.09% | +8.48% |
| 26 Feb 2021 | -2.54σ | -2.68% | About once every 37 trading sessions23 comparable moves / 854 observations | -0.33% | +2.09% | +4.96% |
| 27 Jan 2021 | -3.47σ | -3.96% | About once every 83 trading sessions10 comparable moves / 833 observations | +1.10% | -1.65% | -3.17% |
| 14 Dec 2020 | -3.30σ | -3.18% | About once every 67 trading sessions12 comparable moves / 804 observations | +0.20% | -0.70% | -2.99% |
| 4 Nov 2020 | +3.95σ | +4.81% | About once every 155 trading sessions5 comparable moves / 777 observations | -0.20% | +0.58% | -0.99% |
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.