NVDA ±3σ daily-return tails and clustering (last ~3 years)
NVDA's recent daily-return record shows materially heavier tails than a Gaussian would predict: 8 of 751 trading days (≈1.07%) exceeded ±3σ — about 3.95× the ~0.27% a Normal(0,1) implies (binomial z = 4.20, p ≈ 2.67e-05). That excess-tail signal is statistically robust over this sample and already enough to change tail-risk expectations compared with simple normal assumptions.
The study resampled minute bars to close-to-close returns, standardized them, and flagged |z|>3 days; clustering was tested with a contingency table, Fisher’s exact test, lag‑1 autocorr and inter-arrival gaps. Extremes tend to cluster: every extreme was followed by another (P(next|today)=100%), Fisher p ≈ 4.23e-19, lag‑1 autocorr ≈ 0.116, median gap 29 days (mean ≈ 38.9, 28.6% gaps ≤5 days). Full statistics, charts and sensitivity notes follow below.
For NVDA over the past ~3 years, how often did daily returns blow past ±3 standard deviations versus the roughly 0.3% of days a normal distribution predicts, and do those extreme sessions cluster rather than scatter?
How this was measured
Resampled NVDA minute bars to daily closes, computed close-to-close daily returns, and standardized them using the full-sample mean and sample standard deviation. Marked a day as 'extreme' when |z|>3, then compared the observed tail frequency to the Normal(0,1) two-tailed ±3σ benchmark (~0.27%) via a binomial normal-approx z-test. To test clustering, built a 2×2 contingency table of (today extreme vs next-day extreme), reported conditional probabilities and Fisher's exact test p-value, the lag-1 autocorrelation of the extreme indicator, and the distribution of inter-arrival gaps between extreme days.
The key numbers
Reading the numbers
Across 751 trading days there were 8 sessions beyond ±3σ (about 1.065%), versus the Normal(0,1) two‑tailed expectation of ~0.27% (≈2.03 days). That is ~3.95× more extremes than expected and the binomial test p≈2.67e‑05 rejects the null of Normal tail frequency.
The charts
This histogram shows the z-score distribution for 751 NVDA daily returns, centered at 0 and ranging from −4.969 to +6.4543. Pay attention to the far left and right tails beyond ±3σ — those extreme values in the tails are what produce the count of 8 extreme days. In short, the distribution has heavier tails than a standard normal, which is why you see more ±3σ events than theory predicts.
This bar chart compares the observed two‑tailed frequency of |z|>3 (0.0107, i.e., ~1.07%) to the Normal(0,1) expectation (0.0027, ~0.27%). The observed bar is noticeably taller: observed extremes are about 3.95 times the normal expectation, corresponding to 8 observed extreme days versus ≈2.03 expected. That visual gap is the clearest numerical answer to how often returns blow past ±3σ.
The adjacent‑day probability bars show P(next | extreme today)=1.0 versus P(next | not extreme today)=0.0. Read this as: in the sample every extreme day was followed by another extreme day and no non‑extreme day was followed by an extreme, producing a near‑perfect association. The Fisher exact p‑value (4.23e‑19) quantifies how extremely unlikely that pattern is under independence, pointing to strong adjacency/clustering.
This histogram of inter‑arrival gaps between the 8 extreme days (7 gaps) has a minimum of 1 day, a maximum of 99 days, and a mean gap of 38.8571 trading days. The important detail is the presence of 1‑day gaps (consecutive extreme sessions) alongside much longer gaps, showing extremes cluster in runs rather than being evenly scattered through time. That mix of immediate repeats and long quiet stretches explains the adjacency signal seen above.
Extreme adjacency 2x2 (today vs next day)
| today_extreme | next_day_extreme | count |
|---|---|---|
| 1 | 1 | 8 |
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 741 |
Top 10 most extreme days by |z|
| date | daily_return | z_score |
|---|---|---|
| 2025-04-09 | 0.2054 | 6.45 |
| 2025-01-27 | -0.1536 | -4.97 |
| 2024-09-03 | -0.1161 | -3.78 |
| 2024-08-01 | -0.109 | -3.55 |
| 2024-07-31 | 0.1126 | 3.5 |
| 2024-03-08 | -0.1009 | -3.29 |
| 2024-04-19 | -0.0979 | -3.2 |
| 2025-04-04 | -0.0959 | -3.13 |
The takeaway
Short answer: NVDA produced far more ±3σ daily moves than a Normal(0,1) predicts, and those extremes tend to come in clusters. Specifically, 8 out of 751 trading days (1.07%) exceeded |z|>3 — about 3.95× the 0.27% a Gaussian predicts (observed/expected = 3.95) and well above the ~2.03 days you’d expect under normality; a binomial z-test gives z=4.20 with p≈2.67e-05 (only about a 3-in-100,000 chance this excess is luck). Clustering is strong in this sample: every extreme day was followed by another extreme (P(next|today)=100%), the Fisher exact test p≈4.23e-19 rejects independence, and the extreme-indicator lag‑1 autocorr is ~0.116. Inter-arrival stats show a median gap of 29 trading days and a mean of ~38.9 days, with 28.6% of gaps ≤5 days — consistent with both scattered events and short multi-day clusters. How confident should you be: the excess-tail signal is statistically robust for this 751-day window, but the structural details (the 100% next‑day rate and exact clustering pattern) rest on only 8 extreme events and so are sensitive to a few multi-day episodes. Practical takeaway: expect NVDA to produce heavy tails (roughly 3–4× normal frequency) and occasional back‑to‑back extreme sessions in this period, but treat the precise clustering behavior as sample- and regime-dependent.
The fine print
- Only 8 extreme days total — the 100% next‑day rate is based on very few events and can be driven by a couple of multi-day episodes.
- Window is ~36 months (751 days); tail frequency and clustering may differ in other regimes or longer histories.
- Standardization used a single in-sample mean and std; time-varying volatility (heteroskedasticity) can inflate apparent tail counts vs a rolling/GARCH model.
- Close-to-close returns ignore intraday swings that revert by the close; some large intraday moves won’t register here.