THE SHORT ANSWER
Gold's monthly changes have a center, wide tails and no promised boundary
Across 798 adjacent World Bank monthly-average changes, the median is +0.00%, the sample standard deviation is 4.57%, and the empirical 5th-to-95th percentile interval runs from -5.52% to +8.13%. These statistics describe the full historical sample. They do not impose a normal distribution, cap a future loss or replace product-level risk analysis.
Middle historical monthly change.
Standard deviation, not maximum loss.
Interpolated empirical sample quantiles.
Adjusted Fisher-Pearson coefficient.
INTERACTIVE DISTRIBUTION
Inspect the histogram, empirical box and tail markers together
Change the bin width to see how grouping changes the histogram without changing the observations. Use pointer, touch or keyboard controls to inspect each bucket; the box plot keeps the median, middle half and 5th-to-95th percentile interval visible.
EMPIRICAL BOX AND TAIL MARKERS
Changing bin width changes the visual grouping, not the underlying observations. The box spans the empirical 25th to 75th percentiles; whiskers mark the 5th and 95th percentiles rather than theoretical limits.
Source: World Bank Commodity Price Data (The Pink Sheet), local monthly nominal USD per troy ounce. Source workbook updated 2026-08-04; retrieved 2026-08-07. These charts describe history and are not price forecasts.
FIXED-PERIOD DISTRIBUTION LAB
Did the center and tails stay stable across historical periods?
Compare four fixed periods using the observed range, empirical P5–P95 interval, middle half, median and arithmetic average. Select a row with pointer, touch or arrow keys. The periods expose distribution change; they do not explain its cause or estimate the next month.
2020-01 through 2026-07.
+1.4% arithmetic average.
Historical P5–P95, not a future limit.
Reading boundary: the thin line is the observed minimum–maximum, the thicker line is P5–P95, the box is Q1–Q3, the vertical mark is the median and the diamond is the average. Fixed periods reveal instability but do not identify its cause.
| Segment | Observations | Average | Median | P5 / P95 | Q1 / Q3 | Observed worst / best |
|---|---|---|---|---|---|---|
| 1960–1979 | 239 | +1.2% | +0.0% | -4.9% / +12.1% | +0.0% / +2.3% | -11.7% / +20.6% |
| 1980–1999 | 240 | -0.1% | -0.3% | -6.1% / +7.4% | -2.3% / +1.4% | -16.7% / +48.4% |
| 2000–2019 | 240 | +0.8% | +0.4% | -5.0% / +7.2% | -1.6% / +3.1% | -11.7% / +11.8% |
| 2020–latest (shorter) | 79 | +1.4% | +0.8% | -4.6% / +7.9% | -1.1% / +3.9% | -7.8% / +10.6% |
EMPIRICAL SUMMARY
Central tendency, dispersion, percentiles and observed tails
| Measure | Value | Interpretation |
|---|---|---|
| Average | +0.70% | Arithmetic mean; sensitive to extreme observations |
| Median | +0.00% | Middle observation after sorting |
| Positive frequency | 43.5% | Share above zero; not a forecast probability |
| Sample standard deviation | 4.57% | Dispersion with n - 1 denominator |
| 25th / 75th percentile | -1.48% / +2.44% | Middle half of the empirical sample |
| 5th / 95th percentile | -5.52% / +8.13% | Historical tail markers, not hard bounds |
| Worst / best | -16.69% / +48.35% | 1980-03 and 1980-01 |
| Skewness | 1.99 | Adjusted Fisher-Pearson sample coefficient |
FORMULAS
The page uses empirical statistics and keeps their assumptions visible
(Current monthly average / prior monthly average - 1) x 100.
Square root of squared deviations divided by n - 1.
Sort observed returns and linearly interpolate between adjacent ranks.
Adjusted Fisher-Pearson coefficient using sample standard deviation.
The arithmetic average is not a compound growth rate. Monthly averages also reduce the apparent size of intramonth jumps and reversals. For multi-year compound outcomes, use gold rolling returns; for path losses from a prior peak, use gold drawdown history.
RISK BOUNDARY
A historical percentile is not a future loss ceiling
Monetary systems, inflation, rates, currencies and market access changed across the sample.
A daily or intraday distribution can have different tails and timing.
Premiums, spreads, fees, storage, tax and currency translation alter outcomes.
Volatility can cluster, so calm and turbulent months may arrive in sequences.
Source, formula and limitsWorld Bank monthly history · CC BY 4.0
SOURCE, LICENSE & REPRODUCIBILITY
Every result uses one consistent monthly series
The source is the World Bank Commodity Price Data (The Pink Sheet), licensed CC BY 4.0. It contains 799 monthly gold averages from 1960-01 through 2026-07. The workbook was published 2026-08-04, retrieved 2026-08-07, and recorded with SHA-256 7902a77505ebdc5d202ce65f666c2ee1b04b626f042d7738ed3e6f7d112c8433.
Monthly change = (current monthly average / prior monthly average - 1) × 100. Only adjacent calendar months are used. The result is not a daily close return, intramonth high or low, dealer quote or exact investor fill.
CONTINUE THE RESEARCH
Move from calendar grouping to tails, distribution and holding periods
FREQUENTLY ASKED QUESTIONS
Questions about monthly gold-return evidence
What does a gold return distribution show?
It shows how the 798 adjacent monthly-average percentage changes are spread across loss and gain buckets, along with empirical percentiles and dispersion.
Is the distribution normal?
The page does not assume normality. It reports empirical percentiles and sample skewness because tail observations and asymmetry can make a normal approximation misleading.
What does the 5th percentile mean?
Five percent of the observed monthly-average changes are at or below the interpolated 5th-percentile value in this historical sample. It is not a guaranteed loss boundary.
Why is standard deviation not a maximum loss?
Standard deviation measures sample dispersion around the average. It does not cap outcomes, and extreme observations can exceed one or several standard deviations.
Can this distribution be used as value at risk?
Not by itself. The observations are one overlapping historical path, regimes change, monthly averages smooth extremes and no portfolio size, confidence model or forward assumption is specified.