Commodity Volatility Calculator

Example Data Table

Formula Used

• Log return: rt = ln(Pt / Pt-1) (or simple return (Pt/Pt-1) - 1).
• Sample volatility (per period): σ = stdev(r) using n-1 in the denominator.
• Annualized volatility: σann = σ × √A, where A is 252 (daily), 52 (weekly), or 12 (monthly).
• Parametric VaR (amount): VaR = z × σ × √h × Exposure where z matches the confidence level and h is horizon periods.
• Historical ES (amount): average of returns in the worst (1 − confidence) tail, scaled to the horizon.

How to Use This Calculator

1. Collect a consistent price series (daily, weekly, or monthly).
2. Paste prices as one value per line, optionally with dates.
3. Choose return method and whether to annualize volatility.
4. Enter exposure, horizon, and confidence to estimate risk.
5. Click Calculate Volatility to view results above the form.
6. Use Download CSV or Download PDF for reporting.

Notes for Risk Management

• Higher volatility can imply larger hedge ratios, wider limits, and stronger liquidity planning.
• Annualized volatility helps compare commodities across different sampling frequencies.
• VaR and ES are simplified indicators; validate against your internal policy and scenario tests.
• For structural breaks, consider rolling windows and stress periods.

Volatility Baselines by Frequency

Daily series typically annualize using 252 trading periods, weekly uses 52, and monthly uses 12. The calculator applies σ_ann = σ × √A so teams can compare risk across sampling choices without mixing units. In commodity programs, annualized volatility commonly ranges around 10–25% for liquid metals and 20–45% for crude benchmarks, depending on regime.

From Price Path to Returns

Returns are computed from consecutive prices using either log returns ln(P_t/P_t-1) or simple returns (P_t/P_t-1) − 1. Log returns add cleanly over time and handle large moves symmetrically, which helps when comparing energy, metals, and agriculture. A 2% rise followed by a 2% drop is not neutral in price terms; the return series makes that compounding visible.

Dispersion Measures and Data Hygiene

Volatility is the sample standard deviation of returns with an n−1 denominator. Using sample σ reduces bias in small datasets. Cleaning matters: remove zero or negative prices, keep consistent timestamps, and avoid mixing spot and futures settlements in one series. For weekly data, align to the same weekday close; for monthly, align to month‑end settles.

Annualized Volatility for Policy Limits

Risk limits often reference annualized volatility because it aligns with budget cycles and hedge mandates. If per‑period σ is 1.20% daily, the annualized estimate is about 1.20% × √252 ≈ 19.0%. The tool reports both to support limit setting and monitoring. Many desks track a 30‑day rolling σ and escalate when it exceeds the long‑run baseline by 50%.

Exposure-Based VaR and Expected Shortfall

Parametric VaR estimates potential loss at a confidence level using VaR = z × σ × √h × Exposure. For 95% confidence, z ≈ 1.6449. With exposure 100,000 and daily σ 1.5%, a 10‑day VaR is roughly 1.6449 × 0.015 × √10 × 100,000 ≈ 78,000. Expected Shortfall complements VaR by averaging outcomes in the worst (1−confidence) tail using the historical return distribution, which helps when returns are fat‑tailed.

Operational Reporting and Governance

The CSV export captures assumptions, counts, and computed metrics for documentation. The PDF snapshot supports approvals and audit trails for risk committees by freezing the result view. Record contract codes, currency, and unit conversions so results stay comparable across cycles.

FAQs

1) Should I use log returns or simple returns?

Use log returns for most risk comparisons because they aggregate cleanly across periods. Use simple returns when you need direct percentage interpretation for single-period budgeting and reporting.

2) Why is volatility annualized with a square root?

Under common assumptions, independent returns scale in variance with time. Standard deviation therefore scales with √time, so σ_ann = σ × √A aligns per-period dispersion with annual conventions.

3) What does “sample” standard deviation mean here?

The calculator uses an n−1 denominator to reduce bias when estimating volatility from finite data. This is typical for risk reporting when the series is a sample of a larger return process.

4) How many price points do I need for reliable results?

More is better. A practical minimum is 30–60 returns for monitoring, while limit setting often uses 250+ daily returns. Short samples can understate risk after quiet periods.

5) Why do VaR and Expected Shortfall differ?

VaR is a threshold at a chosen confidence, while Expected Shortfall averages losses beyond that threshold. ES is more sensitive to tail risk and can be more informative for stressed markets.

6) Can I use this for futures exposure in different units?

Yes, but normalize exposure first. Convert contracts into a consistent monetary exposure using contract size, FX rate, and unit conversions. Then VaR and ES outputs map to your reporting currency.