Volatility Risk Calculator

This sample illustrates aligned series values. Use the button above to load them into the calculator.

• Simple return: rt = (Pt/Pt-1) − 1
• Log return: rt = ln(Pt/Pt-1)
• Sample volatility: s = √( Σ(r−m)² / (n−1) )
• Annualized volatility: sa = s × √k, where k is periods per year.
• EWMA variance: σ²t = λσ²t−1 + (1−λ)x²t, using xt=rt−m if demeaning is enabled.
• VaR (normal): VaR = −(μh + σhzα) with α = 1 − confidence.
• CVaR/ES (normal): ES = −(μh + σh φ(zα)/α ).

1. Choose whether you will paste prices or returns.
2. Select a frequency that matches your data (daily, weekly, monthly).
3. Pick a volatility method: standard, EWMA, or rolling window.
4. Set confidence and horizon to evaluate tail risk.
5. Optionally paste a benchmark series to calculate beta and correlation.
6. Press Calculate. Results appear above the form and under the header.
7. Use Download CSV or Download PDF to export a report.

Notes: Parametric VaR assumes approximately normal returns. For non-normal assets, consider stress tests and scenario analysis alongside these outputs.

Volatility as a Core Risk Signal

Volatility summarizes how widely returns vary around their average. Higher dispersion usually means larger uncertainty in future outcomes and larger potential drawdowns. Volatility often clusters, so recent data may deserve extra weight here. This calculator converts raw prices or returns into per-period volatility and an annualized figure, so different assets can be compared on a consistent scale. When paired with downside deviation, you can distinguish between “total noise” and harmful negative moves.

Annualization and Data Frequency Choices

Annualized volatility is computed by multiplying per-period volatility by the square root of k, where k is the number of periods per year. Daily data often uses k≈252, weekly uses 52, and monthly uses 12. The key is consistency: a daily price series should not be interpreted with a monthly factor. If your dataset has gaps, consider cleaning it before estimation to avoid overstating risk.

Method Selection: Standard, Rolling, and EWMA

Sample standard deviation treats all observations equally and is a solid baseline for stable regimes. Rolling volatility focuses on the most recent window, such as 20 trading days, and can reveal fast risk shifts. EWMA assigns heavier weight to recent returns using a decay factor λ (often 0.94 for daily series). Lower λ reacts faster but can be noisier; higher λ smooths volatility but may lag sudden shocks.

Tail Metrics: VaR and Expected Shortfall

VaR estimates a loss threshold that should not be exceeded with a chosen confidence over a given horizon, assuming approximately normal returns. Expected Shortfall (CVaR) goes further by estimating the average loss in the tail beyond VaR. Because ES captures tail severity, it is typically more conservative than VaR. Horizon scaling uses √h for volatility and h for mean, aligning risk to your holding period.

Interpreting Outputs for Portfolio Decisions

Use the risk grade as a quick screening tool, not a final decision. Compare annualized volatility against your risk budget, then check VaR and ES to understand tail exposure. If you provide a benchmark, beta and correlation help separate market-driven risk from idiosyncratic risk. Combine these results with scenario analysis, liquidity limits, and position sizing rules to build resilient portfolios. Review over cycles.

1) What input formats are supported?

Paste numbers separated by new lines, commas, spaces, or semicolons. For prices, use positive closes. For returns, use per-period values in decimal or percent, matching your chosen unit.

2) When should I use log returns?

Log returns are useful for longer horizons and compounding, and they handle proportional moves symmetrically. Use them only when your price series is strictly positive.

3) How do I choose EWMA lambda and rolling window?

For daily data, λ=0.94 is a common starting point. Reduce λ to react faster to new volatility, or increase it to smooth noise. Rolling windows like 20, 60, or 120 periods align with 1, 3, or 6 months.

4) Why do VaR and ES sometimes show as zero?

If the estimated mean over the horizon is strongly positive or volatility is extremely low, the parametric normal tail loss can be clipped at zero. Increase the horizon, lower the confidence, or validate inputs if results seem unrealistic.

5) Can I compute beta and correlation accurately?

Yes, but both series should have the same frequency and similar length. The calculator aligns by truncating to the shortest series. For best results, use matching date ranges and clean missing values beforehand.

6) Is this suitable for crypto or thinly traded assets?

It can provide a quick view, but normal-based VaR may understate fat tails and gaps. Consider shorter windows, stress scenarios, and non-parametric methods alongside these outputs, especially when liquidity and jumps dominate risk.