Calculator Inputs
Example Data Table
| Observation | Closing Price | Comment |
|---|---|---|
| 1 | 100.00 | Starting close |
| 2 | 101.40 | Positive daily move |
| 3 | 100.85 | Minor pullback |
| 4 | 102.30 | Recovery session |
| 5 | 101.70 | Another small decline |
| 6 | 103.10 | Upward continuation |
| 7 | 102.25 | Short-term reversal |
| 8 | 104.55 | Volatile rebound |
These example values also match the sample dataset button in the form.
Formula Used
rt = (Pt / Pt-1) - 1
rt = ln(Pt / Pt-1)
r̄ = Σrt / n
s² = Σ(rt - c)² / d
Here, c is either the mean return or zero, depending on your setting. d is n-1 for sample or n for population.
σ = √s²
HV = σ × √N
N is the number of periods per year, such as 252, 52, or 12.
How to Use This Calculator
- Enter an asset name for clear chart labels and exports.
- Paste closing prices in time order, oldest first.
- Select log or simple returns based on your workflow.
- Choose the rolling window that matches your analysis horizon.
- Set periods per year to fit daily, weekly, or monthly data.
- Decide whether to use sample or population deviation.
- Enable demeaning if you want volatility centered around the average return.
- Add an optional benchmark volatility to compare relative risk.
- Press the calculate button to display the summary, chart, and detailed table.
- Use the CSV or PDF buttons to export your results.
FAQs
1. What does historical volatility measure?
Historical volatility measures how widely an asset’s returns have varied over a chosen lookback period. Higher values mean returns were more dispersed, which usually signals greater realized risk or stronger price swings during the sample.
2. Should I use log returns or simple returns?
Log returns are common in quantitative work because they aggregate neatly across time. Simple returns are easier to interpret in plain percentage terms. For short intervals, both methods often produce similar volatility estimates.
3. Why does the rolling window matter?
The rolling window controls how much recent history enters each volatility estimate. Short windows react faster to shocks. Longer windows smooth noise and highlight broader risk regimes, but they respond more slowly to new conditions.
4. Why is 252 often used for annualization?
Many analysts use 252 because it approximates the number of trading days in a year for equities. Weekly data often uses 52, while monthly data uses 12. Match the annualization factor to your data frequency.
5. Is historical volatility the same as implied volatility?
No. Historical volatility comes from past price behavior. Implied volatility comes from option prices and reflects market expectations about future movement. They are related concepts, but they answer different questions.
6. Does high historical volatility predict future losses?
Not by itself. High realized volatility signals larger past fluctuations, not guaranteed future direction. Prices can rise or fall during high-volatility periods. Use it with trend, valuation, liquidity, and macro context.
7. Can I use weekly or monthly prices?
Yes. The method works with any consistent frequency. Just keep the data spacing uniform and update the periods-per-year input. Mixing daily, weekly, and monthly prices in one series can distort the result.
8. Why can one extreme move change volatility so much?
Volatility is built from squared deviations, so unusually large returns receive much more weight than small ones. A sharp jump or drop can therefore raise both the current estimate and the rolling volatility curve.
Practical Notes
Historical volatility is a realized measure, not a forecast. It is useful for screening, portfolio review, position sizing, risk comparison, and regime detection.
This tool is for education and analysis. It is not investment advice.