Historical Volatility Calculator
Calculate daily and annualized historical volatility from a series of asset prices.
10 prices → 9 log returns
Formula
Log returns are preferred over simple returns for volatility calculations because they are time-additive and more closely approximate a normal distribution.
The sample standard deviation of log returns. Measures the typical daily price fluctuation as a percentage.
Scaled by √252 (trading days per year) to give an annualized figure. Crypto trades 365 days, but 252 is standard for comparability; some analysts use √365.
Examples
- Prices: 60000, 62000, 59000, 61500, 63000, 58500, 64000
- Log returns: 0.0328, -0.0496, 0.0415, 0.0241, -0.0741, 0.0898
- Mean log return = 0.01074
- Std dev of log returns = 0.0594
- Annualized vol = 0.0594 × √252 = 94.3%
- Prices: 1.0000, 1.0002, 0.9998, 1.0001, 0.9999, 1.0003, 1.0000
- Log returns are extremely small (<0.0003)
- Std dev ≈ 0.00019
- Annualized vol = 0.00019 × √252 = 0.30%
- Prices: 5.00, 5.80, 4.50, 6.20, 4.00, 7.00, 5.50
- Log returns: 0.1484, -0.2537, 0.3202, -0.4382, 0.5596, -0.2412
- Mean log return = 0.01586
- Std dev = 0.3506
- Annualized vol = 0.3506 × √252 = 556.4%
Key Concepts
What is Historical Volatility?
Historical volatility (HV) measures how much an asset's price has fluctuated over a past period, expressed as an annualized percentage. It's calculated from the standard deviation of log returns. Unlike implied volatility (from options), HV is backward-looking — it tells you what happened, not what the market expects.
Why Use Log Returns?
Log returns (ln(P_t / P_{t-1})) are used instead of simple percentage returns because they are time-additive (you can sum daily log returns to get the period return), more closely approximate a normal distribution, and handle compounding correctly. This makes them the standard choice for volatility calculations.
The √252 Annualization Factor
Volatility scales with the square root of time, not linearly. If daily volatility is 2%, annual volatility is 2% × √252 ≈ 31.7%, not 2% × 252. This comes from the mathematical property that variance (not standard deviation) is additive for independent observations.
Crypto vs Traditional Volatility
Bitcoin typically has annualized volatility of 50–80%, compared to 15–20% for the S&P 500 and 10–15% for gold. Altcoins can have volatility exceeding 100–200%. This higher volatility means both larger potential gains and larger potential losses.
Volatility Clustering
Financial returns exhibit volatility clustering: high-volatility periods tend to be followed by more high-volatility periods, and calm periods follow calm periods. This means a single volatility number may not capture the current risk regime — recent volatility is often more informative than long-term averages.
Using Volatility for Position Sizing
Higher volatility means you should generally take smaller positions. A common approach: target a fixed dollar risk per trade by dividing your risk budget by the asset's volatility. If your risk budget is $1,000 and daily vol is 5%, you'd size the position at ~$20,000 to risk about $1,000 per day.
How to Calculate and Interpret Historical Volatility
Historical volatility quantifies price uncertainty by measuring the dispersion of past returns. The calculation involves three steps: computing log returns between consecutive prices, calculating the standard deviation of those returns, and annualizing by multiplying by the square root of the number of trading periods in a year.
The annualized volatility figure gives you an intuitive sense of price risk. A crypto asset with 80% annualized volatility means that, under normal conditions, you can expect the price to fluctuate within roughly ±80% over a year (one standard deviation). In reality, crypto returns have fat tails, so extreme moves occur more frequently than a normal distribution predicts.
Comparing volatility across assets helps with portfolio construction and risk management. If you're allocating between a 30% vol asset and an 80% vol asset, equal dollar allocation means the higher-vol asset dominates your portfolio's risk. Volatility-weighted allocation (giving less capital to more volatile assets) creates more balanced risk exposure.
Frequently Asked Questions
Should I use 252 or 365 for crypto annualization?
Both conventions exist. Using √252 aligns with traditional finance standards and makes cross-asset comparisons consistent. Using √365 reflects that crypto markets trade every day. The difference is small (~20%). This calculator uses √252 for consistency with industry standards.
How many price points do I need?
At minimum 10 prices (giving 9 returns) for a rough estimate. For reliable volatility estimates, 30+ prices are recommended. The estimate improves with more data, but very long windows may include different volatility regimes. A 30–60 day window balances precision with relevance.
What's the difference between historical and implied volatility?
Historical volatility is calculated from past prices — it tells you what happened. Implied volatility is derived from options prices — it tells you what the market expects to happen. When IV is higher than HV, options are 'expensive'; when IV is lower, options are 'cheap'. This is the basis of many options trading strategies.
Why does my annualized vol look so high?
Crypto is genuinely very volatile. Daily moves of 3–5% are routine, which annualizes to 50–80%. If you're seeing very high numbers (200%+), check your data for errors, gaps, or stock splits that could create artificially large returns between data points.