Direct Answer
Close-to-close volatility is the sample standard deviation of log returns between successive closing prices, usually annualized. It is the standard historical volatility estimate. Higher values mean larger typical day-to-day swings.
Close-to-Close Volatility: Formula, Meaning, Signals, Examples and How to Use It
How Is Close-to-Close Volatility Calculated?
Close-to-close volatility is the sample standard deviation of log returns between successive closing prices, usually annualized. It is the standard historical volatility estimate.
Formula: sigma = sqrt(252) x sqrt( sum of (r_i - mean(r))^2 / (n - 1) ), where r_i = ln(Close_i / Close_(i-1))
Inputs:
- Closing prices
- Window length n
- Annualization factor (commonly 252 trading days)
Worked example. Five daily log returns of 1.0%, -0.5%, 0.8%, -1.2% and 0.4% annualize to 14.7%. The inputs are illustrative numbers, not market data.
Reading it. Higher values mean larger typical day-to-day swings. It is the usual benchmark to compare with implied volatility, and it is only comparable between series using the same window and annualization.
Limits. It uses only closes, so it misses the movement within the day and is less efficient than range-based estimators. Short windows are noisy, and annualizing with the square root of time assumes returns are independent.
What is Close-to-Close Volatility?
Close-to-close volatility is the sample standard deviation of log returns between successive closing prices, usually annualized. It is the standard historical volatility estimate.
How to use Close-to-Close Volatility
Higher values mean larger typical day-to-day swings. It is the usual benchmark to compare with implied volatility, and it is only comparable between series using the same window and annualization. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime.
Strengths
- Log returns make each daily change additive over time, so variance scales with the number of days under the usual assumptions.
- Only closing prices are needed, and these are the most widely and cleanly published prices, so the estimate can be reproduced from almost any source.
- Reproducible when the formula and data convention are fixed.
Weaknesses and limitations
- The n minus 1 divisor makes the variance estimator unbiased but not the standard deviation, so the volatility figure is slightly low on average.
- Each return uses two closes, so a window of n returns needs n plus 1 prices and the first observation is lost.
- Correlated indicators can create false confidence by repeating the same underlying information.
Editorial and risk note
This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance.
Frequently Asked Questions
Is Close-to-Close Volatility a buy or sell signal?
No. Higher values mean larger typical day-to-day swings. It uses only closes, so it misses the movement within the day and is less efficient than range-based estimators. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions.
What is the best setting for Close-to-Close Volatility?
Close-to-Close Volatility takes these inputs: closing prices; window length n; annualization factor (commonly 252 trading days). There is no universal best setting for the tunable ones, so test them across instruments, regimes and out-of-sample periods and favor stable parameter regions over one historical winner.
Can Close-to-Close Volatility be used by itself?
It uses only closes, so it misses the movement within the day and is less efficient than range-based estimators. Short windows are noisy, and annualizing with the square root of time assumes returns are independent. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.
Does Close-to-Close Volatility work on every timeframe?
The calculation (sigma = sqrt(252) x sqrt( sum of (r_i - mean(r))^2 / (n - 1) ), where r_i = ln(Close_i / Close_(i-1))) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it.
Why does Close-to-Close Volatility give false signals?
The n minus 1 divisor makes the variance estimator unbiased but not the standard deviation, so the volatility figure is slightly low on average. Each return uses two closes, so a window of n returns needs n plus 1 prices and the first observation is lost. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.
How should Close-to-Close Volatility be backtested?
Rebuild Close-to-Close Volatility from closing prices using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline.