Direct Answer
Variance is the average squared deviation of values from their mean. It is the square of standard deviation and is additive across independent sources, which is why it is the basis of many volatility models. Larger variance means a wider spread around the mean.
Variance: Formula, Meaning, Signals, Examples and How to Use It
How Is Variance Calculated?
Variance is the average squared deviation of values from their mean. It is the square of standard deviation and is additive across independent sources, which is why it is the basis of many volatility models.
Formula: s^2 = sum of (x_i - mean)^2 / (n - 1) for a sample; divide by n for a population
Inputs:
- A series of values (returns or prices)
- Window length n
- Sample or population convention
Worked example. The values 3, 5, 7 and 9 have a mean of 6 and a sample variance of 6.67. The inputs are illustrative numbers, not market data.
Reading it. Larger variance means a wider spread around the mean. Its units are squared, so it is hard to read directly; the square root, standard deviation, is the version in the data's units. Variance scales linearly with time for independent returns.
Limits. Squaring makes it very sensitive to outliers and expresses risk in squared units. It treats gains and losses symmetrically, and sample versus population conventions give different numbers for small windows.
What is Variance?
Variance is the average squared deviation of values from their mean. It is the square of standard deviation and is additive across independent sources, which is why it is the basis of many volatility models.
How to use Variance
Larger variance means a wider spread around the mean. Its units are squared, so it is hard to read directly; the square root, standard deviation, is the version in the data's units. Variance scales linearly with time for independent returns. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime.
Strengths
- Because variances of independent components add, a total can be decomposed into contributions from separate sources.
- The N minus 1 form is an unbiased estimator of the population variance, so averages across many windows center on the true value.
- Reproducible when the formula and data convention are fixed.
Weaknesses and limitations
- A change of price units by a factor of 10 changes variance by a factor of 100, so values are hard to compare across instruments.
- Two windows with the same variance can arise from many moderate moves or a few large ones, so the figure does not describe the typical move.
- 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 Variance a buy or sell signal?
No. Larger variance means a wider spread around the mean. Squaring makes it very sensitive to outliers and expresses risk in squared units. 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 Variance?
Variance takes these inputs: a series of values (returns or prices); window length n; sample or population convention. 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 Variance be used by itself?
Squaring makes it very sensitive to outliers and expresses risk in squared units. It treats gains and losses symmetrically, and sample versus population conventions give different numbers for small windows. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.
Does Variance work on every timeframe?
The calculation (s^2 = sum of (x_i - mean)^2 / (n - 1) for a sample; divide by n for a population) 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 Variance give false signals?
A change of price units by a factor of 10 changes variance by a factor of 100, so values are hard to compare across instruments. Two windows with the same variance can arise from many moderate moves or a few large ones, so the figure does not describe the typical move. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.
How should Variance be backtested?
Rebuild Variance from a series of values (returns or 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.