Standard DeviationSD
Standard deviation measures how widely values spread around their average. In trading it is the standard measure of volatility: the more prices or returns swing away from their mean, the higher the standard deviation and the risk.
When people say an asset is "volatile", they usually mean its standard deviation is high. It is the most common way to put a number on risk, and it sits inside many tools, from Bollinger Bands to the Sharpe ratio. This entry explains what standard deviation measures, how to calculate it step by step and where it falls short.
- Category
- Risk Management
- Reading time
- 4 min
- Also called
- Std dev, Volatility (standard deviation), Sigma
- Updated
Standard deviation in plain words
Standard deviation measures how much values vary or disperse around an average, and in markets it is also a measure of volatility.1
The bigger the spread, the higher the standard deviation; the smaller the spread, the lower it is.1
Bollinger Bands use it directly, with outer bands usually set two standard deviations from the middle band.2
How to calculate standard deviation, step by step
Find the average
Mean of the prices or returns.
Find each deviation
Value minus the average.
Square each deviation
Removes negative signs.
Add them up
Sum of squared deviations.
Divide by the count
This is the variance.
Take the square root
That is the standard deviation.
Worked examples
Example 1 — Five closing prices
σ ≈ $1.41Closes: $10, $12, $11, $13, $9.
| Average | $55 ÷ 5 = $11 |
| Squared deviations | 1 + 1 + 0 + 4 + 4 = 10 |
| Variance | 10 ÷ 5 = 2 |
| Standard deviation | √2 ≈ $1.41 |
The steps — mean, deviations, squares, sum, divide and square root — follow the population formula.1
Example 2 — Comparing two assets
B is riskierBoth average 8% a year. Asset A's returns have a standard deviation of 5%, asset B's 20%.
| Asset A | Steadier |
| Asset B | Four times the spread |
With the same average, the higher standard deviation means larger swings and more risk.1 See Volatility.
Example 3 — Bollinger Bands
$46–$5420-day average $50, standard deviation $2.
| Upper band | $50 + 2 × $2 = $54 |
| Lower band | $50 − 2 × $2 = $46 |
Bollinger Bands place the outer bands two standard deviations from the middle band.2
Standard deviation vs other risk measures
| Aspect | Measures | Limitation |
|---|---|---|
| Standard deviation | All swings, up and down | Treats gains as risk |
| Downside deviation | Losses only | Used in Sortino Ratio |
| Max drawdown | Worst peak-to-trough fall | One event only. See Drawdown |
| ATR | Average daily range | In price, not %. See Average True Range |
Where standard deviation is used
Volatility measurement
Comparing how risky assets are.
Bollinger Bands
Setting band width. See Bollinger Bands.
Sharpe ratio
Return per unit of volatility. See Sharpe Ratio.
Position sizing
Smaller positions in more volatile assets. See Volatility Targeting.
Advantages and disadvantages
Advantages
- Standard, widely understood risk measure.
- Easy to compare across assets.
- Feeds many indicators and ratios.
Disadvantages
- Penalises upside swings as much as downside.
- Assumes a roughly normal distribution.
- Underestimates rare extreme moves.
Going deeper
Read as far as you need. Each level builds on the one before it.
Same units as the data
Beginner
Taking the square root brings the measure back to the original units — dollars for prices, percent for returns.1
The 68–95 rule
Intermediate
In a normal distribution about 68% of values fall within one standard deviation and about 95% within two. Market returns have fatter tails, so extremes happen more often. See Normal Distribution.
Population vs sample
Advanced
StockCharts divides by the number of data points, treating them as the whole population; a sample formula divides by one fewer and gives a slightly larger value.1
Common mistakes
Treating it as downside risk
It counts upside swings too.
Trusting the normal curve
Markets have fat tails. See Black Swan.
Comparing different periods
Use the same window and frequency.
Mixing price and return SD
Return-based SD is comparable across assets.
Check your understanding
Test yourself before moving on. Each answer comes with an explanation.
Key points to remember
- Standard deviation measures spread around an average.
- In trading it is the main measure of volatility.
- It is the square root of the variance.
- It powers Bollinger Bands and the Sharpe ratio.
- It treats upside and downside swings alike.
Frequently asked questions
What is a good standard deviation for a stock?
Is volatility the same as standard deviation?
How is annual volatility calculated?
Further learning
- Volatility
What standard deviation measures.
- Bollinger Bands
An indicator built on it.
- Sharpe Ratio
Return per unit of standard deviation.
- Ulcer Index
A downside-only alternative.
Sources
This article is written in our own words. The sources below support the specific facts, rules and figures marked with a number in the text. Links open the original publisher’s page.
- StockCharts ChartSchool. Standard Deviation (Volatility) (opens in a new tab) Checked .
- StockCharts ChartSchool. Bollinger Bands (opens in a new tab) Checked .
Educational content, not financial advice. Examples use hypothetical prices and simplified costs; actual fees, margin rules and regulations vary by broker, market and country. We are not affiliated with any publisher linked above. Last reviewed . Report an error or request a source credit.