No Session Today
View all rates
Intermediate3 min readRisk and Portfolio Management · 9/11

Volatility: How Standard Deviation Measures It

Two stocks can end the week at the same result, one quietly and the other with violent daily swings. Standard deviation is a number that measures that difference.

What you will learn

  • See why the average move alone hides the bumps.
  • Follow the idea behind standard deviation with a simple example.
  • Know how to read the number and its limits.
The lesson as a short video · 20 seconds · Watch on YouTube
In this lesson
  1. The average hides the bumps
  2. The idea behind the calculation
  3. How to read the number
  4. Check yourself
  5. Summary
  6. Related terms

The average hides the bumps

If I tell you a stock's average weekly move was zero, it could be a stock that barely moved, or one that jumped up and down violently every day. Volatility is the word for how far the daily moves stray from that average.

Calm stockStandard deviation 1%
+1%
-1%
+1%
-1%
0%
Volatile stockStandard deviation 3%
+3%
-3%
+3%
-3%
0%
Five trading days; the average move is zero in both
The same average move, but the second stock's daily moves stray much further from it.

The idea behind the calculation

  1. Find the averageThe average of the daily moves over the period.
  2. See how far each day isThe difference between each day's move and the average.
  3. Square the differences and average themSquaring treats negative gaps like positive ones and gives more weight to big moves.
  4. Take the square rootSo the number returns to the same unit as the moves: a percentage.
A worked exampleThe calm stock moved +1%, -1%, +1%, -1% and 0%. The average is zero and the squared gaps sum to 4. The volatile stock moved +3%, -3%, +3%, -3% and 0%, with squares summing to 36. For a sample standard deviation we divide by the number of days minus one, 4, and take the root: a standard deviation of 1% for the first and 3% for the second.

So the dispersion of the second stock's daily returns, measured by standard deviation, is about three times the first. That does not say which stock is better; it says the second is a rougher ride and usually needs a wider stop and a smaller position to keep the risk in pounds close to the first.

How to read the number

You will sometimes see volatility marked "annualised", converted to a yearly scale to make comparison easier. What matters is comparing figures calculated the same way over the same period.

Watch outStandard deviation is calculated from the past; a stock can be calm for months and then swing hard on sudden news. Very large moves also happen in markets more often than this number might suggest.

See volatility on funds

Each fund page on FoudaLens shows volatility next to returns. Compare two funds and look at both numbers together.

Investment funds

Check yourself

1. Two stocks share the same average move. One has a standard deviation of 1%, the other 4%. What does that mean?

The number measures the spread of moves, not their direction or the stock's quality.

2. Why are the differences squared?

Without squaring, gaps above and below the average cancel out.

Summary

  • The average move alone can hide a stock that swings violently.
  • Standard deviation measures how far moves typically stray from their average.
  • It comes from the past; compare it only with figures calculated the same way over the same period.

Related terms

Stop lossNet asset value

Related lessons

Technical IndicatorsThe ATR Indicator: Measuring Price Volatility
Previous · 08Beta and Market RiskNext · 10Maximum Drawdown: The Worst Fall a Portfolio Went Through

Educational content only, not investment advice. Companies and figures in the examples are invented for illustration.