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Volatility Explained: Standard Deviation, Beta and the VIX

Volatility measures how much prices swing. How standard deviation captures it, what beta compares, what the VIX measures, and why volatility is not loss.

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Key takeaways

  • Volatility is how much and how quickly a price moves up and down; a volatile stock has larger swings.
  • The usual measure is the standard deviation of returns, which shows how spread out returns are around their average.
  • Beta compares a stock's past movements with the market's: above 1 means it has tended to swing more than the market, below 1 less.
  • The Cboe Volatility Index, or VIX, measures the market's expectation of near-term volatility in the S&P 500, derived from option prices.
  • Volatility is not the same as loss: it describes the size of swings in both directions, but larger swings do make big losses more likely over a short period.

"Volatile" turns up constantly in market news, but it has a precise meaning: how much, and how quickly, a price moves up and down. A volatile stock makes larger swings, in both directions. Measuring that, and understanding what the measures do and do not say, is the basis for thinking about risk.

Standard deviation: the usual measure

The standard measure of volatility is the standard deviation of returns. OpenStax's Introductory Statistics describes standard deviation as the most common measure of variation, a number that measures how far data values are from their mean: small when values cluster near the average, larger when they are spread out.

A small example. Two stocks each have an average daily return of 0.1% over a week.

Day Stock A Stock B
1 +0.4% +3.0%
2 −0.2% −2.6%
3 +0.3% +2.4%
4 −0.1% −2.9%
5 +0.1% +0.6%

Both average +0.1% a day, but B's returns are scattered much further from that average, so B has a far higher standard deviation, and is far more volatile. A week like B's is what a "volatile stock" feels like: the same average path, with much larger swings around it.

Historical and implied. Volatility calculated from past returns is historical volatility. Implied volatility is inferred from option prices and reflects the volatility the market expects; options are covered in call and put options.

Beta: volatility relative to the market

Beta compares a stock's past movements with a benchmark index:

  • Beta of 1: the stock has tended to move in line with the market.
  • Beta above 1: it has tended to move more. A beta of 1.5 means it rose about 1.5% on average when the market rose 1%, and fell about 1.5% when it fell 1%.
  • Beta below 1: it has tended to move less.

Beta measures only the part of a stock's swings that comes with the market's, sometimes called market or systematic risk; it says nothing about company-specific surprises. It is calculated from past data and can change. FINRA's guide to market capitalisation adds a related tendency: large-cap companies tend to be less vulnerable to market ups and downs than mid-caps, and mid-caps less than small-caps, a generalisation it says is no guarantee for any particular company.

The VIX: expected volatility

Cboe describes the Cboe Volatility Index (VIX) as a leading measure of market expectations of near-term volatility conveyed by S&P 500 index option prices, introduced in 1993. Because it is built from option prices, it is forward-looking: it reflects what option traders are paying for protection, not what has already happened.

Cboe also notes that the VIX has historically had a strong inverse relationship with the S&P 500: it tends to rise when stocks fall. Cboe itself says the VIX is considered by many to be a premier barometer of investor sentiment. VIX futures and options exist, but Cboe stresses that they have unique characteristics, behave differently from other products and need to be understood before use.

Volatility is not the same as loss

A volatile stock swings both ways. Volatility measures the size of the moves, not their direction, so a highly volatile stock can rise a lot as well as fall a lot. But volatility still matters for anyone with money at stake:

  • Short horizons. The larger the swings, the more likely a big fall happens just when you need to sell. Risk tolerance and time horizon looks at this trade-off.
  • Borrowed money. In a margin account, a volatile stock can trigger a margin call on an ordinary bad week.
  • Stop orders. The SEC warns that a short-term intraday price move can trigger a stop order at a price well below the day's close, and larger swings make such moves more likely.

Volatility can be reduced at the portfolio level by holding investments that do not all move together, the idea behind diversification, though market-wide volatility cannot be diversified away.

Seeing volatility in practice

A chart of a volatile stock looks jagged. Learn to Trade Stocks Beginner lets you step through simulated price action with its chart replay and a virtual balance, and its lessons cover risk alongside orders and portfolios. It is one of our education apps, and the statistics behind spread and probability are explained further in our guide to the binomial distribution. The investing basics hub lists the related guides.

Good to know

Frequently asked questions

What is volatility in stocks?
How much a stock's price moves up and down over a period. A stock whose daily moves are often 4% or 5% is more volatile than one that rarely moves more than 1%. Volatility describes the size of the swings, not their direction.
How is volatility measured?
Most commonly by the standard deviation of returns, a statistical measure of how far values are spread from their average. Historical volatility uses past returns; implied volatility is inferred from option prices and reflects expected future movement.
What does a beta of 1.5 mean?
That over the period measured, the stock tended to move about 1.5 times as much as its benchmark index, in the same direction: up about 1.5% on average when the market rose 1%. Beta is calculated from past data and can change.
What is the VIX?
The Cboe Volatility Index, which Cboe describes as a measure of market expectations of near-term volatility conveyed by S&P 500 index option prices. Cboe notes it has had a historically strong inverse relationship with the S&P 500, so it has tended to rise when stocks fall.

Sources

  1. VIX Volatility Products (opens in a new tab)Cboe Global Markets — accessed
  2. 2.7 Measures of the Spread of the Data (Introductory Statistics 2e) (opens in a new tab)OpenStax — accessed
  3. Beta (finance) (opens in a new tab)Wikipedia — accessed
  4. Market Cap Explained (opens in a new tab)FINRA — accessed
  5. Stop, Stop-Limit, and Trailing Stop Orders – Investor Bulletin (opens in a new tab)Investor.gov, U.S. Securities and Exchange Commission — accessed

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