What is 'Volatility'

Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security.

In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market. Market volatility can be seen through the VIX or Volatility Index. The VIX was created by the Chicago Board of Options Exchange as a measure to gauge the 30-day expected volatility of the U.S. stock market derived from real-time quote prices of S&P 500 call and put options. It is effectively a gauge of future bets investors and traders are making on the direction of the markets or individual securities. A high reading on the VIX implies a risky market.

A variable in option pricing formulas showing the extent to which the return of the underlying asset will fluctuate between now and the option's expiration. Volatility, as expressed as a percentage coefficient within option-pricing formulas, arises from daily trading activities. How volatility is measured will affect the value of the coefficient used.

 

Breaking Down 'Volatility'

Volatility refers to the amount of uncertainty or risk related to the size of changes in a security's value. A higher volatility means that a security's value can potentially be spread out over a larger range of values. This means that the price of the security can change dramatically over a short time period in either direction. A lower volatility means that a security's value does not fluctuate dramatically, and tends to be more steady.

One measure of the relative volatility of a particular stock to the market is its beta. A beta approximates the overall volatility of a security's returns against the returns of a relevant benchmark (usually the S&P 500 is used). For example, a stock with a beta value of 1.1 has historically moved 110% for every 100% move in the benchmark, based on price level. Conversely, a stock with a beta of .9 has historically moved 90% for every 100% move in the underlying index.

Calculating Volatility

Volatility is often calculated using variance and standard deviation. The standard deviation is the square root of the variance. 

For simplicity, let's assume we have monthly stock closing prices of $1 through $10. For example, month one is $1, month two is $2, and so on. To calculate variance, follow the five steps below.

  1. Find the mean of the data set. This means adding each value, and then dividing it by the number of values. If we add, $1, plus $2, plus $3, all the way to up to $10, we get $55. This is divided by 10, because we have 10 numbers in our data set. This provides a mean, or average price, of $5.50.
  2. Calculate the difference between each data value and the mean. This is often called deviation. For example, we take $10 - $5.50 = $4.50, then $9 - $5.50 = $3.50. This continues all the way down to the our first data value of $1. Negative numbers are allowed. Since we need each value, these calculation are frequently done in a spreadsheet.
  3. Square the deviations. This will eliminate negative values.
  4. Add the squared deviations together. In our example, this equals 82.5.
  5. Divide the sum of the squared deviations (82.5) by the number of data values.

In this case, the resulting variance is $8.25. The square root is taken to get the standard deviation. This equals $2.87. This is a measure of risk, and shows how values are spread out around the average price. It gives traders an idea of how far the price may deviate from the average. 

Variance and standard deviation in Excel.

If prices are randomly distributed (and often they are not), then about 68% off all data values will fall within one standard deviation. 95% of data values will fall within two standard deviations (2 x 2.87 in our example), and 99.7% of all values will fall within three standard deviations (3 x 2.87). In this case, the values of $1 to $10 are not randomly distribute on a bell curve, rather there is a significant upward bias. Therefore, all the values do not fall within three standard deviations. Despite this limitation, standard deviation is still frequently used by traders, as price data sets often contain up and down movements, which resemble more of a random distribution. 

For additional reading, see A Simplified Approach to Calculating Volatility and Option Volatility.

RELATED TERMS
  1. Downside Risk

    Downside risk is an estimate of a security's potential to suffer ...
  2. Historical Volatility - HV

    Historical volatility is a statistical measure of the dispersion ...
  3. Risk Measures

    Risk measures give investors an idea of the volatility of a fund ...
  4. Dispersion

    Dispersion is a statistical term that describes the size of the ...
  5. Variability

    Variability is the extent to which data points in a statistical ...
  6. Portfolio Variance

    Portfolio variance is the measurement of how the actual returns ...
Related Articles
  1. Investing

    Why Standard Deviation Should Matter to Investors

    Think of standard deviation as a thermometer for risk, or better yet, anxiety.
  2. Investing

    Understanding Volatility Measurements

    Learn how to choose a fund with an optimal risk-reward combination. Find more information about standard deviation, beta, and more.
  3. Investing

    Calculating volatility: A simplified approach

    Though most investors use standard deviation to determine volatility, there's an easier and more accurate way of doing it: the historical method.
  4. Trading

    How To Convert Value At Risk To Different Time Periods

    Volatility is not the only way to measure risk. Learn about the "new science of risk management".
  5. Investing

    How Investment Risk Is Quantified

    FInancial advisors and wealth management firms use a variety of tools based in modern portfolio theory to quantify investment risk.
  6. Investing

    3 Reasons to Ignore Market Volatility (VIX)

    If you can keep your head while those about you are losing theirs, you can make a nice return in roiling markets.
  7. Trading

    Implied vs. Historical Volatility: The Main Differences

    Discover the differences between historical and implied volatility, and how the two metrics can determine whether options sellers or buyers have the advantage.
  8. Investing

    SPLV vs. LGLV: Comparing Low-Volatility ETFs

    Discover the major differences between two competitive low-volatility ETFs, and learn why one may be more suitable for your portfolio than the other.
  9. Investing

    3 Cases When Beta Does Not Measure Volatility of Stocks

    Examine the theoretical and statistical relationship between beta and volatility to identify three factors that limit beta's explanatory value.
  10. Investing

    T Rowe Price Capital Appreciation Fund Risk Statistics Case Study (PRWCX)

    Analyze PRWCX using popular risk metrics that are part of modern portfolio theory (MPT). Explore PRWCX's volatility, correlation and return statistics.
RELATED FAQS
  1. What is the difference between standard deviation and variance?

    Understand the difference between standard deviation and variance; learn how each is calculated and how these concepts are ... Read Answer >>
  2. How can you calculate volatility in Excel?

    Historical volatility is a long-term assessment of risk. Here's how to calculate it in Excel. Read Answer >>
  3. What Is the Formula for Calculating Beta?

    Learn about beta, how to calculate it, and how it's used as a risk measure with examples that include Apple and Tesla. Read Answer >>
  4. Is variance good or bad for stock investors?

    Learn how high variance stocks are good for some investors and how diversified portfolios can reduce variance without compromising ... Read Answer >>
  5. How do you calculate variance in Excel?

    To calculate statistical variance in Microsoft Excel, use the built-in Excel function VAR. Read Answer >>
  6. What is the variance/covariance matrix or parametric method in Value at Risk (VaR)?

    Learn about the value at risk and how to calculate the value at risk of an investment portfolio using the variance-covariance, ... Read Answer >>
Trading Center