When selecting a security for investment, traders look at its historical volatility to help determine the relative risk of a potential trade. Numerous metrics measure volatility in differing contexts, and each trader has their favorites. A firm understanding of the concept of volatility and how it is determined is essential to successful investing.

The most simple definition of volatility is a reflection of the degree to which price moves. A stock with a price that fluctuates wildly—hits new highs and lows or moves erratically—is considered highly volatile. A stock that maintains a relatively stable price has low volatility. A highly volatile stock is inherently riskier, but that risk cuts both ways. When investing in a volatile security, the chance for success is increased as much as the risk of failure. For this reason, many traders with a high-risk tolerance look to multiple measures of volatility to help inform their trade strategies.

### Key Takeaways

- Volatility refers to how quickly markets move, and it is a metric that is closely watched by traders.
- More volatile stocks imply a greater degree of risk and potential losses.
- Standard deviation is the most common way to measure market volatility, and traders can use Bollinger Bands to analyze standard deviation.
- Maximum drawdown is another way to measure stock price volatility, and it is used by speculators, asset allocators, and growth investors to limit their losses.
- Beta measures volatility relative to the stock market, and it can be used to evaluate the relative risks of stocks or determine the diversification benefits of other asset classes.
- The CBOE Volatility Index (VIX) is a common metric used to measure the expected volatility of the S&P 500.
- Investors can hedge to minimize the impact volatility has on their portfolio, or they can embrace volatility and seek to profit from price swings.

#### Calculating Volatility with Average True Range

## Standard Deviation

The primary measure of volatility used by traders and analysts is the standard deviation. This metric reflects the average amount a stock's price has differed from the mean over a period of time. It is calculated by determining the mean price for the established period and then subtracting this figure from each price point. The differences are then squared, summed, and averaged to produce the variance. The formula for standard deviation is as follows:

$\begin{aligned}&\text{Standard Deviation}=\sqrt{\frac{\sum^n_{i=1}(x_i-\bar{x})^2}{n-1}}\\&\textbf{where:}\\&x_i=\text{Value of the }i^{th}\text{ point in the data set}\\&\bar{x}=\text{The mean value of the data set}\\&n=\text{The number of data points in the data set}\end{aligned}$

The standard deviation is calculated in a few steps:

- Find the mean of all data points by adding all data points and dividing by the number of data points.
- Find the variance of each data point by subtracting each data point from the mean (from Step 1.)
- Square each variance, then add all squared variances together.
- Divide the sum of squared variances (from Step 3) by one less than the number of data points.
- Take the square root of the variance (from Step 4); this is the standard deviation.

Because the variance is the product of squares, it is no longer in the original unit of measure. Since price is measured in dollars, a metric that uses dollars squared is not very easy to interpret. Therefore, the standard deviation is calculated by taking the square root of the variance, which brings it back to the same unit of measure as the underlying data set.

Although other volatility metrics are discussed in this article, the standard deviation is by far the most popular. When people say volatility, they usually mean standard deviation.

Chartists use a technical indicator called Bollinger Bands to analyze standard deviation over time. Bollinger Bands are comprised of three lines: the simple moving average (SMA) and two bands placed one standard deviation above and below the SMA. The SMA is essentially a smoothed-out version of the stock's historical price, but it is slower to respond to changes.

The outer bands mirror those changes to reflect the corresponding adjustment to the standard deviation. The standard deviation is shown by the width of the Bollinger Bands. The wider the Bollinger Bands, the more volatile a stock's price is within the given period. A stock with low volatility has very narrow Bollinger Bands that sit close to the SMA.

In the example above, a chart of Snap Inc. (SNAP) with Bollinger Bands enabled is shown. For the most part, the stock traded within the tops and bottoms of the bands over a six-month range. The price was between about $12 and $18 per share. Bollinger Bands are often used as an indicator of the range a security trades between, with the upper band limit indicating a potentially high price to sell at, and the lower band limit indicating a potential low price to buy at.

Because most traders are most interested in losses, downside deviation is often used that only looks at the bottom half of the standard deviation.

## Maximum Drawdown

Another way of dealing with volatility is to find the maximum drawdown. The maximum drawdown is usually given by the largest historical loss for an asset, measured from peak to trough, during a specific time period. In other situations, it is possible to use options to make sure that an investment will not lose more than a certain amount. Some investors choose asset allocations with the highest historical return for a given maximum drawdown.

The value of using maximum drawdown comes from the fact that not all volatility is bad for investors. Large gains are highly desirable, but they also increase the standard deviation of an investment. Crucially, there are ways to pursue large gains while trying to minimize drawdowns.

### Maximum Drawdown Quote

A maximum drawdown may be quoted in dollars or as a percentage of the peak value. When comparing securities, understand the underlying prices as dollar maximum drawdowns may not be a fair comparable base.

Many successful growth investors, such as William J. O'Neil, look for stocks that go up more than the market in an uptrend but stay steady during a downtrend. The idea is that these stocks remain stable because people hold on to winners despite minor or temporary setbacks.

A stop-loss order is another tool commonly employed to limit the maximum drawdown. In this case, the stock or other investment is automatically sold when the price falls to a preset level. However, gaps can occur when the price moves too quickly. Price gaps may prevent a stop-loss order from working in a timely way, and the sale price might still be executed below the preset stop-loss price.

## Beta

Beta measures a security's volatility relative to that of the broader market. A beta of 1 means the security has a volatility that mirrors the degree and direction of the market as a whole. If the S&P 500 takes a sharp dip, the stock in question is likely to follow suit and fall by a similar amount.

Relatively stable securities, such as utilities, have beta values of less than 1, reflecting their lower volatility as compared to the broad market. Stocks in rapidly changing fields, especially in the technology sector, have beta values of more than 1. These types of securities have greater volatility.

A beta of 0 indicates that the underlying security has no market-related volatility. Cash is an excellent example if no inflation is assumed. However, there are low or even negative beta assets that have substantial volatility that is uncorrelated to the stock market.

The beta of the S&P 500 index is 1. A higher beta indicates that when the index goes up or down, that stock will move more than the broader market.

## Is High or Low Volatility Better for Stocks?

Many day traders like high volatility stocks since there are more opportunities for large swings to enter and exit over relatively short periods of time. Long-term buy-and-hold investors, however, often prefer low volatility where there are incremental, steady gains over time. In general, when volatility is rising in the stock market, it can signal increased fear of a downturn.

## What Is Considered Average Stock Volatility?

When looking at the broad stock market, there are various ways to measure the average volatility. When looking at beta, since the S&P 500 index has a reference beta of 1, then 1 is also the average volatility of the market.

On an absolute basis, investors can look to the CBOE Volatility Index, or VIX. This measures the average volatility of the S&P 500 on a rolling three-month basis. Some traders consider a VIX value greater than 30 to be relatively volatile and under 20 to be a low volatility environment. The long-term average for the VIX has been just over 20.

## How Can I Trade Changes in Volatility?

For those looking to speculate on volatility changes, or to trade volatility instruments to hedge existing positions, you can look to VIX futures and ETFs. In addition, options contracts are priced based on the implied volatility of stocks (or indices), and they can be used to make bets on or hedge volatility changes.

## Why Is Stock Volatility Important?

The volatility of a stock (or of the broader stock market) can be seen as an indicator of fear or uncertainty. Prices tend to swing more wildly (both up and down) when investors are unable to make good sense of the economic news or corporate data coming out. An increase in overall volatility can thus be a predictor of a market downturn. Volatility is also a key component for pricing options contracts.

## How Do You Find the Implied Volatility of a Stock?

Implied volatility is determined using computational models such as the Black-Scholes Model or Binomial Model. These models identify factors that may impact an equity's future price, determine outcome likelihoods, and price derivative products like options based on their findings.