 ## Understanding the Standard Deviation of a Stock

The standard deviation of a stock is a useful tool for investors to use when searching for their ideal stock. Some investors prefer a conservative approach, while others like to take a more aggressive route. The standard deviation helps to point them in the right direction.

A few key concepts to take note of regarding standard deviation are:

• The standard deviation of a stock determines the dispersion of a dataset in relation to its mean.
• A high standard deviation represents volatile stocks, while a low standard deviation usually points to consistent blue-chip stocks.
• The greater the standard deviation, the riskier the stock.

## What Is the Standard Deviation of a Stock?

The standard deviation is a statistical measurement that analyzes the dispersion of a dataset in relation to its mean. It’s quantified as the square root of the variance. To calculate the standard deviation as the square root of the variance, the variation must be evaluated between the various data points in relation to the mean. When the data points are a greater distance from the mean, the dataset has a higher deviation. In other words, the more scattered the data points, the higher the standard deviation.

When using the standard deviation in a financial setting, such as applying it to stock market returns, it can assist in providing insight on past volatility of that stock. When the standard deviation is higher, it points to a larger variance between the stock’s prices and the mean. This points to a more vast price range. For example, a high standard deviation will appear for volatile stocks, while a lower standard deviation is present in stocks that are more consistent

## Calculating the Standard Deviation of a Stock

When calculating the standard deviation, you first need to determine the mean and variance of the stock. To calculate the mean, you add together the value of all the data points and then divide that total by the number of data points.

To determine the variance, you take the mean less the value of the data point and square each individual result. Then you add up the squared results for one single total, which is then divided by the number of data points minus one. This result is known as the square root of the variance. This result is used to calculate the standard deviation. While these calculations can be completed on paper, the easiest way to perform them is by using Excel.

When it comes to stock prices, the data set is viewed in dollars and the variance in dollars squared. The standard deviation comes into play because dollars squared is not a helpful unit of measurement. In calculating the standard deviation of the stock, you get the square root of the variance, which returns the value back to its original form, making the data much easier to apply and evaluate.

## Standard Deviation Risk

When it comes to stock returns and investments, the standard deviation is used to determine market volatility and, therefore, risk. A higher risk stock will demonstrate an unpredictable price and a wider range. Stocks that stick close to their means, or range-bound stocks, are considered lower risk because investors can assume, with a fair amount of confidence, that the stocks practice a consistent behavior. When a stock has a wider range and tends to increase, decrease, or gap unpredictably, it’s viewed as a higher risk stock with the potential for a more significant loss.

While a greater risk can sound intimidating, it’s important to remember that when it comes to the stock market, risk isn’t necessarily a bad thing. The greater a stock’s risk, the greater the possibility of a hefty profit.

The use of standard deviation to determine risk in the stock market is applied assuming that most of the market’s stocks’ price activities follow a normal distribution pattern. When stocks are following a normal distribution pattern, their individual values will place either one standard deviation below or above the mean at least 68% of the time. A stock’s value will fall within two standard deviations, above or below, at least 95% of the time.

For instance, if a stock has a mean dollar amount of \$40 and a standard deviation of \$4, investors can reason with 95% certainty that the following closing amount will range between \$32 and \$48. This also means that 5% of the time, the stock’s price can experience increases or decreases outside of this range. When the stock’s standard deviation is high, it is most likely a highly volatile stock. When its standard deviation is low, it’s usually a reliable blue-chip stock.

In taking all this to mind, investors can assume that a low standard deviation points to a less risky investment, while a greater variance and standard deviation reflects a higher risk stock. While 95% of the time, investors can reasonably assume that a stock’s price will stay within two standard deviations of the mean, this is still a decent-sized range. The key idea to remember is that more potential outcomes, the more potential risk.

## Standard Deviation Investments

Standard deviation in investing usually appears in the likeness of Bollinger bands. Bollinger bands, created by John Bollinger in the 1980s, are a number of lines that assist in determining trends in specific stocks. The exponential moving average (EMA) is found at the center of these trend lines, and it shows the average price of the stock over a given period of time. The lines on both sides of this center range anywhere from one to three standard deviations away from the mean. When the stock’s price changes, the outer trend lines also change with the moving average.

While Bollinger bands can be applied in many useful ways, they are commonly used to determine the market’s volatility. Whenever a stock tends to experience significant volatility, the bands will appear further apart. When the volatility lessens, the bands will fall closer together and appear nearer to the exponential moving average. It’s not uncommon for charts that typically see narrow bands to experience random spikes in volatility — for example, after earnings reports or products are released.

A Bollinger band can be a useful chart in investing because it provides a visualization of the standard deviation and makes the identification of highly volatile stock as easy as a quick glance.

## Applying the Standard Deviation of a Stock

Standard deviation can be used throughout the financial world, but it is especially useful when it comes to investing in stocks and determining trading strategies. The use of standard deviation assists in measuring the volatility of the market and stocks as well as predicting stocks’ performance trends.

When it comes to investing, investors can reasonably expect an index fund to have a low standard deviation because the whole goal of an index fund is to match the index. Conversely, investors can expect an aggressive growth fund to have a higher standard deviation compared to standard stocks because the whole point of these funds is to generate exceptionally high returns.

There isn’t necessarily a better level of standard deviation. Some investors may prefer a low standard deviation, while others are attracted to stocks with a high standard deviation. The preferred standard deviation simply depends on the type of investment investors are looking for as well as the amount of risk they are willing to accept. When it comes to applying the standard deviation of a stock to a portfolio, investors should determine how much volatility they are comfortable with as well as their ultimate investment goals. Aggressive investors are typically more eager to take on high volatility stocks, while the more reserved investors tend to avoid them.

Analysts, advisors, and portfolio managers all use standard deviation as one of their top methods of measuring risk. The standard deviation is also listed by investment firms for their mutual funds and other various products. When a significant dispersion is evident, it means that the stock’s return is not sticking to expectations. The standard deviation is a very simple statistic to understand; therefore, it is commonly reported to investors and end clients.

Author:
Jeff Bishop One of the best traders anywhere, over the past 20 years Jeff’s made multi-millions trading stocks, ETFs, and options. He is renowned as an incredible trader with a deep insight and a sensitive pulse on the markets and the economy. Jeff Bishop is CEO and Co-Founder of RagingBull.com.

Even greater than his prowess as a trader is his skill and passion in teaching others how to trade and rake in profits while managing risk. 