What is 'Standard Deviation'
The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. It is calculated as the square root of variance by determining the variation between each data point relative to the mean. If the data points are further from the mean, there is higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.
In finance, standard deviation is a statistical measurement; when applied to the annual rate of return of an investment, it sheds light on the historical volatility of that investment. The greater the standard deviation of a security, the greater the variance between each price and the mean, which shows a larger price range. For example, a volatile stock has a high standard deviation, while the deviation of a stable bluechip stock is usually rather low.
BREAKING DOWN 'Standard Deviation'
In the financial services industry, standard deviation is one of the key fundamental risk measures that analysts, portfolio managers, wealthmanagement advisors and financial planners use. Investment firms report the standard deviation of their mutual funds and other products. A large dispersion shows how much the return on the fund is deviating from the expected normal returns. Because it is easy to understand, this statistic is regularly reported to the end clients and investors.
What's the Difference Between Standard Deviation and Mean?
In its simplest form, the mean is the average of all the data points in a set. In investing, for example, you might want to know the mean closing price for the last 20 days. You can find this by adding the closing prices for each session and dividing by 20. Because markets are fickle, traders and analysts use moving averages that adjust daily to incorporate the most recent data. This means the calculation is always considering the most recent sessions' movements, and older sessions drop off as they become less relevant. One can calculate an exponential moving average by weighting each data point, giving greater significance to more recent data.
Standard deviation is calculated based on the mean. The distance of each data point from the mean is squared, summed and averaged to find the variance. Or to put it another way: Variance is derived by taking the mean of the data points, subtracting the mean from each data point individually, squaring each of these results and then taking another mean of these squares. Standard deviation is the square root of the variance.
Calculating a Standard Deviation
The formula for standard deviation uses three variables. The first variable is to be the value of each point within the data set, traditionally listed as x, with a subnumber denoting each additional variable (x, x1, x2, x3, etc.). The mean, or average, of the data points is applied to the value of the variable M, and the number of data points involved is assigned to the variable n.
To determine the mean value, you must add the values of the data points together, and then divide that total by the number of data points included. For example, if the data points were 5, 7, 3 and 7, the total would be 22. You would then divide 22 by the number of data points, in this case four, resulting in a mean of 5.5. This leads to the following determinations: M = 5.5 and n = 4.
The variance is determined by subtracting the value of the mean from each data point, resulting in 0.5, 1.5, 2.5 and 1.5. Each of those values are then squared, resulting in 0.25, 2.25, 6.25 and 2.25. The square values are then added together, resulting in a total of 11, which is then divided by the value of n1, which is 3 in this instance, resulting in a variance approximately of 3.67.
The square root of the variance is then calculated, which results in a standard deviation measure of approximately 1.915.
Standard Deviation vs. Variance
The variance helps determine the data's spread size when compared to the mean value. As the variance gets bigger, more variation in data values occurs, and there may be a larger gap between one data value and another. If the data values are all close together, the variance will be smaller. This is more difficult to grasp than are standard deviations, however, because variances represent a squared result that may not be meaningfully expressed on the same graph as the original dataset.
Standard deviations are usually easier to picture and apply. The standard deviation is expressed in the same unit of measurement as the data, which isn't necessarily the case with the variance. Using the standard deviation, statisticians may determine if the data has a normal curve or other mathematical relationship. If the data behaves in a normal curve, then 68 percent of the data points will fall within one standard deviation of the average, or mean data point. Bigger variances cause more data points to fall outside the standard deviation. Smaller variances result in more data that is close to average.
What's Standard Deviance Used For?
Standard deviation is an especially useful tool in investing and trading strategies as it helps measure market and security volatility – and predict performance trends.
As it relates to investing, for example, one can expect an index fund to have a low standard deviation versus its benchmark index, as the fund's goal is to replicate the index. On the other hand, one can expect aggressive growth funds to have a high standard deviation from relative stock indices, as their portfolio managers make aggressive bets to generate higherthanaverage returns.
A lower standard deviation isn't necessarily preferable. It all depends on the investments one is making, and one's willingness to assume risk. When dealing with the amount of deviation in their portfolios, investors should consider their personal tolerance for volatility and their overall investment objectives. More aggressive investors may be comfortable with an investment strategy that opts for vehicles with higherthanaverage volatility, while more conservative investors may not.

Variance
Variance is the spread between numbers in a data set and their ... 
Standard Error
Standard error is the standard deviation of a sample population. 
Variance Swap
A variance swap allows counterparties to hedge or speculate directly ... 
Residual Standard Deviation
The residual standard deviation is a statistical term used to ... 
Sales Price Variance
Sales price variance is the difference between the money a business ... 
Risk Measures
Risk measures give investors an idea of the volatility of a fund ...

Trading
Exploring the Exponentially Weighted Moving Average
Learn how to calculate a metric that improves on simple variance. 
Investing
Two Approaches to Building a LowRisk Portfolio
Building a portfolio consisting of lowrisk assets is achieved primarily by using one of two principal lowvolatility strategies. 
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. 
Investing
Financial Ratios Every Investor Should Know
Explore the risk metrics of mutual fund DODFX. Learn how beta, Rsquared, capture ratios and standard deviation measure systematic and volatility risk. 
Insights
Simulating stock prices using excel
Here, we'll use the average of the change in log prices, volatility, normal distribution and Excel to formulate the future prices of an asset. This can amount to a very valuable tool for investors ... 
Investing
FKINX: A Risk Statistics Case Study
Examine important risk metrics for mutual fund FKINX. Discover what beta, standard deviation and Rsquared say about volatility and systematic risk. 
Financial Advisor
Does Your Investment Manager Measure Up?
These key stats will reveal whether your advisor is a league leader or a benchwarmer. 
Investing
5 Ways to Rate Your Portfolio Manager
These five performance ratios will help you measure how good your money manager is at increasing the value of your portfolio. 
Investing
Apple Could Fall By 10 Percent Based On Options
Weak demand for the new iPhone 8 is putting the squeeze on Apple's stock. 
Investing
VHT vs. XLV: Comparing Health Care ETFs
Compare two of the top health care ETFs, the Vanguard Health Care ETF and the SPDR Health Care ETF, and find out which one is a better investment.

What is the difference between standard deviation and average deviation?
Understand the basics of standard deviation and average deviation, including how each is calculated and why standard deviation ... Read Answer >> 
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 >> 
What is the difference between standard deviation and z score?
Understand the basics of standard deviation and Zscore; learn how each is calculated and used in the assessment of market ... Read Answer >> 
How is risk aversion measured in Modern Portfolio Theory (MPT)?
Find out how risk aversion is measured in modern portfolio theory (MPT), how it is reflected in the market and how MPT treats ... Read Answer >> 
How do you calculate variance in Excel?
To calculate statistical variance in Microsoft Excel, use the builtin Excel function VAR. Read Answer >> 
What is the best measure of a stock's volatility?
Understand what metrics are most commonly used to assess a security's volatility compared to its own price history and that ... Read Answer >>