Is Volatility Standard Deviation? Are They the Same Thing?
The answer is yes and no.
Let's start with what volatility and standard deviation are separately and then we will put them together and compare.
What Volatility Is
In general, volatility is how much something tends to move. It is not necessarily a term limited to finance, but this website is about finance and investing, so I give you an example from the stock market:
Consider two stocks. Stock A usually moves only very little, typically something like 0.5% every day. Of course there are some rare days when it moves more (for example when the company reports its quarterly earnings or when there is a big crash of the whole stock market), but the typical moves for this stock are very small. This stock is said to have low volatility. Another stock (stock B) moves much more – 2 or 3 percent on a typical day and sometimes even more. Stock B is much more volatile than stock A – its volatility is much higher.
There are several different approaches to the exact calculation of volatility. The most popular approach is to calculate volatility as standard deviation of returns, but it is not the only way to do it.
Note: Another quite popular way of calculating volatility (although far less popular than the standard deviation method and used mainly by some volatility traders) is the so called non-centered or zero mean historical volatility. The calculation is very similar to the standard deviation method, but there is a little difference. Both methods are described in the user guide of the Historical Volatility Calculator.
What Standard Deviation Is
Standard deviation is a statistic. It is one of the measures that are used in descriptive statistics to describe dispersion (also called variability) in a data set. It has an exact formula that you use to calculate it. It is the square root of variance, or in other words the square root of the average squared deviation from the mean (if this sounds complicated, see Calculating Variance and Standard Deviation in 4 Easy Steps).
Standard deviation has many advantages (e.g. quite straightforward interpretation) and therefore it is widely used in many disciplines, from natural sciences to the stock market.
Why Volatility Is the Same as Standard Deviation
Standard deviation is the way (historical or realized) volatility is usually calculated in finance. Using the most popular calculation method, historical volatility is the standard deviation of logarithmic returns. Therefore, to some extent, volatility and standard deviation are the same, but...
Why Volatility Is Not the Same as Standard Deviation
The meanings of both volatility and standard deviation reach far beyond the area where the two represent the same thing:
Volatility is not always standard deviation. You can describe and measure volatility of a stock (= how much the stock tends to move) using other statistics, for example daily/weekly/monthly range or average true range. These measures have nothing to do with standard deviation. Standard deviation is only one way of calculating and measuring volatility, but not the only one.
Standard deviation, besides being used in finance as a measure of volatility, is used in virtually every other discipline that works with numbers. Volatility of investment returns is only one use of standard deviation, but not the only one.