Is Volatility and Standard Deviation the Same?

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 PDF 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.


Related pages


atr indicator explainedetf correlation calculatorberkshire hathaway hedge fundjohn c hull solutionsblack scholes options pricingcalculating weighted percentagesfx formula in exceltrading option greeksgeometric average return formulaexcel formulas for calculationcalculating annualised returnsharpe nobel prizehow to calculate the coefficient of skewnessstatistics calculator standard deviationdefine skewness and kurtosisvix term structure cboespx options settlementstock price volatility calculatorblack scholes theoreminverse volatility etfexcel standard deviation calculationunderstanding black scholesbsm option pricing modelhow to calculate intrinsic value of a stock using excel13f securitiesweighted average inventory calculatorswiss franc etfhow to use normdist function in exceloptions expirationsarithmetic mean formula for grouped datahow to trade the vixvix 3x etfhow to trade vix futuresstandard deviation formula for excelspy historical returnsblack scholes stock option calculatorbsm modelstoxx 50 europekurtosis calculatorblack scholes option pricing model excelproshares short s&p 500vix index historical datadefinition of sharpe ratiosample variance formula for grouped datafx option pricermacd 2 linesmoothed rsigeorge soros 13fs&p 500 vix short-term futurescolor notepadexcel formula explanationsblack scholes tablefifo and weighted averagemean deviation calculatorkurtosis formula in statisticssma emasquared deviation calculatorhow to manually calculate standard deviationspy historical returnsstandard error of skewnessexcel sample meancboe definitionderivation of variance formulashorting putslatest 13f filingsberkshire hathaway 13f filingcall option implied volatilitytheta black scholesblack shoals modelcompute sample covariancevix short term futuresvxv etfblack scholes excel formulawacc formula with preferred stockrsi indicator pdfrealized yield calculatortheta optionyahoo finance quotes csvdefine contango