Historical Volatility Calculation

This page is a step-by-step guide how to calculate historical volatility. Examples and Excel formulas are available in the Historical Volatility Calculator and Guide.

Although you hear about the concept of historical volatility often, there is confusion regarding how exactly historical volatility is calculated. If you are using several different charting programs, it is quite likely that you will get slightly different historical volatility values for the same security with the same settings with different software. The following is the most common approach – calculating historical volatility as standard deviation of logarithmic returns, based on daily closing prices.

What Historical Volatility Is Mathematically

When talking about historical volatility of securities or security prices, we actually mean historical volatility of returns. It looks like a negligible distinction, but it is very important for the calculation and interpretation of historical volatility. Mathematically, historical volatility is the (usually annualized) standard deviation of returns. If you know how to calculate return in a particular period and how to calculate standard deviation, you already know how to calculate historical volatility. If you’re still not sure, detailed step-by-step guide follows.

Deciding the Parameters

There are 3 parameters we need to set:

I mostly use 1 day (day-to-day returns), 21 or 63 days (representing 1 month or 3 months), and 252 (as there are 252 trading days per year on average).

It is not as important whether you use 20 or 21 days, or 252 or 262 days. Much more important is that you use the same parameters consistently, so your results will be comparable.

Step 1: Calculating Returns

First we need to calculate the continuously compounded return of each period. In our case, we will calculate the day-to-day returns for each of the 21 days (our n=21):

Historical Volatility Formula 1

ln = natural log
Cn = closing price
Cn-1 = previous day closing price

Step 2: Standard Deviation of the Returns

Next we need to calculate the standard deviation of the returns we got in step 1. Standard deviation is the square root of variance, which is the average squared deviation from the mean (if you are not familiar with it, here you can see a detailed explanation of variance and standard deviation calculation).

First, calculate the average of the returns we got in step 1:

Historical Volatility Formula 2

Then, calculate the squared deviation from the average for each of the returns:

Historical Volatility Formula 3

Calculate the average of the squared deviations by summing them up and dividing by n-1 (in our case 21 – 1 = 20). We are dividing by n-1 rather than n, as we are calculating sample standard deviation (we are estimating the standard deviation from a sample – if not familiar, see the difference between population and sample standard deviation).

Historical Volatility Formula 4

Note: This is the variance of the returns.

Calculate standard deviation = square root of variance. The whole formula therefore is:

Historical Volatility Formula 5

Note: It may look scary, but we have just added a square root to the previous formula.

The number we got now (σ) is 1-day historical volatility.

Annualizing Historical Volatility

The only thing left is to annualize the volatility. We do that by multiplying the 1-day volatility by the square root of the number of (trading) days in a year – in our case square root of 252. The result is the annualized volatility.

Calculating Historical Volatility in Excel

In practice, calculating historical volatility manually would be very lengthy (and prone to errors). But it is very easy in Excel. In fact, you do the whole step 2 with the standard deviation function (use STDEV.S for sample standard deviation).

Historical Volatility Calculator

You can download the Historical Volatility Excel Calculator from sesyixo.ru. Besides the most popular HV calculation method described above, the calculator can also calculate HV using two other, alternative methods, including the zero mean (or non-centered) method. There is a user guide that comes with the calculator, which explains all the calculations in more detail.

Get the Historical Volatility Calculator + Guide now


Related pages


how do i buy the vixparametric varoption greek calculatordj euro stoxx 50 historical pricessec 13f faqinterpret skewness and kurtosisshort the vixstandard deviation multiplicationcontango curvefree black scholes calculatorvolatility calculatormedian advantages and disadvantagesetc etfarithmetic basicscoloured notepadstock calculator excelvix quoteskurtosis coefficientdiv yield formulablack scholes gammalong straddle exampledefine option contractwhat is macd histogramarithmetic formulas in excelsharpe ratio interpretationall etf listadvantages and disadvantages of mean median and modecost of ending inventory formulayahoo finance download csvrsi calculation excelnotepad color codeswhat is the formula for standard deviation in excelhow to plot break even graph in excelhow to calculate variance excelfutures vs options differenceshort payoffleptokurtic platykurticstandard deviation calcweighted percentage calculatorxl formulass&p etf shorthow is the dividend yield calculateddow jones highest ever closingnatural log in excel13 f filingscalculating the variance in excelvolatility etnvelocityshares daily inverse vixpopulation mean and standard deviation calculatorwhat does bearish and bullish mean in stocksdefinition of skewness and kurtosishow to trade vix futuresroot excel formulastock price volatility calculatorvxv etfsec form 13 fcentral tendency excelaverage of percentages calculatorexcel standard deviation formulacalculate variance on excelrho option2x s&p 500 etfformula for profit and loss in exceldays calculator excelnotepad background colorotm stockwhat is the formula for variance in excelshorting a put optionhow to calculate arithmetic average returnsample mean calculatorsortino ratio formula