This page is a step-by-step guide how to calculate historical volatility. 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. 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. I mostly use 1 day day-to-day returns , 21 or 63 days representing 1 month or 3 months , and as there are trading days per year on average. It is not as important whether you use 20 or 21 days, or or days. Much more important is that you use the same parameters consistently, so your results will be comparable.
First we need to calculate the continuously compounded return of each period. 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. 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.
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 The result is the annualized volatility. In practice, calculating historical volatility manually would be very lengthy and prone to errors. But it is very easy in Excel. S for sample standard deviation. 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. If you don't agree with any part of this Agreement, please leave the website now. All information is for educational purposes only and may be inaccurate, incomplete, outdated or plain wrong. Macroption is not liable for any damages resulting from using the content. No financial, investment or trading advice is given at any time.
Historical Volatility Calculation This page is a step-by-step guide how to calculate historical volatility. What Historical Volatility Is Mathematically When talking about historical volatility of securities or security prices, we actually mean historical volatility of returns. Deciding the Parameters There are 3 parameters we need to set: Calculating Returns First we need to calculate the continuously compounded return of each period.
Standard Deviation of the Returns Next we need to calculate the standard deviation of the returns we got in step 1. First, calculate the average of the returns we got in step 1: Then, calculate the squared deviation from the average for each of the returns: This is the variance of the returns.
The whole formula therefore is: Annualizing Historical Volatility The only thing left is to annualize the volatility. Calculating Historical Volatility in Excel In practice, calculating historical volatility manually would be very lengthy and prone to errors.More...