Wednesday, 3 February 2016

How is Daily & Historical volatility calculated?

Understand Volatility

The most important parameter “Volatility” in the trading and investment is often neglected by the traders. Only few statistical indicators in the technical study consider the volatility as a key parameter in their combination. Volatility also informs well in advance how the price is going to behave in the near future. The dynamic price action of a financial instrument whether it is a stock or currency or future always follows the internal volatility in it.

The most appropriate and common definition I have derived for the volatility is, “The annualized standard deviation of the price change”. The standard deviation is a statistical calculation and most beautiful work available in the branch of statistics.

At this point you may ask “How the volatility is going to bother you?” Volatility in the financial mathematics is often treated as a discouraging word. The financial translation of the word volatility says, “The risk associated in the investment over a particular time”. When the analyst in the business channel broadcast the news that market is currently volatile we all anticipate something risky. The most general view the trader concludes that “doing the business in the stock or in the financial instrument will increase the risk of failure”. However the fact and the truth reveals that none of those broadcasters have an appropriate scale to measure and inform us a correct number on volatility before pressing the panic button.

Volatility is classically defined as a powerful untrained horse which has all capacity to win the race if trained properly. Same time the powerful horse has the capacity to kill his rider if not guided properly.

Definition of volatility - “it is the risk associated with the price at a particular time”
Mathematical definition - “the annualized standard deviation of the price change”


How to calculate volatility?

1. Estimating the volatility based on the periodic return: In this method we need to calculate the periodic return of the price change and calculate the daily volatility using the standard deviation formula. Below are the steps involved in calculating the daily volatility based on the periodic return. 
I have calculated volatility for NIFTY on 02/02/2016 based on past 1 month data from 01/01/2016 till 02/02/2016. We would compare our manually calculated volatility with NSE NIFTY volatility at the end.

Step 1 :- Find the periodic return by using LN (current price/previous price) as shown in image below
Daily-and-historical-Volatility-Calculation

Continue to calculate log returns till the end 
Daily-and-historical-Volatility-Calculation

Step 2 :- Take periodic return square as shown below 
Daily-and-historical-Volatility-Calculation

Continue to calculate log returns till the end as shown below 
Daily-and-historical-Volatility-Calculation


 Step 3:-  Arithmetic average of the periodic return
Daily-and-historical-Volatility-Calculation

Step 4 :-  Arithmetic average of the square periodic return

Daily-and-historical-Volatility-Calculation



Step 5 :- Variance= Arithmetic average of the square periodic return- (Arithmetic average of the periodic return)2 
Daily-and-historical-Volatility-Calculation

Step 6 :- Daily volatility = Square root of (Variance) 
How-to-calculate-daily-volatility

Step 7 :- Annual volatility = daily volatility X square root of (Number of days in a year)
How-To-calculate-historical-volatility

Final Calculation as shown below
Daily-and-historical-volatility

NSE NIFTY Volatility shown in below image as on 02/02/2016



If you observe our calculation for Daily Volatility i.e 1.044 vis-a-vis Nifty Daily volatility i.e 1.05 , it is almost similar and 
Manually Historical Volatility calculated i.e 19.96 vis-a-vis NIFTY annualised volatility i.e 20 is the same , if we round off 19.96 to nearest value.

You may also download the excel sheet below for your future reference

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3 comments:

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  3. One comment that I have is the number of days for annual volatility.
    Since weekend and no-trading days are not included, it should be 252 instead of 365.

    ReplyDelete