A Study on the Historical Volatility of Various Indices over a Period of Time in the Indian Stock Market with Reference to National Stock Exchange

Volatility is the fluctuation that is present in the time-series of stock prices. Volatility is an abstract concept. Historical volatility is the realized volatility. Historical volatility is the actual price fluctuation of the stocks in the past. The main objective of this paper is to estimate the historical volatility (both intraday and entire series) of various indices in National Stock Exchange namely CNX Bank, S&P CNX Nifty, S&P CNX Defty, CNX Nifty Junior and Nifty Midcap50. Historical volatility is calculated over a period of 6 years 3 quarters from Jan 1^st 2006 to Sep 30^st 2012 for the indices CNX Bank, S&P CNX Nifty, S&P CNX Defty, and CNX Nifty Junior. Historical volatility is computed for the index Nifty Midcap 50 over a period of 5 years from Oct 1^st 2007 to Sep 30^st 2012 because of non-availability of open, high, low prices for the period Jan 1^st 2006 to Sep 30^st 2007 for Nifty Midcap 50.

Historical Volatility is estimated using Close-to-Close Estimator, Parkinson Estimator, Garman- Klass Estimator, Rogers-Satchell-Yoon Estimator and Yang-Zhang Estimator. Microsoft Excel is used for calculation and analysis purpose. Historical volatility is found to be very high in CNX Bank index. Volatility Cone is used as the parameter in various indices namely CNX Bank, S&P CNX Nifty, S&P CNX Defty, CNX Nifty Junior and Nifty Midcap 50. The study takes different rolling periods percentiles of volatility. The study empirically proves that there is a clear reversion to the mean as indicated by the volatility cone.

This paper examines whether there is any significant difference in the historical volatility of 5 indices in National Stock Exchange before and after 2008 recession i.e. 2 years before 2008 (Jan 1^st 2006 to Dec 31^st 2007) and 2 years after 2008 (Jan 1^st 2009 to Dec 31^st 2010) using SPSS Paired Sample T-test. Daily Yang-Zhang historical volatility estimator values are used as input in Paired Sample T-test for the indices S&P CNX Nifty, S&P CNX Defty, CNX Nifty Junior and CNX Bank. Daily Close-to-Close historical volatility estimator values are used as input in Paired Sample T-test for the index Nifty Midcap 50 since closing prices are only available in 2006 and 2007 for Nifty Midcap 50, historical volatility can be computed only using Close-to-Close estimator formula. There is no significant difference in the historical volatility of various indices before and after 2008.

The study also examines whether there is any significant difference in the historical volatility of CNX Bank index one month before and after Reserve Bank of India Credit Policy Announcement and Credit Policy Review dates and if there is any significant difference in historical volatility, the study investigates for that particular date, whether there is any significant difference in the closing prices of CNX Bank index one month before and after Reserve Bank of India Credit Policy Announcement and Credit Policy Review dates.