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Sunday, October 31, 2010

Historical Volatility – Part 1: Definition

Historical Volatility (HV) is a measure of the fluctuations of the stock price (i.e. how volatile the prices had fluctuated) over a certain period of time in the past.

Suppose the daily closing prices of Stock X and Y for the past 10 days are shown as follows:

As can be seen from the data above, regardless of the direction (up or down), the closing prices of Stock X in the past 10 days have fluctuated / changed by $2 to $5, whereas Stock Y by $1 to $3.
Since given the same initial stock price of $100, Stock X has shown bigger fluctuation in terms of dollar, Stock X is said to be more volatile than Stock Y.

Now, suppose Stock Z has an initial stock price of $50 and has also fluctuated by $2 to $5 like Stock X. In this case, given the same fluctuation in terms of dollar but lower stock price than Stock X, Stock Z will be considered to be more volatile than Stock X.
Hence, to get relative measurement of volatility and to compare volatilities among stocks with different prices, it is more accurate to reflect the price change in terms of percentage of the stock price, which is known as “Price Returns”.

Historical Volatility (HV) is therefore obtained by calculating the standard deviation of historical price changes (i.e. price returns) over a specified period in the past.

In Statistics, Standard Deviation measures the dispersion (spread) of a set of data points from its mean (average).
The more disperse (spread out) the data points from its mean, the higher the standard deviation. This deviation is referred by traders as “volatility”.
(Note: Further understanding about standard deviation will be discussed in the future article).

The higher the historical volatility, the bigger fluctuation the stock has experienced. As such, theoretically, the more likely the stock may make big movement in the future too, although this does not give any insight about the trend / which direction it will move to.

Depending of its uses/purposes or data availability, for calculation of HV, we can use historical price data in terms of daily, weekly, monthly, quarterly or yearly.
The common period used to calculate HV is 10 days, 20 days, or 30 days (using daily data).
To allow comparison between volatilities that are calculated using different period, the HV would be annualized.

By expressing HV using annualised standard deviation of % price returns, the figures can be used to compare the volatility across different stocks, regardless of the stock price and the period used for HV calculation.

In conclusion, Historical Volatility can be defined as follow:

Historical Volatility (HV) is the annualised standard deviation of historical price changes (i.e. returns) over a specified period in the past.

In the next posts, we will discuss:
* Formula to calculate HV
* Steps to calculate HV using MS Excel (with example)
* Further understanding about Standard Deviation

Continue to Part 2: Formula to Calculate Historical Volatility.

To view the list of all the series on “Historical Volatility”, please refer to:
More Understanding about HISTORICAL VOLATILITY

Other Learning Resources:
* FREE Trading Educational Videos with Special Feature
* FREE Trading Educational Videos from Trading Experts

Related Topics:
* Understanding Implied Volatility (IV)
* Understanding Option Greek
* Understanding Option’s Time Value
* Learning Candlestick Charts
* Options Trading Basic – Part 1
* Options Trading Basic – Part 2


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