Volatility definition
/What is Volatility?
Volatility defines both the size and frequency of changes in the price of an asset. An asset is considered to be riskier if it has a high level of volatility, since its valuation could be spread across a substantial range. Conversely, a low rate of volatility equates to minimal or moderate pricing changes over a period of time. An option associated with an asset is more valuable when the volatility associated with the asset is high, since the asset holder can realize a large gain by waiting for the price of the asset to spike, and then buying it; the difference between the exercise price of the option and the purchase price are maximized by doing so. A high level of volatility is considered less favorably in regard to a retirement portfolio, since the ending value of the portfolio can be exceedingly difficult to predict.
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How to Calculate Volatility
Volatility is based on the historical price movements of the asset, and is calculated as the standard deviation of the asset price over a period of time. Beta is a measure of volatility, since it measures volatility in comparison to a performance benchmark (typically a major stock index). Thus, a beta of 1.2 means that an asset price changes 120% in relation to a 100% pricing change in the comparison index, while a beta of 0.8 means that the asset price changes 80% in relation to a 100% pricing change in the comparison index.
More specifically, the calculation of volatility requires one to determine the mean of a data set, then calculate the difference between each data item in the data set and the mean, then square the deviations to eliminate negative values, then add together the squared deviations, and finally divide the total of these squared deviations by the number of data items in the data set.