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# Volatility 7 – Volatility Summary

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This is the seventh and final article in a series on volatility. The goal of this series is to clarify the different meanings of the term volatility and to discuss its many possible uses, including describing stock price action, evaluating option prices, choosing option strategies, and forecasting the market. Option traders should strive to gain an accurate understanding of volatility — and its many uses — because volatility affects option prices, trading decisions and risk analysis.

This article summarizes the important points of the previous articles.

The Concept of Volatility

"Volatility" is price change without regard to direction, which can be confusing to traders who think that "up is good and down is bad." With volatility, it is the percentage change that matters, so a 1 percent price rise is equal in volatility terms to a 1 percent price decline.

The volatility of a particular stock's price action is derived from a series of daily closing prices. The daily percentage changes are computed, and then the standard deviation of those percentage changes is calculated. This standard deviation is referred to as the historical volatility of a stock's price.  The stated volatility percentage is the annual standard deviation of stock price movement.

Volatility makes it possible to compare the price fluctuations of the same stock during different time periods, and volatility makes it possible to compare the price fluctuations of two stocks regardless of a difference in price level. Volatility also makes it possible to compare past stock price fluctuations to price fluctuations that are forecast by the options market.

From statistics about normal distributions (bell-shaped curves), approximately 68% of all outcomes occur within one standard deviation of the mean; approximately 95% of all outcomes occur within two standard deviations of the mean; and approximately 99% of outcomes occur within three standard deviations.

Implied Ranges

The stated volatility percentage is the standard deviation of price movement over one year, but price-range probabilities for one year are not useful to short-term traders. So here is a formula that converts the stated volatility — the annual standard deviation — to a period of time chosen by the trader:

Standard Deviation for n days = Stock Price x Volatility x square root of time
Where square root of time =
square root of n days / square root of days per year

The statistics of volatility are a good starting point for traders, because the stock price has a 33% chance (approximately) of closing beyond one standard deviation at expiration. Consequently, a stock price change equal to one-standard deviation is a realistic target for the stock to reach. A trader still has to get the direction right, and there is still the risk that a particular time period will be one of the two-thirds when the stock price does not close beyond the one-standard deviation level.