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Technical Studies: Volatility

The Volatility indicator plots a moving average of a security's standard deviation over a specified time period. It indicates the extent to which the security's price has fluctuated from its average price during that period.

The default parameter is 20 minutes/hours/days/weeks/months, depending on the selected frequency. Twenty (20) is the default period given that 20 trading days is roughly equivalent to one month. The parameter can be customized to plot the standard deviation line over shorter or longer periods.

Interpreting Volatility: According to some technical analysts, "The bigger the base, the bigger the move." Essentially, periods of low volatility (tighter trading ranges) often precede periods of high volatility, or large price swings. And those swings may occur either upward or downward.

The standard deviation line rises when fluctuations in a security's price are at their wildest. This often occurs soon after the security breaks above or below a trading range. In contrast, the standard deviation line is lowest when the security's trading range tightens and prices are relatively stable. The bigger the gap between the closing prices and the average price over the period, the higher the standard deviation line. Conversely, the closer the gap between the closing prices and average price over the period, the lower the standard deviation line.

Calculating Volatility: To calculate Volatility, start by finding the variance.
Variance = Sum of all deviations from the mean, squared, for last n closing prices / n
Where the default value for n is 20, but can be customized.

For a 20-day standard deviation, for example, the average closing price during the 20-day period might be 40.90 while the 20th day's closing price is 38.90. The deviation from the moving average for the twentieth day is -2. The square of -2 is 4. Add that number to the square of the deviation for the previous 19 remaining periods and divide the sum by 20 to arrive at the variance.

Then calculate the standard deviation:
n-period Standard Deviation = Square root of Variance
If Variance = 4.5, then the n-period Standard Deviation = 2.12

Standard Deviation and trading ranges: The standard deviation can be used to determine an expected trading range of a security over a specified time period. A 20-day standard deviation of 2.12 means the security, in all likelihood, stayed within a range of plus-or-minus $2.12 of its average price 66% of the time during the past 20 trading days. If the security's average price during the period was $45, for example, we would expect the security to stay within a range of $42.88 and $47.12 during the period 66% of the time.

Similarly, we'd also expect the security to stay within two standard deviations of its average price 95% of the time within the period. Two standard deviations of $2.12, which is 2 x $2.12, is $4.24. So 95% of the time during the 20-day period, we'd expect the security to stay above $40.76 and below $49.24.

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