Name, Sometimes Called:
Standard Deviation
In statistics, its symbol is the lower case Greek letter sigma ( ).
Brief Description:
The standard deviation is a statistical measure of
dispersion, or volatility in TA terms. It is used as a component
of other TAIs, such as Bollinger Bands.
Definitions, Formulas:
The standard deviation measures dispersion, scatter,
or volatility. It provides a measure of how the raw data is distributed
around a simple moving average or mean.
Begin by selecting the interval for the data to be examined. We
use N = 20.
Then calculate the average (mean) closing price (SMA)
of the N price values
The calculation for the (sample) standard deviation is then
where
SN
= the (20-day sample) standard deviation
= each of the 20 closing price values
Positive Development Calculation:
For this TAI, there is no positive development (NPD).
It is used as a component of other TAIs, such as Bollinger
Bands as well as a measure of volatility.
History:
The standard deviation is a statistical measure with
a long history. Karl Pearson, sometimes called the father of modern
statistics, reportedly introduced the term “standard deviation”
in 1893, although the concept was by then over a century old.
High standard deviation values indicate widely dispersed data (drastically
changing prices). Conversely, low values indicate relatively stable
prices.
This chart below shows the standard deviation indicator applied
to the closing price of Panera Bread (PNRA) from September 2003
through September 2005. Notice the high points near point A on the
Standard Deviation line. Remember that standard deviation is a measure
of volatility, not direction. The peak over 3 standard deviations
to the left of A were on a price rise. The slightly higher peak
to the right of the A were on a price decline.
What constitutes “high” or “low” volatility
is somewhat subjective. Generally standard deviations from zero
to one contain 68% of a given population. From zero to two contain
95%, and zero to three about 99%. Therefore anything above three
is very rare and very volatile. Anything above two is more volatile
than anything below one.
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