Standard
Deviation
If
you spend much time following the market you’ve heard the
term Standard Deviation mentioned.
Standard deviation has nothing to do with the normal
mischievousness of a particular age group.
It is a statistical term, and a concept that can improve
the success of your stock trading.
It’s
also the concept Bollinger Bands is based on.
In simplest of terms, standard deviation is a measure
of how far a particular data point within a group is from
the average. You
can also look at it as a measure of volatility or spread. If all the data points of a group are near the average
the standard deviation of the group would be low and the volatility
would be low. The standard deviation is calculated by adding
the squared variance from the average of all the data points.
You can calculate this with a pencil and piece of paper,
but the good news is it’s a standard key on most any scientific
calculator. All
you do is enter all the values of the group, i.e. the closing
prices of a stock for the last ten days then press the standard
deviation key and it’ll display the standard deviation for
the values entered.
The displayed value will be one standard deviation
from the mean.
Most
of us have run into the concept of standard deviation and
may not have realized it.
The bell curve used to grade students in high school
or college is a representation of the concept of standard
deviation. A
picture of the classic bell curve is an easy way to represent
standard deviation.
A bell shape viewed from the side represents all the
scores in the class if those scores follow a normal distribution.
A vertical line drawn from the highest point of the
bell down to its base would represent the average score.
Most of the scores are grouped around the average score
and these would be roughly within one standard deviation of
the mean. The
scores to the extreme left and right of the bell would be
within 2 or 3 standard deviations of the mean.
With the “normal” distribution of the bell curve the
data points from one stand deviation below the mean to one
standard deviation above the mean represent roughly 68 percent
of the values in the group.
Two standard deviations (plus and minus) encompass
95 percent of the values in the group, and three standard
deviations encompass 99 percent of the values in the group.
A teacher could use standard deviation to assign grades
by simply figuring that any score greater than a value, i.e.
2.5 standard deviations above the mean receives an “A”, etc.
Applying
the concept of standard deviation to investments gives the investor
an idea of where a data point is relative to the mean and how
volatile the markets are.
Bollinger Bands can be applied to any stock using most
charting software. Bollinger
Bands overlay three lines on a stock chart.
The middle line is the moving average over the specified
period, i.e. 14 days.
The top line is the value two standard deviations above
the mean and the lower line is two standard deviations below
the moving average. As the market is more volatile the bands get broader and become
more narrow as volatility is reduced.
How extreme a standard deviation value is depends on
the length of the moving average in consideration.
Sometimes a market commentator will say that a particular
market is 3 or 4 standard deviations above or below it’s given
moving average. A
value 2 standard deviations from its mean is an extreme value.
If the current value of the index or stock is 3 or 4
standard deviations from its moving average then it is very
extreme and often signifies a market top or bottom. This type
of information can help an investor make money and the average
investor can benefit from learning more about standard deviation
and how it is used in stock market analysis.
