Volatility Analysis
($ $ ) $
($ $ ) $
($ $ ) $
($ $ ) $
($ $
2 11 81
4 11 49
6 11 25
8 11 9
10 1
2
2
2
2−=
−=
−=
−=
− 11 1
12 11 1
14 11 9
16 11 25
18 11
2
2
2
2
2) $
($ $ ) $
($ $ ) $
($ $ ) $
($ $ )
=
−=
−=
−=
−=$$
($ $ ) $
(($ $ $ $ $ $
49
20 11 81
81 49 25 9 1
−=^2
=+++++
Standard Deviation11 9 25 49 81 10
330 10 5 74
++++
= =
$ $ $ ) / )
($ / ) $. per hourSince the standard and mean deviations are greater than zero, there is a second‐
order change in prices where momentum is rising. This therefore represents vola-
tile trend action, with respect to the first measure of volatility. If the rates of
change in price were constant, then the standard and mean deviations will be zero.
These are therefore useful quantitative tests for the first measure of volatility. In
this example, the actual average deviation from the mean rate of increase is $5 per
hour, as indicated by the mean deviation value.
If we now assume that the rates of change in price were in fact randomly distrib-
uted instead of rising in a parabolic fashion, and assuming that the random distribu-
tion approximates a normal distribution, we may then use this to find the statistical
properties of the given random rates of change in price. Since one standard deviation,
1SD, is $5.74, we know that 68.2 percent and 95 percent of the random rates of
change in price over a 10‐hour period will occur between ± 1SD and ± 2SD of the
mean rate, respectively. Therefore, 68.2 percent of increases in rate of change in pric-
es over a 10‐hour period would stay within $11 ± $5.74 per hour, that is, between
$5.26 and $16.74 per hour. At the 2SD level, 95.4 percent of the increases in rate of
change in prices over the same number of periods would stay below an upper value
of $11 + (2 × $5.74), that is, $22.48 per hour. This is especially useful information for
the trader and analyst. This means that whenever the increase in the rates of change
in prices falls or rises, there is a 68.2 percent chance that the rates of change in prices
over a 10‐hour period may potentially start to increase once they decline to a rate of
$5.26 per hour, and conversely start to decline once they reach a rate of $16.74 per
hour. At the 2SD level, there is a 95.4 percent chance that the rates of change in prices
may potentially start to decline once they reach a rate of $22.48 per hour.