ThE hAnDbook of TEChnICAl AnAlysIsexample 2: Calculating deviation Values for a Constant rate of Change in price
Assume prices are rising at a constant rate of $2 per hour over a 10‐hour period.
This represents a first‐order change in prices—momentum is flat.
Mean rate of increase per hour
=++++++++($ $ $ $ $ $ $ $ $ 2++==$ ) / 2 2 $ 2 / 2 10 2 2 20 10 $2 2 2 2Mean Deviation is calculated as follows. We find the average of the difference
in absolute values from the mean for each value:
| $ $ | $
| $ $ | $
| $ $ | $
| $ $ | $
| $ $ | $
| $ $ |
2 2 0
2 2 0
2 2 0
2 2 0
2 2 0
2 2
−=
−=
−=
−=
−=
−=$$
| $ $ | $
| $ $ | $
| $ $ | $
| $ $ | $
0
2 2 0
2 2 0
2 2 0
2 2 0
−=
−=
−=
−=
=
Mean Deviation(($ $ $ $ $ $ $ $ $ $ ) / $ /
$
0 0 0 0 0 0 0 0 0 0 10 0 10
0
+++++++++=
= per hourObviously, the standard deviation value would also be zero since it uses the
same difference in values between each rate of change and the mean, which are all
zero in this example.
Since the standard and mean deviations are both zero, there is only a first‐order
change in prices, that is, a constant rate of change in prices where momentum is
flattening. Therefore, there is no volatility in price as far as the first measure of
volatility is concerned. Again, statistical measures of deviation are useful quantita-
tive tests of the first measure of volatility.
We may also use the statistical measures of deviation to quantitatively exam-
ine if reversals that occur at a constant rate of change in price represent volatility
with respect to the first measure. Assume that we have a market that reverses ev-
ery hour and trends at a constant rate of $2 per hour. See Figure 21.18.
Does this represent volatile behavior? As we have already observed, the ques-
tion as to whether a market is volatile or otherwise is a meaningless question. It
is similar to asking if the trend is up or down. Without reference to the lookback
duration, it is impossible to answer the question if a trend is currently up or down.