THE HAnDbook of TEcHnIcAl AnAlySIS(5) Weighting Mode
There are numerous ways to average data. The main difference between the vari-
ous averaging methods lies in the sensitivity toward the latest prices. Some averag-
ing methods tends to give all prices within the N period lookback equal weighting,
that is, they are equal weighted, while others tend to allow the moving average to
react more rapidly to recent prices, giving the later prices more weight within its
averaging. In such cases, we say that the moving average is front weighted, that is,
it has a greater reaction speed or sensitivity to more recent data or prices. A sim-
ple moving average (SMA) is an example of an equal-weighted moving average.
Examples of front-weighted moving averages include the exponential moving
average (EMA) and linearly weighted moving average (LWMA).
Some moving averages are weighted toward the middle of their lookback pe-
riod, that is, they are mid-weighted. One such example is the triangular moving
average. The triangular moving average weighting increases toward the middle
of the lookback period and decreases toward either end of the lookback period.
The triangular moving average is therefore somewhat similar to a centered mov-
ing average. The triangular moving average is created via a process called double
smoothing, where an SMA is created from the rolling values of another SMA.
(1) Simple Moving average A simple moving average (SMA) is the most basic
form of a moving average and is calculated by first dividing the sum of all prices by
its number of periods. Let N equal the lookback period:
Average over periodsN =∑(Closing Prices over periods /NN)
This average value is then rolled forward to the next most recent closing price,
dropping off the oldest closing price in the previous range and adding to it the lat-
est closing price. This process is repeated indefinitely and thus forms the moving
or rolling average. Sometimes the effect of dropping off the last price may cause
the moving average to swing erratically, especially if the value dropped off was
relatively large. Increasing the lookback period or increasing the sensitivity of the
moving average to recent prices via the use of front-weighted moving averages
will help reduce the impact of the drop-off effect on the moving average.
The weighting factor for each period is equal, with each price having an equal
impact on the average value. The percentage of contribution or influence that each
period has on the SMA is (100/N) percent.
So, for a 10 period SMA, the price corresponding to each period has a (100/10) =
10 percent contribution or impact on the average price. See Figure 11.7 for an ex-
ample of a 10-day SMA. The last column on the right represents the moving aver-
age of the last 10 days on the Chicago Board Options Exchange (CBOE) Interest
Rate 10-Year Treasury Note, beginning on May 29, 2009. Figure 11.8 is a plot of
the moving average.
(2) triangular Moving average A triangular moving average is a double
smoothed moving average. The value for each period of the first SMA is aver-
aged a second time over the same number of periods. It is mid-weighted, as can