WMA - Weighted Moving Average

Yesterday I researched and wrote about the Simple Moving Average , At the end of it I commented on how I thought it was a bit crap and missed the majority of the major moves (would only kick in at halfway through an uptrend). I think the reason for this is that all time periods are given equal weight, so when calculating a 15 period SMA, the oldest period has exactly the same amount of weight as the most recent period.

To combat these problems technicians use either the Weighted Moving Average (WMA) or the Exponential Moving Average (EMA). In this article I will focus on the Weighted Moving Average, and will follow it up later with the EMA.

As I've already mentioned, the Weighted Moving Average attempts to place more weight on the more recent periods.

The Calculation

This is also a fairly simple calculation with a slight change from the Simple Moving Average (SMA) calculation. Where the SMA places equal emphasis on each period, the WMA places more on the most recent. This is done by making the weight of the most recent period as the number of periods, the next most recent is the number of periods minus 1 and so on until the oldest period has a weight of only 1. Then you divide the sum of the weighted closing prices by the sum of the weights.

I'm pretty sure that didn't make a whole lot of sense, so let me illustrate:

Weight		Value		Weighted Data
5	*	50	=	250
4	*	30	=	120
3	*	20	=	60
2	*	15	=	30
1	*	12	=	12
15				460

So when we divide 460 (the sum of the weighted data) by 15 (the sum of the weights) we get a little over 30 (30.6666667), when we contrast this with the SMA for this set of data we find that the SMA is 25.4, so it is fairly clear that there is a much stronger bias towards the more recent data. I'm sure that when you run it over more periods in a volatile market such as FOREX the difference is more pronounced.

How to use the Weighted Moving Average

From what I can understand, the Weighted Moving Average should be used exactly the same way as the Simple Moving Average, however the WMA can provide for better results in volatile markets by placing more emphasis on recent data. To recap the most common way that these lines are used: When the short term line crosses the long term line it can indicate either an uptrend or a downtrend.

Below I've included 2 charts, the first is the chart which is on the Simple Moving Average page, the second is the same chart with Weighted Moving Averages as the 2 lines both have the long term average calculated across 50 periods, the short term is calculated across 15 periods.

Chart illustrating the Simple Moving Average, note that often it can take too long for the short term SMA (blue line) to cross the long term SMA (red line).

Chart illustrating the Weighted Moving Average, note that the short term WMA (orange line), crosses the long term WMA much much closer to the start of an up trend.

Next time I will research the Exponential Moving Average. I'm pretty happy with the results generated by the WMA and think that I could quite realistically use it to fairly accurately indicate changes in trends (particularly up trends), so it will be interesting to see what difference there is between the Weighted Moving Average (WMA) and the Exponential Moving Average.

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