Moving Averages: Know The Basics First
The moving
average is probably one of the most used and possibly overused indicators
in the financial markets. In Part 1 of this series of two lessons, let’s look at
the calculation and comparison of simple, exponential and weighted moving
averages.
Simple Moving Average
An average is simply the sum of a data set divided by the number of data
points. Let’s look at a set of grades. Suppose Johnny earns the following
grades:
His average would be the sum of the grades divided by the number of tests:
Now suppose on his next test he scores a 90. If we took a 5-day
“moving” average of his grades we would drop off his oldest grade (67)
and add in his newest grade (90) and then divide by 5. This is illustrated in
Figure 1. Notice how the average “moves” from the oldest 5 data points
to the newest 5 data points, hence the name “moving average.”
Figure 1: A
5-Period Simple Moving Average. Notice how the average “moves” from
the oldest 5 periods to the newest 5 periods.
Exponential Moving Average
An Exponential Moving Average (EMA) takes a percentage of today’s price and
adds in the prior day’s exponential moving average times 1 minus that
percentage. For instance, suppose you wanted a 10% EMA. You would take today’s
price and multiply it by 10% then add that figure to the prior day’s EMA
multiplied by the remaining percent:
(1-.10))
Because most people think in terms of days (time periods) vs. percentages,
the following formula can be used to determine the percentage to be used in the
calculation:
So if you wanted a 20 period EMA you would use 9.52% (2/(20+1)) as your
percentage for the calculation.
As usual, I strongly suggest that you have a computer do all the work, since
the EMA is available in virtually all charting packages. I have yet to meet a
trader that does these calculations by hand.
As you can see, by nature of its calculation, the EMA gives more weight to
the recent periods. This brings us to our next type of moving average: the
weighted moving average.
Weighted Moving Average
The theory behind a weighted moving average (WMA) is that the recent data is
more relevant than past data. Therefore, it puts more “weight” on the
recent data and less weight on the older data. To calculate it, you take the
number of periods you wish to analyze and that becomes the weight for today’s
price. Yesterday’s price would use today’s weight -1 and so on and so forth for
the number of periods. You then divide the sum of the weighted prices by the sum
of the weights.
For example, suppose we took the last five “grades” we used in our
first example and calculated a 5-period WMA. The calculation would be as
follows:
Figure
2: Calculation of a Weighted Moving Average. The number of periods (in this case
5) becomes the “weight” for today. The weight for the remaining days
is reduced by 1 until the last day is found. Therefore, the most recent period
gets the highest weight and the oldest period gets the smallest. The summed
weighted prices are then divided by the sum of the weights
Again, I strongly suggest that you have your computer do all the work.
Comparing the EMA, WMA and Simple Moving Averages
The simple moving average gives equal weight to all data points. By nature,
it is the “true” average. The exponential and weighted moving averages
give the most recent data points the highest rankings or “weightings”.
Therefore, the simple moving average tends to lag (by representing all data
points equally) the exponential and weighted moving averages during large price
changes. However, during “normal” or “flat” markets the
differences become negligible. This is illustrated in Figure
3.
Figure
3: IBM Simple, Exponential and Weighted Moving Averages. Notice during
“normal” or “flat” markets the averages tend to run together
(a). However, once the market begins to make sharp moves (b) and (c) the EMA and
WMA tends to catch up to price faster while the Simple Moving Average tends to
lag.
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So Which One Should You Use?
Deciding between the types of moving averages really becomes a matter of
personal preference. Normally when you hear talk of moving averages, in the
media it normally refers to simple moving averages. Therefore, due to widespread
focus on these numbers, it’s important to give them consideration. The 50- and
200-day (simple) moving averages are most commonly used here. As a trader,
especially during large price moves, you might consider experimenting with
exponential or weighted moving averages.
Looking Ahead
Now that we’ve defined the different types of moving averages we can focus on
characteristics of the indicator and strategies. In Part 2, we’ll look at these
characteristics and general uses of moving averages. We’ll touch upon the fact
that “conventional wisdom” regarding moving averages is often wrong.
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References and Additional Reading
Technical Analysis From A to Z by Steven Achelis. I keep this book on
my desk for quick reference. Mr. Achelis covers most technical indicators
including their calculation and general use in a clear and concise manner.
The 2/20 EMA Breakout System, by Dave Landry, December 1996 issue of
Technical Analysis of Stocks and Commodities.
The
TRADEHARD.COM Guide to Conquering the Markets, Edited by Mark Etzkorn.
The Running Cup and Handle, Chapter 6, pages 74 through 76.
Hit
and Run Trading by Jeff Cooper. Expansion Pivots, Chapter 8, pages 59
through 67.
Street
Smarts by Laurence Connors and Linda Raschke.
The Holy Grail, Chapter 10, pages 79 through 86