March 10, 2006, Newsletter Issue #9: What Are Stock Moving Averages: Simple, Weighted, & Exponential

Tip of the Week

A moving average smoothes out values of adjacent statistical observations and thereby eliminates minor or irregular fluctuations (called "noise"). A moving average is one of the most widely used technical analysis tools in all of trading and is a workhorse for many in the industry. Moving averages are used to identify the market´s or an individual equity´s trend in order to establish positions in the direction of the trend.

While there are numerous methodologies for calculating moving averages, we will deal with the three most commonly used - simple, weighted, and exponential. All are based on the issue´s closing price for the time frame used (daily, weekly, or monthly), the idea being that there are many intra-period battles going on in the market and the war isn´t won until the close. Some studies will base their calculations on intraday spreads between high and low pricing, but we will not pursue that issue here. We will speak of a "10-day" moving average throughout this discussion, though the calculations for weekly and monthly moving averages will follow the same logic.

Simple Moving Average
A simple 10-day moving average consists of successive averages of the 10 most recent days´ closing values. The calculation is very straightforward - simply add up the daily closing values and divide by 10. With each subsequent day, the newest closing value is incorporated into the average and the value of 10 days previous is dropped.

One of the objections some have with the simple moving average calculation is that it assigns equal weight to each of the 10 values. It is not unreasonable to argue that the most current readings should be more important as a reflection of what the stock is doing now. This takes on added importance as the time frame increases (e.g., 20 days). Since the calculation is modified each day by dropping the oldest value in favor of adding the most current one, its fluctuation now becomes a function of just two numbers. That is, if the current value is greater than the one being dropped, the average turns upward. The converse is true - if the current value is lower than that of 10 days ago, the average moves lower.

Weighted Moving Average
Although the weighted averaging process is basically the same as for a simple moving average, more significance, or "weight," is added to the most current readings (on a closing basis).

The weightings may be allocated to suit the individual analyst´s taste and don´t have to be uniformly progressive (10, 9, 8, 7, etc.). The importance here is that you are consistent in your application. For example, there is no reason why the first five days cannot have equal weightings with the progression occurring in days six through 10 (although you are complicating an already cumbersome calculation).

The next step is to multiply the "weighting" by the day´s closing price to come up with a "weighted price."

For example: Price Weighted Calculation
Date Weighting X Closing Price = Weighted Price
6/11/04 1 X 72.12 = 72.12
6/12/04 2 X 72.08 = 144.16
6/13/04 3 X 70.69 = 212.07
6/14/04 4 X 68.90 = 275.60
6/15/04 5 X 68.02 = 340.10
6/18/04 6 X 66.88 = 401.28
6/19/04 7 X 67.32 = 471.24
6/20/04 8 X 69.41 = 555.28
6/21/04 9 X 69.84 = 628.56
6/22/04 10 X 68.83 = 688.30
Sum 55 694.09 = 3788.71

694.09 / 10 = 69.41 simple average
3788.71 / 55 = 68.89 weighted average

Exponential Moving Average
This form of moving average also assigns greater relevance to the more current values. An exponential system is based upon the assignment of a fixed percentage weight to the current price, say 18 percent (could be any weighting; see below for rationale), and all of the remaining weight (82 percent) to the previous value of the moving average itself. The proportional weight assigned to the most recent reading is often called a "smoothing constant."

To determine an exponential "smoothing constant" roughly proportional to a simple moving average of a given time length, divide two by one more than the length of the simple moving average you wish to replicate. It may sound confusing, so let´s look at an example. To find a smoothing constant to construct an exponential moving average comparable to a simple 10-day moving average, divide two by 11 (one more than the 10-day simple). The result is 0.18 (why we chose this number above).

As a starting point, let us assume day one to be the exponential moving average for that point in time. The exponential moving average is updated by multiplying the newest price by 0.18 (our smoothing constant) and adding that to the product of the previous exponential moving average multiplied by 0.82 (the balance of the 100 percent allocation).

Date Closing Exponential Moving Avg.
6/11/04 72.12 Arbitrary start point 71.75
6/12/04 72.08 (0.18 x 72.08 + 0.82 x 71.75 = 71.81)
6/13/04 70.69 (0.18 x 70.69 + 0.82 x 71.81 = 71.61)
6/14/04 68.90 (0.18 x 68.90 + 0.82 x 71.61 = 71.12)
6/15/04 68.02 (0.18 x 68.02 + 0.82 x 71.12 = 70.56)
6/18/04 66.88 (0.18 x 66.88 + 0.82 x 70.56 = 69.90)
6/19/04 67.32 (0.18 x 67.32 + 0.82 x 69.90 = 69.44)
6/20/04 69.41 (0.18 x 69.41 + 0.82 x 69.44 = 69.43)
6/21/04 69.84 (0.18 x 69.84 + 0.82 x 69.43 = 69.51)
6/22/04 68.83 (0.18 x 68.83 + 0.82 x 69.51 = 69.38)

Looking at the three types of moving averages, the largest spread between them is 0.52 points, or just 0.75 percent of the simple 10-day moving average. The issue is thus whether the additional work in calculating the weighted and exponential moving averages is justifiable in terms of providing a trading edge. It appears that the exponential moving average seems to react more quickly than the simple moving average, which could possibly signal a quicker entry or exit point for a trade.

We recommend that whichever moving average you use, stay consistent with that method. Bouncing from a simple to a weighted average will only confuse you and restrict your ability to recognize equities that have historically reacted well around these trendlines.

Time Frames
We commonly use 10-unit and 20-unit simple moving averages. "Unit" refers to the time frame you wish to use - daily, weekly, or monthly. This changing of perspectives is like driving up to the Rocky Mountains. From a great distance, the range appears to be one solid piece of rock emanating from the earth´s crust (think of this as a long-term or monthly chart). As you get a little closer (weekly chart), you start to notice that the "barren" rock is covered with trees and huge fields of snow. Taking a tram up the mountainside (daily chart), you notice pastures of grass surrounding the tree line, an occasional lake nestled into a flat, not to mention a plethora of wildlife. This short-term, or daily, chart reveals things you could only imagine from the long-term perspective.

Each view provides you with a different viewpoint, though each independently does not afford a complete assessment of the mountain. Such is the reasoning behind examining the various chart views and their accompanying moving averages.

The longer term charts and the accompanying longer-term moving averages can aid in determining the overall trend of a stock, index, or market. In fact, we consider the 20-month moving average as the line of demarcation between a bull and bear market.

Summation
There is no perfect moving average style or length. You could probably back-test all sorts of combinations and make a positive case for their predictive reliability for some stock or index. Ultimately, the ideal combination is the one that has worked for you. This brings us back to the concept of consistency. Whatever calculation or duration you use, make it yours and stick with it. Only repetitive trial and error will help you hone your technical skills with respect to moving averages.

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