Weighted Moving Averages: The Basics
Over the years, technicians have found two problems with the simple moving average. The first problem lies in the time frame of the moving average (MA). Most technical analysts believe that price action, the opening or closing stock price, is not enough on which to depend for properly predicting buy or sell signals of the MA's crossover action. To solve this problem, analysts now assign more weight to the most recent price data by using the exponentially smoothed moving average (EMA). (Learn more in Exploring The Exponentially Weighed Moving Average.)
For example, using a 10-day MA, an analyst would take the closing price of the 10th day and multiply this number by 10, the ninth day by nine, the eighth day by eight and so on to the first of the MA. Once the total has been determined, the analyst would then divide the number by the addition of the multipliers. If you add the multipliers of the 10-day MA example, the number is 55. This indicator is known as the linearly weighted moving average. (For related reading, check out Simple Moving Averages Make Trends Stand Out.)
Many technicians are firm believers in the exponentially smoothed moving average (EMA). This indicator has been explained in so many different ways that it confuses students and investors alike. Perhaps the best explanation comes from John J. Murphy's "Technical Analysis Of The Financial Markets", (published by the New York Institute of Finance, 1999):
The exponentially smoothed moving average addresses both of the problems associated with the simple moving average. First, the exponentially smoothed average assigns a greater weight to the more recent data. Therefore, it is a weighted moving average. But while it assigns lesser importance to past price data, it does include in its calculation all the data in the life of the instrument. In addition, the user is able to adjust the weighting to give greater or lesser weight to the most recent day's price, which is added to a percentage of the previous day's value. The sum of both percentage values adds up to 100.
For example, the last day's price could be assigned a weight of 10% (.10), which is added to the previous days' weight of 90% (.90). This gives the last day 10% of the total weighting. This would be the equivalent to a 20-day average, by giving the last days price a smaller value of 5% (.05).
|Figure 1: Exponentially Smoothed Moving Average|
The above chart shows the Nasdaq Composite Index from the first week in Aug. 2000 to June 1, 2001. As you can clearly see, the EMA, which in this case is using the closing price data over a nine-day period, has definite sell signals on the Sept. 8 (marked by a black down arrow). This was the day that the index broke below the 4,000 level. The second black arrow shows another down leg that technicians were actually expecting. The Nasdaq could not generate enough volume and interest from the retail investors to break the 3,000 mark. It then dove down again to bottom out at 1619.58 on Apr. 4. The uptrend of Apr. 12 is marked by an arrow. Here the index closed at 1,961.46, and technicians began to see institutional fund managers starting to pick up some bargains like Cisco, Microsoft and some of the energy-related issues. (Read our related articles: Moving Average Envelopes: Refining A Popular Trading Tool and Moving Average Bounce.)