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In order to get a quick impression of the chart technical condition of an underlying instrument, moving averages are a real classic and standard tool among indicators. This chapter explains that there is a multitude of variants and interpretation possibilities.

## How to use a Moving Average?

One of the most important questions in any investment or trade decision is the question of market direction. What is the trend phase? Is the market going down or up in the time window under consideration? This is just as important for the investor who is positioning himself on the horizon of a few months or years as for the trader who may only want to position himself on the horizon of a few days or hours.

On a higher level, it makes sense to open positions in the direction of the overriding trend. This is easy to read, but it is the art of being able to recognize this overriding trend direction.

Trends often last longer than initially assumed. In addition, the trader also knows the actual market dynamics in the considered time window on his side, which increases the chance of winning trades. The fact that trends can last for a long time and become even more severe is shown by a simple example, the DAX price trend of the past years. Here, for example, a beginning upward trend phase can be seen in 2003, although this was interrupted by temporary consolidations, some of which lasted for months. But it continued until 2007. 2007 to 2009 and the year 2011 were marked by sharp corrections. The downward trend in 2011 began quite harmlessly in May, but intensified massively into the summer. Since September 2011, however, the DAX has been rising again at a higher level.

The aim is to participate in such trend phases with trading as long as they last. The actual turning point at which the trend ends can generally hardly be determined realistically. On the way there, however, positions can be built up profitably following the trend. If a trend change occurs, set and followed stop levels help to avoid missing the exit.

There are various methods for charting a trend or the superior market direction. A simple method to get an overview of the market condition of strongly tending markets, such as the stock markets, are moving averages.

After trend lines, moving averages are the most well-known tools used by technical analysts. This fact is due to the fact that the concept of moving averages is easy to understand and also easy to demonstrate due to its usefulness in trend markets. A moving average is a method of calculating the average value of a security or indicator over a specified number of time periods. The term “moving average” implies that the average changes.

In its basic form, a moving average is no more than a smoothing of the line chart with its closing prices. Moving averages are trend-following indicators, which means firstly that they lag behind prices (“trend-following”) and secondly that their direction indicates the direction of the trend. Due to this characteristic, moving averages can signal when a new trend has started or when an old trend has ended or reversed.

### The calculation of a simple moving average

When calculating a moving average, a mathematical analysis of a security’s average over a predetermined period of time is carried out. If the price of the security changes over time, the average price moves up or down. A simple moving average is calculated by adding the closing prices of a security over a certain period of time (for example, 10 days). This sum is then divided by the number of time periods. The result is the average price of the security over this particular time period. For example, to calculate a 10-day moving average of Intel, we first add together Intel’s closing prices for the previous 10 days. Then we divide this sum by 10 to get the average price of Intel over the past 10 days. We can then mark the result as the first point on the chart. To get the second point, we would leave out the first day and take the average from the second day to the eleventh day. And so it goes on and on. In this way, a moving average line is created, in which the average of the last 10 days is always formed. In practice, the charting software does these calculations and the moving average is usually displayed as a line in a bar chart.

There are two points of criticism of simple moving averages:

Firstly, it is criticized that only the time period covered by the average (for example 50 days) is considered. The second criticism is that the simple moving average is weighted equally every day. With a 50-day line, the last day receives the same weighting as the first day of the calculation period. Accordingly, in this example, the price of each day is assigned a weight of 2%. For this reason, there was also a demand for a higher weighting of the most recent price movements.

### Other types of moving averages

#### a) Linear weighted moving average

To address the weighting issue, some technical analysts use a linear weighted moving average. A weighted moving average is calculated by multiplying each previous day by a weighting factor. Table 1 below shows how a 5-day linear weighted moving average is calculated.

As you can easily see, more weight is given to today’s, the last price (5 x 30) than to the price five days earlier (1 x 20).

However, the linear weighted moving average does not take into account the problem that only the price movements that are part of the calculation basis are included.

#### b) Exponentially smoothed moving average

This type of moving average refers to both problems mentioned in connection with the simple moving average.

An exponential moving average is calculated to give less weight to older closing prices and more weight to the most recent data. For this reason it is also a weighted moving average.

With this type of moving average, the Technical Analyst is able to change the weighting by giving more or less weight to the most recent price data. This is done by assigning a certain percentage to the last day of the selected time period. This value is then added to the value of the previous day. The sum of both percentage values is 100.

For example, to calculate a 10% exponentially smoothed moving average from Intel, we do the following:

First, we take today’s closing price and multiply it by 10%. We then add this product to the value of yesterday’s moving average, multiplied by 90% (100% – 10% = 90%).

The formula used to calculate an exponentially smoothed moving average is

EMA = [(current closing price) x 0.09] + [(yesterday’s EMA) x 0.91]

Proponents of the exponentially smoothed moving average argue that the exponentially smoothed moving average follows the trend better than a simple moving average. But other analysts argue that this advantage is only marginal and that exponentially smoothed moving averages are too fast. In Figure 1 below, you can see the difference between the S&P 500 (daily interval) and the two 50-day lines. Note and see in the chart that both averages have advantages and disadvantages and you should choose the one that suits the market and your trading style better.

### Moving averages as a filter

For the sake of simplicity, the simple moving average will be considered here using the DAX as an example. Such a moving average is nothing more than the sum of the last closing prices divided by the number of closing prices considered. It therefore represents the average closing price of the number of closing prices considered. Now the question arises how many closing prices should be considered. There are no limits to the imagination, any length of period is possible. Frequently observed are, above all, the moving averages with the lengths 200, 50 and 20. The 200 moving average covers almost the trading period of a year, the 20 moving average that of a month. It is advisable to adjust the moving average to the cyclical nature of the underlying instrument if necessary.

This simple effectiveness will be demonstrated by way of example. Here you can see a daily chart since 2009 of the German DAX index. The 200 moving average is shown in red and the 50 moving average in blue. For the medium-term oriented investor to invest, it is advisable to look at the 200 moving average. As long as the index is above the moving average and the moving average is rising, the investment is made. If the price falls below it, the investment ends. Thus, the upward movement of around 1,000 points from 2009 to 2010 could be followed with very simple means. Shortly before the crash in 2011, investors would have exited. A buy signal would have been active since around 6,350 points since 2012. As of February 2014, this signal has caused investors to lose 3,300 points. It is characteristic for sideways phases that this method delivers many false signals. However, if the investor catches a pronounced trend movement, the gains from this trend movement more than compensate for the losses from any previous false signals.

This very simple principle offers nowhere near the possibility of entering or exiting in the area of turning points, but it is generally sufficient to observe the course of the price once a month in order to be present during major trend phases. When looking at the 50 moving average, it becomes clear that it is much closer to the price trend. Here, the above-mentioned method generates more frequent entries and exits. However, these come much earlier and offer the opportunity to participate more comprehensively, especially in strong trend phases.