Moving Average (MA) for receiving buy or sell signals and MACD for determining the trading position size

In general, we can say that such indicators are quite good at showing the direction of the dominant trend. Their weaknesses include the facts that they are somewhat lagging and also do not work well during flats. Within this class, we will look at the indicators Moving Average (MA) and Moving Average Convergence / Divergence (MACD).

The moving average is one of the simplest indicators. Mathematically, this is the average price of the financial instrument under analysis for the last n periods. The difference between the moving average and the simple average is that when the next price bar is formed, it is included in the calculation, and the bar which was the last onebefore that is excluded from the calculation. Thus, it is as though the average were to “slide” to the right along with the formation of new prices. Let us have a look at the figure.

Figure 13. Constructing a moving average

The latest (current, instantaneous) value of the MA at the point x indicated by a red circle, is a simple arithmetic average (the sum of the values divided by their number) for n last prices of this financial instrument. Area B, shown in the figure in yellow, is the averaging period, i.e. the number of bars taken to calculate the MA value. The longer the averaging period, the less flexible the MA will be, and the laterit will react to the emerging trend. However, it will be better at filtering out small and insignificant price changes. The shorter the MA period, the more sensitiveit will be, but it will also react to price changes that do not comprise a trend.

The arrow in the figure indicates the direction of movement for this period (i.e. with the appearance of a new price, this interval will move one bar to the right). In the figure, we can see that at the beginning of the period under consideration there is a section equal to n (designated as A), for which the value of the moving average with averaging period n cannot be determined, since there is not enough data.

As can be seen from the figure, the MA shows the general direction of the trend developmentrather well, smoothing out the small fluctuations in the price that are irrelevant for trading. Incidentally, we should note that the MA indicator itself can be considered as a simplest digital filter (DF). The lagging is due to the very nature of the MA. The lagging value is equal to half the averaging period.

Completing the description of this indicator, we should note that there are many options for calculating moving averages. First, we can take not only n closing prices (Close)as the initial data array for the calculation of the MA, but also such values as the Typical Price (Typical Price = (High + Low + Close) / 3), the Median Price (Median price = (High + Low) / 2), or other certain price parameters. Also, another MA indicator can be used as input parameters (and any other indicator whatsoever). In this case, the price is called “doubly smoothed”. By analogy, the price can be smoothed three times, four times, etc. However, we must remember that each smoothing increases the lagging. Secondly, there are different types of moving average (simple, exponential, weighted, smoothened, etc.). In addition, there is a whole subclass of dynamic moving averages, which are supposed to adjust to the market. In a flat (where the traditional MA performs poorly), the averaging period of the dynamic MA increases to reduce the number of false signals. Once the indicator identifies the beginning of active movement, the MA period decreases sharply to reflect the emerging trend more flexibly.

The Moving Average Convergence / Divergence. This indicator is constructed on the basis of two exponential moving averages and is calculated as the difference between them. One of them is called “fast”, the other is“slow” (in accordance with their periods). Obviously, the fast moving average can be either above the slow one, or below it. Consequently, the values of the difference between them can be both positive and negative numbers. In the chart, these values are displayed in the form of a histogram (as a rule), although they can be represented by an ordinary curve. Also, the indicator has a signal line, which is a simple moving average of the values of the histogram.

Figure 14. Constructing the MACD

The MACD can be interpreted based on several characteristics.

Firstly, it is the intersections:

• buy when the histogram crosses the signal line upwards;
• sell when the histogram crosses the signal line downwards.

Secondly, it is the overbought / oversold zone, which an analyst can determine depending on how far (compared to recent values) the histogram is from the zero value.

Thirdly, it is the divergences. A bullish divergence occurs when the MACD histogram forms new highs, and the price fails to form them. A bearish divergence is the situation when the histogram forms new lows, and the price fails to do so. Divergences in overbought and oversold zones are considered to be the strongest and most significant signals.

Figure 15. Bullish divergence of the MACD

The figure shows that at point a, the price has generated a local high, which corresponds to a MACD highat point a`. The MACD indicator has formed a new highat point b`, which exceeds the previous one. At the same time, the price did not even reach level aat point b.

Let us also note the fact that MACD is constructed in a separate area of the chart (unlike the MA, which is shown directly in the price chart).

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