The Moving Average (MA) indicator calculates the moving average value of market prices within a certain period of time to obtain a trend value, which is used as a tool for analyzing price trends. Its purpose is to form a trend chart based on average values.
Its a highly frequently used chart-based trading tool. The advantage of the moving average lies in its ability to mitigate price volatility, eliminate some short-term and irregular fluctuations, and make the price trend look smoother. Especially in short-term trading, traders use very small time frames, such as 1-minute or 3-minute charts for trading. The smaller the time frame, the stronger the randomness. At this time, candlestick traders often get into relatively big trouble. And in such cases, the moving average can play a relatively good role.
There are many types of moving averages. The three most commonly used ones are the simple moving average, the weighted moving average, and the exponential moving average. There are certain differences in structure and application among these three types of moving averages, which need to be discussed separately.
Simple Moving Average (SMA)
The Simple Moving Average is the most widely used. For traders, there is no need to pursue an overly complex average. From experience, the simple moving average is sufficient for use. The calculation method of the simple moving average is to sum up the data to be calculated and then divide by the total number of observed data. The number obtained at this time is the so-called average value. At this time, a new observed data is added to the summation data sequence, such as the closing price of the day, and at the same time, the first item of the original data sequence is removed. The new sum obtained is divided by the total number of data to get a new average value. By repeating this process continuously, a series of average values can be obtained. Then connect these average values with lines in the chart, and a simple moving average is obtained.
The SMA is an arithmetic moving average calculated by adding the elements in a time series and dividing the sum by the number of time periods. It is the most popular technical analysis tool used by traders. All elements in the SMA have the same weight. If the moving average period is 5, then each element in the SMA will have a weight of 20% (1/5) in the SMA.
The SMA is usually used to identify the trend direction, but it can also be used to generate potential trading signals.
The formula for calculating the SMA is simple:
SMA = (sum of data points within the moving average period) / (total number of periods)
Weighted Moving Average(WMA)
A Weighted Moving Average refers to a moving average that assigns specific weights to each data point within the moving average period when calculating the average value. The exponential moving average is a type of WMA, where elements during the moving average period are assigned weights that increase exponentially.
The linearly weighted moving average (LWMA), often also referred to as the weighted moving average (WMA), is calculated by assigning linearly increasing weights to the elements within the moving average period.
If the moving average period contains ten data entries, the most recent element (the tenth element) will be multiplied by ten, the ninth element will be multiplied by nine, and so on until the multiplier for the first element is one.
Then the sum of all these linearly weighted elements is added together and divided by the sum of the multipliers. If there are 10 elements, the sum will be divided by 55 (n(n + 1)/2). The following figure plots the SMA (red line), EMA (green line), and LWMA (purple line) over a 30 -day period.
It can be seen from the above figure that, like the exponential moving average, the WMA responds more quickly to changes in the price curve than the simple moving average.
However, its response to fluctuations is slightly slower than that of the EMA.
The slow response to fluctuations is because the LWMA focuses more on the most recent data than the EMA. In the case of the EMA, the weight of each new data point is continuously increased exponentially.
Exponential Moving Average（EMA）
The simple moving average is sometimes too simple and is not very effective when there are peaks in security prices. The exponential moving average gives more weight to the most recent period.
This makes them more reliable than the SMA and better represents the recent performance of the security, so they can be used to create a better moving average strategy.
The EMA is calculated as follows:
Weighted multiplier = 2 / (moving average period + 1)
EMA = ((closing price – previous day/bar EMA) × multiplier) + previous day/bar EMA
Rewritten as: EMA = (closing price) × multiplier + (previous day/bar EMA) × (1 – multiplier)
The latest data of the shorter-period EMA has a greater weight than that of the longer-period EMA. For example, the weight of a 10-period EMA is 18.18% (2/11), while the weight of a 20-period EMA is 9.52% (2/21).
It is called an exponential moving average because the weight of each item in the moving average period increases exponentially compared to the weight of its previous item. The exponential moving average responds more quickly than the simple moving average, as shown in the following figure.
In the figure below, the blue line represents the daily closing price, the red line represents the 30-day SMA, and the green line represents the 30-day EMA.
Below I have mentioned an excerpt from the book “Technical Analysis of the Financial Markets” by John J. Murphy, which was published by the New York Institute of Finance in 1999. This work contains one of the best explanations regarding the advantages of the exponentially weighted moving average compared to the simple moving average.
The process is as follows:
“The exponentially smoothed moving average addresses two problems associated with the simple moving average. First, the exponentially smoothed average assigns greater weight to more recent data. Therefore, it is a weighted moving average.
However, although it places less emphasis on past price data, its calculation does include all data throughout the life cycle of the instrument.
Furthermore, the user can adjust the weights to give a greater or smaller weight to the price of the most recent day and add it to a certain percentage of the previous day’s value. The sum of the two percentage values is 100.”
Triangular Moving Average (TMA)
First, calculate the simple moving average (SMA):
SMA = (D1 + D2 + D3 +….. + Dn) / n
Next, calculate the average of the SMA:
TMA = (SMA1 + SMA2 + SMA3 +…. + SMAn) / n
Consider the chart above, which includes the daily closing price curve (blue line), the 30 -day SMA (red line), and the 30 -day TMA (green line). It can be seen that the TMA is much smoother than the SMA. The fluctuation waves of the TMA are longer and more stable than those of the SMA.
Due to the double averaging, the TMA has a greater lag than other moving averages such as the SMA and EMA. It can be seen that it takes a longer time for the TMA to respond to price fluctuations.
Compared with the signals generated by the SMA, the trading signals generated by the TMA during the trend cycle will be farther away from the peaks and troughs of the cycle, so less profit will be obtained by using the TMA.
However, during the consolidation period, the TMA will not generate as many trading signals as the SMA, which will prevent traders from holding unnecessary positions and thus reduce trading costs.
Variable Moving Average (VMA)
The variable moving average is an exponentially weighted moving average developed by Tushar Chande in 1991. Chande suggested that the performance of the exponential moving average can be improved by using the volatility index (VI) to adjust the smoothing period when market conditions change. Volatility is an indicator that measures how fast prices change over time.
The volatility index shows the market’s forecast of volatility for the next 30 days.
The purpose of developing the VMA is to slow down the averaging during the price consolidation period to avoid invalid trading signals, and to speed up the averaging during the market trend to make full use of the trend price.
The method for calculating the variable moving average is given below:
VMA = ( * VI * closing price) + (1 – ( * VI)) * VMA[1]
where,
= 2 / (N + 1)
VI = a measure of volatility or trend strength
N = the smoothing period determined by the user
VMA [1] = the previous value of the variable moving average
Reproduction Notes：InvestFancy » Moving Average