Moving Averages

A Moving Average is one of the oldest and most widely used indicators. It allows for calculating the average value of a security over a given period p, where the term "moving" implies that this fixed period p shifts with each new trading session. Each new moving average value is therefore the average of the p previous prices before the current session. Moving averages are generally calculated using closing prices.

Several types of moving averages exist, the most common being:

• The "Simple" or "Arithmetic" Moving Average (SMA)
• The "Exponential" Moving Average (EMA)
• The "Smoothed" Moving Average (also known as "Smoothed" or "Rolling" Moving Average)
• The "Weighted" Moving Average (WMA)
• The "Triangular" Moving Average (TMA)
• The "Variable" Moving Average (VMA)
• The "Volume-Weighted" Moving Average
• The "Zero Lag" Moving Average (ZLMA)

The periods used for plotting moving averages depend on the time horizon objective. Generally, the following periods are used:

• 5 to 13 sessions for very short-term
• 14 to 25 sessions for short-term
• 26 to 49 sessions for short/medium-term
• 50 to 99 sessions for medium-term
• 100 to 200 sessions for long-term

The only difference between these various types of moving averages is the weight assigned to the prices within the chosen period.

1. The Arithmetic Moving Average gives equal weight to all prices in the period according to the formula:

   

2. The Exponential Moving Average gives more importance to recent prices according to the formula:

   

   The weight of prices decreases exponentially as they move further away from recent prices.

   

   The prices within the period account for approximately 86% of the average.

3. The Smoothed Moving Average, designed by Welles Wilder, is analogous to the exponential moving average but with a smaller coefficient k. It allows for smoothing prices by eliminating short-term fluctuations.

   

   The weight of prices decreases exponentially as they move further away from recent prices. For example, the weighting for a period p=10 looks like this:

   

   The prices within the period account for approximately 63% of the average.

4. The Weighted Moving Average gives more importance to recent prices according to the formula:

   

   The weight of prices decreases linearly:

   

5. The Triangular Moving Average is similar to the exponential moving average or the weighted moving average, except for the weighting system which is different. Exponential and weighted moving averages assign most of their weight to the most recent data. With the triangular moving average, the majority of the weight is assigned to the median portion of the period's data.

   

6. The Variable Moving Average is an exponential moving average that automatically adjusts the smoothing constant based on the volatility of the data series.

   The more volatile the data, the larger the smoothing constant used in the calculation, which consequently gives more weight to the most recent data. The reasoning is inverse for less volatile data.

7. The Volume-Weighted Moving Average was developed by Dick Arms, best known for inventing the Arms Index and the equi-volume graphical representation method. It is an original moving average calculation method that integrates volume into the calculation. It is calculated as follows:

   1. Calculation of average volume using all timeframes on the chart.
   2. Calculation of the volume unit or "volume increment" by multiplying the average volume by 0.67.
   3. Calculation of the volume ratio for each timeframe by dividing the actual volumes of the timeframe by the volume increment.
   4. Starting from the most recent timeframe and working backwards, we multiply the price of each timeframe by the period's volume ratio and cumulatively add these values until the total reaches the specified number of volume units. Only a portion of the last timeframe's volume is generally used.

8. The Zero Lag Moving Average is a variant of the exponential moving average aiming to reduce the lag of the average. It is calculated as follows:

   

   A classic exponential moving average applied to instruments changing linearly tends to produce a result close to the value at the midpoint of the period. The Zero Lag Moving Average compensates for this lag by calculating the average of the latest price increased by the difference with the median price of the period.

Examples

Interpretation

A moving average represents an average of prices; therefore, when it is below the prices, it indicates a bullish trend, and conversely, it indicates a bearish trend when the moving average is above the prices.

In theory, a buy signal is obtained when the moving average crosses above the price, and a sell signal when the moving average crosses below the price.

However, depending on the volatility of the asset, there may be false signals because the moving average might cross the price curve for only a few days before returning to its previous trend. To improve the probability of signal detection, confirmation of the signal by another indicator is sometimes desirable.

One can also use the crossover of moving averages of different periods to determine buy and sell signals.