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The Moving Average (MA)

The Moving Average (MA) is a very popular trend indicator that can be used to determine the presence and direction of a trend. They are one of the most versatile tools that can be applied to price charts and are widely used as part of mechanical trading systems and strategies. The Moving Average was developed early part of the 20th century, pioneered initially by a market analyst named Richard Schabacker who used it to identify trends in the stock market. Schabacker's concept was further refined by other market technicians, including Robert Edwards and John Magee, who helped popularize the use of moving averages in their book: Technical Analysis of Stock Trends of 1948.

A Moving Average (MA) smooths out the erratic nature of price action by averaging price data over a specified look-back period. This can be an average of the closing price, the opening price, the high or the low; although the closing price is the most commonly used price data. Thus, a 5-day MA of the closing price is the average of the price close over the last 5 days.

As the MA averages past price data, they are lagging indicators that follow, rather than predict, price action. Thus, moving averages identify trends only after they have been established. Furthermore, a MA with longer look-back period is smoother and less sensitive to price changes than a shorter period MA but it has a greater degree of lag.

Types of Moving Averages

There are three popular types of Moving Averages: the Simple Moving Average (SMA); the Exponential Moving Average (EMA), the Smoothed Moving Average (SMMA), and the Linear Weighted Moving Average (LWMA). There are also less popular Moving Averages, such as the Triangular Moving Average (TMA), the Variable Moving Average (VMA) and the Volume Adjusted Moving Average (VAMA).

The Simple Moving Average (SMA)

The Simple MA is simply the average of the price data for the look-back period under analysis with no extra weighting given to any of the data. Thus, a 5-day MA is calculated simply by calculating the sum of the price for the past 5 days and dividing the result by 5, with the formula being:

SMA_n = ( price₁ + price₂ + ... + price_n ) ÷ n

where n is the look-back period of the SMA as specified by the trader.

The SMA has two weaknesses which can make it rather erratic. First, the SMA is sensitive to the price that is dropped as the new SMA is calculated. If the price that is dropped is well above average it can cause the SMA to drop appreciably and if the price that is dropped is way below average, it can cause the SMA to increase appreciably. Secondly, the SMA is sensitive to the latest price that is added to the calculation. If the price that is added is well above average it can cause the SMA to increase appreciably and if the price that is added is way below average, it can cause the SMA to decrease appreciably.

The Exponential Moving Average (EMA)

The Exponential MA is a refinement of the SMA that attempts to assign more weight to the most recent data, making it less sensitive to the price that is dropped from the calculation, and reduces lag. This is accomplished by applying a smoothing constant to a SMA and then calculating the EMA. Thus, the EMA is calculated in three stage: First, calculate the SMA for the look-back period (n); Second, calculate the Smoothing Constant (Sm) using the formula:

Sm = ( 2 ÷ ( n + 1 ) )

and finally, calculate the EMA using the formula:

EMA = ( price − previous EMA ) × Sm + previous EMA

The Smoothed Moving Average (SMMA)

The Smoothed (MA) is a combination of a SMA and an EMA. It gives the recent prices an equal weighting as the historic prices as it takes all available price data into account. This is achieved by subtracting the previous period’s SMMA from today’s price and adding the result to the previous period’s SMMA to find the current period’s SMMA. The formula for the SMMA starts by calculating the SMA with the same look-back period as the SMMA and dividing it by the look-back period:

SMMA₁ = SMA( n ) ÷ n

where n is the specified look-back period for the SMMA. The subsequent SMMA values are calculated using the formula:

SMMA( i ) = ( ( SMMA( i − 1 ) × n ) − SMMA( i − 1 ) + CLOSE( i ) ) ÷ n

where n is the look-back period of the SMMA, SMMA( i ) is the SMMA of the current bar, CLOSE( i ) is the current closing price.

The SMMA is almost identical to an EMA of twice the look-back period. In other words, 20-period SMMA is almost identical to a 40-period EMA.

The Linear Weighted Moving Average (LWMA)

The Linear Weighted MA is yet another refinement of the SMA that also attempts to assign more weight to the most recent data. However, it accomplished this by multiplying each price data by its position in the data stream with the oldest price data occupying position 1 and the latest price data occupying position n where n is the look-back period of the WMA as specified by the trader. The sum of the results is then divided by the summation of n. The formula is:

LWMA_n = ( ( price₁ × 1 ) + ( price₂ × 2 ) + ... + ( price_n × n ) ÷ ( n × ( n + 1 ) ) ) ÷ 2

Triangular Moving Average (TMA)

The Triangular (MA) is another refinement of the SMA that attempts to improve the indicator's sensitivity to the price action. The TMA attempts to do this by implementing a form of "double smoothing". First a SMA is calculated, then for each subsequent price bar a SMA of the SMA is calculated. This process gives more weight to the middle part of the data interval. The formula used is:

TMA_n = ( SMA _-1 + SMA _-2 + ... + SMA _-n ) ÷ n

where n is the look-back period of the TMA as specified by the trader.

Unfortunately, double smoothing does not overcome indicator lag and a number of traders prefer displacing the TMA to the left of the chart by half the look-back period, and extrapolating the "missing" data to the current bar. However, no form of extrapolation is 100% accurate resulting in the redrawing of the indicator as the data becomes available.

The Linear Weighted Moving Average (LWMA)

The Linear Weighted MA is yet another refinement of the SMA that also attempts to assign more weight to the most recent data. However, it accomplished this by multiplying each price data by its position in the data stream with the oldest price data occupying position 1 and the latest price data occupying position n where n is the look-back period of the WMA as specified by the trader. The sum of the results is then divided by the summation of n. The formula is:

LWMA_n = ( ( price₁ × 1 ) + ( price₂ × 2 ) + ... + ( price_n × n ) ÷ ( n × ( n + 1 ) ) ) ÷ 2

The Variable Moving Average (VMA)

A variable MA is an adaptation of the EMA that was developed by Tushar Chande in 1992. It uses price volatility, as indicated by a 9-period Chande Momentum Oscillator (CMO), to adjust the smoothing constant of the data series. When the volatility is higher, the smoothing constant is higher, which gives the current data more weight. Conversely, when the volatility is lower, the smoothing constant is lower, which gives the current data less weight. This makes the VMA more sensitive during periods of volatility and less sensitive during periods of low volatility, allowing the MA to be more reliable in both high and low volatility markets.

The Volume Adjusted Moving Average (VAMA)

The Volume Adjusted MA was developed by Richard W. Arms, Jr. It assigns weight to the data based on the volume of that period. Thus, the period with the most volume will have the greatest weight in determining the MA, while the period with the lowest volume will have the least weight.

A volume adjusted moving average is calculated by first assigning the weighting to each period using the formula:

( price × volume ) ÷ volume

Then a simple moving average is applied to the results for each period under analysis.

How to trade with Moving Averages?

There are two primary ways in which traders use Moving Averages to generate trade signals. These are crossovers of two or more Moving Averages and price bounce off the Moving Average. However, Moving Averages are also used as part of trading strategies, where they confirm or filter trade signals.

Moving Average Crossovers

The Moving Average MA crossover generally requires two Moving Averages: a fast moving MA, with a short look-back period, and a slow moving MA with a longer look-back period. The fast MA is close to the price action while the slow MA acts as a signal line. These crossovers can be bullish or bearish, with a bullish crossover being called the golden cross and the bearish crossover being called the death cross. The fast Moving Average can be replaced with the price action itself, which is a Moving Average with a look-back period of 1 and result in what is referred to as a price crossover.

The Golden Cross

The golden cross is a bullish crossover that occurs when a fast Moving Average crosses up over a slower Moving Average (MA), having been below that slower MA. The fast MA will have a shorter look-back period than the slow MA. The golden cross suggests that the trend is turning bullish and is a buy signal.

The Death Cross

The death cross is the bearish counterpart to the golden cross. It occurs when a fast MA crosses down below a slower MA, having been above that slower MA previously. As was the case with the golden cross, the fast MA will have a shorter look-back period than the slow MA. The death cross suggests that the trend is turning bearish and is a sell signal.

Triple Moving Average Crossover

A third Moving Average (MA), even slower MA, can also be added to the price chart. This MA acts as a trade filter, requiring a crossover of the two faster Moving Averages, and requiring both of the faster Moving Averages to cross over the slowest MA before a trade signal is generated.

In other words, in a bullish triple MA crossover, the fastest MA must first cross up over the slower MA, then both those Moving Averages must cross up over the slowest MA before a buy signal is generated. In a bearish triple MA crossover, the fast MA must cross down below the slow MA and both the fast and slow Moving Averages must then cross down below the slowest MA before a sell signal is generated. The result is a more reliable trade signal as the triple crossover requires more confirmation than the standard crossover. However, the triple crossover will also generate fewer trade signals and will have a greater degree of lag than the standard crossover.

Price Bounce

The Moving Average (MA) price bounces off the MA; it also generates potential trade signals. The price bounce requires only one MA but it does require the existence of a strong trend. The strength of the trend can be gleaned from the slope of the MA, or from other trend strength indicators, such as the Average Directional Index (ADX) or the Trend Strength Indicator (TSI).

The direction of the trend is relevant to the trade signal generated by the price bounce. In an uptrend, the price will pull back to the MA where it could bounce off the MA to the upside. When the price does bounce off the MA in an uptrend, it confirms the strength of the current uptrend and generates a potential buy signal. In a downtrend, the price will pull back to the MA before potentially bouncing off the MA to the downside. When this happens, it confirms the strength of the downtrend and generates a potential sell signal.

Here the Moving Average is treated as a dynamic support and resistance line that the price action fails to penetrate. This confirms that the strength of the trend has not dissipated, and that the trend has a far greater probability of continuing than reversing.

Advantages and Disadvantages of Moving Averages

Moving Averages Frequently Asked Questions

What does a Moving Average indicate?

A Moving Average (MA) is an average of the price movement of a security over a specified period of time. It indicates the existence and direction of a trend.

What is the purpose of Moving Averages?

Moving Averages are used to smooth out the random price movements of a security so that the trader can better understand the price movement over a period of time.

Can Moving Averages be used to trade futures?

Yes, Moving Averages are very versatile and can be used to trade any financial asset class, from stocks and forex, to bonds, commodities and futures.

Why is an EMA better than a SMA?

The Exponential Moving Average (SMA) assigns equal importance to each data point it averages. This makes it sensitive to the price data point falling out of the scope of the SMA and the latest price data point. The Exponential Moving Average (EMA), on the other hand, gives the later price data point more significance, making it less sensitive to the price data point falling out of the scope. This also reduces the amount of lag the EMA experiences.

What is the Golden Cross?

The golden cross is a bullish crossover signal that is generated when a fast MA crosses up over a slower MA. The fast MA will have a shorter look-back period than the slow MA.

What is the Death Cross?

The death cross is the opposite of the golden cross. It is a bearish crossover signal that is generated when a fast MA crosses down over a slower MA. The fast MA will have a shorter look-back period than the slow MA.

Summary

Applied as an overlay on top of the price chart, the simplicity and versatility of the Moving Average (MA), as well as its effectiveness, makes the MA a cornerstone of technical analysis. There are also various types of Moving Averages that average the price data slightly differently. Of the various types of Moving Averages, the Exponential Moving Average (EMA) is generally preferred as it assigns greater importance to more recent price data.

However, the MA is a lagging indicator that reacts to price data rather than predicting it. This may result in traders missing optimal trade entry or exit points at the very start or very end of a trend. The MA is also prone to generating false signals, particularly in non-trending, range-bound markets.