 # Education Excerpt: SMA, LWMA, GMA, TMA, EMA

Education
NASDAQ:AAPL   Apple Inc 9219 views
We decided to publish second part of the paper on moving averages. The first part detailed Simple Moving Average . In the second part we decided to present: linearly weighted moving average (LWMA), geometric moving average ( GMA ), triangular moving average (TMA) and exponentially smoothed moving average ( EMA ).

The first part can be read by clicking on chart below:

Possible uses of the moving average
• Identification of trends
• Identification of price extremes
• Identification of support and resistance levels
• Identification of signals

Identification of trend
The moving average can be used as simple tool to determine prevailing trend. Simplest way to determine current trend using moving average is to compare current value of security to current value of moving average. If value of moving average is below price of the security, then trend is considered to be upward. Contrary to that when value of moving average is above price of the security then trend is considered to be downward. Another method of determining trend is to use two same moving averages but with different length (different number of hours or days, etc.). These two moving averages would be then plotted on graph as two simple lines occasionally crossing. Trend would be considered upward when shorter moving average would be above longer moving average. Opposite to that, if shorter moving average would be below longer moving average then trend would be regarded to be down.

Illustration 1.01
Picture above depicts daily chart of XAUUSD . It is observable that price continued to rise most of the time when it was above 10-day SMA . It is also observable that when price dropped below 10-day SMA then it continued to decline further.

Identification of price extremes
Analyst can find another utilization of moving average in finding the price extremes. This is possible due to natural tendency of price to move back towards its moving average after it deviated too far from it.

Illustration 1.02
Graph above depicts General Motors on daily time frame. It is visible that when price deviated too far from its 10-day SMA then retracement followed. However, it is not a rule that price will retrace full length back to moving average once it deviated too far from it.

Identification of support and resistance levels
Another possible use of moving averages lies in using them as specific support and resistance levels. In rising markets price has tendency to correct towards moving average before continuing to rise further. Similarly, in declining markets price tends to suddenly increase towards moving average and then drop and continue lower.

Identification of signals
Generally, when moving average with lower period interval crosses above moving average with longer period interval it is considered bullish signal. On the other hand, when moving average with longer period interval crosses above moving average with lower period interval it is considered bearish signal. These crossovers can serve as specific buy and sell signals in markets that are trending.

Illustration 1.03
Picture above shows same graph of General motors as is depicted in Illustration 1.02. However, instead of one 10-day SMA this graph also includes 20-day SMA . It is easily identifiable where these two moving averages cross each other and by doing so generate specific buy and sell signals. However, we have to note that in non-trending markets this method lacks utility since moving averages tend to produce a lot of false signals.

The Linearly Weighted Moving Average (LWMA)
The Linearly Weighted Moving Average (LWMA) is very similar to the Simple Moving Average ( SMA ) we introduced in our previous education excerpt. But while SMA gives each time period involved in the calculation same weight LWMA differentiates between the weight linked to each time interval. Normally, 10-day SMA calculation would be conducted by summing up each value per time period and then dividing this result by total number of time intervals (which would be 10 in this particular example). In this calculation each time period (each day) would have 10% weight. However, as mentioned before, LWMA gives each time interval different weight. This unequal redistribution of weight can be achieved in two simple steps. In the first step analyst multiplies each day's value and sums up resulting values together. Then in the second step analyst divides resulting value (from the first step) by the sum of all multipliers. For example, in 10-day LWMA first day's value would be multiplied by 10. Then second day's value would be multiplied by 9; and third day's value would be multiplied by 8 (continuing up to 10 days where last day's value would be multiplied by 1). Resulting value for each time interval would be then summed up and divided by 55 (multipliers: 10+9+8+7+6+5+4+3+2+1 = 55). This simple change in formula would result in giving 10th (most recent day) day in the calculation twice the weight of 5th day and ten times the weight of the 1st day. Calculation of 10-day LWMA for 11th day would then involve weighting data from 2nd day up to 11th day while dropping the 1st day's value from data set being used in the calculation. Assigning different weight to each time interval helps to give more relevance to the most recent days as opposed to giving less importance to days before that.

Formula
LWMA = [(Pn * W1) + (Pn-1 * W2) + (Pn-2 * W3)] / summation of W
P = price for the period
n = period
W = the assigned weight to each period (highest weight goes first and then it linearly declines)

Illustration 1.04
Chart above depicts two different moving averages. First is 10-day SMA (blue) and second is 10-day LWMA (yellow). While these two moving averages have same length they are different in shape. This is because of unequal redistribution of weight. This allows LWMA to act in advance of SMA .

Geometric Moving Average ( GMA )
The Geometric Moving Average ( GMA ) is another form of moving average. But rather than using price in its calculation GMA uses percentage changes between the previous time period and the current time period. This type of moving average distributes weight equally as SMA . In addition to that it suffers from lag. When SMA and GMA (with same length) are plotted on same graph they are not different in shape or dimensions. Therefore they would overlay each other.

The Triangular Moving Average (TMA)
The Triangular Moving Average (TMA) is another type of moving average that is different from previous types of moving averages in that it is double smoothed. Its calculation begins with taking SMA with predetermined number of bars. After that these results are being used to take SMA of former SMA . However, length of second SMA is only half of that used in calculation of original SMA . For example, 20-day SMA would be smoothed through calculation of 10-day SMA that would use data from 20-day SMA . The result can be then plotted on graph and it is depicted as smoothed line. TMA represents the trend better since it is double smoothed, however, at cost of sensitivity to trend changes. When TMA and SMA (with same length) are plotted on same graph they are different in shape and dimensions.

Illustration 1.05
Picture above shows daily graph of PEP . Three moving averages are depicted: SMA , LWMA, TMA. They all observe same 10-days, however, each acts differently.

The Exponentially Smoothed Moving Average ( EMA )
The Exponentially Smoothed Moving Average ( EMA ) is type of moving average that weights importance on the most recent data. Decrease in weight from one time interval (one day) to another is exponential; and unlike SMA and LWMA exponential moving average has ability to use information outside the length of the moving average. Result from calculation of EMA can be then plotted on graph similarly like result from SMA , LWMA or any other moving average. EMA is considered to be more responsive to trend changes and it can be used when analyst is concerned with effect of lag (which is stronger in SMA and LWMA).

Formula
EMA = Pricet x k + SMAy x (1-k)
t = today
k (multiplier) = 2/(number of days in period +1)
SMA = simple moving average of closing price
y = yesterday

Illustration 1.06
Picture above depicts daily graph of Raytheon . It also depicts 10-day SMA and 20-day EMA . It is visible that many fake signals took place once market started to trade sideways.

Disclaimer: This content is purely educational.