Technical Studies: Simple and Exponential Moving Averages

Moving averages smoothen out the price fluctuations of a security or index by revealing its average closing price over a selected period.

Moving averages are reactive, as they are based on the historical price action of the security or index. They are plotted based on the selected frequency (minutes/hours/days/weeks/months). If a stock is trading above its 50-day moving average, then investors are more bullish (positive) about that stock now than they have been, on average, during the last 50 trading days. Similarly, if the stock is trading below its 50-day moving average, then investors are more bearish (negative) about that stock now than they have been, on average, during the last 50 trading days.

Intersection points are also important when viewing moving averages. If a stock crosses its 50-day moving average trending downward, for example, this could be interpreted as a signal to sell. Similarly, if the stock crosses its 50-day moving average trending upward, this could be interpreted as a signal to buy.

Ten-day and 20-day moving averages are considered useful for pinpointing very short-term price trends. Fifty-day averages are considered useful for showing intermediate-term price trends. And 100-day and 200-day moving averages are considered useful for interpreting longer-term price trends.

Simple Moving Average (SMA) Calculation: The default SMA is simply the average closing price of the security for the past 50 trading periods (minutes/hours/days/weeks/months, based on the selected frequency) divided by 50, plotted on a chart. The SMA calculation is as follows:
SMA = Sum of the last n trading periods / n
Where the default value for n is 50, but can be customized.

Exponential Moving Average (EMA) Calculation: Compared to the SMA, the EMA puts more weight on recent price action. As a rule, EMAs calculated over shorter periods will follow the price line more closely than longer periods. A 10-period EMA will follow the price line more closely than a 20-period EMA, particularly when the price action is volatile.

The default EMA is the closing price during the last 20 trading periods (minutes/hours/days/weeks/months, based on the selected frequency).

In order to calculate EMA, first determine the exponent:
Exponent = 2 / (Number of Periods + 1)
Note: The Exponent for a 20-period MA is 0.0952 [or 2 / (20 + 1)]

Then calculate the EMA:
EMA = (Today's close × Exponent) + (previous EMA × (1 - Exponent))

For the 20-period EMA example,
EMA = (Today's close × 0.0952) + (previous EMA × (1 - 0.0952))