Exponential Moving Average (EMA)

An Exponential Moving Average is another type of moving average. A simple moving average, the price data has an equal weight in the computation of the average. Also, the oldest price data is removed from the moving average as a new price is added to the computation. The exponential moving average assigns a weight to the futures price data as the average is calculated. Thus, the oldest price data in the exponential moving average is never removed, but it has only a minimal impact on the moving average. This study displays the exponential moving averages as a crossover system. You may select up to three different averages. Generally, the lengths are short, intermediate, and long term. A commonly used system is 4, 9, and 18 intervals. An interval may be in ticks, minutes, days, weeks or months; it is a function of the commodity chart type.

A buy signal occurs when the short and intermediate term averages cross from below to above the longer term average. Conversely, a sell signal is issued when the short and intermediate term averages cross from above to below the longer term average. You can use the same signals with two moving averages, but most market technicians suggest using longer term averages when trading only two exponential moving averages in a crossover system.

Another trading approach is to use the current price concept. If the current commodity price is above the exponential moving averages, you buy. Liquidate that position when the current commodity price crosses below either moving average. For a short position, sell when the current commodity price is below the exponential moving average. Liquidate that position when current commodity price rises above the exponential moving averages.

As you use exponential moving averages, do not confuse them with simple moving averages. An exponential moving average behaves quite differently than a simple moving average. It is a function of the weighting factor or length of the average.

Parameters:

• Period1 (4) - the number of bars, or period, used to calculate the first moving average.
• Period2 (9) - the number of bars, or period, used to calculate the second moving average.
• Period3 (18) - the number of bars, or period, used to calculate the third moving average.

Computation

The formula to calculate an exponential moving average is as follows:

EMAt = EMAt-1 + (k * (Pt - EMAt-1))

• EMAt is the exponential moving average for the current period.
• EMAt-1 is the exponential moving average for the previous period.
• Pt is the price for the current period.
• k is the exponential smoothing constant.

FutureSource does not ask you to specify the smoothing constants. It asks you to specify the length of the moving average. You can then determine the smoothing constant from the formula listed below.

If you specify an exponential moving average length of 10, the smoothing constant is 0.18. The formula to determine the smoothing constant is:

k = 2 / (n + 1)

• k is the smoothing constant
• n is the length of the moving average.

Now, substitute the above values in the formula.

k = 2 / (10 + 1) = 2 / 11 =.1818

Conversely, if you know the smoothing constant, you must derive the length of the moving average. In this example, use a smoothing constant of .125 You can solve the above equation for the value of n, which produces the following formula:

n = (2 / k) - 1

Now, substitute the above values for the equation.

n = (2 /.125) - 1 = 16 - 1 = 15

Please remember that FutureSource always asks for the length of the moving average, not the smoothing constant. If you know the smoothing constant, you use the above formula to determine the length of the moving average. If you set the length of the moving average and want to know the smoothing constant, use the formula to solve for the smoothing constant or k.

Note: There are several variations to the above formula.