Moving Average

Moving Averages are one of the most popular and easy to use tools available to the technical analyst. By using an average of prices, moving averages smooth a data series and make it easier to spot trends. This can be especially helpful in volatile markets.

A moving average (MA) is an average of data for a certain number of time periods. It "moves" because for each calculation, we use the latest x number of time periods' data.  There are two major types of Moving Averages:  "Simple" and "Exponential".
 

Simple Moving Average

A simple moving average (SMA) is formed by finding the average price of a currency or commodity over a set number of periods. Most often, the closing price is used to compute the moving average. For example: a 5-day moving average would be calculated by adding the closing prices for the last 5 days and dividing the total by 5.

A moving average moves because as the newest period is added, the oldest period is dropped. If the next closing price in the average is 15, then this new period would be added and the oldest day, which is 10, would be dropped. The new 5-day moving average would be calculated as follows:

Over the last 2 days, the moving average moved from 12 to 13. As new days are added, the old days will be subtracted and the moving average will continue to move over time.

moving averages are lagging indicators and will always be behind the price. Because moving averages are lagging indicators, they fit in the category of trend following. When prices are trending, moving averages work well. However, when prices are not trending, moving averages do not work
 

Exponential Moving Average

In order to reduce the lag in simple moving averages, technicians sometimes use exponential moving averages, or exponentially weighted moving averages. Exponential moving averages reduce the lag by applying more weight to recent prices relative to older prices. The weighting applied to the most recent price depends on the length of the moving average. The shorter the exponential moving average is, the more weight that will be applied to the most recent price. For example: a 10-period exponential moving average weighs the most recent price 18.18% and a 20-period exponential moving average weighs the most recent price 9.52%. The method for calculating the exponential moving average is fairly complicated. The important thing to remember is that the exponential moving average puts more weight on recent prices. As such, it will react quicker to recent price changes than a simple moving average. For those who wish to see an example formula for an exponential moving average, one is provided below. Others may prefer to skip this section and move on the comparison of the moving averages.

Exponential Moving Average Calculation

The formula for an exponential moving average is:

X = (K x (C - P)) + P

X = Current EMA
C = Current Price
P = Previous period's EMA*
K = Smoothing constant
(*A SMA is used for first period's calculation)

The smoothing constant applies the appropriate weighting to the most recent price relative to the previous exponential moving average. The formula for the smoothing constant is:

K = 2/(1+N)
N = Number of periods for EMA

For a 10-period EMA, the smoothing constant would be .1818.

The EMA formula works by weighting the difference between the current period's price and the previous period's EMA and adding the result to the previous period's EMA. There are two possible outcomes: the weighted difference is either positive or negative.

1. If the current price (C) is higher than the previous period's EMA (P), the difference will be positive (C - P). The positive difference is weighted by multiplying it by the constant ((C - P) x K) and the answer is added to the previous period's EMA, resulting in a new EMA that is higher ((C - P) x K) + P.
   
2. If the current price is lower than the previous period's EMA, the difference will be negative (C - P). The negative difference is weighted by multiplying it by the constant ((C - P) x K) and the final result is added to the previous period's EMA, resulting in a new EMA that is lower ((C - P) x K) + P.