Moving Average

There are several types of moving averages. The most basic is the simple moving average (SMA), which is the sum of closing prices over a particular period divided by the number of days in that period.

For example, a five-day simple moving average would be the sum of the closing prices of the five most recent trading days, divided by five; a 20-day moving average would be the sum of the 20 most recent closing prices divided by 20, and so on. Each day the most recent closing price is added to the equation and the most distant day is dropped off.

A weighted moving average (WMA), the most simple of which is referred to as a linearly weighted moving average, multiplies closing prices by a weighting factor that emphasizes recent price action. The oldest price in the calculation is multiplied by 1, the second oldest by 2, the third oldest by 3, etc.

For example, a standard five-day weighted moving average would multiply the closing price of the fifth most recent trading day (five trading days ago) by one, the fourth most recent trading day by two, the third most recent trading day by three, the second most recent trading day by four, and the most recent trading day by five. These products would be summed and then divided by the sum of the weighting factors (in this case, 1 + 2 + 3 + 4 + 5 = 15) to derive the linearly weighted moving average value for the current day. Other weighting schemes can be used to increase or decrease the emphasis of more recent prices.

An exponential moving average (EMA) is actually a specific type of weighted moving average. It uses a constant (a smoothing factor) between 0 and 1 in the following manner: the current closing price (C) multiplied by the smoothing constant (S) added to the product of the previous day's exponential moving average value (PEMA) and 1 minus the smoothing factor, or:

• Today's EMA = S*C + (1 - S)*PEMA

While the description and formula seems somewhat confusing, the approach is actually simpler to calculate than other moving averages because all you need is today's closing price and yesterday's EMA value.

Final notes: The preceding descriptions use daily closing prices. Moving averages can, of course, be constructed on intra-day, weekly or monthly time frames, and substituting the open, low, high or average price of a bar for the closing price.

Over the long run, most studies have shown the practical differences of the these three moving averages types to be negligible. Using one over the other can only be considered a matter of personal preference. In fact, some traders dislike standard weighted and exponential moving averages because they feel these calculations distort recent price action.

One distinct type of moving average is the Adaptive Moving Average (AMA), which dynamically adjusts the number of days in the moving average calculation to current market volatility: In high volatility-periods the number of days would increase (making the average less sensitive and less prone to whipsaws), and in low-volatility periods the number of days would decrease (making the average more sensitive to smaller price swings).

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