A:

Moving averages are one of the most popularÂ tools used by active traders to measure momentum. The primary difference between aÂ simple moving average,Â weighted moving average and exponential moving average is the formulaÂ used to create them.

## Simple Moving Average

The simple moving average (SMA) was prevalent before the rise of computers due to the ease in calculating. The increase in processing power has made other types of moving averages and technical indicators easier to use. A moving average is calculated from the average of the closing prices for the time period being examined. A moving average most often uses daily closing prices, but it can also be calculated for other timeframes. Other price data such as the opening price or the median price may also be used. At the end of the new price period, that data is added to the calculation, while theÂ oldest price dataÂ in the series is eliminated.

For a simple moving average, the formula is the sum ofÂ the data points over a given period divided by the number of periods. For example, the closing prices of Apple IncÂ (AAPL) from June 20-26, 2014 were as follows:

 Date Closing Price of AAPL June 26 \$90.90 June 25 \$90.36 June 24 \$90.28 June 23 \$90.83 June 20 \$90.91

A five-period moving average, based on the prices above, would be calculated using the following formula:

(P1+P2+P3+P4+P5)/5

P = Period

(\$90.90+\$90.36+\$90.28+\$90.83+\$90.91)/5 = \$90.656

Based on the equation above, the average price over the period listed above was \$90.66. Using moving averages is an effective method for eliminating strong price fluctuations. The key limitation is that data points from older data areÂ not weighted any differently than data points nearÂ the beginning of the dataÂ set. This is where weighted moving averages come into play.

## Weighted Moving Average

Weighted moving averages assign a heavier weighting to more current data points since they are more relevant than data points in the distant past. The sum of the weighting should add up to 1 (or 100%). In the case of the simple moving average, the weightings are equally distributed, which is why they are not shown in the table above.

For example:

 Date Closing Price of AAPL Weighting June 26 \$90.90 5/15 June 25 \$90.36 4/15 June 24 \$90.28 3/15 June 23 \$90.83 2/15 June 20 \$90.91 1/15

The weighted average is calculated by multiplying the given price by its associated weighting andÂ totalingÂ the values. The denominator of the WMA is the sum of the number of price periods as a triangular number.Â In the example above, the weighted 5-day moving average would be \$90.62.

((90.9*(5/15))+(90.36*(4/15))+(90.28*(3/15))+(90.83*(2/15))+(90.91*(1/15)))

In this example, the recent data point was given the highest weighting out of an arbitrary 15 points. You can weigh the values out of any value you see fit. The lower value from the weighted average above relative to the simple average suggests the recent selling pressure could be more significant than some traders anticipate. For most traders, the most popular choice when using weightedÂ moving averages is to use a higher weighting for recent values. (For more information, see:Â Moving Average Tutorial.)

## Exponential Moving Averages

Exponential moving averages (EMAs),Â are also weighted towardÂ the most recent prices, but the rate of decrease between the one price and its preceding price is not consistent. The difference in decrease is exponential. Rather than every preceding weight being 1.0 smaller than the weight in front of it, you might have a difference between the first two period weights of 1.0, a difference of 1.2 for the two periods after those, and so on.

Calculating an EMA involves a couple of steps. The first step is to determine the SMA for the time period, which is the first data point in the EMA formula. Then, a multiplier is calculated by taking 2 divided by the number of time periods plus 1. The final step is to take the closing price minus the prior day EMA, times the multiplier plus the prior day EMA. (For related reading, see: What is the exponential moving average (EMA) formula and how is the EMA calculated?)

## Which Moving Average Is More Effective?

Because anÂ exponential moving averageÂ (EMA) uses an exponentially weighted multiplier to give more weight to recent prices, some believe it provides a more effective indicator to determine trend when compared with aÂ WMAÂ or SMA. Some believe that the EMA is more responsive to changes in trend. On the other hand, the more basic smoothing provided by the SMA may make it better for finding simple support and resistance areas on a chart. In general, moving averages smooth price data that can otherwise be visuallyÂ noisy.

The functions of an EMA and a WMA are similar, relying more heavily on the most recent prices and placing less value on older prices. Traders use these over SMAs if they are concerned about the effects of lags in data reducing the responsiveness of the moving average indicator.

All moving averages have a significant drawback in that they areÂ lagging indicators. Since moving averages are based on prior data, they suffer a time lag before they reflect a change in trend. A stock price may move sharply before a moving average can show a trend change. A shorter moving average suffers from less lag than a longer moving average.

Still, this lag is useful for certain technical indicators known as moving average crossovers. The technical indicator known as theÂ death crossÂ occurs when the 50-day SMA crosses below the 200-day SMA, and it is considered a bearish signal. An opposite indicator known as the golden cross is created when the 50-day SMA crosses above the 200-day SMA, and it is considered a bullish signal. (For related reading, see: How to Use a Moving Average to Buy Stocks.)

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