How to Calculate EWMA

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An exponential weighted moving average is one of the metrics investors use to measure a stock's historical volatility. The weighting gives a higher value to more-recent data points. Weighting these items exponentially increases the difference in value between older and newer pieces of data.

Choosing a Smoothing Factor

Before you can calculate any type of weighted average, you must choose a smoothing factor between zero and one. The smoothing factor determines the impact of the weighting on each data point. You can express the smoothing factor as a decimal or a percentage.

Setting the Weights

To determine the weight for the first item, subtract the smoothing factor from one and convert the result to a percentage. Multiply the weight for the first item by the smoothing factor to find the weight for the next item. Repeat this step for each data point in your series. For example, if your smoothing factor is 0.90, the weight for the first item would be 10 percent. The second weight would be 90 percent of this, or 9 percent.

Calculating the EWMA

Multiply each data value by itself to get the square of the item. Multiply this result by the weighting factor you calculated for that item to find the EWMA variance. Take the square root of the variance to find the volatility of the stock.


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