The exponential moving average (EMA) is a weighted moving average (WMA) that gives more weighting, or importance, to recent price data than the simple moving average (SMA) does. The EMA responds more quickly to recent price changes than the SMA. The formula for calculating the EMA just involves using a multiplier and starting with the SMA.
The calculation for the SMA is very straightforward. The SMA for any given number of time periods is simply the sum of the stock's closing prices for that number of time periods, divided by that same number. So, for example, a 10day SMA is just the sum of the closing prices for the past 10 days, divided by 10.
The three steps to calculating the EMA are:
 Calculate the SMA.
 Calculate the multiplier for weighting the EMA.
 Calculate the current EMA.
The mathematical formula, in this case for calculating a 10period EMA, looks like this:
SMA: 10period sum ÷ 10
Calculating the weighting multiplier: [2 ÷ (selected time period + 1)] = [2 ÷ (10 + 1)] = 0.1818 or 18.18%
Calculating the EMA: [Closing priceEMA (previous day)] x multiplier + EMA (previous day)
The weighting given to the most recent price is greater for a shorterperiod EMA than for a longerperiod EMA. For example, an 18.18% multiplier is applied to the most recent price data for a 10 EMA, whereas for a 20 EMA, only a 9.52% multiplier weighting is used. There are also slight variations of the EMA arrived at by using the open, high, low or median price instead of using the closing price.
Using the EMA: Moving Average Ribbons
Traders use moving averages in devising their trading strategies. They do this via moving average ribbons, which plot a large number of moving averages onto a price chart. Though seemingly complex based on the sheer volume of concurrent lines, ribbons create an effective and simple way of visualizing the dynamic relationship between short, intermediate and longterm trends. Traders and analysts rely on ribbons to identify turning points, continuations, overbought/oversold conditions, to define areas of support and resistance, and to measure price trend strengths..
Defined by their characteristic threedimensional shape that seems to flow and twist across a price chart, moving average ribbons are very simple to create and interpret. They generate buy and sell signals whenever the moving average lines all converge at one point. Traders look to buy on occasions when shorterterm moving averages cross above the longerterm moving averages from below, and look to sell when shorter moving averages cross below from above.
To construct a moving average ribbon, simply plot a large number of moving averages of varying time period lengths on a price chart at the same time. Common parameters include eight or more moving averages and intervals that range from a twoday moving average to a 200 or 400day moving average. For ease of analysis, keep the type of moving average consistent across the ribbon – all EMAs, for example.
When the ribbon folds – all of the moving averages converge into one close point on the chart – trend strength is likely weakening and possibly pointing to a reversal. The opposite is true if the moving averages are fanning and moving apart from each other, suggesting that prices are ranging and that a trend is strong or strengthening.
Downtrends are highlighted by shorter moving averages crossing below longer moving averages. Uptrends, conversely, show shorter moving averages crossing above longer moving averages. In these circumstances, the shortterm moving averages act as leading indicators that are confirmed as longerterm averages trend towards them.
The number and type of moving averages vary considerably between traders, based on investment strategies and the underlying security or index. But EMAs are especially popular, because they give more weight to recent prices, lagging less than other averages. Some common ribbon examples involve eight separate EM lines, ranging in length from a few days to multiple months.

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