What Is the Exponential Moving Average (EMA)?

The exponential moving average (EMA) is a technical chart indicator that tracks the price of an investment such as a stock or a commodity o🔯ver time.

Like the simple moving average (SMA), the EMA tracks price trends over time. But the EMA is a weighted moving average that gives more importance to recent price data within the timeline being tracke🌜d.

Watching several EMAs at🃏 the same time is easy to do with moving average ribbons.

Traders and analysts rely on moving averages and ribbons to identify turning points, continuations, and overbought or oversold conditions. They also can be used to 澳洲幸运5开奖号码历史查询:def♓ine areas of support and res♏istance and to measure the strength of price trends.

Calculating EMA

The EMA is designed to improve on a 澳洲幸运5开奖号码历史查询:simple moving average by giving more weight to the most recent price data, which is considered more relevant to investors than older data. Since new data carries greater weight, the EMA responds more quickly 𒁃than the SMA to price cꦯhanges.

The formula for calculating the EMA starts with the SMA and uses a multiplier. There are three steps in the calculation (although 澳洲幸运5开奖号码历史查询:chart applications do the math for you):

1. Compute the SMA
2. Calculate the multiplier for weighting the EMA
3. Calculate the current EMA

The calculation for the SMA is the same as computing an average or mean. That is, the SMA for any given number of time periods is the sum of 澳洲幸运5开奖号码历史查询:closing prices for that number of time periods, divided by that same numbe🥃r. So, for example, a 10-day SMA is just the sum of the closing prices for the past 10 days, di🌳vided by 10.

The mathematical formula looks like this:

$\begin{aligned}&\text{SMA} = \frac { A_1 + A_2 + ... + A_n }{ n } \\&\textbf{where:} \\&A_n = \text{Price of an asset at period } n \\&n = \text{Number of total periods} \\\end{aligned}$​SMA=nA1​+A2​+...+An​​where:An​=Price of an a💦sset at period nn=Number of total periods​

The formula for calculating♚ the weigh🍬ting multiplier looks like this:

$\begin{aligned} \text{Weighted multiplier} &= 2 \div (\text{selected time period} + 1) \\ &= 2 \div (10 + 1) \\ &= 0.1818 \\ &= 18.18\% \\ \end{aligned}$Weighted multiplier​=2÷(selected time period+1)=2÷(10+1)=0.1818=18.18%​

In both cases, we’re assuming a 10-day SMA.

So when it comes 𒐪to calculat🍰ing the EMA of a stock:

$\begin{aligned} &EMA = \text{Price}(t) \times k + EMA(y) \times (1-k) \\ &\textbf{where:}\\ &t=\text{today}\\ &y=\text{yesterday}\\ &N=\text{number of days in EMA}\\ &k=2 \div (N + 1)\\ \end{aligned}$​EMA=Price(t)×k+EMA(y)×(1−k)where:t=todayy=yesterdayN=number of days in EMAk=2÷(N+1)​

The weighting given to the most recent price is greater for a shorter-period EMA than for a longer-period EMA. For example, an 18.18% multiplꦡier is applied to the most recent price data for a 10-day EMA, as we did above, whereas for a 20-day EMA, only a 9.52% multiplier weighting is used.

There are aꦺlso slight variations of th💎e 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 sometimes watch 澳洲幸运5开奖号码历史查询:moving average ribbons, which plot a number of moving 🍸averages onto a price chart rather than just one moving average.

Thoug♎h seemingly complex based on the sheer number of concurrent lines, ribbons are easy to see on charting applications and offer a simple way of visualizing the dynamic relationship between trends in the short, intermediate, and long term.

Defined by their characteristic three-dimensional shape that seems to flow and twist across a price chart, moving average ribbons are easy to interpret. The indicators trigger buy and 澳洲幸运5开奖号码历史查询:sell signals whenever the moving aver൲age lines all converg🌳e at one point.

Traders look to buy on occasions when shorter-term moving averages cross above the longer-t𒊎erm moving averages from 🦂below and look to sell when shorter moving averages cross below from above.

How to Create a Moving Average Ribbon

To construct a 澳洲幸运5开奖号码历史查询:moving average ribbon, plot a large number of moving averag♛es of varying time ไlengths on a price chart.

Common parameters include eight or more moving averages and intervals that range from a two-dꦦay moving average to 🎃a 200- or 400-day moving average.

When the ribbon folds—when 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, s๊uggesting that prices are ranging and that a trend is strong or strengthening.

Downtrends are often chꦐaracterized by shorter moving averages crossing below longer moving averages.

Uptrends show shorter 🦩moving averages crossing above longer moving averages.

In these circumstances, the short-term moving averages act as 澳洲幸运5开奖号码历史查询:leading indicators that are ꦏconfirmed as longer-term averages trend towarꦐd them.

The Bottom Line

The preferred number and type of moving averages can vary considerably between traders, based on 澳洲幸运5开奖号码历史查询:investment strategies and the underlying security or index. But EMAs are especially popular because they give more weight to recent ꦛprices, responding earlier⛄ than other averages.

Some common moving average ribbon examples in𒊎volve eight separate EMA lines, ranging in length from a few days to many months.