# EMA - Exponential Moving Average

Updated: 2024-03-12

Unlike the SMA, the EMA gives more weight to recent data, making it quicker to respond to price changes.

## Calculating

### Formula

EMA = (Close - Previous EMA) * Multiplier + Previous EMA

Where:

• Close: the closing price for a given period (Price today/now). Here close prices is for example
• N: the period of the EMA.
• Multiplier: 2 / (N + 1)
• Previous EMA is the EMA of the previous period.

The EMA for the first period is just the Close price.

But for subsequent periods, it’s calculated as follows:

• EMA = (Close - Previous EMA) * Multiplier + Previous EMA
• EMA[i] = (Close[i] - EMA[i-1]) * 2/(N+1) + EMA[i-1]

However, the EMA’s calculation is slightly more complex for the initial period because there is no previous EMA. In this case, we use the SMA as the first EMA:

EMA(first period) = SMA


Example:

Let’s calculate a 5-minute EMA at Minute 6 with the following market data:

MinuteOpenHighLowCloseEMA
1$10.0$11.0$9.5$10.0-
2$10.1$12.1$10.0$12.0-
3$12.2$15.2$12.0$15.0-
4$15.1$15.1$13.9$14.0-
5$14.1$16.1$14.0$16.013.4(SMA)
6$16.1$16.1$14.9$15.015.67
7$15.1$17.1$15.0$17.0
8$17.1$17.1$15.9$16.0
9$16.1$18.1$16.0$18.0

Can be calculated from first price

Here, N = 5, so Multiplier = 2 / (5 + 1) = 0.33.

• SMA(5) = (10.0 + 12.0 + 15.0 + 14.0 + 16.0) / 5 = 13.4
• This value becomes the first EMA (EMA[5]). Now, to calculate the EMA for the 6th minute, we use the EMA formula:
EMA[6] = (Close[6] - EMA[5]) * multiplier + EMA[5]
= (15.0 - 13.4) * 0.33 + 13.4
= 14.13


## Pros and Cons

Pros:

• More responsive: By giving more weight to recent prices, the EMA can adapt faster to price changes.
• Combines trend and momentum: The EMA not only captures the overall trend but also shows the asset’s momentum.
• Often used for High frequency trading.

Cons:

• More prone to false signals: The sensitivity of the EMA can sometimes lead to false signals, especially in volatile markets.
• Complex calculation: Compared to the SMA, the EMA’s calculation is slightly more complex, especially for longer periods.

## Example of signals

Like the SMA, traders often use two EMAs: a short-term one and a long-term one. When the short-term EMA crosses above the long-term EMA, it’s a bullish (buy) signal, and when it crosses below, it’s a bearish (sell) signal.

True Positive:

In minute 7, the short EMA crosses above the long EMA, which is a buy signal. The price then goes up, confirming this was a correct signal.

In a stable uptrend, the short-term EMA might cross above the long-term EMA, correctly suggesting that it’s a good time to enter a long position.

False Positive:

In minute 11, the short EMA dips below the long EMA, suggesting a sell signal. However, the price increases in the next minute, making this a false signal.

In a volatile market, the price might swing up and down sharply, causing the short-term EMA to cross the long-term EMA back and forth, generating multiple buy and sell signals that could be misleading.

In real trading, EMA can be used in combination with other indicators such as MACD (Moving Average Convergence Divergence) or Bollinger Bands.

For instance, a trader might look for the short-term EMA to cross above the long-term EMA and the MACD to cross above its signal line as a confirmation for a long position.