# EMA - Exponential Moving Average

### On This Page

## About

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

Minute | Open | High | Low | Close | EMA |
---|---|---|---|---|---|

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 | $16.0 | 13.4(SMA) |

6 | $16.1 | $16.1 | $14.9 | $15.0 | 15.67 |

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.

## Use in Real Trading

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.