## Exponentially Smoothed Moving Average

### This lesson will cover the following

- er who uses smaller time fram
- What is the so called “drop-off effect”?
- How to estimate the value of an exponential moving average?
- SMA or EMA – which one to use?

The most criticized aspect of simple moving averages is the so called ”drop-off effect”. In case the most recent price shows little change, while the earliest price, now being dropped off, shows significant change, the moving average can be influenced by this discarding of older data. If a large change in the moving average occurs as a result of the deletion of early data, this could generate a false signal.

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Despite that very early data is not necessarily as relevant when determining price movement in the future as the most recent prices, it still may provide information of some value. The SMA completely ignores the older data, which remains outside of the length of the moving average. In order to maintain this older information in the calculation of the moving average, technical analysts calculate and use the so called exponential moving average (EMA).

When calculating a SMA for a certain number of days, each day is given equal importance, equal weight, which means that each days data will have an equal impact upon the value of the simple moving average. On the other hand, an EMA gives different weights depending on the recentness of data. Most recent data is given greater relevance (greater weight), while earliest data is given less weight.

## How to calculate an Exponential Moving Average?

Let us look again at the example we provide in the previous article. We have estimated that a 10-day SMA has a value of 0.8921.

Trading Day | Close Price |

1 | 0.87777 |

2 | 0.88196 |

3 | 0.89143 |

4 | 0.89649 |

5 | 0.90522 |

6 | 0.89942 |

7 | 0.88975 |

8 | 0.88993 |

9 | 0.89257 |

10 | 0.89665 |

10-day SMA | 0.89212 |

Let us assume that on the 9th day AUD/USD pair closed not at 0.89257, but at a lower level, say 0.88488, because of a disappointing retail sales report released out of Australia. What will be the influence upon the value of the SMA?

Trading Day | Close Price |

1 | 0.87777 |

2 | 0.88196 |

3 | 0.89143 |

4 | 0.89649 |

5 | 0.90522 |

6 | 0.89942 |

7 | 0.88975 |

8 | 0.88993 |

9 | 0.88488 |

10 | 0.89665 |

10-day SMA | 0.89135 |

We can see that the value of the 10-day SMA has decreased, because of a change in data regarding only a single day. Tables above show how equally-weighted data influence the overall value of the SMA. As it is a short-term SMA, its value can change only due to some extraordinary price action during one single day.

However, this effect can be smoothed out by using a different way of data averaging. In this case a technical analyst uses the Exponential Moving Average (EMA). It can be calculated by using the following formula:

**EMA (i) = EMA (i-1) + SF*[P(i) – EMA (i-1)]**, where

P (i) refers to the price in period (i), which is most often the closing price;

EMA (i) refers to the most recent value of the EMA;

EMA (i-1) refers to the previous recent value of the EMA;

SF refers to a smoothing factor, which is calculated as follows;

SF = 2/(n+1), where n represents the number of periods the EMA uses.

Trading Day | Total number of days (n) | Smoothing Factor | Close Price P (i) | EMA (i-1) | EMA (I) |

1 | 10 | 0.182 | 0.87777 | 0.89290 | 0.89015 |

2 | 10 | 0.182 | 0.88196 | 0.89533 | 0.89290 |

3 | 10 | 0.182 | 0.89143 | 0.89620 | 0.89533 |

4 | 10 | 0.182 | 0.89649 | 0.89613 | 0.89620 |

5 | 10 | 0.182 | 0.90522 | 0.89411 | 0.89613 |

6 | 10 | 0.182 | 0.89942 | 0.89293 | 0.89411 |

7 | 10 | 0.182 | 0.88975 | 0.89364 | 0.89293 |

8 | 10 | 0.182 | 0.88993 | 0.89447 | 0.89364 |

9 | 10 | 0.182 | 0.89257 | 0.89489 | 0.89447 |

10 | 10 | 0.182 | 0.89665 | 0.89450 | 0.89489 |

In the table above we used exactly the same closing prices and the same candles as when calculating the SMA in the previous article. Beginner traders should take note, that the EMA (i-1) value for the 10th day (which in our case is the earliest period) is the closing price of candle number 11, which stands before the ten successive closing prices in the table, or 0.89450. Thus, we begin constructing the table in a bottom up manner. Now, let us see the following graph:

Here we can see a 10-day SMA (the black line) and a 10-day EMA (the blue line). Usually the EMA will change its direction more rapidly than the SMA, because of the additional weighting it places on the most recent data. The graph shows that during the most recent 4 periods (days) the EMA moves below the SMA. That is because the AUD/USD pair demonstrates a clear downward movement during these most recent four days. Therefore, the EMA reflects most recent sentiment more distinctly.

Notice that during the first 12 days (the 12 consecutive green candles to the left) the EMA remains above the SMA and then reacts earlier to the change in sentiment (the 8 consecutive red candles). So, we can say, that the EMA better reflects what market players are doing now than the SMA. This also explains why a number of oscillators use an EMA and most particularly the MACD, which we shall discuss next.

## EMA or SMA – which to choose?

The EMA has greater agility and usually reacts faster to changes in general market sentiment and respectively price action, while the SMA reacts in a slower manner. Thus, the SMA better smooths out fakeouts and extraordinary price movement.

For a trader who uses smaller time frames and is willing to catch the trend fast, the EMA will be a more appropriate choice. With the EMA he/she will be able to recognize and enter the trend earlier, than if using the SMA. A negative side in this case can be the probability to be stopped out (traders stop-loss could be triggered), if a fakeout or unusual spikes and splashes occur. As the EMA reacts faster to most recent price action, it could signal that the trend has already reversed and that the trader should exit his/her trade, probably at a loss. In the mean time, however, the market may continue its prior move in the direction of traders position.

For a trader who uses longer time frames the SMA will probably be a better choice, because of its smoothness. In a longer term the trend usually lasts for a prolonged period of time, which makes the immediate recognition not so important. In this case a trader expects a smooth movement and a weak reaction to unusual spikes and splashes, as the latter actually do not change the trend itself. A negative side can be the omission of a good entry point, because the SMA tend to show a huge delay after the trend has begun.

The bottom line is that different trading styles require different parameters of the moving average. Short-term traders, who enter into, say 25 trades per month, may use a 4-day SMA, while long-term traders, who enter into, say 3-4 trades per month, may use a 20-day EMA. Both trading styles could be almost equally effective. Thus, we cannot say that a 4-day SMA is more appropriate than a 20-day EMA.

It again comes to experimentation and practice. If a trader finds out that a moving average is the indicator, which best suits his/her trading strategy, then he/she will have to take time and experiment in order to decide which type of moving averages and what period to use.