EMA

Yaser Rahmati | یاسر رحمتی

The EMA is a type of moving average that places a greater weight and significance on the most recent data points. It's often used in technical analysis of financial markets. Here's how to calculate it:

Exponential Moving Average (EMA)

Step 1: Understand the Concept

The EMA smoothes out the data to identify trends over a period. Unlike the simple moving average (SMA), which assigns equal weight to all observations, the EMA assigns greater weight to the most recent observations.

Step 2: Choose a Period

Decide the period for your EMA. Common periods are 10-day, 20-day, 50-day, etc. The period you choose will determine how sensitive your EMA is to changes in the data. Shorter periods are more sensitive, while longer periods are less sensitive.

Step 3: Calculate the Smoothing Factor (α)

The smoothing factor α (alpha) determines how much weight is given to the most recent observation. It is calculated as:

$$\alpha=\frac{2}{N+1}$$

where 𝑁 is the chosen period.

Step 4: Compute the Initial EMA

For the first calculation, you need an initial EMA value. This is typically the SMA of the first N periods.

$$SMA=\frac{\sum_{i=1}^{N}P_{i}}{N}$$

Where 𝑃𝑖 ​ is the price at time 𝑖 .

Step 5: Compute the EMA

Once you have the initial EMA, you can use the formula to compute the EMA for subsequent periods.

$$EMA_{today}=(P_{today}\times \alpha)+(EMA_{yesterday}\times (1-\alpha))$$

Where:

• Ptoday is the current price.

• EMAyesterday​ is the EMA value of the previous day.

Example Calculation

Let's calculate a 10-day EMA for a given set of prices.

Step 1: Data and Period

Assume the following prices for 10 days: 22, 24, 23, 25, 26, 27, 28, 29, 30, 31.

$$Period \; N = 10$$

Step 2: Calculate the Smoothing Factor (α)

$$\alpha=\frac{2}{N+1}=\frac{2}{11}=0.1818$$

Step 3: Compute the Initial EMA (SMA of first 10 days)

$$SMA=\frac{22+24+23+25+26+27+28+29+30+31}{10}=\frac{265}{10}=26.5$$

This SMA serves as the initial EMA.

Step 4: Compute the EMA for subsequent days

Let's calculate the EMA for day 11 (assuming the price is 32 on day 11):

$$EMA_{day11}=(P_{day11}\times \alpha)+(EMA_{day10}\times (1-\alpha)) \\ EMA_{day11}=(32×0.1818)+(26.5×(1−0.1818)) \\ EMA_{day11}=5.8176+21.697=27.5146$$

Step 5: Repeat for Subsequent Days

Continue this process for each subsequent day using the formula provided.

Sensitivity to Recent Data

• SMA: All data points within the selected period are equally weighted. This means SMA reacts more slowly to recent price changes.

• EMA: Recent prices are weighted more heavily than older prices. As a result, EMA reacts more quickly to price changes and can be more useful for capturing short-term trends.

Use in Trend Analysis

• SMA: Due to its equal weighting, SMA is often used for identifying longer-term trends and for smoothing out short-term fluctuations.

• EMA: EMA is preferred when the focus is on capturing shorter-term trends and reacting to recent price movements more quickly. This makes EMA useful in volatile markets.

Lag

• SMA: The lag in SMA is more pronounced due to its equal weighting of all data points within the period.

• EMA: The lag in EMA is less pronounced because of the higher weighting on recent prices. This allows EMA to respond faster to changes in the market.

Practical Application

• SMA: Commonly used for:

  • Long-term trend analysis.

  • Smoothing data to see the overall direction without much noise.

  • Basic signal generation (e.g., Golden Cross and Death Cross in moving average crossover strategies).

• EMA: Commonly used for:

  • Short-term trading strategies.

  • Identifying recent price trends more quickly.

  • Technical indicators (e.g., MACD - Moving Average Convergence Divergence, which uses EMA).