Skip to content
Reversion Docs

Indicator Formula

Technical Details — Exponential Moving Average (EMA)

Section titled “Technical Details — Exponential Moving Average (EMA)”

Overview

Section titled “Overview”

The Exponential Moving Average (EMA) applies exponentially decreasing weights to older data points, ensuring recent prices have more influence. The multiplier $$\alpha = 2/(n+1)$$ controls how quickly old data decays.

Mathematical Derivation

Step 1 — Calculate Multiplier

Section titled “Step 1 — Calculate Multiplier”

Purpose: Determine the weighting factor for new data.

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

Where:

  • $$n$$ = Period (lookback length)
  • $$\alpha$$ = Smoothing multiplier

What This Measures: How much weight to give the most recent price

Step 2 — Apply EMA Recursion

Section titled “Step 2 — Apply EMA Recursion”

Purpose: Blend new price with previous EMA.

$$EMA[t] = Close[t] \times \alpha + EMA[t-1] \times (1 - \alpha)$$

Where:

  • $$Close[t]$$ = Current closing price
  • $$EMA[t-1]$$ = Previous EMA value

What This Measures: Exponentially weighted average of all historical prices

Compact Formula Summary

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

$$EMA[t] = Close[t] \times \alpha + EMA[t-1] \times (1 - \alpha)$$

Default Parameter: Period (n) = 14

Complete Calculation Example

With Period = 10, α = 2/11 = 0.1818. If EMA[t-1] = 44.50 and Close[t] = 45.00:

$$EMA = 45.00 \times 0.1818 + 44.50 \times 0.8182 = 8.18 + 36.41 = 44.59$$

The EMA moved toward the new price but didn’t jump all the way — it blended new and old data.

Key Takeaways from the Example
  1. Recursive Calculation: EMA depends on its previous value, creating an infinite memory that decays exponentially
  2. Recent Price Emphasis: Newer bars have more weight, making EMA more responsive than SMA
  3. No Drop-Off Effect: Unlike SMA, EMA never fully drops old bars — they just decay toward zero influence
  4. Most Popular MA: EMA’s balance of responsiveness and smoothness makes it the default choice for most strategies