An exponential moving average (EMA) is a moving average that applies exponentially decaying weights to past prices, giving the most recent closes the greatest influence. Compared with a simple moving average of the same length, an EMA turns sooner when price changes direction, trading some smoothness for responsiveness.
The EMA is built from a smoothing factor, k = 2 ÷ (N + 1), and each new value is the latest close times k plus the previous EMA times (1 − k). Because every past price still contributes a shrinking amount, the EMA carries the whole history while emphasizing the present. Common lengths — 9, 21, 50, 200 — serve as trend filters and crossover signals, with the 50/200 cross the classic golden/death cross.
The faster response cuts lag but raises sensitivity to noise, so EMAs can whipsaw in ranges just as SMAs do. The EMA-cross baselines in Secuora’s research at /strategy lost money after costs over twelve months on BTC — responsiveness is not the same as a profitable edge once fees are counted.
For a 9-period EMA, k = 2 ÷ (9 + 1) = 0.2. If the prior EMA is $100 and the new close is $110: (110 × 0.2) + (100 × 0.8) = 22 + 80 = $102.