Why do traders reach for an exponential moving average?

The simple moving average has two nuisances: every bar in the window counts equally, and an old bar rolling off the back can jolt the line when nothing happened today. The exponential moving average fixes both by refusing to have a back end at all.

The formula

Pick a period n and compute the smoothing multiplier:

k = 2 ÷ (n + 1)

Then each bar:

EMA_today = (Close_today × k) + (EMA_yesterday × (1 − k))

The series is normally seeded with a simple average of the first n closes, after which it feeds on itself forever.

A worked example

For n = 10, k = 2 ÷ 11 ≈ 0.182.

Yesterday's EMA was 100.0 and today's close is 110.0:

110 × 0.182 + 100 × 0.818 = 20.0 + 81.8 = 101.8

Another 110 close tomorrow: 110 × 0.182 + 101.8 × 0.818 = 20.0 + 83.3 = 103.3.

Over the same two bars — taking the ten closes before the jump to have all been 100 — a 10-day simple average would print 101.0 and 102.0. The EMA is ahead — and both are behind the price, exactly as the lag lesson promised.

The two responses to the same step, side by side. First the simple one, which arrives exactly:

Then the exponential one, which leads it for a week and then never quite gets there:

Where the weights go

Unpack the recursion and you get a decaying ladder: today's close carries 18.2% of the value, yesterday's 18.2% × 81.8% ≈ 14.9%, the day before ≈ 12.2%, and so on. The weights shrink geometrically but never reach zero, so an EMA technically remembers every bar it has ever seen. No bar ever "falls off", which is why the EMA has no drop-off effect — and also why its value depends slightly on where you started the calculation.

Which one should you use?

Not a quality ranking. It's the same dial from the lag lesson:

• EMA — reacts sooner, whipsaws more, better suited to questions about recent behaviour.
• SMA — calmer, later, and easier to reason about because every bar's contribution is obvious.

A trader who prefers one is expressing a preference about noise tolerance, not a discovery about markets. Both are summaries of the past with different memory profiles.

In the data

An exponential average has to start somewhere, and the usual seed is a plain simple average. Below are the first two values of Apple's 20-day EMA and of its 20-day SMA for a history beginning on 2 January 2026:

The first EMA value is identical to the SMA: it is not an exponential average at all yet. The weighting only starts to bite from the second row, so two series compared near the start of a history can agree for reasons that have nothing to do with the market.

Try it now

1. Read the two schematics above bar by bar and find the point where the simple average overtakes the exponential one. Then say why that has to happen, using nothing but the two formulas.
2. Compute one EMA step by hand against real numbers: take the day-before value of Apple's published 20-day EMA, the first table below, the latest close, the latest session's close in the second table, and k = 2 ÷ 21 ≈ 0.0952. Matching the published latest value is a genuinely satisfying two minutes.

3. Check the seam while you are there. In the two tables in the section above, compare the first EMA value with the first SMA value, confirm they are identical, then look at the second rows, where the weighting starts to bite.