Explainer · Kresmion Research
What Is a Moving Average? SMA and EMA Explained
A moving average is the average closing price over a fixed number of recent periods, recalculated each period so the window slides forward through the data. The result is one smoothed line drawn on top of the price.
Moving averages are the first overlay most people add to a chart, and the first one they misread. This page covers the arithmetic, how the simple and exponential versions differ, and what the named crossings describe. All figures below are invented. It is descriptive throughout.
What a moving average measures
A raw price series is noisy, and the shape underneath is hard to see. A moving average replaces each close with the average of that close and the N-1 closes before it. Plot that number, then repeat next period after dropping the oldest close and adding the newest.
The window slides forward one step at a time, which is where the name comes from. The line is in the same units as price, so it sits over the same bars that show what a candlestick chart shows, and it does not exist for the first N-1 periods.
The simple moving average, worked by hand
The simple moving average, or SMA, weights every close in the window equally. Take a hypothetical stock with five daily closes, in dollars: 40, 42, 41, 43, 44. Add them: 40 + 42 + 41 + 43 + 44 = 210, and divide by five. The 5 period SMA is 42.00.
Now step the window forward one day. The stock closes at 48, and the oldest close, 40, falls out. The window is now 42, 41, 43, 44, 48, which sums to 218, so the average is 43.60.
The average moved 1.60 while the price moved 4.00, from 44 to 48. That gap is the smoothing. It rose because a high close entered the window and a low close, the 40, left it: an SMA can turn on the day an old value drops out, with nothing new happening.
The exponential moving average
The exponential moving average, or EMA, asks the same question with different weights: the newest close counts most, and each older close fades as it ages. No close leaves the calculation outright; its influence just shrinks.
The weighting comes from a smoothing factor, 2 divided by (N + 1). For a 5 period EMA that is 2 / 6, or about 0.333, so each new value is (today's close x 0.333) + (yesterday's EMA x 0.667). Seed the EMA with the 5 period SMA of 42.00, the usual starting point, and apply the close of 48: (48 x 0.333) + (42 x 0.667) = 16.0 + 28.0 = 44.00, against 43.60 for the SMA. The two lines got there differently. The EMA moved 2.00 on the weight of the new close alone. The SMA moved 1.60, and part of that came from the 40 leaving the window rather than from the 48 arriving.
An EMA turns sooner than an SMA of the same length, which also means it turns on small moves the simple average would have absorbed: a shorter reaction time and a noisier line are the same property.
Why the window length changes what you see
The window length is the only thing that says which time horizon the line describes. A 20 period average of daily bars summarises about a month of trading; a 200 period average covers roughly ten months. Run both over one series and they disagree most of the time, because they describe different spans of history.
The longer average also lags more, for a mechanical reason: every moving average is computed entirely from closes that have already printed, with no forward-looking term in the arithmetic. It can only turn after the underlying series has, and the more closes sit in the window, the more new data it takes to shift it.
The conventions people refer to
Two readings come up constantly. The first is whether the latest close sits above or below a long average, say a 200 period line: a statement about where today's close sits relative to the average of the last 200 closes, today's included, and nothing more. The second is a crossing of two averages: a shorter average crossing up through a longer one is widely called a golden cross, and the same crossing downward a death cross. Those names are old folklore attached to a geometric event.
Both describe past data. Because both lines are built only from closes that already happened, a crossing is confirmed only after the move that caused it sits in the series: by the time a 50 period line crosses a 200 period line, the closes that pulled it across are weeks old.
Where moving averages help and where they mislead
They help as a readability tool: a smoothed line makes a choppy series legible at a glance. Kresmion's terminal charts support moving average overlays, simple, exponential, weighted and Hull, added on top of the candlesticks for any stock, index or crypto pair.
They mislead in three ways. In a sideways series, a short and a long average cross repeatedly with no sustained move either way: the arithmetic is fine, there is no shape to smooth. On a different bar interval the same label means a different line, since 50 daily bars cover about ten weeks and 50 hourly bars about eight sessions. And the line only knows the price: nothing about the size of the company underneath it, which is what market cap measures, or how much movement the market is pricing in, closer to what the VIX tracks.
Key takeaways
| Point | Detail |
|---|---|
| Definition | The average of the last N closes, recomputed each period as the window slides. |
| SMA | Every close counts equally, so a value dropping out can move the line by itself. |
| EMA | Newest close weighted most, via a factor of 2 / (N + 1), so the line turns sooner. |
| Lag is structural | Built only from closes already printed, so it turns after the series does. |
| Crossings | Golden cross and death cross name the geometry of two lines meeting, in past data only. |
Frequently asked questions
What is the 50 day moving average?
It is the average of the last 50 daily closes, recalculated after every session: each day the newest close enters and the close from 50 sessions earlier drops out. Fifty sessions is about ten weeks of trading.
What is the difference between the SMA and the EMA?
The SMA gives every close in its window the same weight. The EMA weights the newest close most and fades older closes gradually, using a factor of 2 divided by (N + 1). An EMA therefore turns before an SMA of the same length, and also reacts to small moves the SMA smooths away.
Does a golden cross predict a price rise?
No. A golden cross is the moment a shorter moving average crosses up through a longer one, and both lines come from closes that have already printed. It records something that happened in the recent past, and results after such crossings vary widely across markets and samples.
What does it mean when a stock trades above its 200 day moving average?
It means the latest close is higher than the average of the previous 200 closes. That is the entire content of the statement, and the line keeps moving as new closes enter and old ones leave.
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Source: standard definitions of the simple and exponential moving average. All prices here are invented for illustration. This page is information, not investment advice. Kresmion Research.
- · Simple and exponential moving average arithmetic is standard; every figure in this page is a hypothetical worked example.
- · Kresmion's terminal charts support simple, exponential, weighted and Hull moving average overlays.
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