The MACD: the distance between two averages
The distance between two averages on a real chart
InteractiveClick any session: the page gives you that day's MACD, the signal line and the histogram, and what they say together.
Where the MACD comes from
You take two exponential averages of the closes: a fast one over 12 sessions and a slow one over 26. The fast one follows price closely, the slow one lags. When price accelerates the two move apart; when it slows they come back together.
Fig. 1 · Two averages on the same price
- The fast average sits close to price and turns early. Twelve sessions is not many: a few new closes are enough to make it turn.
- The slow one arrives later. Twenty-six sessions weigh for far longer, and that lag is exactly what makes the distance between the two visible.
The MACD is exactly that distance: fast average minus slow average. Drawn in a panel of its own it becomes a line that rises when the two move apart upward and falls when they move apart downward.
Fig. 2 · The distance becomes a line
- The MACD is zero when the two averages touch. It is not a level of market equilibrium: it is simply the point where fast and slow sit at the same price.
- It is positive when the fast one is above the slow one, negative when it is below. The sign says which of the two is in charge, not whether price is high or low.
- It has no fixed limits. Unlike the RSI it does not run from 0 to 100: it can grow for as long as the two averages move apart, which is why there is no absolutely "high" MACD.
The signal line
On the MACD line you calculate another exponential average, over 9 sessions: that is the signal line. It serves one purpose, to give a point of comparison: if the MACD is above its own average, it is moving faster than it was.
Fig. 3 · The MACD and its signal
- When the MACD moves above the signal it is called a cross to the upside. It means the distance between the two averages is growing faster than it was.
- When it moves below, a cross to the downside. These are the only two events this pair of lines can produce, and they happen often.
- Crosses always come after the price move. They are averages of averages: part of the run has already happened by the time one line cuts the other.
Crosses are the most common way of watching this indicator, and also why it disappoints anyone relying on it alone: there are many of them, and they arrive when part of the move has already happened.
The histogram
The histogram is the distance between the two lines: MACD minus signal, drawn as bars. It adds no new information, it makes it readable: when the bars lengthen the two lines are moving apart, when they shorten they are coming together and a cross is near.
Fig. 4 · The histogram is the distance
- A bar above zero: the MACD is above the signal. The taller the bar, the further apart the two lines are.
- Shortening bars say the cross is getting closer. That is the one thing the histogram really adds: you see it earlier, because you see the distance.
The arithmetic, step by step
Here are the first three Amazon sessions where all three parts exist. The histogram is a subtraction: anyone can redo it by hand with the numbers in the table.
| Session | Close | MACD | signal | The histogram is the difference |
|---|---|---|---|---|
| $220.22 | 3.245 | 5.023 | 3.245 − 5.023 = -1.778 | |
| $224.19 | 3.093 | 4.637 | 3.093 − 4.637 = -1.544 | |
| $227.61 | 3.212 | 4.352 | 3.212 − 4.352 = -1.140 |
MACD numbers are in the same unit as price: they are euros or dollars of distance between two averages, not percentages. That is why two stocks at very different prices have MACD values that cannot be compared.
The three ways of reading it
People using the MACD watch three different things, and they do not say the same thing: the cross with the signal, the width of the histogram, and the move above or below zero.
Fig. 5 · The zero line
- Above zero the fast average is above the slow one. It is the slowest of the three conditions: by the time it happens, the move has been under way for a while.
- Crossing zero is the moment the two averages actually touch. It comes well after the cross with the signal, and that is why it says something different.
1The cross with the signal
- The quickest of the three, and also the most frequent.
- In a directionless stretch they cross over and over.
2The width of the histogram
- It says whether the two lines are moving apart or coming together.
- It shortens before the cross happens.
3The move through zero
- The slowest of the three: the two averages have actually crossed.
- It comes well after the cross with the signal.
Find a cross to the upside
On the chart, green dots are crosses to the upside and red ones to the downside. Click a session where the MACD moves above the signal: the page tells you whether you got it.
Click a session on the chart above.
What the MACD is not
It is not a bounded oscillator. Unlike the RSI it does not run from 0 to 100: it is a distance, and it can grow for as long as the two averages move apart. There is no absolutely "high" or "low" reading.
It anticipates nothing. It is made of averages, which is to say of the past: it moves after price, always. Looking for an early warning in something built on lag is looking for what is not there.
It is not a system. There are many crosses, and this page does not count how many "work": that would not be a measurement, it would be a story. The MACD describes how two averages are moving, and that is already something.
Deeper dives: the moving average · the RSI · the ADX · the trend · trading volume · the stop loss.
Where to go from here
The indicators · Momentum and oscillatorsThe other indicators in the «Momentum and oscillators» family
RSI — Relative Strength Index
- an oscillator from 0 to 100: the strength of gains against losses
- 70 and 30, the 50 line, divergences
- find overbought on the real chart and change the settings
The other lessons in the guide
What is technical analysis
- the study of price and volume to recognise the trend and the levels
- three premises: price discounts everything, trends, history repeats
- exercise: uptrend, downtrend or sideways on three real charts
Candlestick chart
- the four prices of a session: body and shadows
- green and red, long and short bodies, long shadows, the doji
- find the candle on a real chart: the judge says yes or no with the numbers
Uptrend: higher highs and higher lows
- higher highs and higher lows: how to recognize an uptrend
- swing points, and the two signals that end a trend
- mark the higher lows yourself on a real chart
Frequently asked questions
What is the MACD?
It is the difference between two exponential averages of the closes, a fast one over twelve sessions and a slow one over twenty-six. Drawn as a line, it measures how far apart the two averages are: it rises when they move apart upward and falls when they move apart downward.
What is the signal line?
It is the nine-session exponential average of the MACD line. It works as a point of comparison: when the MACD moves above it, that is a cross to the upside; when it moves below, a cross to the downside.
What does the MACD histogram measure?
The distance between the MACD line and its signal line, drawn as bars. It adds no information: it makes visible whether the two lines are moving apart or coming together, and therefore whether a cross is near.
Does the MACD lead price?
No. It is built on averages, that is on prices that have already happened, so it always moves after price. It describes how two averages are moving: useful for reading a stretch of chart, not for predicting one.
Method and sources
| Source |
|---|
| Gerald Appel, Technical Analysis: Power Tools for Active Investors |
The Amazon prices run from to : real sessions from our archive, over a fixed window. The sessions before the start get the averages going and are not shown. This guide explains how the tools work: it does not contain investment recommendations and promises no returns. Our method · license · report an error.
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