Moving Average Convergence Divergence (MACD)

Reviewed 12 August 2026 · Sourced from Gerald Appel’s own 2003 interview, Thomas Aspray’s 1988 articles and current platform documentation

What MACD actually is

Someone shares a chart with you. Under the price there is a second panel: two wiggly lines, a row of bars behind them, and a label reading MACD — Moving Average Convergence Divergence. The video says it “confirmed momentum” before the move. You assume there is mathematics in that panel you don’t have, and that the name is long because the idea is hard.

The idea is a subtraction.

That is it. Take the shorter average, take the longer average, subtract. Plot the answer. Everything else on the panel is built out of that one number.

Now the name makes sense, because the name is literal. Two moving averages of the same price can only do two things relative to each other: close in, or pull apart. Convergence is closing in — the two averages drifting toward the same value, which drives the subtraction toward zero. Divergence is pulling apart, which drives it away from zero in whichever direction the shorter average went. MACD is a distance meter between two averages, with a sign on it.

It comes from Gerald Appel, a money manager and newsletter writer, in the late 1970s. Appel put a date on it himself in a September 2003 interview in Technical Analysis of STOCKS & COMMODITIES: “MACD was originally invented in about 1977, but the way I use it has evolved over the years.” Thomas Aspray, in the same magazine in 1988, credits it identically — “Convergence/Divergence was developed by Gerald Appel.”

The three parts, and what each one is made of

Most confusion about MACD is really confusion about which of the three things on the panel you are looking at. They are built in a chain, each derived from the one before it.

Read down that middle column and one thing should jump out. The signal line is an average of an average. It is not calculated from price at all — its only input is the MACD line, which was itself built from two averages of price. Price is two smoothing steps away from it. That is the most important structural fact about this indicator, and the whole of the lag problem lives in it.

The histogram is not volume

This is the most common misreading of the panel, and it is entirely the fault of the drawing. Vertical bars rising and falling from a zero line look exactly like volume bars, because volume is also drawn as vertical bars.

Two consequences of histogram = MACD − signal follow from the definition and cost nothing to remember. The histogram is positive whenever the MACD line is above its signal line and negative whenever it is below. And — this trips up people who think they are watching two independent things — the histogram crossing zero and the MACD line crossing its signal line are one event happening once. The gap is zero exactly when the two lines touch.

The histogram also is not Appel’s. Thomas Aspray added it, introducing it in Technical Analysis of STOCKS & COMMODITIES as the MACD Histogram/Momentum indicator. The date is genuinely contested: TradingView’s documentation says 1986, while the magazine’s own author archive lists Aspray’s earliest MACD article as August 1988. Both cannot be right. The attribution to Aspray is solid; the year sits in the ledger below as unverified.

Where 12, 26 and 9 came from

Open MACD on any platform and it loads 12, 26, 9. The numbers have the settled look of something derived — as though somebody optimized them, published the work, and the industry adopted the result. Here is the honest position on that.

The defaults are documented. Their derivation is not. StockCharts’ ChartSchool gives the 12-day EMA, the 26-day EMA and the nine-day EMA of the MACD line as the standard configuration, so what your chart loads is verifiable today. What no source reachable for this page publishes is why those three numbers. No derivation, no optimization study, no body that ratified it. It is convention — true because enough software ships it that enough people look at it.

You will run into a specific origin story: that 12 and 26 encode a two-week and a one-month lookback from an era when markets traded six days a week including Saturday mornings, making 12 two weeks and 26 roughly a month. It is repeated on forums, in courses and in a great many articles. This page could not trace it to any primary source — not to Appel, not to the magazine that published him, not to a platform’s documentation. It may well be true. It is recorded here as unverified rather than laundered into the prose as history.

Appel’s own words complicate it further, in an interesting direction. In 2003 he said the original description of MACD “used different combinations of time frames than we use nowadays to a certain degree.” Read that carefully: the man who invented the indicator is saying the settings in circulation are not necessarily the ones he originally published. So the common claim that “Appel chose 12/26/9” is doing more work than the record supports.

One thing Appel is clear about is what he set out to build. Asked why, he said: “I was just looking for new indicators! I was looking for a quality indicator that would be readily interpretable, that would not create so many whipsaws as to be confusing, and that would still be relatively simple to maintain.” Hold onto that phrase — “not create so many whipsaws” — because whipsaw is still the failure mode this indicator is best known for, by the admission of the person who tried to design it out.

Why it cannot lead price

MACD is filed under “momentum indicators,” and momentum sounds forward-looking. The filing is misleading. MACD is a lagging indicator wearing momentum’s clothes, and that is not a matter of opinion or of how well you read it. It is structural.

An exponential moving average is a weighted average of closing prices that have already printed. That is its only ingredient. An average of past data cannot contain information that is not in the past data. Subtracting one such average from another does not create foresight; it produces a second quantity that is also entirely a function of prices that already happened. Whatever MACD tells you, price told it first.

The double lag

Then it happens twice. Price moves. The two EMAs respond with a delay, because they are averages. The MACD line changes only after they do. And the signal line — a 9-period EMA of the MACD line — responds only after that. Two smoothing steps between price and the signal line, each paying its own delay.

The second delay is easy to put a number on. The standard EMA multiplier is 2 ÷ (n + 1), so a 9-period EMA covers 20% of the remaining distance to its input on each new bar. Suppose the MACD line jumps and then holds perfectly still. Here is how much of that finished move the signal line has absorbed, bar by bar — our own arithmetic from the multiplier, not a sourced figure:

Eleven bars to substantially finish reacting to a move that was already over before the first row — and the MACD line had itself already lagged price to get there. On a daily chart that is most of a month of catching up.

Nobody has to take this from us. Aspray, who built the histogram, opens his 1988 article by conceding it: the MACD “is an excellent indicator, but its signals often lag when run on weekly data.” He built the histogram in response to that exact problem.

Zero-line crossings versus signal-line crossings

Two different events get called “a MACD crossover,” they mean different things, and a large share of the articles you will read treat them as interchangeable.

A zero-line crossing

The MACD line equals zero at exactly the moment the 12-period EMA and the 26-period EMA are equal — because MACD is the difference between them, and a difference is zero when two things are the same. So MACD crossing zero is not a separate phenomenon needing its own theory. It is the two moving averages crossing each other, reported on a different axis. If you already watch a 12 and a 26 cross on the price chart, the zero line tells you nothing new; it is the same event in a different costume.

A signal-line crossing

This one has no equivalent on the price chart. The MACD line crossing its signal line means the current gap between the two averages has moved above or below the recent average size of that same gap. That is a statement about the rate of change of the gap, not about where the averages sit.

Which is why a signal-line crossing carries no information about their positions. MACD can be at −3.00 — both averages far apart, the short one well below the long one — and still cross above its signal line, because the gap merely stopped widening as fast as it recently had been. Two averages nowhere near each other, no change in their order, and a crossing all the same.

And no, this page will not give you a hit rate. Not for zero-line crossings, not for signal-line crossings, not for the histogram. No study reachable for this page establishes how often either event is followed by anything in particular, over any horizon, on any instrument. Percentages in this corner of the internet are overwhelmingly invented, and a plausible number with no source behind it is worse than no number at all.

Divergence: the most-cited signal and the least reliable

Ask about MACD in a trading forum and you will get divergence. It is the signal the indicator is famous for. It also deserves the most suspicion, for two independent reasons.

First, what it is. Divergence here means price and MACD disagreeing at their extremes. Price grinds out a high that exceeds its previous high, but MACD’s matching peak comes in lower than its previous peak. Or price makes a lower low while MACD makes a higher low. Note the terminology collision: this “divergence” is price-versus-indicator, and it has nothing to do with the “divergence” in the indicator’s own name, which means the two averages pulling apart.

Mechanically the idea is reasonable. Price reached further this time, but the gap between the two averages did not open as wide as it did last time. The move covered more ground with less separation behind it. As a description of the arithmetic, that is fair.

Problem one: it was not in the original

Appel, in his own words in 2003, on the tool as he first published it: the original description “had no particular references to divergences.” The most-cited MACD signal is not part of the indicator as its inventor introduced it. It accumulated afterwards. That does not make it wrong — ideas can be improved by other people, and Appel says in the same breath that interpretation has gotten better over the years. It does mean nobody gets to invoke Appel’s authority for it, which is quietly what “a classic MACD signal” does.

Problem two: it persists, and then it gets counted backwards

A divergence is not a moment. It can sit there for weeks or months while price keeps going, printing higher high after higher high with MACD peaks stepping down the whole way. StockCharts states the consequence plainly: “Divergences should be taken with caution. Bearish divergences are commonplace in a strong uptrend, while bullish divergences occur often in a strong downtrend.” Commonplace in a strong uptrend — the condition is most abundant precisely where acting on it would have been most costly.

So: divergence is a real, definable pattern. Treat it as a description of what has already happened on the chart, which is all any of this ever is. Divergence and the tools stacked with it are Stage 4 of the Technical Analysis course.

Why a MACD reading is not comparable to anything

This is the property almost nobody explains, and it changes what you are allowed to do with the number.

RSI is bounded: its formula cannot produce a value below 0 or above 100, on any instrument, at any price, ever. That bounding is what lets an RSI of 68 mean the same kind of thing on a $9 stock and a $900 stock. MACD has no bounds at all. StockCharts puts the consequence directly: “Because the MACD is unbounded, it is not particularly useful for identifying overbought and oversold levels.” There is no ceiling for a reading to be high relative to.

The deeper problem is units. MACD is a dollar amount subtracted from a dollar amount, so a reading is denominated in dollars per share of that particular stock. Not a percentage, not a ratio, not a score. StockCharts again: MACD values “are dependent on the price of the underlying security,” and therefore “it is not possible to compare MACD values for a group of securities with varying prices.”

The same trap runs along the time axis for a single stock. A stock that traded at $20 five years ago and $200 today is a stock whose MACD scale grew roughly tenfold with it. A reading of 1.00 was a substantial separation at $20 and is a rounding error at $200. “MACD is higher than it has been in years” can be a statement about nothing but the share price. Comparing today’s reading to one from before a large price change, or from before a split, is comparing two different units.

The fix is the arithmetic in the example: divide the gap by the slower average and you have a percentage, which travels between stocks and across time. That is exactly what a percentage-based version of this same indicator does, and it is why one exists. It is not what plain MACD gives you.

What’s confirmed, what isn’t, and what’s only convention

Every indicator page on this site carries this breakdown, because a technical indicator mixes documented history with numbers nobody ever justified, and prose alone hides the difference.

What trips people up

• Thinking the histogram is volume. Vertical bars around a zero line, so the shape invites it. There is no volume data in MACD at all — the bars measure the distance between two lines in their own panel. Volume is a separate measurement, off the exchange tape.
• Counting a histogram zero-cross and a signal-line cross as two events. They are one event. The histogram is the gap between those two lines, so it reaches zero exactly when they touch.
• Confusing a zero-line cross with a signal-line cross. A zero-line cross is the 12 and 26 EMAs crossing each other. A signal-line cross is the gap moving relative to its own recent average, and says nothing about where the averages sit — MACD can cross its signal line while sitting deep in negative territory.
• Expecting an indicator built from past averages to lead. It cannot. Price moves first, the EMAs follow, the MACD line follows them, and the signal line follows that. Two smoothing steps, two delays.
• Comparing readings between two stocks, or across years. A reading is denominated in that stock’s own dollars, and the scale grows with the share price. +4.00 on a $400 stock and +0.08 on an $8 stock can be the identical move, as the worked example shows exactly.
• Running it on a range and trusting the crossings. Flat price means the two averages sit together, which means MACD hovers near zero, which means its sign flips on noise. Appel built the tool trying to reduce whipsaws and it still whipsaws.
• Adding a second momentum indicator for “confirmation.” MACD and RSI are both computed from the same recent closes. Agreement between them is substantially built in, so it feels like a second opinion while mostly being the same one restated.
• Believing any percentage attached to it. No named study reachable for this page puts a hit rate on any MACD signal. A confident number with no citation is the loudest warning sign on a trading page.
• Trading rent money on it. No indicator changes what a loss does to a household with no cushion under it. The behavior side of the market, and its five-question pre-trade checklist, exist for this reason.

The figures on this page are checked against the source that publishes them, and dated. Published rates move after the release named above — the linked source always carries the current number. This page explains a term; it does not recommend a product.