What Is a Triangle Chart Pattern, and What Did Testing Find?

A triangle chart pattern is a stretch of price action where the swing highs and the swing lows close in on each other, so each push up falls short of the last one while each dip holds above the one before. The definition tested below fixes nothing else about it: it says only which way those two sequences run.

Make that description precise enough for a computer and the shape starts to look fragile. Lo, Mamaysky and Wang did that for ten classical patterns in a 2000 NBER working paper, and the triangle turned up in simulated random prices nearly as often as in real ones. Here is the definition, the counts, the test results, and what they are worth on a funded account.

What is a triangle chart pattern?

A triangle is a stretch of narrowing price movement, with the highs stepping down and the lows stepping up. The CFTC's glossary runs A to Z on one page and has no entry for it, nor for a wedge or a pennant, so there is no official definition there to appeal to. The nearest official vocabulary is its Congestion entry, whose second sense covers a stretch of trading in which price fluctuation is repetitious and limited.

The glossary does define the activity the pattern belongs to. Charting, in its futures-market sense, is plotting price trends, price averages, volume and open interest on a graph, and a Chartist is a technical trader acting on signals read off those graphs. The Technical Analysis entry then attaches a condition that the rest of this post is effectively a test of: the approach draws on price changes, rates of change, volume and open interest while leaving fundamentals aside, and works consistently only where the random-walk view of price movement is wrong.

The triangle therefore arrives as a charting convention, and like the head and shoulders and the double top and double bottom it has to be pinned down before anyone can count it.

How is a triangle defined precisely enough to test?

By the ordering of five consecutive swing points. In their NBER working paper on technical analysis, Lo, Mamaysky and Wang wrote formal definitions for ten classical patterns so an algorithm could find them, and their Definition 3 is the triangle. A triangle top needs the first swing point to be a high, each successive high to be lower than the one before it, and the intervening lows to rise. A triangle bottom is the mirror: first swing point a low, each low higher than the last, and the two highs between them falling. They take the ten shapes from traditional charting, citing chapters VII to X of Edwards and Magee (1966).

Notice what is absent. The definition carries no tolerance percentage, where the same authors' rectangle pins its tops and its bottoms each to a 0.75 percent band around their average and their double top pins the two peaks to a 1.5 percent band around theirs. The triangle is specified entirely by which way the inequalities point.

Getting from raw prices to "swing points" takes the other half of the machinery. The authors smooth each price history with a kernel regression and read local maxima and minima off the smoothed curve, inside rolling windows of 38 trading days, so a pattern counts only if it completes inside that window. One charting platform handles the same problem with a threshold on move size: Quantower's ZigZag documentation says the indicator locates extrema and, at its default setting of 5 percent, leaves anything smaller off the chart. Either way, the swing points you see are the output of a threshold somebody chose.

What separates a triangle from a broadening formation?

The direction of two inequalities, and nothing else. In Lo, Mamaysky and Wang's scheme, the triangle and the broadening formation are built from the same five alternating swing points; the triangle has falling highs and rising lows, the broadening formation has rising highs and falling lows. Their Definition 2 and Definition 3 are exact reflections of each other.

That matters because the two shapes behaved very differently in the same data set.

Both shapes failed to separate from the unconditional case in that sample, and failed differently: a rising-volume condition took the broadening top to the edge of significance, while it moved the triangle top from 0.393 only as far as 0.368.

How often do triangles appear, and how often in random data?

Often enough to count in the thousands across 35 years of US stock data, and a random walk produced almost as many. The algorithm found 1,294 triangle tops and 1,193 triangle bottoms across NYSE and AMEX stocks between 1962 and 1996. Run over simulated geometric Brownian motion — a random walk calibrated to each stock's own mean and standard deviation — the identical detector produced 1,049 triangle tops and 1,176 triangle bottoms.

Set that beside the other patterns in the same table. Real prices gave 1,611 head and shoulders against 577 in the simulation, 2,076 double tops against 535, and 1,482 rectangle tops against 122. The triangle bottom's real-versus-simulated counts, 1,193 and 1,176, are within two percent of each other.

The Nasdaq sample tilts further. There the data produced 850 triangle tops and 789 triangle bottoms while the simulation produced 1,169 and 1,309 — more triangles in the random series than in the market.

Be careful what this establishes. The authors call their simulated sample one realisation of geometric Brownian motion, which they say makes its relative frequencies hard to generalise from. What it shows is that spotting triangles is weak evidence that anything non-random is happening, in a way that spotting rectangles apparently is not. The sample behind every count above is 50 stocks per five-year subperiod across seven subperiods, drawn from each fifth of the market-capitalisation range.

Does the triangle pattern predict anything?

In Lo, Mamaysky and Wang's NYSE/AMEX sample, the triangle top came closer than any of the other nine patterns to showing nothing at all: it carried the largest Kolmogorov-Smirnov p-value of the ten and the smallest goodness-of-fit statistic. The authors measured the one-day return beginning three days after a pattern concluded and asked whether those returns were distributed differently from returns generally. That is a test of information content, with no trade attached.

On the NYSE/AMEX sample, the test told conditional returns apart from unconditional ones at the 5 percent level for five of the ten shapes: head and shoulders, broadening bottom, rectangle top, rectangle bottom and double top. The triangle top returned a p-value of 0.393, the largest of the ten, and the triangle bottom 0.185. Their goodness-of-fit test sets the spread of conditional returns across deciles against the 10 percent per decile an uninformative signal would give; it put the triangle top among the three failures at 0.212, with the triangle bottom scraping through at 0.047.

The Nasdaq sample reversed it. Every one of the ten was significant at 5 percent there, triangles included, with the triangle top posting the largest test statistic in that row, and the authors point out that the Nasdaq sample contained far fewer detections, so the test had less power there.

A second study reaches the triangle from another direction. Park and Irwin's review records that Zhou and Dong (2004) applied fuzzy-logic pattern definitions to 1,451 US stocks from 1962 to 2000 and reported significant cumulative abnormal returns of around 3 percent over 120 days for head and shoulders, inverse head and shoulders, rectangle tops and rectangle bottoms. Triangles are absent from that list, and the review adds that among stocks priced over $2.00 the significance dropped sharply or vanished.

Does falling volume confirm a triangle?

The study behind the numbers above does test a volume condition, but not the one a chartist means: it is a share-turnover trend measured across halves of a five-year subperiod, not volume inside the triangle. Lo, Mamaysky and Wang compared each stock's average share turnover in the first half of each subperiod against the second, calling it a decreasing-volume case when the earlier figure exceeded the later by more than 20 percent and an increasing-volume case in the opposite situation. So the label attaches to years of a stock's trading activity, and the days that form the shape are nowhere in it.

Read with that limit in place, the counts are still striking. Of the triangle tops detected in the NYSE/AMEX sample, 666 fell in decreasing-volume periods against 300 in increasing-volume periods; for triangle bottoms the split was 710 to 222. Broadening tops went the other way, 143 against 409.

The statistical result is where the triangle does best in the NYSE/AMEX sample. Adding the declining-volume condition reduced significance for most patterns and raised it for the triangle bottom, which the authors read as a possible role for volume trend there; the triangle bottom was also the only NYSE/AMEX pattern whose rising-volume and falling-volume distributions differed significantly from each other, at p = 0.046. In the Nasdaq sample that same comparison separated widest for the triangle top, at 0.005, and the authors name it the exception there. Both sit in a paper that describes volume trend as providing little incremental information.

Has the triangle been tested on futures?

Not in the studies Park and Irwin's review tabulates. Their Table 7 summarises eleven chart-pattern studies from 1988 to 2004, and its "markets considered" column lists spot currencies and exchange rates, individual NYSE, AMEX, Nasdaq and FTSE stocks, closed-end funds, S&P 500 stocks and the NYSE Composite Index. No futures market appears in any of the eleven entries.

The review is blunt about the category's methods too. Every one of those studies except Leigh, Paz and Purvis (2002) skipped parameter optimisation and out-of-sample testing and paid little attention to data snooping, and results varied by pattern, market and sample period. Across the wider set of 92 modern studies the review covers, 58 reported positive results for technical trading, 24 negative and 10 mixed, under the same warning about data snooping and after-the-fact rule selection. A replication of the ten-pattern procedure on UK stocks, by Dawson and Steeley (2003), found the conditional return distributions did differ while the average market-adjusted return came out negative across every pattern and period tested.

Two gaps follow. A US equity index future is not a US stock, and a daily-bar study is not evidence about a shape drawn on a five-minute chart. Nothing above is evidence about a triangle on the E-mini.

What does a triangle mean on a funded futures account?

On a funded account, a triangle amounts to a stop level and a count of how many attempts the account can absorb — arithmetic you can do, sitting alongside a pattern whose evidence is thin. The studies above say nothing about whether the next triangle resolves up or down, so the part under your control is the size of each attempt.

Start from the account. Take your maximum drawdown from the pricing page, divide by the dollars you intend to risk per attempt, and the quotient is the number of consecutive failures the account survives; halving the risk doubles that count and changes nothing about the pattern. Our position sizing post works the same division through with contract sizes and tick values. The accounts here are simulated, with a real payout on the profits.

The trailing line adds a second constraint, since it follows your highest closing balance and never retreats. How the drawdown moves sets out the mechanics. A triangle that breaks your way intraday and gives the move back before the close leaves the line where it was and buys no extra room for the next attempt.

A shape that returned a p-value of 0.393 in the study that defined it precisely enough to count is no reason to add contracts, and the definitions tested above carry no entry, no stop and no target, so nothing in them speaks to a breakout rule built on one. Our risk disclosure sets out what the outcomes look like for most people who try this.

FAQ

Do ascending, descending and symmetrical triangles test differently?

The studies cited here cannot say, because none of them splits the pattern that way. Lo, Mamaysky and Wang's Definition 3 specifies a single triangle top and a single triangle bottom from the ordering of five swing points, with no condition on the slope of either boundary, and Zhou and Dong's fuzzy-logic version as summarised by Park and Irwin uses the same pair. Any claim that one variant performs better than another rests on something other than these papers.

Is the triangle the most common chart pattern?

No. In the NYSE/AMEX sample from 1962 to 1996, double tops and bottoms were the most frequently detected of the ten, at 2,076 and 2,075, then head and shoulders and its inverse, at 1,611 and 1,654. Triangle tops came to 1,294 and triangle bottoms to 1,193 — below the rectangles at 1,482 and 1,616, and above the broadening formations at 725 and 748.

Does a triangle breakout come with a price target?

Not in anything tested here. The ten definitions in the NBER paper stop at the geometry of the swing points; they contain no entry trigger, no stop and no objective, so the studies measure what returns did after a shape completed rather than what a trade in it would have earned.

How long does a triangle take to form?

In the tested definition, up to 38 trading days — roughly two months of daily bars. The algorithm fits its kernel regression to rolling windows of that length and only registers a pattern that completes inside one, so anything slower is invisible to it. Quantower's ZigZag, by contrast, filters swings by size rather than duration, showing moves of 5 percent or more at its default setting.