Support and Resistance
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In short
Support is a price at which buying is expected to appear; resistance is a price at which selling is expected to appear.
Scope. This article describes how levels are constructed, what happens at them in a series with no mechanism, and what the research has found where a mechanism does exist. It gives no levels to watch and no rules for acting at one. Last of the four-article technical cluster introduced in Technical Analysis: What It Is and What the Evidence Says. It is also the article in the cluster where the evidence is strongest in favour, and the article where the evidence against is most easily demonstrated — both of which are reported below.
Practitioners treat both as horizontal or sloping regions on a chart where a move is likely to slow, stop or reverse, and the concept is probably the most widely used idea in the whole of technical analysis.
It is also the one idea in this cluster with a documented mechanism, which makes it the most interesting of the four and the one that requires the most care to report accurately.
How levels are constructed
Prior turning points. The most common construction: a price where the market previously stopped and reversed is marked and watched on the reasoning that participants remember it.
Round numbers. Whole units, halves and other psychologically salient prices, on the reasoning that people place orders at numbers they can state easily.
Trendlines. A sloping line drawn through two or more prior lows or highs, extended forward as a moving boundary.
Moving averages used as dynamic levels. A widely watched average treated as a floor or ceiling that travels with the price. The construction and lag of these averages is set out in the previous article.
Fibonacci retracements. Horizontal lines placed at fixed proportions of a completed move, conventionally 23.6%, 38.2%, 50% and 61.8%.
Pivot points. Levels computed mechanically from the previous period's high, low and close.
The polarity convention holds that a resistance level, once broken, becomes support, and vice versa. It is a convention rather than a finding.
Two constructions worth doing the arithmetic on
The pivot family is fully mechanical. From a previous period's high, low and close, the central pivot is the average of the three, and the surrounding levels are reflections of the high and low around it.
| Input or level | Formula | Value |
|---|---|---|
| Previous high · low · close | Given (illustrative) | $104.00 · $98.00 · $102.50 |
| Pivot P | (H + L + C) / 3 | $101.50 |
| R1 · S1 | 2P − L · 2P − H | $105.00 · $99.00 |
| R2 · S2 | P + (H − L) · P − (H − L) | $107.50 · $95.50 |
The Fibonacci retracement percentages do come from the golden ratio, which is worth confirming rather than assuming — with one exception that is rarely mentioned.
| Quoted retracement | Derivation | Computed value |
|---|---|---|
| 61.8% | 1 / φ | 0.618034 |
| 38.2% | 1 / φ² | 0.381966 |
| 23.6% | 1 / φ³ | 0.236068 |
| 50% | None | Not a Fibonacci ratio |
Worked example
Worked example — three of the four retracements are what they claim to be, and one is not. Using φ = 1.618034, the quoted 61.8%, 38.2% and 23.6% reproduce 1/φ, 1/φ² and 1/φ³ to six decimal places. The 50% line, which sits between them on every charting package and is often the most watched of the four, has no connection to the Fibonacci sequence at all — it is the midpoint of a move, included by convention. That does not make it worse than the others; it makes the numerological framing of the set inaccurate, and a reader who has been told the levels are mathematically derived should know that one of the most-used of them is not.
The density problem
A framework that always identifies a level nearby cannot be tested by observing that price stopped near a level. This is measurable, and the measurement is the strongest argument in this article.
On 200 synthetic driftless random-walk paths of 500 trading days each, at each day the levels available to a chartist using only history up to that point were assembled: every prior swing high and low over a five-day window, a grid of round numbers at $5 intervals across the range traded, the 50-day and 200-day moving averages, and the four retracements of the range to date.
| Measurement | Result |
|---|---|
| Distinct levels on the chart by day 500 | 76 on average |
| Days on which price sits within 1% of at least one level | 89.2% |
| Range across paths | 59.6% to 100.0% |
Worked example — price is almost always at a level. A one-year chart carries around 76 distinct levels under ordinary construction rules, and on 89% of days the price is within 1% of one of them. The observation it reversed at a level is therefore close to unfalsifiable: on a random series with nothing in it, nine days in ten qualify. The problem is not that levels are wrong — it is that the supply of them is large enough that any outcome can be attributed to one after the fact. Anyone evaluating this method, favourably or otherwise, has to fix the levels in advance and count both the hits and the misses, which is exactly what the strongest study in the field did.
What happens at a level when nothing is happening
The second measurement is the base rate. On 400 synthetic paths of 600 days, every occasion on which price came within 0.25% of a prior swing high was recorded, and the following ten days were examined to see whether price first fell 1% away from the level or first rose 1% through it. This produced 44,690 touch events.
| Outcome within ten days of touching a prior swing high | Share of all events | Share of resolved events |
|---|---|---|
| Turned away from the level first | 49.4% | 49.6% |
| Broke through the level first | 50.3% | 50.4% |
| Neither, within ten days | 0.3% | — |
Worked example
Worked example — the level held, and the level broke, are both routine. With no mechanism in the data whatsoever, a level turns price away 49.6% of the time and fails 50.4% of the time. Both narratives are therefore available on roughly half of all occasions by construction, which is why chart commentary can accommodate any outcome without strain: the level held and the level broke, confirming the breakout describe a coin flip. The corollary is the useful part: any real effect has to be measured as a departure from roughly 50%, not as a collection of occasions when a level worked. (The near-even split is what the symmetry of a driftless walk requires; the density figure depends on the level-construction rules stated above and would move with them, though not enough to change the conclusion.)
The evidence in favour, which is real and is narrower than it is usually reported
The strongest empirical result anywhere in this cluster concerns support and resistance. A study published in the Federal Reserve Bank of New York's Economic Policy Review in 2000 tested support and resistance levels that six firms active in the foreign-exchange market actually published to their customers during 1996 to 1998. Critically, it benchmarked the behaviour of exchange rates at those published levels against behaviour at 10,000 sets of arbitrarily chosen levels — the exact discipline the density problem above demands. The finding was strong evidence that the published levels helped predict intraday trend interruptions, with predictive power persisting for at least several business days after publication, and varying substantially across the currencies and the firms examined.
Subsequent work by the same author proposed a mechanism rather than leaving the result unexplained: the clustering of stop-loss and take-profit orders, with take-profit orders concentrated at round numbers and stop-loss orders just beyond them. That is an account of why levels would matter which does not require anyone to believe the chart is predictive — it says that orders physically accumulate at salient prices, and accumulated orders move prices when they execute.
What that result licenses, and what it does not. It licenses the statement that support and resistance is not merely pattern-seeking, that a documented mechanism exists, and that in at least one market at one horizon the effect was measurable against a proper benchmark. It does not license generalising to a reader's own chart. The levels tested were published in advance by identifiable providers, so they were fixed rather than chosen after the fact; the market was foreign exchange, which is centralised around a dealer network and behaves differently from equities; the horizon was intraday; and performance varied by firm, meaning some providers' levels carried the result and others' did not. A level drawn by oneself, after the fact, on a daily equity chart is a different object from the one that was tested.
The reflexivity that sits underneath all of it
The mechanism cuts both ways, and this is the honest place to end the cluster. If enough participants watch a level, orders cluster there and the level becomes self-fulfilling. But if enough participants anticipate the cluster, they act before it and the level stops working — and if enough anticipate that, they act before that. A level's usefulness is a function of how many people are watching it and how many of those are trying to be early, neither of which is observable from the chart.
That instability is not a flaw in the idea; it is the idea. Support and resistance is a claim about the behaviour of other participants, which means it cannot be a stable property of a price the way a company's revenue is a stable property of a company. It is the clearest illustration in this pillar of the difference between analysing a business and analysing a market's expectations about one — and it is why this portal stops at describing the practice.
Frequently asked
8 questions
What are support and resistance?
Support is a price where buying is expected to appear, resistance a price where selling is expected to appear. Both are claims about where a move might slow or reverse, constructed from prior turning points, round numbers, trendlines, moving averages, retracements or pivot formulas.
Do support and resistance levels work?
The most rigorous test found that levels published in advance by foreign-exchange firms did help predict intraday trend interruptions, benchmarked against 10,000 sets of arbitrary levels, with a plausible mechanism in order clustering. That result is real and narrow: it concerns pre-published levels, in foreign exchange, intraday, with performance varying by provider. It does not transfer automatically to a level drawn after the fact on a daily equity chart.
Why does it matter how many levels a chart has?
Because on a random series with about 76 levels available, price sits within 1% of one on 89% of days. Observing that price reversed near a level is therefore close to unfalsifiable, and any test has to fix the levels in advance and count the misses.
How often does a level hold?
On synthetic data with no mechanism in it, 49.6% of touches turned price away and 50.4% broke through. Both outcomes are routine, so a real effect has to show as a departure from roughly 50% rather than as a collection of occasions when a level worked.
Are Fibonacci retracements really based on the Fibonacci sequence?
Three of the four are: 61.8%, 38.2% and 23.6% reproduce 1/φ, 1/φ² and 1/φ³ exactly. The 50% line has no connection to the sequence at all — it is simply the midpoint of a move, included by convention.
How are pivot points calculated?
The central pivot is the average of the previous period's high, low and close. The first resistance and support are reflections of the low and high around that pivot, and the second pair adds and subtracts the previous range. The arithmetic is fully mechanical, which is why different chart packages produce identical pivots.
Why do round numbers come up so often?
Because orders cluster at prices people can state easily. Work following the foreign-exchange study proposed exactly this: take-profit orders concentrating at round numbers and stop-loss orders just beyond them, with the accumulated orders moving prices when they execute.
If everyone watches a level, does it stop working?
That is the reflexivity problem and it has no stable answer. Enough watchers make a level self-fulfilling; enough participants anticipating those watchers make it self-defeating. A level's usefulness depends on how many are watching and how many are trying to be early, and neither is visible on the chart.
References
- Federal Reserve Bank of New York — Osler (2000), Support for Resistance: Technical Analysis and Intraday Exchange Rates, Economic Policy Review 6(2) —
- Federal Reserve Bank of New York Staff Report 125 — Currency Orders and Exchange-Rate Dynamics —
- Park and Irwin (2007) — What Do We Know About the Profitability of Technical Analysis?, Journal of Economic Surveys 21(4) —
Educational and informational only — not investment advice, a recommendation, or an offer to buy or sell any security. Investing involves risk, including the possible loss of principal. Worked examples use fictional companies and figures.