Data basis: DAX, FTSE, NQ, DOW, M5 candles built from M1 data, 2015–2026, 26,795 activated sequences (double bottom and mirrored double top), 13,635 pullback entries, 17,862 run endings. Horizon 24 h, sequences non-overlapping. Benchmark: driftless random walk, p = d(stop) / (d(stop) + d(target)). Pullback entries net of spread and slippage. Lookahead-free: activation on a completed close. No trading recommendation.
Fibonacci extensions are among the most widely used tools in chart analysis. The claim behind them is a forecast: after a structure — here a double bottom with an intermediate high — price has an elevated tendency to reach certain multiples of the first leg, and the zone from 1.618 to 2.0 is held to be a "terminal zone" where moves end.
The problem with such claims is that they almost always appear without a benchmark. "Price reached 1.618 in two thirds of cases" sounds like a statement about Fibonacci. It is, at first, only a statement about distances: how often one level is reached before another depends on how far away each is — with no market structure at all.
So we put the rule against the only fair comparison: a driftless random walk with the same distances.
1. The construction
A double bottom is defined mechanically: two swing lows at a similar level (tolerance 25% of the leg height), an intermediate high between them, separation 3 to 60 M5 candles, leg at least three times the median candle range. The leg runs from the low (0) to the intermediate high (1.0). Activation is the first M5 close above the intermediate high. Double tops are tested mirrored.
Three tests:
- A) Magnet: after activation, does price reach the 1.618 extension before falling below the double-bottom low?
- B) Pullback entry: after activation, a retrace to 0.5 of the leg, long there, stop at the low, target 1.618.
- C) Termination: where does the maximum run end? Density per 0.1-leg band.
The benchmark for A and B: a driftless random walk starting between a stop and a target reaches the target first with probability p = d(stop) / (d(stop) + d(target)). This quantity is computed for every sequence from its actual geometry and averaged. Only a hit rate above this p would be a Fibonacci effect.
2. Test A: the magnet is weaker than chance
| Market | Sequences | 1.618 before low break | Random walk | t | 2.0 reached |
|---|---|---|---|---|---|
| DAX | 6,824 | 67% | 71% | −6.3 | 52% |
| FTSE | 6,878 | 66% | 70% | −6.5 | 53% |
| NQ | 6,391 | 67% | 71% | −7.5 | 52% |
| DOW | 6,702 | 67% | 71% | −6.7 | 53% |
| Pooled | 26,795 | 67% | 71% | −13.5 | — |
The Fibonacci hit rate is four percentage points lower than the random-walk expectation on each of the four markets, every time at |t| > 6, pooled t = −13.5. This is not a borderline case. Price reaches the 1.618 extension less often than a random path with the same distances would.
The 67% is no evidence of a magnet. It is almost entirely geometry: after activation, price is already above the intermediate high, the low is far away, the 1.618 mark comparatively close. The random-walk p of 71% shows that the target is, on average, the nearer level. A "magnet" that hits less often than chance at equal distance is not one.
One detail supports the result rather than weakening it: the 24 h horizon only counts sequences in which one of the two levels was reached. This truncation favours the nearer level — on average, the target. Despite that advantage, the hit rate sits below the benchmark.
3. Test B: the 0.5 pullback is a fair coin
| Market | Entries | Win rate | Random walk | avgR |
|---|---|---|---|---|
| DAX | 3,459 | 35% | 34% | +0.03 |
| FTSE | 3,535 | 35% | 36% | −0.03 |
| NQ | 3,232 | 36% | 35% | +0.04 |
| DOW | 3,409 | 36% | 34% | +0.05 |
| Pooled | 13,635 | 35.5% | 34.8% | +0.020 (t = +1.8 on the win rate) |
The classic entry — wait for the retrace to half the leg, stop below the low, target 1.618 — wins in 35.5% of cases. The random walk with the same geometry would come to 34.8%. The 0.7 percentage-point difference sits at t = +1.8, below the significance threshold of |t| ≥ 2. After costs, +0.020 R per trade remains, negative on the FTSE.
The bracket has a reward-to-risk ratio of about 2.2 to 1 (target 1.118 leg units against a risk of 0.5). With a win rate matching chance, the expectancy of such a bracket is zero by construction; the small positive deviation is just enough to cover costs. That is the result one expects from a setup with no information content.
4. Test C: where runs end — no terminal zone
If 1.618 to 2.0 is a zone where moves typically run out, the density of run endings should show a hump there. For 17,862 sequences we measured how far the maximum run went before the low was broken or the horizon ended.
| Band (leg units) | Share | Band | Share |
|---|---|---|---|
| 1.0–1.1 | 2.9% | 1.6–1.7 | 6.7% |
| 1.1–1.2 | 8.2% | 1.7–1.8 | 5.9% |
| 1.2–1.3 | 9.6% | 1.8–1.9 | 5.3% |
| 1.3–1.4 | 9.5% | 1.9–2.0 | 4.8% |
| 1.4–1.5 | 8.7% | 2.0–2.1 | 4.4% |
| 1.5–1.6 | 7.7% | 2.5–2.6 | 2.8% |
The distribution peaks at 1.2–1.3 and then declines monotonically. From 1.6 to 2.0 the share per band falls from 6.7% to 4.8%, without any irregularity. The 1.618–2.0 zone is not where runs end — it is a section of a smoothly falling curve describing that long runs are rarer than short ones. That holds for any price series, including a random one.
The initial peak is geometry too, not a finding: a run must have exceeded activation (1.0) to be counted at all, and the most common continuation of a break is a short one.
5. What this means
In all three tests, the Fibonacci zones deliver nothing the distance geometry does not already dictate. The magnet hits less often than chance, the pullback entry is a coin flip that covers costs, and the terminal zone does not exist in the distribution.
This is not a statement that Fibonacci traders cannot be profitable. It is a statement about where their edge does not come from: not from the levels. Anyone making money with Fibonacci zones is making it with something else — context, timing, risk management — and the zones are a coordinate system, not a forecast.
The methodological point is the more important one. A hit rate without a benchmark is not information. 67% sounds like a finding until one knows that pure geometry would predict 71%. This comparison — a random walk with the same distances — is mandatory for every level claim in our work, and the Fibonacci rule is a clean example of why. Nor is it the only pattern to end this way: the 1h pin bar behaves against its benchmark exactly like an arbitrary candle.
6. Limits
- One mechanical double-bottom definition. Fractal wings 3, tolerance 25%, separation 3–60 candles, leg ≥ 3× median range. Discretionary Fibonacci users draw differently and more selectively. We tested the rule, not the eye.
- Only 1.618 and 2.0 as targets, only 0.5 as entry. Other ratios (1.272, 0.618) were not tested. With a magnet below chance on all four markets, a hidden effect at another ratio is unlikely but not ruled out.
- Random walk without drift and without volatility structure. The benchmark is deliberately simple. A model with an intraday volatility profile would shift the expectation slightly — in which direction was not measured.
- M5 discretisation, fills exactly at the level. Absolute R values of such bracket simulations carry a small bias; what is robust is the comparison against the benchmark with identical construction, not the absolute +0.020 R.
- 24 h horizon. Sequences without resolution within 24 h do not count in test A. The direction of this bias favours the nearer level, i.e. the hypothesis.
- In-sample. There was no parameter to optimise in the sense of a search, but the definition was fixed before the test and not checked out-of-sample.