Fibonacci Levels

Mathematical

Ancient mathematics applied to price charts — the maths is certain, the application is not.

The sequence dates to Leonardo of Pisa, 1202. Its use on price charts is a 20th-century idea.

What it claims

On NEPSE the swings these levels are measured from are often truncated by the daily circuit band, so the high or low used is a price the market never freely chose. That after a move, price often pauses or reverses at levels set by proportions derived from the Fibonacci sequence — most commonly 38.2%, 50% and 61.8% of the preceding move.

How it works

1Each number in the sequence is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21.
2The ratio between neighbours converges on roughly 1.618, and its inverse on 0.618.
3Retracements are drawn from the start to the end of a move, marking 23.6%, 38.2%, 50%, 61.8% and 78.6%.
4Extensions project past the move — 127.2%, 161.8%, 261.8% — to estimate targets.
5The 50% level is not a Fibonacci ratio at all; it is included by convention.

The mathematics, which is not in dispute

The sequence appeared in Leonardo of Pisa's *Liber Abaci* in 1202. Each number is the sum of the two before it, and the ratio between neighbours converges on roughly 1.618 — a proportion that genuinely turns up in plant growth, shell spirals and other natural structures.

Ratio	Where it comes from	Level used
0.618	Any number divided by the next one	61.8% retracement
0.382	Any number divided by the one two places on	38.2% retracement
0.236	Divided by the one three places on	23.6% retracement
1.618	The golden ratio itself	161.8% extension
0.500	Not a Fibonacci ratio at all	50% — included by convention

How the levels are drawn

Retracement levels on a completed move

Levels are drawn from the low to the high of a move. Price often pauses near them — partly because a great many traders draw the same lines.

You pick a move you consider complete — a low to a high — and the tool divides that distance at the ratios. The levels then act as candidate places where a pullback might stop.

The choice of which swing to measure is entirely yours, and different choices give completely different levels. This is the same weakness Elliott Wave has, in a smaller form.

Why they appear to work

There is no mechanism by which a shell spiral should govern a share price, and nobody has proposed a credible one. The honest explanation is simpler and more useful.

A very large number of traders draw the same lines. Every platform ships the tool with the same defaults.
Orders cluster there because of that. Buy orders, stop losses and profit targets accumulate at the same prices.
Price reacts to the orders, not to the ratio. The level matters because people made it matter.

This is a self-fulfilling effect rather than a natural law — and it is still a real effect. Round numbers work the same way and nobody claims mysticism for those. Treat a Fibonacci level as a place where other participants are likely to act, which is a perfectly good reason to watch it, and not as a place price is obliged to turn.

How much weight it can carry

The sequence is real mathematics with genuine appearances in nature. Whether prices respect it is a separate question, and the honest answer is that these levels work partly because a great many traders draw the same lines and act on them. That is a self-fulfilling effect, not a natural law — which still makes the levels worth knowing, for the same reason round numbers are. Treat them as places where others may act, not as places price must turn.

Mathematical. The underlying mathematics is settled. Whether markets obey it is a separate question, and a more doubtful one.

On NEPSE specifically

Fibonacci levels are drawn from a completed swing, and NEPSE's daily circuit limits truncate swings: a move that would have run further was stopped by the band, not by sellers. Levels measured from a circuit-capped high or low are measured from a number the market never actually chose. On thinly traded stocks the swing highs themselves are often single prints, which is a weak basis for a proportional level.

The vocabulary

The 7 terms you need to follow any discussion of this method.

Fibonacci sequence: The number series where each term is the sum of the two before it. The ratios between its terms are the source of the retracement levels traders use.; 1, 1, 2, 3, 5, 8, 13, 21, 34...
Golden ratioalso: Phi: The proportion the Fibonacci sequence converges toward, roughly 1.618, and its inverse 0.618. It is the origin of the 61.8% retracement level.; Approximately 1.618
Fibonacci retracement: Horizontal levels drawn at set proportions of a prior move, used to anticipate where a pullback might stop.
Fibonacci extension: Projected levels beyond a completed move, used to estimate where a trend might run to.; Common levels: 127.2%, 161.8%, 261.8%
Retracement level: A proportion of a prior move where price might pause or reverse. The commonly watched levels are 38.2%, 50% and 61.8%.
Support: A price level where buying has repeatedly been strong enough to stop a fall.
Resistance: A price level where selling has repeatedly been strong enough to stop a rise.

All 180 terms in the glossary →

What the research says

We found no papers testing this method. Searching arXiv’s quantitative-finance archive for it returns nothing. That does not prove the method does not work — but it does mean nobody has published a test of it there, and you should weigh it accordingly. By contrast, the indicators page lists a dozen.