🌀 Fibonacci retracements, extensions and pivot points

🎯 In 30 seconds: Fibonacci retracements divide a finished swing into slices (23.6%, 38.2%, 50%, 61.8% and 78.6%) and mark where a pullback might pause. Extensions project the same ratios beyond the swing to suggest targets. Pivot points take one bar’s high, low and close and turn them into seven levels for the next bar. None of these levels has a reason to hold on its own. They are useful as pre-planned places to watch how price behaves, and they are most interesting when they line up with an older support or resistance zone.

Where the ratios come from

The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and each number is the sum of the two before it. Divide any number by the next one and the answer settles near 0.618. Divide by the number two places ahead and you get about 0.382. Three places ahead gives about 0.236.

Charting software adds two more lines by habit. The 50% line is not a Fibonacci ratio at all. It comes from the older idea that a market often gives back about half of a move before resuming. The 78.6% line is the square root of 0.618.

There is no physical law that makes markets respect these numbers. The honest case for them is narrower: many people draw the same lines, so orders can cluster there, and a fixed set of ratios gives you a consistent way to describe a pullback.

Drawing a retracement step by step

1. Pick a finished swing. For a rally, choose the swing low where it started (A) and the swing high where it ended (B). Use clear turning points that other traders would also pick, not a random wiggle.
2. Measure the range. Range = B minus A.
3. Subtract each ratio from the top. Level = B minus (ratio × range). For a decline, flip it: level = swing low plus (ratio × range).
4. Wait. The lines only matter if price comes back to them.

Worked example with a hypothetical stock, ZEXA. It rallies from a swing low of $40 to a swing high of $60. The range is $20.

How people read retracements

• Shallow pullbacks (23.6% to 38.2%) are read as a sign of eager buyers. The trend is strong enough that dips get bought quickly.
• The middle zone (38.2% to 61.8%) is where most traders expect a normal pullback to end. It is also wide: on ZEXA it covers almost $5.
• Deep pullbacks (beyond 61.8%) raise doubts. If price closes below 78.6%, many traders treat the swing as broken, because most of the rally is gone.

The key word is reaction. A level is a place to look for evidence, such as a strong candle, a pickup in volume, or a higher low on a shorter time frame. Price drifting through a line without pausing tells you the line did nothing this time.

Retracements carry more weight when they agree with something else. If the 50% line on ZEXA sits next to an old breakout level near $50, and a rising 50-day average is close by, that cluster is worth more than any single line. The chapter on support and resistance zones explains how to judge the older levels.

Extensions: projecting past the swing

Extensions ask how far the next leg might run. The common version uses three points: the start of the swing (A), its end (B) and the end of the pullback (C). You add a multiple of the first swing to point C.

Continuing the example, ZEXA pulls back to C = $50 and starts rising again. The first swing was $20.

• 100% projection: $50 + 1.0 × $20 = $70. The second leg matches the first.
• 161.8% projection: $50 + 1.618 × $20 = $82.36.
• 61.8% projection: $50 + 0.618 × $20 = $62.36, just above the old high.

A second method skips point C and extends the original swing from A: 127.2% gives $40 + 1.272 × $20 = $65.44, and 161.8% gives $72.36. Different tools use different methods under the same name, so check which one you are looking at.

Treat extensions as places to consider taking partial profits or tightening a stop. They are a planning aid. A trend that has a reason to keep going will often run straight past them.

Pivot points from yesterday’s bar

Floor pivot points come from the days when traders on exchange floors needed quick levels before the open. They use only the prior bar’s high (H), low (L) and close (C).

• Pivot (P) = (H + L + C) / 3
• R1 = 2 × P minus L, and S1 = 2 × P minus H
• R2 = P + (H minus L), and S2 = P minus (H minus L)
• R3 = H + 2 × (P minus L), and S3 = L minus 2 × (H minus P)

Worked example: yesterday a hypothetical stock traded between $98 and $104 and closed at $102.

The default pairing is daily pivots on intraday charts, built from yesterday’s regular session. Swing traders sometimes use weekly pivots (from last week’s bar) on daily charts, and monthly pivots on weekly charts.

Common readings: opening above P tilts the session toward buyers, and below P toward sellers. R1 and S1 are the levels most often tested in a normal day. R3 and S3 are reached mainly on days with big news. Some traders use the next level out as a profit target and the level behind them as a stop reference.

Where these levels mislead

• Hindsight fit. After the fact you can always find a swing whose ratios match the turn. Only lines drawn before the turn count.
• No context. Pivots are pure arithmetic. They know nothing about earnings dates, gaps or the trend.
• Gaps. A stock that gaps past several levels at the open makes them irrelevant for that day.
• Testing is hard. David Aronson argues that methods relying on judgment cannot be tested until they are written as exact rules. If you want to know whether a level helps, define the swing points and the entry rule precisely and test it, as shown in Testing an idea.

Sources

• John J. Murphy, Technical Analysis of the Financial Markets (1999), on percentage retracements and Fibonacci ratios
• Perry J. Kaufman, Trading Systems and Methods, on pivot point calculations
• David Aronson, Evidence-Based Technical Analysis (2007), on subjective versus objective methods
• Moneydesks Technical Analysis tool: Fibonacci retracement drawing and floor pivot points in the Indicator guide