How to Draw Fibonacci Retracements: What 0.382, 0.5 and 0.618 Really Are

What retracement levels are

After a big move in one direction, price often gives back part of it. Fibonacci retracement is a way to estimate where that pullback might stop: you divide the size of the previous move (the swing) by fixed ratios and draw horizontal lines. The lines themselves are simple arithmetic, so anyone who picks the same two points gets the same values. What differs is which high and low you pick as the swing, and that is also the weakness this article spends the most time on.

How to draw them: from the low to the high

For an upswing, draw from the low to the high; each level is high − (high − low) × ratio. With a low of 100 and a high of 150, the swing is 50 and the levels are as below. 0% is the high and 100% is the low itself; a pullback all the way to 100% has retraced the entire swing. For a downswing, only the direction is reversed: draw from the high to the low and calculate low + swing × ratio. This site's Fibonacci tool automatically takes the highest high and lowest low in the chosen range as the swing, and tells upswings from downswings by which of the two came first.

• 23.6%: 150 − 50 × 0.236 = 138.2
• 38.2%: 130.9
• 50%: 125
• 61.8%: 119.1
• 78.6%: 110.7

Where the ratios come from

The Fibonacci sequence, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…, makes each number by adding the two before it. As the numbers grow, one number divided by the next approaches 0.618, divided by the number two places later it approaches 0.382, and divided by the number three places later it approaches 0.236. For example, 34 ÷ 55 ≈ 0.618, 21 ÷ 55 ≈ 0.382 and 13 ÷ 55 ≈ 0.236. 78.6% is the square root of 0.618 (about 0.786); the 161.8% extension level is the golden ratio, 1.618, and 127.2% is the square root of 1.618. This site's tool calculates extensions as the prices 127.2, 161.8 and 261.8% of the swing away from the swing's starting point, but the reference point for measuring extensions can differ between tools.

50% is not a Fibonacci ratio

The 50% level that always appears in the list is not a ratio from the Fibonacci sequence. The ratios from the sequence settle on values such as 0.618, 0.382 and 0.236 as the numbers grow, and 0.5 is not among them. 50% is commonly explained as having joined the list from a convention of treating a retracement of about half a move as important. Values like 78.6%, which put a sequence ratio through one more calculation, are mixed in as well, so the list of levels itself differs slightly between tools and people. Having Fibonacci in the name does not mean every line rests on the same basis.

The biggest weakness: which swing do you pick?

Every level comes from the swing's two points, so changing just one point moves all the levels. If the swing in the first figure starts from the intermediate low B (116) instead of the lowest low A (100), the same bounce is no longer a bounce off the 61.8% level but a move that has retraced almost the entire swing. Whether you use wick tips or bodies, and whether you pick the swing on the daily or the 4-hour chart, also changes the values. The thing to be most careful about is that if you pick a suitable swing after the bounce is over, any bounce can be explained by one of the levels.

Prices where other evidence overlaps

The Fibonacci levels that draw attention are usually prices where other evidence overlaps. When a previous high or low, a support or resistance zone where price has stopped several times, a moving average or a price zone with heavy traded volume sits near a level, more people are likely to be watching that price. In the first figure, too, the 61.8% level (119.1) lies within the price zone where the rally paused for a while (about 116 to 121.7). But when price stops at such a spot, you cannot tell whether it stopped because of the ratio or because of the other evidence that overlapped it. Looking at the price zones where swings cluster with the Support & Resistance Finder is one way to check for this kind of overlap.

A sober look at predictive power

The evidence that Fibonacci levels have any special predictive power is weak. For a start, the levels are tightly packed. The five lines from 23.6% to 78.6% sit every 12 to 17% of the swing, so wherever a pullback stops, there is bound to be a level nearby. Even if you count only 3% of the swing above and below each of the five levels as 'near', 30% of the range from 0% to 100% is near one level or another. When many people watch the same line, orders can gather at that price and it can actually stop there, but that is closer to a result of people's habits than a property of the ratio. How often price bounced at the levels was not measured in this article.