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# What is a Fibonacci Retracement?

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• Written By: John Lister
• Edited By: Kristen Osborne
2003-2016
Conjecture Corporation
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Fibonacci retracement is a technique used for predicting financial market behavior. It is based on a mathematical sequence known as Fibonacci's sequence or Fibonnaci's numbers. The theory is that this sequence mirrors the way markets fluctuate and then "correct" themselves. While some sources believe the Fibonacci retracement is effective, its reliability can be overstated, particularly by people selling financial advice services.

Fibonacci's sequence is named after the mathematician who introduced it to Europe, Leonardo of Pisa. The name is a contraction of filius Bonnacio, or "son of Bonnacio." The sequence follows one simple rule: each number is the sum of the two previous numbers in the sequence. The first ten numbers in the sequence are thus 0, 1, 1, 2, 3, 5, 8, 13, 21 and 34. There is a mathematical formula for calculating the sequence without having to go step by step through the list. This formula is the basis of the solution to several mathematical problems.

Using Fibonacci retracement is a technique based around another characteristic of the sequence. This is that each number is approximately 1.618 times the previous number. Rather neatly, this also means each number is 61.8% of the one that follows it. In similar fashion, each number is 38.2% of the number two along in the sequence, and 23.6% of the number three places along. These three percentages form the basis of analysis under Fibonacci retracement.

Somebody using the technique will plot a graph beginning with an extreme high and low for the value being tracked, which will usually be a market index, but could be an individual stock. This high and low will be the highest and lowest recorded figures in the period of past history used for the analysis and will be logged on the graph as 100% and 0% respectively. The analyst will then draw vertical lines representing the 61.8%, 38.2% and 23.6% marks. It's important to note that these percentages refer to the gap between the high and low figures; they don't represent, for example, 61.8% of the higher figure itself.

The theory is that when the value being tracked fluctuates upwards or downwards, it will often briefly reverse direction when it hits one of the values that represent the 61.8%, 38.2% and 23.6% points. In some cases, there may be an overall pattern of movement in one direction, but with multiple temporary reversals as each point is reached. Though this pattern is far from guaranteed to occur, most analysis suggests it happens too often to be merely coincidental. The most common explanation is that the gap between each of the points represents the aggregate effect of investors' psychological response to market movements, particularly the way they try to predict when the market is going to turn.