The Fibonacci sequence, named after an Italian scholar of the same name, is a simple mathematical series where each number is the sum of the two preceding numbers. It starts as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89

The sequence is sometimes called ‘nature’s code’ because the numbers recur repeatedly in the natural world. An apple always has five pips, arranged like a star, and flowers always have three, five, eight, 13 or 21 petals.

Similarly, rows of seeds in sunflowers or pinecones always add up to Fibonacci numbers, because it is the most efficient way to pack lots of seeds into a small space.

Curiously, excluding the numbers zero, one, two and three, if you divide any Fibonacci number by the number after it, you get a similar answer: roughly 0.62 or 62%. The Greeks called this number Phi, representing physical perfection, and it has since become known as ‘the golden ratio’.

At the same time, if you divide any number greater than three by the second number that follows it, the results are around 0.38 or 38%.

Applying Fibonacci numbers to share trading produces horizontal lines on a chart which can indicate support and resistance levels for a share price. The main Fibonacci ‘retracement levels’ are 23.6%, 38.2%, 50%, 61.8% and 78.6%.

This article uses the example of insurance firm Direct Line (DLG). Having loaded the chart on Shares’ website, go to the Settings cog, select Drawings and then Fibonacci Retracement Levels.

Point the cursor at the October/November 2020 low in the share price (around 262p), hold down and move the cursor to the peak in the share price in January 2021 (around 340p), and release.

This should produce a series of purple lines across the chart showing support and resistance levels for the share price. Interestingly, the first drop in the price to around 300p knocks off roughly 40p or half of the price rise from the October/November low, consistent with the 50% retracement level.

Subsequently, both the 38.2%, 50% and 61.8% Fibonacci levels have provided alternately support and resistance levels for the share price.

It is important not to anchor your expectations on these levels as prices can and often do overshoot and undershoot them, but they can provide a rough guide to future support and resistance levels which can be useful for investors seeking clues as to the direction of share prices.

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