# 3 Important Uses of Fibonacci Numbers

An example of the power of math can be found in Fibonacci numbers. Fibonacci numbers are a sequence discovered by Italian mathematician Leonardo Fibonacci in the 13th century. The sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and 89 on to infinity. The sequence has a series of interesting properties. The sum of any two consecutive numbers equals the next highest number. After the first four numbers, the ratio of any number to its next highest number approaches 0.618. The ratio of alternate numbers approach .382. These ratios are often simplified to the key Fibonacci levels—38%, 50%, and 62%.

While many of the features of Fibonacci sequences appear throughout nature, investors have harnessed their power to predict stock prices. The most popular Fibonacci-based investment system is Elliot wave theory. Given the subjective nature of the various waves and the complexity of the process, I have never used Elliot Wave in my investments. Instead, I use the following three simple applications of Fibonacci retracement levels:

1. Levels of support and resistance – A weakness of retracements is they can only be measured by looking backward. However, these reviews offer impressive patterns. Reviewing Apple’s (AAPL) decline from a peak of \$202 to a low of \$79.60, we see support after 62% of the decline (red arrows) that led the price higher. Also, we see a gap through the same support (red circle) that led to the ultimate low. Applying Fibonacci levels at these events would have revealed a downside price target.
2. Trend changes – Prices often consolidate near retracement levels. Regardless of a trend’s potential, approaching retracements will slow the pace.
3. Price targets – The most applicable use of Fibonacci levels are price targets. When AAPL bottomed at \$79.60 and began rallying, the 38% retracement level of \$126 was an obvious price target. When the shares reached the price in a quick fashion, no one should have been surprised.

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Fibonacci levels are both mystic and useful. Learn to use them and take the mystery out of this technical pattern.

Sean Hannon, CFA, CFP is a professional fund manager.

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