I’ve mentioned in blogs of days past about Fibonacci ratios and how they are used by market technicians and traders to determine support and resistance levels, but I never defined them. Seeing as how popular they are and how they really do reflect price movement, I thought I’d provide a short overview of the subject so that you’ll know what they are when people mention them.

**What is a Fibonacci number?**

The famous Fibonacci number sequence was named for an Italian mathematician, Leonardo di Pisa–aka Fibonacci, who wrote about the number sequence (although he did not invent it) as well as introducing the Arabic number system to Europe in his 13th century bestseller, *Liber Abaci*, known in English as the* Book of Calculation*. Eight hundred years later, Dan Brown also used Fibonacci numbers as an integral part of his bestseller, *The Davinci Code*. If you’re one of the few people on the planet who hasn’t read this book, let me explain Fibonacci numbers. They are nothing but the sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233… where each successive number is formed by the addition of the previous two numbers. The **golden mean** or **golden ratio**, is an approximation formed by the ratio of two adjacent numbers in the sequence. The larger the numbers, the better the approximation. For example, 5/8 = 0.625, but 144/233 = 0.6180 which is a much better approximation to the golden mean. (233/144 = 1.6180 is also called the golden mean, FYI.)

**Why are they significant?**

The golden mean has significance in many areas of art and science, and it also plays a prominent role in stock chart analysis. But the 61.8% level is not the only level of significance–levels formed by other ratios provided insight into trading psychology, too. These other levels are determined by the ratio of two Fibonacci numbers separated by one, two, or three numbers. For example, the next important Fibonacci level is given by 89/233 = 0.382 or the 38.2% level. Of lesser importance is the next level, given by 55/233 = 0.236 or the 23.6% level. You should note that although the 50% retracement level is *not* a Fibonacci level (I know it can be derived from 1/2 but from no other Fibonacci numbers) it *is* considered to be an important psychological trading level and so technicians include it in their analysis.

What these Fibonacci levels do is provide a clue as to intermediate levels of price support and resistance between two extremes. To find these levels, subtract the vertical distance between two extreme points and divide that by the key Fibonacci ratios of 23.6% (0.236), 38.2% (0.382), 50% (o.50), and 61.8% (0.618). Note that Fibonnaci levels aren’t always exact but they do provide decent ballpark numbers. The figure below is a recent chart of the S&P along with key Fibonacci levels.

**Conclusion**

Many charting programs include Fibonacci ratios in the form of retracement levels, arcs, and fans. Note that the strength of a level intensifies with each price test so that when the level is finally broken, the price movement will be particularly strong and trades made on that breakout generally have a much better chance of success.

As with other indicators, Fibonacci ratios aren’t always accurate, so use them as a guide to your trading rather than as an overall trading strategy. They are particularly useful in placing stop-losses or setting price targets. Some traders use pullbacks to Fibonacci levels to add to existing positions. Fibonacci ratios are also used in Elliott Wave Theory, Gann retracement levels, and in Gartley Patterns.

The intro to candle sticks was great. Thanks!