Fibonacci numbers and ratios

Fibonacci numbers and ratios

Fibonacci, a famous 13th century mathematician discovered a number sequence called “the Fibonacci sequence,” adding the two previous numbers in the sequence to come up with the next number: 1, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13, 8 + 13 = 21, 13 + 21 = 34 and so on to infinity.

Importantly, after the first several numbers in the Fibonacci sequence, the ratio of any number to the next higher number is approximately 0.618, and the next lower number is 1.618. These two figures (0.618 and 1.618) are known as the Golden Ratio or Golden Mean. Its proportions are pleasing to the human eyes and ears and appear throughout nature and in biology, art, music and architecture. A few examples of shapes based on the Golden Ratio include playing cards, sunflowers, snail shells, the galaxies of outer space, hurricanes and even DNA molecules.

Two Fibonacci technical percentage ratios that are particularly important to traders are 38.2% and 61.8%. Most market technicians will track a “retracement” of a price uptrend from its beginning to its most recent peak, and those retracements in price often stop at these Fibonacci ratios, indicating places where markets may turn or show signs of strength. Other important retracement percentages include 75%, 50% and 33%. For example, if a price trend starts at zero, peaks at 100, and then declines to 50, it would be a 50% retracement. The same levels can be applied to a market that is in a downtrend and then experiences an upside “correction.” Perhaps it is a self-fulfilling prophecy, but traders know where these price retracement levels are, and the market frequently respects them.

What is most fascinating about Fibonacci numbers, the Golden Ratio and the Elliott Wave Principle as they are applied to technical analysis of markets is that these principles are a reflection of human nature and human behavior. The longer you are in the trading business and study the behavior of markets, the more you will realize that human behavior patterns and market price movement patterns are deeply intertwined. If you want to figure out prices, you need to figure out the trading crowd.