Fibonacci Trend Lines
Fibonacci was a mathematician living in the 13th century who discovered the "Fibonacci numbers." These numbers belong to a sequence where each successive number is the sum of the two previous numbers. (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on).
As the sequence reaches larger numbers, the quotient of consecutive numbers yields a surprisingly consistent proportion of 1.618 (or its inverse 0.618). This proportion is known by many names: the golden ratio, the golden mean, the divine proportion, and seems to be a fundamental proportion for the building blocks of nature.
Some traders apply the Fibonacci numbers to financial markets, and watch closely the important percentages drawn from these numbers (23.6%, 38.2%, 61.8%, 161.8% and 261.8%). They see these percentages as invisible support/resistance zones where prices may hesitate and/or reverse, and use them to predict interaction between trend and countertrend movements. (For example, the extent of retracement contrary to an underlying trend, or the distance that a new high or low might travel).
With a compass-like movement, three curved lines are drawn at 38.2%, 50% and 61.8%, from the desired point. These lines anticipate the support and resistance levels and possible ranges.
Fibonacci fans are diagonal lines indicating areas of support and resistance. After the high and low of the chart is located, an invisible vertical line is drawn though the rightmost point. This invisible line is then divided into 38.2%, 50% and 61.8%, and lines are drawn from the origin through each of these points.
Fibonacci retracements are horizontal lines indicating areas of support or resistance. They are calculated by first locating the high and low of the chart, then six lines are drawn: at 0% (the low on the chart), 23.6% 38.2%, 50%, 61.8%, and 100% (the high on the chart). Fibonacci extensions are also drawn at 161.8%, 261.8%, 423.6%.
After a significant price movement up or down, the new support and resistance levels may settle at or near these lines.
Note: Fibonacci retracements work best in trending markets with clearly defined swings where (in an uptrend) the highs get consistently higher along with the retrenchment lows (and vice versa for a downtrend).
Fibonacci Time Zone
Fibonacci time zones are a series of vertical lines spaced in increments that conform to the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, etc.). These lines indicate areas in which major price movement may be expected.