A Fibonacci fan is a charting technique that uses Fibonacci ratios to predict support and resistance levels.
Fibonacci fans are sets of trendlines drawn from a trough or peak through a set of points dictated by Fibonacci retracements. To create them, a trader draws a trendline off which to base the fan, usually covering the low and high prices of a security over a given period of time. To reach retracement levels, the trader divides the difference in price at the low and high end by ratios determined by the Fibonacci series, typically 23.6 percent, 38.2 percent, 50 percent and 61.8 percent. The lines formed by connecting the starting point for the base trendline and each retracement level create the Fibonacci fan.
Traders can use the lines of the Fibonacci fan to predict key points of resistance or support, at which they might expect price trends to reverse. Once a trader identifies patterns within a chart, they can use those patterns to predict future price movements and future levels of support and resistance. Traders use the predictions to time their trades.
The Fibonacci sequence begins with the digits zero and one, then proceeds infinitely with the next number in the sequence equal to the sum of the two numbers preceding it (e.g., 0, 1, 1, 2, 3, 5, 8, 13, 21, 35, etc.). The proportion of any adjacent terms equals approximately 1.618, represented in mathematics by the Greek letter phi, and coincidentally underlies a huge number of naturally occurring patterns. For unknown reasons, stock prices appear to behave in patterns consistent with the Fibonacci ratio as well.
Technical analyses based upon Fibonacci ratios exist for both the price and time axes of charts. Analysts can also use retracements to produce arcs or fans using arithmetic or logarithmic scales. Nobody appears to know whether these tools work because stock markets exhibit some form of natural pattern or because many investors use Fibonacci ratios to predict price movements, making them a self-fulfilling prophecy. In any event, key support and resistance levels tend to occur frequently at the 61.8-percent level on both uptrends and downtrends.
To derive the three key ratios typically used in technical analysis based upon the Fibonacci series, you simply find the proportion of one number in the series to its neighbors. Adjacent numbers produce the inverse of phi, or 0.618, corresponding to a retracement level at 61.8 percent. Numbers two places apart in the sequence yield a ratio of 38.2 percent, and numbers three places apart yield a ratio of 23.6 percent.