# Fibonacci Retracements & Extensions

#### Introduction

The use of Fibonacci levels in trading is based on the principle that the ratios of the Fibonacci sequence tend to coincide with key support and resistance zones, often signaling key pivot areas of price movement. Thus, Fibonacci levels are commonly used as a tool by technical chartists when analyzing markets. Why these levels work (i.e. the origin and history of their significance) is beyond the scope of this article, but it is worth mentioning that the behaviors of markets tend to follow patterns and behaviors found in nature. For a comprehensive overview of the history of the Fibonacci sequence and its prevalence in nature, art, music, math, etc., please refer to the background section of this website.

#### Fibonacci Sequence

The Fibonacci sequence begins with the numbers 0 and 1 and is comprised of subsequent numbers in which the next number in the series is the sum of the two previous numbers (1+2=3, 2+3=5, 3+5=8, 8+5=13 . . .)

The output produces the following sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 . . .

#### Fibonacci Ratios

When a number in the Fibonacci series is divided by the number preceding it, the quotients themselves approach the Fibonacci constant (Φ) also known as the Golden Ratio (1.618):

1/1 = 1,   2/1 = 2,   3/2 = 1.5,   5/3 = 1.666…,   8/5 = 1.6,   13/8 = 1.625,   21/13 = 1.61538,   34/21 = 1.619,   55/34 = 1.6176…, and   89/55 = 1.618

The inverse process (e.g. 55/89 instead of 89/55) also produces a constant: 0.618, or φ. Skipping a number in the sequence (e.g. 55/144 and 144/55) produces two more constants: .382 and 2.618. The ratios of the Fibonacci sequence can be represented through horizontal lines calculated between the start and end point of a measurement. These lines will be applied to an active price chart. #### Fibonacci Retracements

Traders apply these Fibonacci levels to help interpret market behavior and to isolate higher probability setups and market pivots. To apply these levels, chartists map an area from 0 to 1, where 1 represents the starting point, and 0 represents the ending point. Fibonacci ratios (levels) .236, .382, .5, .618, and .786 are then mapped between the starting and ending point. See the chart below of the S&P 500. Note the starting point at the 2007 peak, and the ending point at the 2009 low, and consider the market action at points A, B, C, and D.

A: Prices find support at the .618 level, and bounce.
B: The entire retracement from the 2009 low abruptly reverses at the same .618 level.
C: The reversal stops at the .382 level and continues its march higher.
D: A cluster of consolidation occurs at the .786 level.

As we will see later in the section covering Fibonacci extensions, it is remarkable to note the price action as the S&P 500 marches to new highs on the chart. The next major cluster of resistance occurs right at the 1.618 extension (F). Those who criticize the reliability of Fibonacci retracements argue that “Fib” levels are not always honored by the markets. In other words, sometimes a market will find support at a .618 level, while other times support will be found at .5, or at no Fibonacci level at all.

I think this argument misinterprets the value of the study. Fibonacci retracements are not predictors of the future, they are levels that help to establish and improve probabilities, particularly when used in combination with other market indicators.

#### Applying Fibonacci Retracements

Some of the criticism surrounding the reliability of Fibonacci levels is no doubt related to lack of technique. It is standard practice across the industry to apply Fibonacci bands (both extensions and retracements) using the pivot cycle highs and lows of a period, and therefore the definitions in this section reference these points for standard use as the default application of the tool.

However, respected market technician Connie Brown, author of the definitive book on the subject, Fibonacci Analysis, makes the case (referencing W.D. Gann) that sometimes the Fibonacci bands are best applied beginning at the secondary pivot high or low.

W.D. Gann stated in his stock course that he often found the secondary swing away from the actual bottom, or the secondary high after the end of a trend, to be of greater value than the actual price that ends the prior trend . . . I have found this to be true and will show you how markets give us internal price clues that tell us when we should make adjustments like this and when we should not.” -Brown, Constance. Fibonacci Analysis (Bloomberg Financial) . Wiley. Kindle Edition.

Amongst practitioners, the technique employed by Brown and Gann in using the secondary highs and lows for certain charts remains a perfectly valid – and often more accurate – application of the tools. Look at the charts below of the 20-Year Treasury Bond ETF: TLT.

The Fibonacci levels applied in Chart A using the standard method creates targets that would appear to be completely unreliable. However, applying the tool at the secondary high as the starting point on the same chart – as in Chart B – reveals a pattern that honors Fibonacci levels more accurately.  