The Fibonacci numbers play an important role in technical analysis and most traders are familiar with using them to determine future price levels. However, far fewer are aware that the Fibonacci number sequence can also be used to identify potential turn dates.

**The Fibonacci number sequence**

The Fibonacci number sequence is used by day traders, investors and other stock market participants to try to predict future price levels within the stock market.

The number sequence was known to Indian mathematicians as early as the 6^{th} century. However it was 13th century Italian mathematician, Leonardo Pisano Bogollo, also known as Leonardo of Pisa or Leonardo Fibonacci, who is credited with introducing it to the western world.

The Fibonacci sequence is as follows, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc., where each successive number is the sum of the two previous numbers. The sequence extends to infinity and contains many unique mathematical properties.

For example, a number divided by the previous number approximates to 1.618 (21/13=1.6153, 34/21=1.6190, 55/34=1.6176, 89/55=1.6181), and the approximation nears 1.6180 as the numbers increase. When a number is divided by the next highest number it approximates to .6180 (13/21=.6190, 21/34=.6176, 34/55=.6181, 55/89=.6179 etc…). Again the approximation nears .6180 as the numbers increase.

As stockcharts.com points out, *“1.618 refers to the Golden Ratio or Golden Mean, also called Phi. The inverse of 1.618 is .618. These ratios can be found throughout nature, architecture, art and biology. In his book, Elliott Wave Principle, Robert Prechter quotes William Hoffer from the December 1975 issue of Smithsonian Magazine:*

*….the proportion of .618034 to 1 is the mathematical basis for the shape of playing cards and the Parthenon, sunflowers and snail shells, Greek vases and the spiral galaxies of outer space. The Greeks based much of their art and architecture upon this proportion. They called it the golden mean.”*

**Common usage**

Fibonacci numbers are most commonly used in technical analysis to determine potential areas of support and resistance. For example after a stock (or index) makes a reversal, technicians will use the Fibonacci sequence to plot various levels at which the stock might find support.

Known as Fibonacci retracements these levels are mathematical relationships, expressed as ratios, derived from the Fibonacci sequence. Fibonacci retracements are based on the idea that markets will retrace a predictable portion of a move, after which they will continue to move in the original direction.

A Fibonacci retracement level is created by taking two extreme points on a chart (high to low) and dividing the vertical distance by the key Fibonacci ratios. The retracement begins at 0.0% and extends to 100.0%, which represents a complete reversal of the original move.

The key Fibonacci ratios are 0%, 23.6%, 38.2%, 61.8% and 100%. The 61.8% retracement is derived from .618.

A 38.2% retracement is considered a natural retracement within a healthy trend and usually implies that the trend will continue. A 61.8% retracement implies that a new trend is about to manifest, while a 50% retracement implies indecision.

The chart below shows the Fibonacci retracement levels plotted from the March 2009 low in the Dow, to the May 2011 intermediate term top. The Dow retraced 38.2% of the entire move before finding support and continuing its advance.

**A 4 year chart of the Dow Jones Industrial Average** (Click on the chart for a larger version)

*Chart courtesy of stockcharts.com*

This usage of the Fibonacci number sequence to determine potential price levels is very common within technical analysis. However, far fewer market participants are aware that the sequence can also be applied to time. I.e. to identify potential turn dates.

Often referred to as Fibonacci Time Zones, and consisting of a series of vertical lines that extend along the X axis of a chart, this indicator is used to forecast reversals based on elapsed time. A major low or high is usually chosen as the starting point with subsequent lines drawn at intervals determined by the Fibonacci sequence.

At first the lines are generally too tightly clustered to be of use. However after the first five zones, the zones expand quite quickly as the sequence unfolds. Potential reversal, or pivot, points can be found by looking ahead 8, 13, 21, 34, 55, 89, 144 and 233 days, all of which are Fibonacci numbers.

A vertical line drawn 8 days after the major turning point represent the 6th Fibonacci Time Zone, while one drawn 13 days after represent the 7th Fibonacci Time Zone, etc. The Fibonacci Time Zones extend outwards as follows:

- 8th zone = 21 days
- 9th zone = 34 days
- 10th zone = 55 days
- 11th zone = 89 days
- 12th zone = 144 days
- 13th zone = 233 days

Market technicians, often referred to as chartists, extend the Fibonacci Time Zones into the future to anticipate potential reversal points.

**Appling Fibonacci Time Zones to the S&P 500**

On 6 March 2009 the S&P 500 index made a major low at 666.79. If we use this low at the starting point and overlay the Fibonacci Time Zones, we see that these time zones have corresponded with many of the major market turning points over the past few years.

**A 4 year chart of the S&P 500 index** (Click on the chart for a larger version)

*Chart courtesy of stockcharts.com*

Fibonacci Time Zones are best used in conjunction with an indicator such as the Relative Strength Index (RSI) which shows overbought or oversold conditions within the market. That’s because, as the S&P 500 chart shows, extreme readings on the RSI often correspond with key turning points.

The next potential turning point for the S&P 500 falls on 28 January 2013 and could well mark a major market top. Those looking to time the market should watch for overbought conditions in the run up to this turn date, since they could signal that a major reversal is imminent.