There are investors and traders that have been misinformed. They believe the application of Fibonacci ratios to stock market movements in price and time have been fully explored, suggesting there is nothing new in the remarkable discovery of Italy’s favorite son, Leonard Fibonacci, for investing and trading applications. Research at Long Wave Dynamics (LWD) suggests our understanding of the Fibonacci sequence and ratios, and their implication for human action and market cycles have barely scratched the surface. LWD has pioneered a new school of Fibonacci application in price and time. Deep mystery as old as time itself is manifesting itself in Fibonacci ratios in daily stock charts that will stun and amaze, if only you are willing to look.

Leonard Fibonacci was a citizen of thirteenth century Pisa, the Italian village of leaning tower fame. Fibonacci is widely accepted as the greatest mathematician of the middle ages, but the jury is still out. Fibonacci may well be recognized as the greatest mathematician of all time before the wobbling orb of earth stops spinning. Historically, Leonard Fibonacci was known for providing the first explanation of Hindu-Arabic numeral system to the Western world. More recently, in the last century, he is better known for discovering the Fibonacci sequence, 1,2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc., which produces Fibonacci ratios, 61.8%, 38.2%, 23.6%, etc. and Fibonacci spirals, all of which are proving to be the living space-time backbone of growth and decay in much of nature.

Joseph and Frances Gies revealed in their book *Leonard of Pisa*, that Leonardo da Vinci along with other artists and architects of the Renaissance consciously employed the golden ratio in their art and designs, unaware of Fibonacci numbers and the natural manifestations of the golden ratio. The Gies also reported that Johannes Kepler wrote of the divine section, the golden ratio, as symbolizing God creating like from like, and that in the 1920s Yale University professor Jay Hambidge coined the term dynamic symmetry to describe the symmetry of growth where the golden ratio is discovered, as opposed to the static symmetry of simple division.

There are critics of Fibonacci ratios applied to art, architecture and natural spirals, and some have valid points. Critics note that spirals in seashells, galaxies and other places often used to illustrate Fibonacci ratios do equate to the golden ratio. The Fibonacci spiral pattern is often clearly there, but the exact ratio measurements are off, sometimes significantly. What critics may often be missing is the time element to an unfolding Fibonacci phenomenon that a still picture may not capture. The light from the stars in the spiral galaxy below began the journey to the camera lens at different times, so exact Fibonacci ratios in the spiral may not be evident.

There are also those that criticize Fibonacci ratios applied to stock market activity. However, the advantage of Fibonacci ratios applied to stock market activity is that stock prices are a rather exacting science; otherwise, trades could not clear to the satisfaction of buyers and sellers at the end of the day. Stock cycle tops and bottoms occur at specific prices, on specific dates, and at specific times. In this article, you will read a very exact application of Fibonacci ratios to stock prices that span decades of space-time.

Spiral galaxies are beautiful and interesting, but using a new school of Fibonacci market cycle analysis to trade the E-mini futures contract or to know when to exit current stock positions for what will invariably be a greater value-buying proposition for large cap stocks at a stock market cycle low in the future is our real interest. This is where the Long Wave Dynamics Formula Timing plan enters stage left in your space-time continuum of investing and trading. The objective is to provide perspective and clarification regarding what appears to be market chaos, but where just under the surface is a fractal order in any market that will produce shock and awe in the thoughtful observer.

For starters, the Long Wave Dynamics Formula timing plan requires that you identify the Level 1 Fibonacci grid, which is the intraday low and intraday high of the most important move you can discover in the market you are studying. There is not sufficient space here to explain why the intraday low and high are essential, just take our word for it. As they say, a picture is worth a thousand words, and pictures are provided. Below is the Level 1 grid in the S&P 500, which identified the most critical Fibonacci targets in the entire 1982-2007 bull market.

Once you have located the Level 1 high and low Fibonacci grid target in any market, you drill-down into the next level of the grids between any adjacent Fibonacci ratios. This applies to all the Fibonacci ranges of every Level of Fibonacci grid. It is important to note that over the 61.8% target the method uses the inverse of the Fibonacci grids below 38.2% to produce the grid targets on the way to the 100% of the given grid. This grid ratio process is explained in detail in the Long Wave Dynamic Formula Timing Plan for subscribers. Below is the current Level 2 grid of the entire 1982-2007 bull market.

The new school of Fibonacci ratios applied to markets recognizes that all Fibonacci targets are important, but that the 38.2% and the 61.8% targets are especially important, because they divide every Fibonacci grid into 1) Solitude range, 2) Normal range, and 3) the Frenzy range. You will recognize that the market plunge into March 2009 reversed right on the 38.2% target of the entire Level 1 grid. This was clearly an important turn in the Fibonacci Dynamic Web. Mr. Market refused to drop out of the Normal range of the entire Level 1 grid and into the Solitude range. In fact, he has insisted on climbing back up the entire Level 1 grid of the Normal range, bursting into the Frenzy range only recently. Whether he can manage to remain in the Frenzy range is an important matter for any market observer.

What the observant investor or trader will immediately recognize is that the show put on for all the world to see in March 2009 was repeated on a smaller market cycle scale when Mr Market plunged into July 1, 2010. Just below the S&P 500 61.8% target at 1013 the market reversed, refusing to drop back into the normal range of the entire Fibonacci Dynamic Web of the 1982-2007 bull market.

This is where it gets interesting. Since Mr. Market has now broken into the new Level 2 grid above 1228, the 76.4% target in the Level 1 grid, he has been diligently climbing the Level 2 grid in pursuit of the 38.2% target in the Level 2 grid at 1278.95. Mr. Market knows that if he cannot get into the Normal range of the Level 2 grid, he risks dropping back through the 1228 target, where market gravity will attempt to pull Mr. Market back into the Normal range of that Level 2 grid.

This pattern of Mr. Market in the Fibonacci Dynamic web is evident down to the lowest possible level, i.e., to a hundredth of a point. Drilling down into the deeper and deeper fractal levels of the market you will recognize this character in Mr. Market even between your sips of coffee, as you try to map out your investing and trading strategy for the New Year. Put that coffee down as you observe the chart below. I would hate to have you burn yourself when you see the chart below.

After trying to break out over the 1259 target in the Level 2 grid on December 22, 2010, Mr. Market backed off into the morning of December 27, 2010, to make another run for that 1259 target. Where did it turn around on the morning of December 22, 2010? It turned on the exact Fibonacci golden ratio of the Level 4 grid at 1241.58. If that is not granular enough for you, note the high on December 28, 2010, at 1259.90, the golden ratio target in the Level 5 grid. These grids are generated from an intraday low in 1982 and an intraday high in 2007. Consider the implications. There are powerful forces at work in the universe that manifest in Fibonacci ratios.

The point is that what appears to be chaos is anything but. There is remarkable order to market activity, right down to the penny, every day, every hour and every second. Obviously, these deeper levels of market activity are not necessarily useful to investors and traders. However, they are the smaller scale versions of the larger moves the market makes, like the March 2009 low and the July 2010 low. All these market moves are ruled by Fibonacci ratios that were discovered long before the electricity that executes your investment and trading orders. You ignore such deep universal order at your peril.

Price is one thing. Time is another. Even more exciting than what Mr. Market is up to with Fibonacci ratios in price, is how Mr. Market respects Fibonacci cycles in time. Long Wave Dynamics research has discovered that Mr. Market is just as enamored with Fibonacci in time as he is with price. Currently, the cycles in price and time have been juiced with trillions of dollars in central bank monetary and government fiscal stimulus. Aggressive monetary and fiscal stimulus has proven the make the cycles run long in System Dynamics research at MIT by Jay Forrester.

In spite of the stimulus, Mother Nature is patient and gets her way. There are degrees of freedom in Fibonacci ratios in price and time in the large cycles and the smaller cycles. The current 20-week cycle is pushing the envelope and running way long, but it will turn down and bottom, sooner rather than later. It will do so based on Fibonacci cycles with degrees of freedom in price and time. It is now time for serious investors and traders to consider the implications of the new school of Fibonacci market cycle analysis. The Long Wave Dynamics Formula Timing Plan provides actionable information to improve performance and reduce risks for investors and traders based on Fibonacci cycles in price and time.

David Knox Barker is author of *Jubilee on Wall Street; An Optimistic Look at the Global Financial Crash*, Updated and Expanded Edition (2009). He is the founder of LongWaveDynamics.com, and the publisher and editor of *The Long Wave Dynamics Letter. *Permission is granted for this article to be reprinted if credit is given to the author and a link is provided to LongWaveDynamics.com.