To some, Fibonacci was a crazy mathematician, to others Fibonacci is an incredibly potent forecasting tool. Everybody is entitled to their opinion and this article is not designed to convert non-believers. After all, if you disregard Fibonacci analysis, it's your loss.

If you are on the fence about what to believe or would like to know more, consider this. The April 2010 S&P market top occurred within 10 points of a prominent Fibonacci resistance.

Following this top, the S&P tumbled 17%. The subsequent bottom at S&P 1,010 in July 2010 was struck within 4 points of Fibonacci support. Even the March post-Japan earthquake low occurred against Fibonacci resistance. The three most pivotal turning points in the last year were framed by Fibonacci support/resistance.

Coincidence? Let’s take a look at some real life trading examples to determine the value of Fibonacci analysis.

Fibonacci. Why Relevant?

Fibonacci, a 12th century Italian mathematician, was the first to mathematically express an aesthetical proportion that’s fascinated and influenced mankind for thousands of years.

This proportion is known as Phi or the Golden Mean and is derived from the Fibonacci sequence. The Fibonacci sequence starts out like this:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.

Each number of the sequence is the sum of the two preceding numbers. The ratio of each successive pair of numbers in the series approximates Phi. The ratios of successive numbers in the series quickly converge on Phi. After the 40th number in the series, the ratio is accurate to 15 decimal places. Fibonacci numbers have certain defining properties:

Division of the preceding number by the subsequent numbers tends to 0.618. Division of the subsequent number by the preceding number tends to 1.618. Division of a number by the second preceding number tends to 2.618.
Division of a number by the second subsequent number tends to 0.382.

The Golden Mean is found in the universe, humans, animals, plants, DNA, music, the bible, ancient architecture, and biology (see March 2011 ETF Profit Strategy Newsletter for a detailed explanation).

In biology, we find that a majority of flowers are adorned with a Fibonacci number of petals. Lilies have 3, buttercups 5, delphinium 8, Marigold 13 and sunflowers either 34, 55 or 89 depending on size. Sunflower seeds are arranged in a number of clockwise and anti-clockwise spirals containing 55 or 89 seeds.

Humans - Fibonacci Programmed

The Golden Ratio is also found in architecture and can be seen in the Great Pyramids of Egypt, the Parthenon in Greece, Notre Dame in Paris, Taj Mahal in India, the CN Tower in Toronto, and the United Nations building in New York.

It could be said that the Golden Ratio is in our DNA - literally. The DNA molecule, the program for all life, is based on the Fibonacci sequence. It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. 34 and 21 are numbers in the Fibonacci series and their ratio closely approximates Phi.

Fibonacci and Tradable Markets

To visually express the price performance of various markets - whether stocks (NYSEArca: VTI), bonds (NYSEArca: SHY), gold (NYSEArca: GLD), silver (NYSEArca: SLV), or commodities (NYSEArca: CSG) – we have created charts. Charts, like the architectural beacons mentioned above, are a creation of men.

With humans’ subconscious admiration for pleasing Fibonacci patterns, would it be outrageous that investors primal emotions – fear and greed – expressed in charts adhere to certain Fibonacci relationships. Research suggests this isn’t a far stretch.

Too Accurate to Dismiss

Like any other forecasting tool, Fibonacci analysis is not infallible, but look at the chart below and evaluate if knowing major Fibonacci retracement levels wouldn’t have helped steer your investment decisions in the right direction.

                                                     

The chart plots monthly S&P 500 candles against common Fibonacci retracement levels (yellow lines). At first glance it becomes obvious that the April 2010 top and the July 2010 bottom occurred precisely against Fibonacci resistance and support (white circles).

Hindsight is always 20/20, but the following excerpts from the ETF Profit Strategy Newsletter illustrate the value of including Fibonacci analysis in real-time trading.

April 16, 2010: “The pieces are in place for a major decline. We are simply waiting for the proverbial first domino to fall over and set off a chain reaction.” – A few days later the S&P reversed within a few points of the 61.8% Fibonacci resistance and fell 17%.

July 5, 2010: “Considering that the S&P is butting against the 100-week SMA, lower accelerations band, 38.2% Fibonacci retracement levels, round number resistance at 1,000, and weekly s1 at 994, there is a good chance we will see some sort of a bounce develop from the 990 - 1,015 area.” – The S&P bottomed the same day. The “some sort of bounce” turned into one of the most tenacious rallies in decades.

Fractal and Useful

Like many aspects of chart analysis, Fibonacci retracement levels are fractal and apply to multiple timeframes as long as used correctly.

In addition to determining how much of the previous rally/decline might be retraced by a future move, Fibonacci projections can help determine how far a rally might carry.

Based on the initial up leg from the 2002 low, one Fibonacci projections pegged a market top at S&P 1,555. The S&P rallied a bit further but topped at 1,576 and declined 910 points thereafter.

Another Fibonacci projection pinpointed the 1987 market top at Dow 2,746. To this day the cause for the biggest one-day meltdown in 1987 remains a mystery. One Fibonacci projection identified 2,746 as an important resistance level. With pinpoint accuracy the Dow (DJI: ^DJI) hit 2,746 and tumbled some 25% thereafter. The S&P (SNP: ^GSPC) and Nasdaq (Nasdaq: ^IXIC) followed suit.

The exact details of the 1987 crash will remain an unsolved mystery, but it appears that Fibonacci resistance is part of the puzzle.

If You are Still in Doubt

In mid-February the ETF Profit Strategy Newsletter expected a correction and used Fibonacci support levels to determine the scope of the correction: "If stocks don't fall below 1,255 and 1,229, we expect new recovery highs."

The March market bottom came right against the 1,255 (1,249 was the actual low) projected Fibonacci support, which kept the larger up trend alive and well. The next major Fibonacci resistance has now become the new up side target.

The ETF Profit Strategy Newsletter incorporates Fibonacci analysis into its comprehensive system of technical analysis. The latest forecast includes the new up side target along with the near-term support level that needs to hold to keep the immediate up trend in place.