TimingCube - TimingCube - Fibonacci and the Golden Ratio - Golden ratio, Fibonacci numbers, Elliott wave, dow theory, Fibonacci retracements

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Signal Update

Current Signal Performance as of

Signal Type	Trade Date	Index	Return since issued
		Nasdaq 100
		Russell 2000
		S&P 500
		QQQQ

Cumulative Returns since First TimingCube Live Signal () as of

Index	Long Only	Long Only with Margin	Long & Short	Long & Short with Margin	Buy & Hold
Nasdaq 100
Russell 2000
S&P 500
QQQQ

Note: QQQQ returns are included for continuity sake.

Market Update

After seven straight weeks of driving the Nasdaq Composite and other indices higher, investors took a small breather. In the absence of anything to lead markets higher, the story of the week became one of increased oil and energy prices. A surge in natural gas prices to all time record levels, above $15 per 1,000 cubic feet, and oil moving back above $60 per barrel, fanned inflation worries anew. Crude oil prices were boosted further by renewed Al Qaeda threats on oil installations.

On Friday, as energy prices eased off their highs, investors turned their attention to next week's Federal Open Market Committee meeting. While a quarter percent increase seems to be a given, all eyes will be on the commentary released after the meeting for any clues which could indicate that the Fed would pause future increases. With such uncertainty the trading was light but the day's gains helped erase some of the week's decline.

The market is clearly in need of a rest after the prolonged advance, and this week resulted in mild consolidation action close to the unchanged level. For the week, the Nasdaq 100 lost the most with a 0.96% decline followed by the S&P 500 and Russell 2000 with respective losses of 0.45% and 0.26%. Our signal remains a Buy.

Trend Timing School

Fibonacci and the Golden Ratio

The mention of Fibonacci's magic number in last week's article on Breakouts was not meant as a tease, and for those of you consumed with curiosity we will attempt to explain further.

Most technical indicators used in stock market investing are artificial man-made contraptions that have no importance or meaning but that which we collectively give them. All but one in fact. The lone exception is the Golden Ratio which is a number built into many things in nature, such as the spiral of a nautilus sea shell, the disposition of leaves (or petals or seeds) in some plants like sunflowers, rabbit breeding patterns, and many geometric shapes. The Golden Ratio (or Number or Mean or Section), is known under many names such as Phi and Divine Proportion. The Golden Ratio is said to be the most economical way to harmoniously arrange living volumes, with less effort and maximum efficiency.

Since it exists in nature the number was not invented but rather discovered by many through the ages, but it is most frequently attributed to Leonardo Pisano, better know by his pen-name Fibonacci. He was a twelfth century Italian mathematician and his studies and writings popularized the ratio and its properties. Some say he discovered the ratio while modeling rabbit population growth, others say he was studying the Great Pyramid of Gizeh. Regardless, he could have read about it in earlier works by the Greeks Plato, Euclid and Pythagoras. The Golden Ratio was, and still is, used extensively in architecture and art, and stock market investments.

The Fibonacci numbers are simply based on the sequence of numbers in which each successive number is the sum of the two previous ones:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, etc.

As the numbers get larger, the ratio between two successive numbers in the series approaches 0.618 (try it: 233 / 377 for example). The numbers satisfy the equation:

F_n+2 = F_n+1 + F_n with F₁ = F₂ = 1

and the mathematicians find the actual value of 0.618 (with thousands of decimals mind you) by solving the equation:

x = 1/x - 1

Trust them, we do.

All of this is well and good, but what does this have to do with investing, you may ask. A number of astute souls reasoned that since human activity was determined by the laws of nature, stock market movements should also be influenced by them. Ralph Nelson Elliott (of Elliott Wave fame) and other researchers found that stock market retracements would often be 0.618 or 0.382 (the reciprocal) of the previous move. Note that the Fibonacci sequence also allows for a 50% retracement, which is one divided by two. Percentage retracements are useful to calculate how far a countertrend movement may go. They can signal in advance when the market may reverse and resume the direction of the original trend by offering resistance zones. Others in the investment community, such as William Gann and Dow Theory proponents had devised theories on retracements but they were based on a more rudimentary one third and two thirds ratio.

The reason this discussion is timely is depicted in Chart 1 below.

S&P 500 Fibonacci retracement lines

Following the Fibonacci number theorem, after the prolonged bear market which took the
S&P 500 from its all time high of 1,553.11 in March 2000 to the low of 768.67 in October 2002, it had to retrace through the major resistance lines shown at 23.6%, 50% and, 61.8%. By breaking and staying above the 61.8% level technical chartist believe that the market effectively erased any remaining effects of the bear market and entered a new bull phase, thus confirming the breakout detected by other indicators. The Dow Jones had already broken that retracement level, but the Nasdaq Composite has only retraced 28.5% of its bear market decline.

We want to agree with the message carried by the S&P 500 and Dow Jones Fibonacci breakouts, but we will keep watching what the market does from here to make sure we remain on the right side of the trend.