Fibonacci Ｓequence

Leonardo Fibonacci, the great 13th century Italian mathematician (1175–1250) created the “Fibonacci sequence” to explain behavior in nature mathematically. History has it that the first question he posed was how many rabbits would be created in one year starting with one pair.

Etching of Leonardo Fibonacci
The sequence is actually quite simple. Start with "1" and add the previous number to create the next. So, 1 + 0= 1, 1 + 1 =2, 2 +1 =3, 3 + 2=5, 5 +3 =8….and so on…so the sequence is…0,1,1,2,3,5,8,13,21,34,55,89,144,233 and so on. Mathematicians have been enamored with the sequence ever since. It not only predicted rabbits' explosive reproduction numbers, but accurately measures a wide array of activity and behavior in nature.

Over time, this sequence was used by the master painters to define the dimensions of their paintings. There is something “pleasing” to humans about the proportions defined by the sequence. Think of 3x5 index cards, or how many times most people knock on a door, or ring the phone….3 is the most common, 5 is second. Humans have 5 senses, five fingers. The patterns of the spiral of sunflowers seeds also can be explained using the sequence.

The Fibonacci sequence also gives us the “golden mean” used in many mathematical calculations. The golden mean is 1.61—which is arrived at by dividing a Fibonacci number by the previous number. For example 89/55=1.61. Going the other direction 55/89=.61—which is how market technicians come up with Fibonacci retracements. Skip a number, 55/144=.38, the next retracement. I could go on with the many combinations used by market technicians. Suffice it to say the harmony of these numbers in nature was the cornerstone of much of W.D. Gann’s work to explain grain markets' pricing behaviors.

The other application of the sequence by Gann was with respect to time. Consider how 21- and 55-day moving averages are a favorite of purist technicians. It was this aspect of time when applied to the “birth dates” of markets that I wish to concentrate on—specifically for the Treasury market.

On August 22, l977, the Chicago Board of Trade started trading 30-year bond futures. This year, August 22 falls on a Monday. It will be the THIRTY-FOURTH ANNIVERSARY (34 is a Fibonacci number). My goal is not to make a market prediction as much as to share a fascinating possibility.

The next Fibonacci number is 55, it's a difference of 21, which could determine the length of the next cycle. If this Gann cycle is accurate, it may mean a cycle high in price, a cycle low in rates in the Treasury complex could occur possibly on August 22, or thereabouts. Another way to look at this would be, that it may be the BEGINNING OF A 21-YEAR CYCLE in lower prices, higher rates.

Simply stated, if this measure were truly predictive, it could mean the end of a bull cycle and the beginning of a bear cycle in Treasury prices. This may not mean that once the cycle's low yield is reached, the market will immediately reverse. Yet, if you were to look back , over time it could show up as an important turning point in the market.

There have been several large changes over the years in the bond contract, like a coupon change 11 years ago from an 8-percent coupon to the current 6-percent coupon. I can’t say if that would distort Gann’s theories. At the margins I hope readers find this interesting. Yet for those of you out there that believe in a higher order to human behavior, this could prove to be a prediction that W.D Gann might have mailed into CNBC if he was alive today.