# Fibonacci Phi Mate Turn Dates - Forecasting Tops and Bottoms

By: Robert McHugh | Mon, Feb 13, 2006

It is important to understand that markets -- and especially equity markets -- seek order. The order they seek often falls into neat, precise Fibonacci Ratio time and price intervals. In the charts we annotate each week, we often point out price retracements and advances that proceed, stop, and turn at precise Fibonacci Ratios in relation to prior price movements. What we have noted to be true, is that price trend tops, bottoms, and reversals also occur very often at precise Fibonacci time intervals with other turn dates.

Before going further, for the benefit of new readers, here's a thumbnail sketch of the mathematics of Fibonacci numbers and ratios, and why they might be integral to financial markets:

While Fibonacci numbers and ratios have existed since the Creation, a 12th century mathematician, Leonardo Fibonacci, is largely credited with identifying the unique sequence and ratios, and their prevalence throughout nature.

The sequence goes like this: It starts with the number 1 and then adds that number to itself to get the next number. It then takes those two numbers and adds them together to get the next number in sequence. Each number next in sequence is the sum of the prior two numbers in the sequence, ad infinitum. Thus the sequence looks like this: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, etc... The ratios between these numbers are unique in that each addend is either .382 or .618 of the sum. For example, 13 plus 21 equals 34. 21 is .618 of 34. 13 is .382 of 34. .618 plus .382 equals a complete 1.00. This holds true for all pairs. These pairs are known as phi mates. The world around us is filled with these ratios and relationships. Robert R. Prechter, Jr.'s amazing book, The Wave Principle of Human Social Behavior and the New Science of Socionomics, New Classics Library, 2002, does a terrific job running down how Fibonacci numbers and ratios are everywhere throughout nature. What is so amazing is that market price and time movements are also dominated by Fibonacci numbers and ratios.

About two years ago, we took notice that when the Dow Industrials ended their two-decade Bull Market on January 14th 2000, something spectacular occurred. It was as if that date was to become one of the most meaningful in the history of the markets. Yet, no one that I am aware of has identified it as such. What is so special about January 14th, 2000? Yes, the Dow Jones Industrial Average topped then, six years ago, but so what? Yes, it can be said that January 14th, 2000 marked the official start of primary Dow Theory Bear market. Again, what's the big deal?

Since this dramatic date, every single market top or bottom of measurable significance has occurred precisely in a Fibonacci .618 to .382 ratio of trading days from either that starting date 1/14/00, or another top or bottom that has occurred since 1/14/2000, based upon closing balances. This is astonishing! A mathematical formula has been 100 percent correct in predicting market tops or bottoms in the Dow Industrials since the Dow Theory Bear began on January 14th, 2000! Each, an exact Fibonacci ratio number of trading days from the Bear's start and from another top or bottom during that Bear. And the trend continues. And nobody is talking about it! You didn't hear about this from your Merrill Lynch research department folks, nor the happy faces on CNBC. Nope.

Here is an example of what we are talking about. October 9th, 2002's low for the Bear market came 687 trading days from the start of the Bear on January 14th 2000. This number of trading days happens to be essentially 61.8 percent of the number of trading days from 1/14/00 to a significant Bear market top, June 23, 2004's top, which occurred 1,115 trading days from 1/14/00. The ratio 687 to 1,115 essentially equals .618 -- phi.

Here's another example. September 6th, 2000's top is 162 trading days from 1/14/00. September 21st, 2001's bottom is 423 trading days from the start of the Bear, 1/14/00. The ratio of 162 to 423 is a Fibonacci 1.0 minus phi, or .382.

Again, let me repeat, there is a either a .382 or .618 ratio relationship for every single meaningful top or bottom since January 14th, 2000 with another top or bottom since January 14th, 2000. The chart on page 4 chronicles every major top and bottom since 1/14/2000 and identifies each's phi mate, the other top or bottom that it shares a .382 or .618 ratio number of trading days relationship with.

What is fascinating is that in the early going, these Fibonacci phi ratios might be off a few thousandths of a percent here or there, but the further out from January 14th, 2000, the more precise the ratios got, often hitting .382 or .618 right on the nose.

This log of phi mates chronicles the amazing Fibonacci pattern that earmarks the current Dow Theory Bear market as something unusual in the making, a Bear market of particular significance in the annals of market history. On page 4 we list 31 tops and bottoms since 1/14/2000 that have a phi mate. 31 pairs over a five-year period. I'm sorry, but this is not a random occurrence. This is nothing short of bizarre. There is no logical explanation for it from a human perspective. It is not coincidence. I would love for one of my University mathematics professor subscribers with the time and interest to calculate the probability that all 30 consecutive pairs of tops and bottoms could be random. How's that for an article my fine-feathered Ph.D. friends? Do the calculation and I'll give you credit, be delighted to include the article in my Guest Articles section. Something huge, something surreal is going on here.

You know what I believe is going on? I'll tell you what I think is going on. I think God has a sense of humor. I think God gets a kick out of the arrogance of mankind. I think God is saying, "Hey mankind, the billions of transactions you millions of people conduct with hundreds of thousands of different points of view based upon tens of thousands of strategies based upon thousands of advisors and news reports all mingle together to result in prices that move exactly how I decide they will; will top and bottom when I tell them to, that ultimately I am in control, and here is the proof, so humble yourselves and seek my face." That's what I think God is saying. To me it is either God, or a random sequence that is astronomically improbable. That's just my take. I'd love to hear yours.

At some point I believe God will say, "I've made my point," and the amazing ratio relationships will cease. But in the meantime, it is worthwhile, I believe, to project what the possible tops and bottoms might be in 2006 based upon this pattern's continuance.

Based upon the assumption that this Fibonacci phi relationship formula between tops and bottoms since January 14th, 2000 will continue, we have calculated the probable turn dates for 2006, including minor as well as major prior tops and bottoms as mates. It should be understood that since the dates we are now projecting are so far out from January 14th, 2000, that dates that hit the .382 or .618 timeframes can vary by plus or minus 1 to 5 days. In other words, if we say 2/24/06 is a likely turn date, it means that 2/21/06 to 3/1/06 also may calculate to a phi mate approximate .382/.618 ratio.

* 3/7/2000's low is 38.0% of the total # of trading days from 1/14/2000's High to 5/26/2000's Low
* 5/26/2000's Low is 38.0% of the total # of trading days from 1/14/00's High to 12/20/00's Low
* 9/6/2000's High is 38.3% of the total # of trading days from 1/14/00's High to 9/21/01's Low
* 10/18/2000's Low is 38.8% of the total # of trading days from 1/14/00's High to 1/4/02's High
* 11/6/2000's High is 37.6% of the total # of trading days from 1/14/00's High to 3/19/02's High
* 11/22/2000's Low is 37.9% of the total # of trading days from 1/14/00's High to 4/29/02's Low
* 12/5/2000's High is 38.7% of the total # of trading days from 1/14/00's High to 5/14/02's High
* 1/3/2001's High is 37.6% of the total # of trading days from 1/14/00's High to 8/22/02's High
* 3/22/2001's High is 37.9% of the total # of trading days from 1/14/00's High to 3/11/03's Low
* 5/21/2001's High is 62.6% of the total # of trading days from 1/14/00's High to 3/19/02's High
* 9/5/2001's High is 38.0% of the total # of trading days from 1/14/00's High to 5/17/04's Low
* 9/21/2001's Low is 61.6% of the total # of trading days from 1/14/00's High to 10/9/02's Low
* 1/4/2002's High is 61.5% of the total # of trading days from 1/14/00's High to 3/31/03's Low
* 3/19/2002's High is 63.4% of the total # of trading days from 1/14/00's High to 6/17/03's High
* 7/23/2002's Low is 61.7% of the total # of trading days from 1/14/00's High to 2/11/04's High
* 8/22/2002's High is 62.1% of the total # of trading days from 1/14/00's High to 3/24/04's Low
* 10/9/2002's Low is 61.6% of the total # of trading days from 1/14/00's High to 6/23/04's Low
* 11/6/2002's Top is 61.5% of the total # of trading days from 1/14/00's High to 8/12/04's Low
* 11/27/02's High is 61.8% of the total # of trading days from 1/14/00's High to 9/7/04's High
* 12/27/02's Low is 61.8% of the total # of trading days from 1/14/00's High to 10/25/04's Low
* 1/14/03's High is 61.8% of the total # of trading days from 1/14/00's High to 11/18/04's Minor Top
* 12/5/01's Minor High is 38.2% of the total # of trading days from 1/14/00's High to 12/28/04's High
* 12/14/01's Low is 38.2% of the total # of trading days from 1/14/00's High to 1/24/2005's Low
* 1/4/02's Major Top is 38.3 % of the total # of trading days from 1/14/00's High to 3/4/05's Top
* 1/29/02's Low is 38.6% of the total # of trading days from 1/14/00's High to 4/20/05's Low
* 6/17/03's Top is 61.7% of the total # of trading days from 1/14/00's High to 7/28/05's High
* 3/19/02's High is 38.2% of the total # of trading days from 1/14/00's High to 9/12/05's High
* 3/19/02's High is 37.5% (Fib 3/8ths) of the total # of trading days from 1/14/00 to 10/21/05's Low
* 4/29/02's Low is 38.2% of the total # of trading days from 1/14/00's High to 12/30/05's Low
* 9/30/03's Minor Low is 61.8% of the total # of trading days from 1/14/00's High to 1/11/2006's High
* 10/14/03's Minor Top is 61.8% of the total # of trading days from 1/14/00's High to 2/7/2006's Low

Probable Tops/Bottoms Turn Dates in the
Dow Jones Industrial Average for the First Three Months of 2006
Based Upon Fibonacci phi Golden Ratio Relationships
With Other Tops/Bottoms From 1/14/2000

 1/11/2006's Top: In issue 259 we noted the next turn is due on or within a day or so of January 12th, 2006. In fact, a closing top was reached on January 11th, 2006 and equities sold off hard for the first time in 2006 on January 12th. 1/11/2006 was 1,507 trading days from the Dow Industrial's all-time top of 1/14/2000. Its phi mate is 9/30/03's bottom, which came 932 trading days from the 1/14/00 all-time top. 1/11/2006 is 575 trading days away from 9/30/03. 932/1,507 = .618, and 575/1,507 = .382. 2/7/2006's Low: In issue 266 we noted the next turn is due on or within a day or so of February 6th, 2006. In fact, a minor closing bottom was reached on February 7th, 2006, at 10,749.76. February 7th is 1,525 trading days from January 14th, 2000 and is 583 trading days from October 14th, 2003's minor top -- which is 942 trading days from 1/14/00. 942/1,525 = .618 and 583/1,525 = .382 -- on the nose.

For those of you bothered that some of these turn dates calculate extremely close, but not exactly as .382/.618 ratios, let me say this. In the overall scheme of what we are talking about here, a few thousandths of a percentage point is non-consequential, especially considering the end-point is to be able to project future market turn dates. But if you need a better explanation, perhaps this: Phi/phi is not really a ratio. It is a number that has no end. Its decimals continue forever -- infinity. If you were ever wondering if you could come close to infinity, well numbers like pi and phi are close examples of eternity. Divide the Fibonacci numbers 13 by 34, or 21 by 34 (note: 13 + 21 = 34). You come close to .382 and .618 ratios, but never quite get exactly there. .618 is a reasonable approximation of phi. Here's something else interesting. Phi is the value 1.618 whereas phi is the value .618. If you multiply Phi by phi you get the value 1.0. This is truly an amazing number.

"Honor the Lord from your wealth,
And from the first of all your produce;
So your barns will be filled with plenty,
And your vats will overflow with new wine."

Proverbs 3:9, 10

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## Author: Robert McHugh

Robert McHugh Ph.D. is President and CEO of Main Line Investors, Inc., a registered investment advisor in the Commonwealth of Pennsylvania, and can be reached at www.technicalindicatorindex.com. The statements, opinions and analyses presented in this newsletter are provided as a general information and education service only. Opinions, estimates and probabilities expressed herein constitute the judgment of the author as of the date indicated and are subject to change without notice. Nothing contained in this newsletter is intended to be, nor shall it be construed as, investment advice, nor is it to be relied upon in making any investment or other decision. Prior to making any investment decision, you are advised to consult with your broker, investment advisor or other appropriate tax or financial professional to determine the suitability of any investment. Neither Main Line Investors, Inc. nor Robert D. McHugh, Jr., Ph.D. Editor shall be responsible or have any liability for investment decisions based upon, or the results obtained from, the information provided.