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Larry Pesavento
 Preface
Over the past 20 years the use and misuse of the Fibonacci Summation series has proliferatedto the point that commentators on the nation’s TV business channels are now resident experts.I lay no claim to being an expert. I have, however, studied the subject of Fibonacci numbers ex-tensively, especially how it relates to trading. I have always taken the pragmatic position that ifI could not use what I was studying to help in trading, then I was not interested in pursuing itany further. If this material can stimulate your interest in the subject, then introducing you tothe subject will have been worthwhile. A word of caution, this material is based on the prob-abilities of trading. The art of trading is one of risk management. Amos Hostetter, one of thefounders of Commodity Corporation in Princeton, New Jersey, used to say, “Take care of lossesand the profits will take care of themselves.” I use this quote a lot because I believe it is very im-portant!
 
The pattern recognition methodology illustrated in the text will be of interest to anyonethat has ever traded using technical charts. I can say with confidence that there are very fewwho have researched patterns to the extent I have. Some of the references date back to the early1900s. Each of these patterns is based on ratio and proportion. A technical chart is nothing morethan a road map with a price and time axis. These patterns repeat with a great deal of regular-ity. Some of my best students have been airline pilots. They seem to approach trading like theyapproach flying, following a flight plan. The similarities to trading are numerous.
Finally, one of my goals in writing this book is to expose you to the subject of ancient ge-ometry. Fibonacci numbers are an integral part of the numbers that make up the subject ofancient geometry. It will be of interest to some of you that many of these sacred ratios havetheir origin in the cosmos. I will not spend a significant amount of time relating my experiencesin astro-harmonics research. The subject is too vast for me to consider here. More importantly,it is not necessary for profitable trading.Contents
 
IMtrOGUCTION «2... sssscssessssneenessssnsesnsscessssecssconsenasensuansenesesenaraaeaee xiHarmonic and Vibratory NUMbEIS.............scsscsssseeseeseeeseeneenes 1Geometrics Of a Price Chart ...........ssssssssscsssssssncsesseescssssecsees 13The Primary Patterns ............c.:sscscssssserssssssesseesssesssseesnenssenseees 21Classical Chart Patterns Using Ratio and Proportion....... 71Bonus Paitern: The Buitterfly ...........:.ssssssssssccssssscssecesseceeneces 83The Opening Price .........cccssscsecseccsccsseecensseeseersrnscetareoreceneras 89Entry TeChniquess ............s:cesccsscssossessssennenssessccnceeseesensescasenseas 97It’s Different THis Time ...........sccccccesceececnsesseeescenscessesncessserses 103The Non Random Nature of Chaos Theory .........s1sssssssses 115APPeCNdiCe ............csssssesnsenssescorsscesceensesscennsessersseesccsenneensscess 133
| Description of the Gartley “222” Pattern... 133
Il Some Practical Tips on Cycles .................-. 150
Ili Some More Practical Tips on Cycles ......... 155
IV Additional Reading ...............::.ssssscsssscesnees 160Stock Trading Using Pattern Recognition and Geometric Ratios
 
Introduction
Leonardo de Pisa de Fibonacci and Beyond
O: the eastern seaboard of Italy, about an hour’s drive from Florence, lies the town of Pisa. Itwas here that Fibonacci was born. He was a thirteenth century mathematician who primarilyworked for the royal families of Italy. The work for which he is most famous is the Libre Abaci(Book of Calculations). His award for this work was the present day equivalent of the NobelPeace Prize. Fibonacci was largely responsible for the use of arithmetic numbers versus Romannumerals. Before Fibonacci, the number 30 was written XXX. After his Libre Abaci, it was writ-ten 30.
 
Legend describes his journey to Egypt as one of great discoveries. He went to Egypt tostudy the mathematical relationships contained in the pyramids.
Those of you who really want to study the math contained in the pyramids should readPeter Thompkin's book The Secret of the Great Pyramids. It is not my intention to explore all ofthe geometry in the pyramids, only the Fibonacci Summation series. Fibonacci found this serieswhen he studied the Great Pyramid at Giza. The series is the sum of the two previous numbers0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 to infinity. Dividing one number by the next afterthe eighth sequence yields 21+ 34 = .618. This just happens to be the relationship of the heightof the Great Pyramid to its base.
Base= 2.00Half Base=1.00Height = 1.27Slope=1.618
Diagonal = 1.902 V(2.618 +1)
This additive series of numbers is based on the equation: Phi+1=Phi squared (6 +1=07).Larry Pesavento
ato Calro
Phin Golden Cross
Length of cross = 3517.5 metersWidth of cross = 2173.5 metersLW = @ (phi)
0 600
Lititititits
The Golden Spiral is formedby the numbers 89, 55, 34, 21,13, 8, 5,3, 2and1
 Stock Trading Using Pattern Recognition and Geometric Ratios
 
What Fibonacci did for me was to open my eyes! These are the relationships that are con-stantly in the market, | first started using Fibonacci numbers in 1974 at the urging of John Hill,Sr. of the Commodity Research Institute of Hendersonville North Carolina. | read all of Elliott'spapers and his correspondence with Charles Collins. Years later, Frost and Prechter wrote thebook Elliott Wave Theory, which explained the wave structure and the use of Fibonacci numbers.It concerned me that not all the waves were .382, 500, .618, 1.618, It was not until 1988 that]began using the square root numbers of the Fibonacci series V.618 = .786 and ¥1.618 = 1.27.Armed with these two square root relationships, the wave structure can be more easily ex-plained. Bryce Gilmore's first book, Geometry of Markets, brought the ratios to the public's atten-tion. The Elliott Wave Newsletter has never used these ratios as far as 1 know, I used to fax infor-mation to them on the square root numbers, but they never responded. Robert Miner of the Dy-namic Traders Group in Tucson, Arizona, uses all of the harmonic ratios. It is my opinion thathis newsletter and technical work is the best in our business. If you don't have the time to dothe work, Robert Miner, one of the best technicians on this planet, will do it for you at a smallmonthly cost. This reminds me of one of my favorite quotes from my friend and fellow trader,Jim Twentyman “Defy Human Nature—Do the work yourself."
What this book is going to do is illustrate how to use the Fibonacci ratios, their squareroots, and their reciprocals to determine the structure of wave vibrations. Of al] the books Ihave in my library, none of the Elliott Wave material covers this important concept. I am goingto keep it as simple as possible. If you can glean only one or two concepts or patterns, then thismaterial will not have been written in vain. I can promise you this much. If you study the ratiosand patterns shown here, you will! realize that markets have a definite pattern hidden withintheir chaos. Sorting through this chaos can enlighten you. The goal here is not to try to predictthe future or even to know what is going to happen next, No one knows that! (Well, there is Onewho knows, but He doesn’t trade,) It is not necessary to know what is going to happen in 5 days.what 1s necessary is to determine how much risk and profit potential is available im the next 5days. Probability is the name of the game. Risk contro] is of tantamount importance. Winnersthink in terms of how much they can lose, Losers focus on how much they can win, “Take careof your losses and the profits uall take care of themselves." —A.B.H.
By the time I have finished, I hope you will see the correlation of geometric patterns tothe ratios and proportions illustrated. It is going to be as simple as I can make it for you.Should you want more elaborate reading material it will be listed in the bibliography.
The material here has always proven exciting to me and my fellow traders who also sub-scribe to this approach to the market. In my opinion, it answers the question, “Can there be orderin the chaos of the market?" 1 wish I could have known this much about the market 20 years ago!
One more thought about the square root number from the golden mean. These numberswere first revealed in William Garrett’s incredible book The Torque Analysis of Stock MarketCycles. This is hands-down the best book on cycles | have ever read. There were only 200 copiessold in 1972, The remainder were destroyed by Prentice-Hall due to lack of interest. The bookwas recently republished by Ruff Publishing (509-448-6739). An excellent choice for every library.Larry Pesaventoa
There are a lot of charts in this book, I know of no other way to illustrate these concepts.Charts were selected from all areas, from commodities to the Dow Jones stocks, Several differ-ent time frames were selected because these patterns are found in all time frames,
Do not be disappointed if you do not see the traditional Elliott Wave pattern labeling. It isnot neccesary when you are using short term pattern recognition. What is important is the ra-tio and proportion of each wave. Frankly, I never felt too comfortable about exactly identifyingthe precise Elliott Wave count. This was brought to my attention most vividly several years agoat my trading house in Pismo Beach, California, Bryce Gilmore and Robert Miner were discuss-ing TBonds. They both came up with different Elliott Wave counts. They humbly admitted thatthey were both right! And these are two of the best technicians I have ever met. Bryce intro-duced the technician to the true geometry of the market, with his software program and book,Wave Trader, | count him as ane. of my very good friends and I will always be indebted to him.Although Elliott Wave devotees may cringe at this thought, you need not be overly concernedwith wave labeling, but the square roots and their reciprocals can go a long way in analyzing awave in the true Elliott sense,Stock Trading Using Pattern Recognition and Geometric Ratios
~~
 
Harmonic and Vibratory Numbers
I included the section on Harmonic and Vi-bratory numbers early in this book so thereader will begin to think in terms of repeti-tions and swings.
Reluctance to share some of their mostprecious trading secrets is probably inherentin all traders, 1 am no exception. What you willobserve in this chapter is, in my opinion, oneof the best kept secrets in technical analysis.These harmonic, or vibratory numbers as I re-fer to them, can be incredibly useful for profitprojection and stop placement. Every com-modity, stock, or speculative instrument hasits own vibratory number, It is as natural aseach element on a chemical chart having itsown number. Traders who specialize in tradingone speculative vehicle use these numbers allthe time. They don’t know why, except thatthey repeat day after day. The next few pagesand charts will describe these numbers and il-lustrate their usage. Make no mistake aboutthis section: it could be one of the most effec-tive tools you can use as a trader.
My first interest in these harmonic or vi-bratory numbers occurred in 1979 while I wasoperating the commodity department forDrexel Burnham Lambert in southern Califor-nia. Jim. Twentyman was working with me andoccupied the adjoining office. A small windowwas located between the offices so we couldtalk without using the phone. Jim had justmoved from Conti Commodities where he wasa very successful broker/trader. He was nowhelping me manage my C.T.A. firm, A.V.M. As-sociates. Jim purchased a Wang computer in1977 to do research on cycles and numbers.He also took a two year sabbatical to study theworks of the legendary trader W.D. Gann.
I had access to the library of the Invest-
ment Center Bookstore in West Los Angeles.This library had the finest collection of booksthat I had ever seen. Any book that I everheard about was there, including rare astrologi-cal books and old technical books from the1920s and 1930s, Once you go through this vin-tage material you will realize there is not a Jotthat is new to technical analysis. Most assur-edly there are new concepts and ideas, butmost material can be traced back to earliertraders. I think you will agree that the conceptof harmonic or vibratory numbers fits into the“new idea” bracket.
The easiest way to describe why har-monic numbers work the way they do is to usean analogy. Suppose you were to drop a rockinto a pool of water. (See illustration below.)Once the rock hits the water, waves will vi-brate from the center of impact until the
Why Harmonic Numbers Work
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Larry Pesavento
thrust of the rock hitting the water dissipates.There are four things that will determine theconsistency and duration of the waves: 1) Theheight from which the rock was dropped; 2)The weight of the rock; 3) The depth of thewater,
Markets react to thrust in much the sameway. Typically, a new announcement or sched-uled economic report will cause this thrust inthe speculative markets, Currently, the finan-cial markets respond to Gross National Prod-uct, employment data, both the Producer PriceIndex and Consumer Price Index, plus manyothers, Veteran traders remember vividly howthe Money Supply numbers of M’ and M?would shock the markets each week. Now youmust search to find these economic numbers.Soon a new leader of economic fundamentalswill emerge and the current leaders will taketheir place in the history books.
Jim Twentyman has an obsession withcorrect data. He has the best data I have everseen, It is flawless! What Jim and I did was tocategorize all the price swings over a fiveminute bar chart in all major commodities.The S&P data was done in 1985. We enteredcach of these into the Wang computer byhand. The computer would then search forvalues of the price swing and report the fre-quency distribution of each price swing. Whenthe distribution is skewed you would get aPoisson distribution and your first hint of aharmonic or vibratory number, It was then ap-parent that the only way you could prove thistheory was to look at thousands of charts tosee if the premise was valid. We tested the ideaand found it statistically accurate and quiteuseful in technical analysis.
Technicians will agree that chart analysisis tantamount to reading a road map. There isan X axis and a Y axis. Chartists depict the Xaxis for time and the Y axis for price. Once the
 
coordinates are found, you know the exactspot where price and time meet. This informa-tion is not going to tell you what will happennext. Nothing can do that! What it does tellyou is that a pattern may be completed at thattime. The neural network I am using does justthat; and harmonic numbers help with this es-timation. It has categorized these patterns intime and price.
As a trader, | must decide when to enterand exit the market, This is what trading is allabout. I then ask myself two questions: 1) Isthe pattern and ratio signal present? and 2)Can | afford to take the risk? If the answer toboth of these questions is “yes,” then I musttake the trade. No one can tell which tradeswill be successful. This is a game of probabili-ties, but the odds and payoffs are on my side.
The only way you can use harmonicnumbers is to go through example after ex-ample yourself and see how they work. It isnot necessary to know why they work—theyjust work! Revealing something as importantas those numbers used to be of concern to me.Jim Twentyman put my mind at ease with thisoriginal quote: “Defy human nature—do thework yourself!" That sums it up! Most traderswant the work done for them. Is it laziness,lack of commitment or desire? I really don'tknow. What I do know is that only 10-15 per-cent of those reading this book will actually goforward and study intraday charts to prove thevalue of Harmonic Numbers.
The harmonic numbers illustrated hereare ones that | am sure work. (There is a bigclue on how to find vibratory numbers if youare interested and I'll give you that clue if youcall me in Tucson, Arizona: 520/529-0469.)Stock Trading Using Pattern Recognition and Geometric Ratios
3
Order from chaos in theFibonacci Summation series?
I found it helpful over the years to viewany market as a vibration from some energypoint. What happened leaves clues to the fu-ture of price movements. The Fibonacci Sum-mation Series is related to chaos theory.Within the chaos of market action are identifi-able patterns that repeat with great frequency.One of the unusual properties of the Fibonacciseries can be illustrated by the following ex-ample; take any two numbers from 1 to infin-ity. Any two numbers will work, but | will startwith 124 and 963. Notice what happens whenyou do the following: add the sum of
 
 
 
 
 
 
 
124
+ 963
1 1087+ 963
2 = 2050+ 1087
3 = 3137+ 2050
4 = 5187+ 3137
5 = 68324+ 5187
6 = 13,511+ 68324
7 = 21,835+ 13,521
8 =35,346
When you divide the seventh harmonic vibra-tion by the eighth harmonic vibration you getthe number .618 (21,835 35,346 = 618). Oncethe eighth harmonic is reached there will bevirtually no change in the ratio of the numbersas you approach infinity. This is a good ex-
ample of how two random numbers can be re-lated in the future. Price and time patternsshow the same characteristics when they re-peat.
S&P—The S&P 500 has a total of five har-monic numbers; three primary and two sec-ondary numbers. Secondary harmonic num-bers are important in strongly trending mar-kets. Primary harmonic numbers are: 270, 350,540. Secondary harmonic numbers are: 170,110.
Treasury Bonds—Treasury Bonds have aharmonic number of 20. When Treasury Bondsexceed 20 Sticks they will most often proceedto 40 ticks. In strongly trending markets, mul-tiples of the tick harmonic should be expected(i.6., 2x20, 3x20, 4x20).
Dow Jones Industrials—The DowJones Industrials have a total of three har-monic numbers: two primary (3S and 105) andone secondary (70).Larry Pesavento
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 Stock Trading Using Pattern Recognition and Geometric Ratios 11
Proportions of ImportanceSacred Ratios from 1-5
~ Reciprocal
1.000 = = 1.0001.272 .; =M1 .41428
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we ae: cso me BTL1.902 = 0.5262.000 oo ‘4 = 0.5002.236 V5 OF = 0.4473.000 eae oe3.142 :4.000
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These ratios are not “sacred” in the religious sense, but they aresacred to the study of geometry. Just about every price ewing imagin-able can be found using one of these ratios. For trading the patterns/ use, you only need to look for tive ratios: .618, .786, 1.00, 1.27 and1.618.
it can be very helpful to know the market you are following isvibratory to .707 or 1.414 instead of the 618 or 1,618.
Finding out why the market did not make one of five ratios can bevery important in determining what it is going to do next. The followingcharts are examples of ¥2 and 1/V2.
 Procter & Gamble (PG) Butterfly PatternDaily Utilizing the Root 2 Numbers
ig Butterfly Top
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Dupont (DD) Head and Shoulders PatternUtilizing the Root 2 Numbers
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 Stock Trading Using Pattern Recognition and Geometric Ratios 13
The Geometric Characteristics of aPrice Chart
» Technicians use price charts to interpretwhat the next move is most likely to be.Me » Let us consider the tollowing?*. a
 
           
    
?N - N “O- ‘>. ~ 2,|| : \A price chart is a square... with two triangles of equal height
1.27 (1.618)
it also contains a pyramid... and a circle.
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              Lary Pesavento
 
Geometric Principlesby Bryce Gilmore
Philosophical Geometry
Ancient philosophers taught pupils thearts of Sacred Geometry in order to developtheir faculty of intuition.
Geometry attempts to recapture the or-derly movement from an infinite formlessnessto an endless interconnected array of forms,and in recreating this mysterious passage fromone to two, it renders it symbolically viable.
The practice of Sacred Geometry is oneof the essential techniques of self-development.
Geometry deals with pure form, andphilosophical geometry reenacts the unfoldingof each form out of the preceding one.
The Canon of Proportion
The binding natural law of mathematicsas we know it today originates from the cos-mos. It was not invented by man, just revealedto him through his study of the planets.
The Seventh Wonder of the AncientWorld, the Great Pyramid of Giza, holds withinits structure all the math “secrets” we need toknow.
The pyramid is a graphic representationof the Earth and Moon and their combinedmovements around the Sun. It demonstratesthe binding relationships between the square,circle, and the Golden Mean,
Modern day scientific studies have (amongother things) confirmed the measurements ofthe Moon and the Earth
The radius of the Moon is 1090 miles andthe radius of the Earth is 3960 miles. A com-bined total of 5040 miles (Plato's mysticalnumber and in calendar days equal to 720wecks, 2 times 360, 3 times 240, 4 times 180, 5times 144, and & times 90).
A square encompassing a circle repre-senting the Earth has four sides, each equal tothe diameter of the Earth, i.e., 3920 by 2 or7920 miles. The petimeter of this square calcu-jates to 31680 miles (4 times 7920, 44 times720, 88 times 360, 132 times 240, 176 times180, 220 times 144, and 342 times 90).
 Stock Trading Using Pattern Recognition and Geometric Ratios 15——{E_—_—___—————
If the Moon and the Earth were placed Using the Pythagorean theorem, i.e., theside by side (see illustration on previous | length of the hypotenuse in a right triangle (90page), the distance between the two centers | degree triangle) will be equal to the squarewould be equal to the sum of the radii, i.¢., | root of the sum of the squares of the other two3920 plus 1080, which equals 5040 miles. A | sides,
circle drawn using the combined radii of 5040 Hypotenuse = square root [(5040 x 5040)would have a circumference of 2 m ror 2x 22/ | + (3960 x 3960)] = 6409 miles.7 x 5040, which equals 31680. If we call the base of the triangle the
The relationship of the circle's circumfer- | Earth's radius, i.e., 3960, then the hypotenuseence to the square's perimeter is 1.000:1.000. | 6409.6 as a ratio of the base 3960 is 6409:3960This geometric exercise is known as squaring | or 1.618:1.000.the circle. Pi is the Pythagorean measure of The irrational number 1,272 is the square22/7 used to calculate the dimensions in a | root of 1.618, Le., 1.272 = ¥1.618.circle or sphere. In decimal form Pi is the irra- It can be demonstrated by this exercisetional number 3.14159. where the designers of the Great Pyramid of-
The radius of the circle 5040 (1080 + | Giza procured their measurements. It can also3960) as a factor of the Earth’s radius is equal | be seen that the irrational numbers of d=to 5040:3960 or 1.2727:1.000. And 1.272 is | 1.618 and x = 3.14159 are related,
mathematically the square root of 1.618, 1/4 (3.142) = 0.786 (1/N.618)1/4 is the harmonic ratio from the square andSquaring the Circle 1,618 is the Golden Mean.
Harmonic Ratios from the SquareThe Diagonal of the Square(Root 2 = 1.4142)
The square is bounded by four equal
sides at right angles to each other,SQUARING THE CIRCLE Using the Pythagorean theorem we can
Perimeter of the square is equal calculate the diagonal length. This numberto carcumterance of the Grcie. will always maintain the same relationship toany side of the square (1.4142:1).
A square with sides equal to 1.000 has adiagonal of: ¥(1? + 1*) or V2, which is 1.4142.
The diagonal of any square relates as1.4142:1,000 with its side.
Expanding a square by the ratio of its di-A hypotenuse calculation for a right- agonal produces the Harmonic Ratio Series.
 
SQUARE =6,000 CIRCLE = 8.000
angled triangle using the 5