Shocking Truth About Fibonacci Numbers

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ng shocki truthabout fi bonacci numbers ByEdwar dDobson 3 8513 213455 89144233377

The Shocking Truth About Fibonacci Numbers What Are Fibonacci Numbers? Fort he“uni ni t i at e d”whoar eunf ami l i arwi t hFi bonac c inumbe r s ,t he yar ea sequence of numbers (a series, in math parlance) initially discovered by an 11th century Italian mathematician. The sequence starts with the digits 0 and 1, then progresses to the next number by adding the last two numbers in the series together. Hence,t hes um of0and1i s1…t he n1+1=2,2+1=3,3+2=5,5+3=8,8+5=13, ands oo n…. t hust hef i r s ts e ve ral numbers in the series are 0, 1, 2, 3, 5, 8, 13, 21, 34, 55,89,144,233,377,610,987,1597……. WhyAr eFi bonac c iNumbe r s“Spe c i al ”? It is commonly thought and has been widely written about that the numbers in the Fibonacci series occur and are manifested throughout nature, art, architecture, financial markets, and many other areas. Is There Any Special Relationship Between the Numbers? Any given number in the series (after 5) approximates 1.618 times the number preceding it. The higher the number, the closer it approximates this ratio. Any given number approximates .618 of the number following. Between alternate numbers, the second higher number approximates 2.618 times the first number (e.g., 233 versus 89). Between alternate numbers, the second number down has the ratio of .382 (the inverse of 2.618) to the first number (e.g., 55 versus 144). There are many other relationships such as these which are consistent between the numbers. Where Can I Learn More About Fibonacci Numbers? Traders Press publishes a short booklet, authored by yours truly way back in 1984, t i t l e d “Unde r s t andi ng Fi bo nac c iNumbe r s ” which furnishes much more information about Fibonacci numbers, interesting facts about them, how they may be used in trading, and a bibliography listing other sources of information. This booklet is available on www.traderspress.com for a nominal price, and is available only as an e-book at present. How Do Traders Use Fibonacci in the Markets? When a stock, commodity or index makes a price move (either up or down) from point A to point B, then the price reacts part of the distance traveled in the AB move, the extent of this reaction frequently approximates a Fibonacci ratio of the distance of the preceding move (e.g. .382 or .618). This is known as a Fibonacci retracement, and the ending point of the reaction is labeled point C. If the original trend reasserts itself, the distance traveled from point C to the point where this new price move culminates at point D (the C-D move) frequently approximates a Fibonacci proportion or ratio (e.g. C-D distance = 1.618 x A-B distance). This is

known as a Fibonacci extension. This is an extremely simplified and incomplete explanation and example and is shown only to illustrate the types of principles used by traders who employ Fibonacci concepts in their timing and analysis. But How About the Numbers Themselves? There has been much written about using the numbers themselves in the markets. For example, if a price low occurs at point A, a subsequent high is “s uppos e d” t o oc c ur34,55, 89, or 144 price bars later. The actual numbers themselves are purported to have great significance in many ways. Many who have wr i t t e naboutt he m al mos ti mbuet he m wi t h“magi c al ”properties and qualities. I nde e d,whe none“Googl e s ”t het e r ms“magi c ”and“Fi bonac c inumbe r s ”t oge t he r , almost THIRTY THOUSAND entries pop up! I Used to Believe That The Numbers We r e“Magi c ”Mys e l f When I first learned about Fibonacci numbers (and relationships) in the e ar l y1980’ s ,Iwasi ntrigued. I spent years observing how consistently Fibonacci r e l at i ons hi psa ndr at i o s“pl aye do ut ”i nmar ke tac t i on.I n1979,Iha dwr i t t e nand self-publ i s he dabookt i t l e d“ The Trading Rule That Can Make You Rich*”( before I had ever learned about Fibonacci numbers and relationships). This book dealt with a highly consistent pattern of market behavior. When the book was reprinted in 1985, I added a chapter which dealt with Fibonacci relationships and how they correlated with the main concept dealt with in the book. (Check this book out on r ade r ss ay t he y havef ound i the l pf uli nt he i r www.traderspress.com …many t t r adi ng) .I nf l ue nc e dbyt he“popul arwi s dom”,Ibe c amet hor oughl y convinced that Fi bonac c inumbe r st he ms e l ve swe r ea“bi gde al ”andhe l d“magi c alpowe r s ”. What Changed Your Mind? One day, years ago, I received an e-mail from my old friend Greg Morris. Upon r e f l e c t i ngon whati ts ai d and “c he c ki ng i tout ” mys e l f ,Iwas shocked! Essentially, it said that there is no real significance to the actual Fibonacci numbers themselves, but only to the ratios and relationships of .382, .618, 1.618, and so on. Years later, Greg wrote briefly about what he told me in that e-mail in his excellent book “The Complete Guide to Market Breadth Indicators” ( avai l abl e on www.traderspress.com ) …butIdoNOT be l i e vewhatheha dt os ayi sc ommon kno wl e dge …. he nc et hi sl i t t l et ongue -in-cheek treatise which has been rattling around in my head ever since Greg made me aware of the fact that FIBONACCI NUMBERS THEMSELVES ARE NOT MAGIC…. what is important is the relationships between them, not the numbers themselves. What I discovered from my friend Greg is that THE SAME “FI BONACCI ” RELATIONSHIPS exist between the numbers in ANY NUMBER SERIES constructed in the same manner as the Fibonacci series, that is, by adding the last two numbers in the series to obtain the next number! To me, this was in incredible r e ve l at i on…. s oIqui c kl ys e tt owor k on a spreadsheet to prove this point to myself.

Le t ’ sSt ar tt heSe r i e sWi t h2and19 Greg suggested starting the series with the numbers 2 and 19 rather than 0 and 1. I did so and was amazed at the results…. af t e rgetting a few numbers into the calculations, it became apparent that the exact same relationships existed between the numbers thus obtained as existed between the numbers in the Fibonacci series. I decided to see what would happen if the series were started with random numbers, e ve nwhe r et hef i r s tors e c ondonewasane gat i venumbe r …we l ll oandbe hol d,t he results were exactly the same: NO MATTER WHAT TWO NUMBERS, POSITIVE OR NEGATIVE, WERE USED TO START THE SERIES, THE RESULT WAS ALWAYSTHE SAME…. THE SO CALLED “FI BONACCI ”RELATI ONSHI PS EXISTED BETWEEN THE RANDOMLY CHOSEN NUMBERS!! Even using two negative numbers to begin the series gave the same result. See the Excel spreadsheet below ( Whe r e ’ st heBe e f ?)i fyo udon’ tbe l i e vei t ! Gr e g’ sWonde r f ulSe ns eofHumor Il ovemyf r i e ndGr e g’ s“dr y”s e ns eofhumor …whe nIas ke dhi m why he had chosen the numbers 2 and 19 to illustrate his point, he told me to reflect on what the 2nd and 19th l e t t e r soft heal phabe twe r e ….We l l ,t he y ar e“B” and “S”…. B. S. Apparent l yt hi si swhathet houghtoft he“magi c ”ofFi bonac c i numbers themselves, as opposed to the relationships between them.

Whe r e ’ st heBe e f ? This Excel s pr e ads he e tqui c kl yi l l us t r at e st hepoi nt …c he c ki toutyour s e l f ! Where's The Beef? Fibonacci #

Ratio

Start

Ratio

Start

Ratio

29

Start

Ratio

-15

Start

1

2

1

19

5

-32

7

2

21

34

-47

-4

Ratio

-11

3

1.500

40

1.905

39

1.147

-79

1.681

3

5

1.667

61

1.525

73

1.872

-126

1.595

-1

-0.750 -0.333

8

1.600

101

1.656

112

1.534

-205

1.627

2

-2.000

13

1.625

162

1.604

185

1.652

-331

1.615

1

0.500

21

1.615

263

1.623

297

1.605

-536

1.619

3

3.000

34

1.619

425

1.616

482

1.623

-867

1.618

4

1.333

55

1.618

688

1.619

779

1.616

-1403

1.618

7

1.750

89

1.618

1113

1.618

1261

1.619

-2270

1.618

11

1.571

144

1.618

1801

1.618

2040

1.618

-3673

1.618

18

1.636

233

1.618

2914

1.618

3301

1.618

-5943

1.618

29

1.611

377

1.618

4715

1.618

5341

1.618

-9616

1.618

47

1.621

610

1.618

7629

1.618

8642

1.618

-15559

1.618

76

1.617

987

1.618

12344

1.618

13983

1.618

-25175

1.618

123

1.618

1597

1.618

19973

1.618

22625

1.618

-40734

1.618

199

1.618

2584

1.618

32317

1.618

36608

1.618

-65909

1.618

322

1.618

4181

1.618

52290

1.618

59233

1.618

-106643

1.618

521

1.618

6765

1.618

84607

1.618

95841

1.618

-172552

1.618

843

1.618

10946

1.618

136897

1.618

155074

1.618

-279195

1.618

1364

1.618

17711

1.618

221504

1.618

250915

1.618

-451747

1.618

2207

1.618

28657

1.618

358401

1.618

405989

1.618

-730942

1.618

3571

1.618

46368

1.618

579905

1.618

656904

1.618

-1182689

1.618

5778

1.618

75025

1.618

938306

1.618

1062893

1.618

-1913631

1.618

9349

1.618

121393

1.618

1518211

1.618

1719797

1.618

-3096320

1.618

15127

1.618

196418

1.618

2456517

1.618

2782690

1.618

-5009951

1.618

24476

1.618

317811

1.618

3974728

1.618

4502487

1.618

-8106271

1.618

39603

1.618

514229

1.618

6431245

1.618

7285177

1.618

-13116222

1.618

64079

1.618

832040

1.618

10405973

1.618

11787664

1.618

-21222493

1.618

103682

1.618

1346269

1.618

16837218

1.618

19072841

1.618

-34338715

1.618

167761

1.618

2178309

1.618

27243191

1.618

30860505

1.618

-55561208

1.618

271443

1.618

3524578

1.618

44080409

1.618

49933346

1.618

-89899923

1.618

439204

1.618

5702887

1.618

71323600

1.618

80793851

1.618

-145461131

1.618

710647

1.618

9227465

1.618

115404009

1.618

130727197

1.618

-235361054

1.618

1149851

1.618

14930352

1.618

186727609

1.618

211521048

1.618

-380822185

1.618

1860498

1.618

24157817

1.618

302131618

1.618

342248245

1.618

-616183239

1.618

3010349

1.618

39088169

1.618

488859227

1.618

553769293

1.618

-997005424

1.618

4870847

1.618

63245986

1.618

790990845

1.618

896017538

1.618

-1613188663

1.618

7881196

1.618

102334155

1.618

1279850072

1.618

1449786831

1.618

-2610194087

1.618

12752043

1.618

165580141

1.618

2070840917

1.618

2345804369

1.618

-4223382750

1.618

20633239

1.618

267914296

1.618

3350690989

1.618

3795591200

1.618

-6833576837

1.618

33385282

1.618

433494437

1.618

5421531906

1.618

6141395569

1.618

-1.1057E+10

1.618

54018521

1.618

701408733

1.618

8772222895

1.618

9936986769

1.618

-1.7891E+10

1.618

87403803

1.618

1134903170

1.618

1.4194E+10

1.618

1.6078E+10

1.618

-2.8947E+10

1.618

1.41E+08

1.618

1836311903

1.618

2.2966E+10

1.618

2.6015E+10

1.618

-4.6838E+10

1.618

2.29E+08

1.618

Le t ’ sNotGe tTooCar r i e dAwayHe r e … Before you completely dismiss the usefulness of Fibonacci, let me say this about i t …I have studied Fibonacci relationships in the markets for many ye ar s …. and I have found few other concepts or tools that are as helpful or as consistent. I ’ ms pe aki nghe r eoft hemaj orr e l at i ons hi ps ,s uc has. 61 8,. 382,1. 618 and so forth (there are others), and not the numbers themselves. As a matter of fact, using these relationships is one of the major inputs that I use to this day in my own t r adi ng…andIhi ghl yr e c omme ndt hati fyouar enott hor oughl yf a mi l i arwi t ht he associated concepts, that you take the t i meandt r oubl et ol e ar nabo utt he m…t he n decide whether or not they deserve a place in your own approach to trading. There are a number of excellent books on the subject which I highly recommend, all of which are available on the Traders Press website, www.traderspress.com . You can s e ar c hf ort hef ol l owi ngt i t l e st he r ebyt i t l eorbyt heaut hor ’ sl as tname .Is ugge s t that you take a look at these and consider adding one or more of them to your trading library: Carolyn Boroden, Fibonacci Trading (http://www.traderspress.com/detail.php?PKey=592 ) Michael Jardine, New Frontiers in Fibonacci Trading (http://www.traderspress.com/detail.php?PKey=266 ) Connie Brown, Fibonacci Analysis (http://www.traderspress.com/detail.php?PKey=601 )

There are a number of other worthwhile items available on Fibonacci as it relates to trading.Toc he c kt he m out ,doas e ar c hoft he“Fi bonac c i ”c at e gor yont he website: http://www.traderspress.com/categoryResults.php?S_CatID=40&Submit=Search+Categories

I ’ m hopi ngt hi sl i t t l e“t ongue -in-c he e k”ar t i c l ebr oughtas mi l et oyourf ac e , made your day a bit more enjoyable, and contributed in some small way to further your understanding and knowledge of Fibonacci numbers and relationships.

Edward Dobson Greenville SC

September 3, 2008

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Edwar dDobsonwasbor ni nCal i f or ni a andr ai sedi nSout hCar ol i na.Atage12,hi s f at heri nst i l l edi nhi m ani nt er estf or i nvest i ngi nst ocks.Thi sbecameal i f el ong passi on,whi chcamet oencompasst r adi ng i nsecur i t i es,opt i ons,andf ut ur es.Af t er col l egeandmi l i t ar ydut y ,hewasabr oker wi t hSmi t hBar neyandPai neWebberf or23 year s,speci al i zi ngi nopt i onsandf ut ur es. I n1992,hel ef tt hebr oker agebusi nesst o devot ef ul lt i met ohi spubl i shi ngbusi ness, Tr ader sPr ess( f oundedi n1975) ,andt o t r adi ng.Hei scur r ent l yanact i vet r aderand st i l lact i vei nhi sbusi ness.