Financial Markets and Nature: The Fibonacci Connection

Transcription

1 Financial Markets and Nature: The Fibonacci Connection Robert S. Vagg I see a certain order in the Universe, and math is one way of making it visible May Sarton ( )

2 Disclaimer The author believes that the information contained in this presentation has been obtained from sources that are accurate. The author accepts no liability for any damage caused by any error in, or omission from, the presentation. The content of the presentation is general information intended as a guide only and should not be relied upon in isolation. It has been prepared without taking account of any individual s financial situation or objectives. It therefore should not be considered as providing anything other than general advice. Individuals should seek appropriate advice from a licensed financial advisor before taking any action stemming from the content of this presentation. I guess I should warn you, if I turn out to be particularly clear, you ve probably misunderstood what I ve said.. Alan Greenspan

3 Nature: An Unpredictable Chaotic Complex System

4 Nature: An Unpredictable Chaotic Complex System The logarithmic spiral a natural growth structure

5 The Nature of the Stock Market Meeting Human Needs Basic Need Secure Housing Food Sustenance Mobility Communication Well-being Market Sector Property Trusts, Financials, Materials, (Defence) Consumer (Staples) Energy, Healthcare Utilities, Industrials, (Transport) Telecommunications, Information Technology Healthcare, Consumer (Discretionary)

6 Natural Growth and Growth Structures 10,000 All Ordinaries Price Index ( ) 10,000 1,000 Linear Trend Dynamic Growth Volatility Static Growth Pattern 1,000 Volatility 100 Linear Trend

7 Three Natural Irrational Numbers Irrational Number: A number that is neither a whole number nor a simple ratio of two whole numbers e (the natural growth base) = Stock Market Relevance describes compound growth > Price Trend Growth π (pi) = describes cyclical growth > Price Volatility Φ (phi) = describes both???

8 Sectioning a Line: The Golden Proportion B A (100%) C Question: How must a line be sectioned so that the ratio of the lengths B:C = A:B? Answer: B:C = A:B = ( Φ ) x = ( Φ 2 ) / = ( Φ 2 ) (61.8%) (38.2%) / = ( Φ 1 ) / = ( Φ 1 ) x = ( Φ 0 ) x = ( Φ 0 ) / = ( Φ -1 ) / = ( Φ -1 ) x = ( Φ -2 ) / = ( Φ -2 )

9 Φ and the Pentagon (Pentangle) B A Relative Lengths AB = % F E AC = Φ DE = % EF = % C D Φ =

10 The Fibonacci Sequence Leonardo Fibonacci (ca ) (Leonardo da Pisa) Fibonacci described the first known recursive number sequence. In the sequence each number is equal to the sum of the previous two (e.g = 13). 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, / 233 = ( Φ 2 ) 377 / 233 = ( Φ 1 ) 144 / 233 = ( Φ -1 ) / 233 = ( Φ -2 ) As the sequence progresses the ratio of each successive pair of numbers converges to (phi).

11 Simple Growth by Regular Branching Growth Rule: Each branch two months old or more produces a new shoot every month Branches Months

12 Continuous Linear Branching B A Maximum branch reduction factor (B/A) = 1/1.618 = 0.618

13 2-Dimensional Growth by Expanding Squares Logarithmic Spiral

14 The Growth Spiral (Logarithmic Spiral) in Nature Ram Horn Low-Pressure Weather System Fossil Shell Aloe Succulent Pinwheel Galaxy (Ursa Major Constellation)

15 Leaf Structure (Phyllotaxis) and Spiral Growth Sunflower phyllotaxis

16 Leaf Structure (Phyllotaxis) and the Golden Angle The Golden Angle : o 2π / Φ = 360 o /1.618 = 360 o x = o Sunflower phyllotaxis 360 o x = o

17 Floret Structures: Products of the Golden Angle 34 Coneflower 34 x 55 Sunflower 55 x 89 Daisy 21 x 34 21

18 Non-Fibonacci Plants: Lucas Phyllotaxis 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843,. 843 / 322 = ( Φ 2 ) 521 / 322 = ( Φ 1 ) 199 / 322 = ( Φ -1 ) / 322 = ( Φ -2 ) Fuchsia (4 petals) Cacti: 4 x 7 spirals 11 x 18 spirals 29 ribs

19 Φ in the Human Form A shell-like Ear Facial Dimensions Designed for Survival Dimensions of the Hand and Arm

20 Φ in the Human Form A well- formed spiral

21 10 base-pairs 3.4 nm The Structure of B-DNA: Φ in the Genes A Right-Handed Double Helix Major Groove decagon Minor Groove 2.1 nm 1,000,000,000 nm = 1 metre axial view D.Harel, R.Unger & J.L.Sussman, TIBS, 11, (1986).

22 A Plot of the Fibonacci Sequence Fibonacci Series (Linear Plot) Fibonacci Series (Log Plot) Series Number Series Number The Fibonacci Sequence represents simple compound (or exponential) growth Growth Rate = 61.8% per period Growth Multiplier = ( = phi = Φ)

23 Phi Growth in the Stock Market Phi Growth = simple compound growth at a 61.8% growth rate Is all compound growth equivalent to Phi Growth?? Yes - If compound growth is not expressed as per annum To calculate a Phi Growth period (n) for an annual growth rate of R n (years) = log(1.618) / log(1+r)

24 37-year Trend Growth: Rio Tinto Ltd ( )

25 Seasonal Growth: The Phi Cycle of Growth and Consolidation Primary Support/Resistance Levels

26 BHP Ltd (BHP): The Phi Cycle of Growth and Consolidation Primary Support/Resistance Levels

27 Stock Market Volatility R.N. Elliott ( ) Systematic studies of US markets by both Gann and Elliott identified repeating patterns of market volatility. Gann used units of 1 /8, Elliott used Fibonacci ratios. W.D. Gann ( ) % X? 4 1 C A B Retracement or Correction (X=?) Strength Elliott Gann Strong 38.2% 37.5% Moderate 50.0% 50.0% Weak 61.8% 62.5% 2 Basic Elliott Wave Structure

28 A Strong Elliott Wave: All Ordinaries Price Index - Nov Mar 2003 Bull-Bear Cycle (38.2%) Romanesque Broccoli (100%) 3 9/11 A B C (61.8%) Numbersmith Research

29 A Weak Elliott Wave: All Ordinaries Price Index - Major Support/Resistance Levels - The Debt Cycle B Nautilus Shell (100%) (61.8%) A (38.2%) C Numbersmith Research

30 Climbing the Stairs All Ordinaries Trend Termination Levels 10, ,000 Trend Termination Levels % -38.2% , , Numbersmith Research

31 A Natural Growth Pattern The Phi Cycle Growth in Stages 10,000 All Ordinaries Price Index ( ) , , , Numbersmith Research

32 Woolworths Ltd (WOW) Growth + Consolidation $100 Woolworths Ltd (WOW) ( ) $100 $50 $50 Secondary Grow th 29% pa $20 Secondary Grow th 52% pa Primary Growth 17.2% pa $20 $10 $10 $5 $5 $2 Secondary Grow th 71% pa $2 $1 Jan- 93 Numbersmith Research 2011 Jan- 94 Jan- 95 Jan- 96 Jan- 97 Jan- 98 Jan- 99 Jan- 00 Jan- 01 Jan- 02 Updated M arch 2011 Jan- 03 Jan- 04 Jan- 05 Jan- 06 Jan- 07 Jan- 08 Jan- 09 Jan- 10 Jan- 11 Jan- 12 $1

33 Three Price-Growth Trend Patterns Three ways to move from A to B C Relative Path Lengths Growth in Steps = units Price B 1 unit A 1 unit Time

34 Three Price-Growth Trend Patterns Three ways to move from A to B C Relative Path Lengths Growth in Steps = units Price B 2 Smooth Linear Growth = ( 2 ) units 2 1 unit A 1 unit Time

35 Three Price-Growth Trend Patterns Three ways to move from A to B C Relative Path Lengths Growth in Steps = units Price B Smooth Linear Growth = ( 2 ) units Growth + Consolidation = ( ) units A Φ = Time Growth Consolidation

36 The Phi Growth Process As the Fibonacci sequence progresses the ratio of each successive pair of numbers converges to (phi). 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987. Phi Growth is NOT specific to the Fibonacci sequence of numbers. It may be produced by beginning with any two numbers and summing each successive pair to form a series. For example: beginning with 31 and / 1274 = / 2061 = , 4, 35, 39, 74, 113, 187, 300, 487, 787, 1274, 2061, 3335.

37 Compound Growth at Reduced Efficiency At 100% efficiency (Fibonacci), compound growth rate = 61.8% 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987. X At 90% efficiency, compound growth rate = 50.0% [ e.g. 1.8 = (1+1) x 0.90 ] 1, 1, 1.8, 2.5, 3.9, 5.8, 8.7, 13.0, 19.5, 29.3, 43.9, 65.9, X The inefficient use of growth resources results in a weaker structure!!! A weakened Nautilus shell constructed at only 90% efficiency would be wasteful of resources, be susceptible to attack by predators, and would not survive. 65.9

38 The Significance of Phi (Φ) In the Fibonacci Series The Fibonacci Ratio (Φ) is NOT dependent upon the particular numbers in the Fibonacci Series. It is generated not by the NUMBER selection, but by the use of an iterative PROCEDURE that is 100% EFFICIENT. That procedure is the mathematical process of ADDITION. For example: = 13 and NOT anything less!! (e.g at 90% efficiency) The Ratio therefore represents COMPOUND GROWTH occurring at MAXIMUM EFFICIENCY.

39 The Significance of Phi (Φ) In Nature The Natural world does not tolerate inefficiency - Only the strong survive. Life forms unable to use growth resources to maximum efficiency either die off or are consumed by stronger competitors (for those resources). In Nature only the survivors of a highly competitive system are available for scientific analyses. Phi (Φ) constantly appears in the results of those analyses.

40 The Significance of Phi (Φ) In Financial Markets In establishing efficient (deregulated) financial markets, we create a highly competitive system that parallels that found in the Natural environment. In the Financial World the primary resource required for growth is CAPITAL (both monetary and intellectual). The survivors in that competitive environment are the businesses that are most able to attract capital to allow growth (i.e. the most PROFITABLE). The most profitable business are those that are the most CAPITAL EFFICIENT. Businesses that are NOT capital efficient will either die off (enter receivership) or be consumed by competitors (M&A activity).

41 Conclusions In both the Natural and Financial worlds, Φ is observed in growth patterns that indicate the MOST EFFICIENT USE OF RESOURCES Stock Market Trend Growth (Strength) Φ describes the process of COMPOUNDING Stock Market Volatility (Risk) Φ describes normal LIMITS of market volatility and the market s major TURNING POINTS

42 The Milky Way: A Guide to the Galaxy 26,000 light years You Are Here