Finance and the Fibonacci SequenceBy Benjamin R. Hull

History

• Leonardo of Pisa (1170-1240)– Financial engineer; analyzed business problems– Brought Arabic Number system to the West

• Liber Abaci (1202)– Tools to calculate present value, compound

interest, geometric series…– Rabbit problem• First western appearance of Fibonacci sequence

Liber Abaci

Rabbits!

The Golden Ratio

• Biology• Architecture• = = 1.6180339…– Approximate: Divide n+1 Fibonacci number by nth

The Fibonacci Sequence

• 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

Technical Trading

• Pioneered by Charles Dow• A Random Walk Down Wall Street– Burton G. Malkiel– Cannot predict future trends based on past ones– Spread of information– Crowd instinct and mass psychology• Individuals want to break even ($40 to $50 drop

example)• Price rise causes bandwagon effect

Strategy

• Identify trends and act based on possible future movements

• Support and Resistance– Lines represent potential turnaround points– Support: Price passes and continues rising– Resistance: Price does not pass and drops

Fibonacci Ratios• Probabilities based on Fibonacci percentage Ratios

– 100%, 61,8%, 38.2%, 23.6%, 0.0%– 50%, 78.6%, 76.4%

• Fibonacci Ratios:• = 1 = 100%• 0.61803… 61.8%• 0.386196… 38.6%• … 23.6%• 0 = 0.0%• Other Ratios:• 1 - 0.76394… 76.4%• 1 - = 0.78615… … 78.6%• 0.5 = 50.0%

Pictures

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SourcesBooks:• “Fibonacci and the Financial Revolution”, Goetzmann, William N., The Origins of Value (pages 123-144). Oxford

University Press Inc., New York, 2005. • “Fibonacci Numbers”, N. N. Vorobev, Addison Wesley, Massachusetts, 2nd Edition, 1994. • “A Random Walk Down Wall Street”, Malkiel, Burton G., W. W. Norton and Company, New York, 6nd Edition,

1996. • “Technical Analysis from A to Z”, Achelis, Steven B., McGraw Hill, New York, Second Edition, 2001.• “Fibonacci and Lucas Numbers, and the Golden Section”, S. Vajda, Halsted Press: a division of John Wiley and

Sons, New York, 2nd Edition, 1994.

Pictures and Other Sources:• http://upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Fibonacci.jpg/220px-Fibonacci.jpg• http://en.wikipedia.org/wiki/File:The_Parthenon_in_Athens.jpg• http://www.mathacademy.com/pr/prime/articles/fibonac/fibonac_8.gif• http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons

%2F0%2F04%2FLiber_abbaci_magliab_f124r.jpg&h=zAQFTteev&s=1• http://upload.wikimedia.org/wikipedia/commons/1/1c/Fibretracement.png• http://stockcharts.com/school/doku.php?id=chart_school:chart_analysis:fibonacci_fan• http://www.landlearn.net.au/newsletter/2008term3/images/rabbit-family-tree.png• http://theinsanium.blogspot.com/2011/01/fibonaccis-rabbits.html• http://en.wikipedia.org/wiki/Fibonacci_retracement• http://blog.afraidtotrade.com/wp-content/uploads/112208-2335-fibonacci13.png