# Finance and the Fibonacci Sequence

Finance and the Fibonacci Sequence By 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 s Sources

Books: 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: