Finance and the Fibonacci Sequence By Benjamin R. Hull

History Leonardo of Pisa ( ) – 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

The Fibonacci Sequence

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

Pictures

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Sources Books: Fibonacci and the Financial Revolution, Goetzmann, William N., The Origins of Value (pages ). Oxford University Press Inc., New York, Fibonacci Numbers, N. N. Vorobev, Addison Wesley, Massachusetts, 2nd Edition, A Random Walk Down Wall Street, Malkiel, Burton G., W. W. Norton and Company, New York, 6nd Edition, Technical Analysis from A to Z, Achelis, Steven B., McGraw Hill, New York, Second Edition, Fibonacci and Lucas Numbers, and the Golden Section, S. Vajda, Halsted Press: a division of John Wiley and Sons, New York, 2nd Edition, Pictures and Other Sources: http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2F0%2F04%2FLiber_abbaci_magliab_f124r.jpg&h=z AQFTteev&s=