Download Finance and the Fibonacci Sequence - Chi

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
• 𝜑
1+√(5)
=
2
= 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, …
• 𝐹𝑛 = 𝐹𝑛−1 + 𝐹𝑛−2
• 𝐹𝑛 =
1
√5
∙
1+ 5 𝑛
(
)
2
1
−
√5
∙
1−√5 𝑛
(
)
2
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:
0
1+√(5)
(
) = 1 = 100%
2
−1
1+√(5)
(
) = 0.61803… ≈ 61.8%
2
−2
1+√(5)
(
) = 0.386196…≈ 38.6%
2
−3
•
1+√(5)
(
2
)
•
(
1+√(5)
2
)
•
Other Ratios:
•
1-(
•
1-
•
1
2
= 0.23606…≈ 23.6%
−∞
1+√(5)
2
1+√(5)
(
2
= 0 = 0.0%
−3
) = 0.76394… ≈ 76.4%
1
2
−
) = 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:
•
•
•
•
•
•
•
•
•
•
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=z
AQFTteev&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