Technical Analysis Work?, YEUNG et al, 2002
Yeung et al. found that using Fibonacci Retracements failed
When trading cost is factored in, only Bollinger Bands seem to
have statistical significance.
about the Golden Ratio, Markowsky, 1992
The golden ratio has captured the popular imagination and is discussed
in many books and articles. Generally, its mathematical properties
are correctly stated, but much of what is presented about it in
art, architecture, literature, and esthetics is false and seriously
misleading. Unfortunately, these statements about the golden ratio
have achieved the status of common knowledge and are widely repeated.
This paper discusses some of the most commonly repeated misconceptions.
cult of the golden ratio, Gardner, 1994
The efforts of phi cultists to find golden rectangles in architecture,
painting, and sculpture reached absurd heights. My discussion here
of what can be called pseudomathematics is based mainly on George
Markowsky's sensible paper, "Misconceptions About the Golden
The internet is cluttered with "educational" sites that
have documents on "Fibonacci numbers in nature" and similar
topics. A search of the internet, or your local library, will convince
you that the Fibonacci series has attracted the lunatic fringe who
look for mysticism in numbers. You will find fantastic claims. Of
course all of this is patently nonsense.
and the Financial Revolution , GOETZMANN, 2003
"This paper examines the contribution of Leonardo of Pisa [Fibonacci]
to the history of financial mathematics. Evidence in Leonardo's
Liber Abaci (1202) suggests that he was the first to develop present
value analysis for comparing the economic value of alternative contractual
cash flows. He also developed a general method for expressing investment
returns, and solved a wide range of complex interest rate problems.
The paper argues that his advances in the mathematics of finance
were stimulated by the commercial revolution in the Mediterranean
during his lifetime, and in turn, his discoveries significantly
influenced the evolution of capitalist enterprise and public finance
in Europe in the centuries that followed. Fibonacci's discount rates
were more culturally influential than his famous series".
- The Man and the Markets, Douglas, S&P's Economic Research
"Everybody with exposure to the commentary of technical analysts
has come across the name Fibonacci or its common abbreviation, Fibo.
We hear of Fibonacci retracements, Fibonacci levels, Fibonacci targets
and Fibonacci fans among others. These Fibonacci comments are often
supplied with a number such as 0.382 or 0.618. We are told that
Fibonacci can help to forecast support and/or resistance as well
as to suggest potential target levels for existing trends. Some
analysts even use Fibonacci in efforts to calculate the timing of
future market turning points. While there is little empirical evidence
to support the statistical reliability of the regular formation
of many of the relationships mentioned above, observations over
time have shown that these relationships do appear often enough
to be considered a useful part of the technical analysts' toolbox".