We're not talking of self-styled 'fab' Fabrice Tourre, the former Goldman Sachs trader convicted on six counts of securities fraud, nor Jérôme Kerviel, who managed to lose €4.9bn (£3.76bn) while working at Société Générale. Nor JPMorgan's London Whale, whose trading positions dwarfed all others, nor Mr 'Copper' Hamanaka of Sumitomo Corporation who tried to corner the market.
We're thinking Leonardo, son of Bonacci (the good natured one), known as Fibonacci who lived roughly between 1170 and 1240 in Italy. His father, wanting the very best for his son, sent him to study maths in Bugia, a flourishing centre of Islam in north Africa. First mastering the spoken word, he then grasped the advantages of Hindu-Arabic numerical annotations over the Roman ones, then in his book Liber Abaci introduced these to Europe. Nine figures separate from the alphabet and a symbol for zero (emptiness) to keep the digits in the correct columns.
The book contained a sequence known to Indian mathematicians solving the growth of rabbit populations: "How many pairs of rabbits will be produced... beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?" The solution: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377… and so on. The next number being the summation of the previous two where the smaller one is 0.618 per cent of the larger which is 1.618 times the size of its predecessor. From these, other Fibonacci numbers can be derived including 23.6, 38.2, 76.4, and 2.618.
This ratio, known as the Golden Mean, is used extensively in art and describes many features of the natural world, including seeds on a sunflower, the spiral of a nautilus shell, and the shape of waves in the sea. The latter links to financial markets where most agree that they move in stages, Elliott Wave insisting there are five legs in a bull market and three in a bear. The ratio between impulsive and corrective moves is often a Fibonacci number.
Fibonacci retracement
Fibonacci projection
Technical analyst veteran Glynn Bradney uses of Fibonacci numbers as deviations around a mean regression. Rather than using the common one or two standard deviations I have found that in quiet markets 0.618 works well and in volatile ones 1.618 captures most market moves.
Standard deviation
Finally, the legendary WD Gann developed a system of angles used to describe market trends. The 45 degree line, where one unit of price takes one unit of time to achieve, is his starting point. Then a fan of angles is plotted (2X1, 3X1, 4X1, 1X2, 1X3, 1X4).
Go on, experiment.
Gann fan
