This name refers to a set of mathematical and graphical
considerations, based on the eponymous series. This latter, formalised by the
famous 13th century Italian mathematician, is expressed
as:
the sum of the two preceding terms (i.e. Un+2 =
Un+1 + Un), with the first two terms being 1 and 1 (i.e.
U0 = U1 = 1).
The first terms of the series are thus: 1, 1, 2, 3, 5, 8,
13, 21, 34, 55, … This series has very numerous interesting properties, the most
useful being the limit of two consecutive terms of this series. Indeed, the
Un+1/Un ratio aims at the golden ratio (about
0.618) for n infinitely high.
In the field of finance, this ratio and its fractions
are used to determine resistance and support levels as well as targets. The
main proportions used are 38.2 %, 50 % and 61.8 %. They are used to determine
what is called “retracements”.
Let us take the example of a stock, which
following the announcement of good news or a speculation wave, rises from 100
(the level around which it usually evolves) to 300 in a few weeks. If a decrease
occurs from the 300 level, corresponding to profit taking or the awareness of
the excess of the increase, it can be interesting to measure the extent of this
correction before a new upward move, or at least a rebound or the end of the
bearish trend, occurs.
In this case, we can expect the stock to find a support
after having dropped by 38.2 % of the upward move. This latter representing
300-100 = 200, the fall extent is 0.382 x 200 = 76.4. A support could thus
appear at 300 – 76.4 = 223.6. The most confident investors could thus buy the
stock on this level. Of course, a similar analysis could be done in the case of
a fall corrected by an upward move.
Quite often, the levels determined by these ratios also
correspond to supports or resistances, which get stronger as time goes
by. Apart from the role of corrections target, Fibonacci ratios can also
constitute thresholds, encouraging the sale of one’s stocks after a sufficiently
significant rise.