FIBONACCI : a leading indicator

This name refers to a set of mathematical and graphical considerations, based on the eponymous series. This latter, formalised by the famous 13^th century Italian mathematician, is expressed as:

the sum of the two preceding terms (i.e. U_n+2 = U_n+1 + U_n), 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 U_n+1/U_n 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.