Fibonacci trading. It's a math sequence that few retail investors use when planning their trades, one left mainly to technical traders at institutions.
It's reliability is questionable, though fanatics claim it's the finest of models.
The idea is derived from the Fibonacci sequence, a series of numbers starting with the digits 0 and 1, with each subsequent figure the sum of the preceding pair (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.). Leonardo of Pisa, commonly known as Fibonacci, was one of the most revered mathematicians during the Middle Ages, and the first to popularize the series in Liber Abaci. a paper published in 1202 (the sequence was developed in Southern Asia and parts of India centuries earlier, but did not make it west).
Or, if you're just interested in seeing the series in nature, click here >
Using the Fibonacci series, investors can create resistance and support levels. The theory purports that following a stock's move (either up or down), it will face a wave of corrections, corresponding to Fibonacci ratios.
Those key ratios are derived from the division of one Fibonacci number by another Fibonacci figure one, two or three places further in the sequence: 0 divided by 1, or 0; 1 divided by 1, or 1; 1 divided by 2, or 0.5; 55 divided by 89, or 0.618; 55 divided by 144, or 0.382; 55 divided by 233, or 0.236.
Continuing out, dividing any number in the series by the consecutive figure in the series calculates to 0.618, and its inverse, 1.618. The latter is also known as the golden ratio, but we'll delve into later.
To use those ratios, pull the stock's trading chart that you're interested in up, setting its lowest point at 0 and it's highest at 1. Between those figures, draw in horizontal lines at the proper points where 0.618, 0.5, 0.382, and 0.236 sit between 0 and 1. These will become the resistance and support levels for the share price.
Find the high and the low on the chart, and then draw arcs that pass through these three points: 32.8 percent, 50 percent and 61.8 percent. These arcs anticipate the stock's support levels, resistance
levels and range of movements. Forex-Central recommends setting stop-loss targets because a stock's movement does not necessarily follow the Fibonacci rule.
If a stock is trending higher and you believe a decline is coming, the order of the arcs will go 0.382 (for support), 0.618 (for resistance), and 0.5 (also for support, though many times the last arc does not occur and the price can simply move higher). If the stock is trending lower and you believe it will begin to advance, the order of the arcs will go 0.618 (for resistance), 0.382 (for support), and 0.5 (for resistance).
The graph below illustrates one trade that fell between those lines.
Here's another look, this time from Investopedia. Traders will often use the 0.618 ratio as a target when a stock breaks above its expected range:
When testing this in real-time, and to trade on the Fibonacci rule, you would only have points 0 and 1 (Forex-Central also says to wait when deciding on the top and bottom points, as the stock may still be moving).
Fibonacci retracements on stock prices are far from perfect. Arcs are not necessarily in any specific order (meaning, a stock that declined, but that is now increasing, may only hit the 0.382 mark before turning negative again). Take a look at this graph from Investopedia that also shows how random the movements can be:
Leonardo of Pisa was also credited with creating some of the earliest formulas traders could use in the 1200s. In a 2004 Yale School of Management paper by William Goetzmann, "Fibonacci and the Financial Revolution," Goetzmann argues that Leonardo was the first mathematician to use the present value theorem, or the equation used by nearly every Fortune 500 company when valuing capital plans and payments.
As for the Golden Rule, it occurs when the sum of two quantities create a third number, and the ratio of that third number is to the larger of the quantities, as the larger quantity is to the smaller one (i.e. in the equation, A + B = C, A is to B as B is to C).