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Fibonacci in Forex: When Rabbits Give You Valuable Trading Advice

admin on August 27th, 2008

Leonardo Fibonacci (1170-1250) was an Italian mathematician, considered by many to be the most talended of the Middle Ages. He popularized a number series, which would later be named after him, as a model of the rabbit population growth generation by generation, but it will later be discovered that these number can be applied to a variety of other situations, including forex trading.

A Little Bit of Maths

The series starts with the numbers 0 and 1, and the next are the sum of the last two: so, putting it all together, the series starts with the numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.

The mathematical limit

lim(i->+inf) { Fib(i)/Fib(i+1) }

or, in simpler terms, the ratio of an arbitrarily big number in the Fibonacci series and its successor, is 0.618, while the limit

lim(i->+inf) { Fib(i)/Fib(i+2) }

or the ratio of a Fibonacci number and the one two places after it in the sequence, yields 0.382. Subtracting these two numbers gives 0.236, their average is 0.500, and their sum is 1.000. Finally, 1.000 – 0.236 = 0.764.

Fibonacci Applied to Forex: Retracement and Extension Levels

The numbers we just learned about — 0, 0.236, 0.382, 0.500, 0.618, 0.764 and 1.000 — are called the “Fibonacci retracement levels”. With calculations similar to those we made in the last section we could also obtain the ratios of 0, 0.382, 0.618, 1.000, 1.382 and 1.618, which are referred to as the “Fibonacci extension levels”.

Once you find the “highest high” quickly followed by a “lowest low” and using them as the extremes to plot the Fibonacci retracement or extension levels on your trading platform, these ratios represent the levels, relative to the highest high/lowest low range, at which the pair is more likely to find a support or resistance level, that is, levels at which the pair will revert its trend.

Advanced Techniques: Fibonacci Fan and Others

Retracement and extension levels are not the only application of these ratios to currency trading: in fact, there are many other tools relying on them. We won’t have time here to discuss all of them, but it’s still worth mentioning another commonly used tool: the Fibonacci fan, which uses the ratios to plot support/resistance levels, this time with the trend lines converging to a single point (hence the term “fan”).

What Makes Fibonacci Reliable

It has been speculated that, although Fibonacci ratios can be very useful while trading, their effectiveness comes from its very widespread use among investors, which ends up influencing the market and the investor themselves, rather than because it is effective per se.

Although we don’t have a definite answer to this matter, it’s still worth pointing out that influencing a market which involves movements worth several trillion dollars every day wouldn’t certainly be something easy to achieve.

One way or another, knowing how to use these tools, although not too easy at first, will really help you along in your trading experience.