# How A Centuries-Old Math Sequence Can Help Predict Market Moves

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When, as a young trainee in a London dealing room, I was first introduced to Fibonacci numbers I was, as are most people, skeptical. The analysis consists of calculating significant levels based on a relationship between the numbers in a mathematical sequence, the discovery of which dates back centuries. Simple logic tells us that while that sequence may throw up some interesting coincidences, the chances of them affecting the price of stocks, currencies or commodities in a modern market are at best remote.

Over time, however, I learned that they often do, but maybe not for any magical or mystical reason, and that they are particularly important to traders after a break of a level takes prices into uncharted territory. That makes them worth understanding now.

The Fibonacci sequence is one where the next number is arrived at by adding the last two, starting with 0 and 1. Thus it begins 0,1,1,2,3,5,8,13,21, and so on. It is first found in early Indian mathematics, but is named for an Italian mathematician who wrote about it in 1202, introducing it to Western math.

The significance to traders and technical analysts is not in the sequence itself, but in something derived from it, the so-called “golden ratio.” The quotient of adjacent terms in the sequence is roughly 1.618 or the inverse, 0.618. As a ratio, 1.618 comes up frequently in nature, ranging from the arrangement of seeds in a sunflower head to the ratio of the length of your whole arm when compared to your arm from the elbow down.

61.8% and 38.2% (subtract 61.8 from 100) are therefore considered key percentages in many things, and are used by traders as likely stopping points for the retracement of a move. Extrapolating further you get 23.6% and 78.6%, which are also considered significant, if not to the same degree.

The skeptical among you are no doubt saying at this point that as fascinating as that repeating ratio may be in some ways, it cannot possibly influence market pricing, and logically you would be right. What you are forgetting, however, is the most basic reason market prices move and movements stop.

They move because one side of the constant battle between sellers and buyers is more motivated and aggressive than the other, and they stop because the opposite side of that balance reassert themselves. Why they do that at any given time is almost irrelevant, and a centuries old mathematical sequence is as good a reason as any. Put simply, Fibonacci levels, or “fibs” as they are often known, work because enough traders use them.

Nothing else is needed.

They are, as I said, particularly useful when something is literally off the charts. When a major resistance level has been broken and the subsequent move up has been, to all intents and purposes, a straight line, pivot points for any retracement are hard to find. There are no support or resistance levels available on a straight-line move, and this is uncharted territory, so nor are there any available from the past. Even if the move has hesitated in places, the levels formed are usually based on one touch and have not caused any major reversal, so they are weak and unreliable. Fibs give you at least a shot of calculating a level to buy on a drop-back.

The fact is, they do work a surprising amount of times. The chart below, for example, is for the S&P 500. It is a bit messy with all the fib levels on there, but you should be able to see that we hit the 38.2% retracement level this morning, and bounced significantly off it.

Or this, a chart for WTI oil futures that shows a bounce off the 38.2% retracement level twice and then a bounce off the 78.6% level once we broke through.

A couple of warnings should be given at this point. First, like any technical analysis, fib levels are affected by how you use them. In the example above you could, say, have taken the August low as your starting point rather than the September one that I used. Interestingly though, if you do, the 23.6% retracement level is at the same place as the 38.2 from the shorter dated move. However you look at it, Fibs apply.

The second thing to be aware of that while this is based on a math concept and math is usually precise, from a trading perspective these are approximate levels. Natural market momentum will often push through them or a determination not to miss the boat on the turnaround will lead to buyers coming in just before the exact level. Entry points and stops need to take that into account.

With those two things in mind, consider using Fibonacci levels if you don’t already, particularly if you are looking to buy on a pullback in stocks. They are not perfect by any means, but traders pay enough attention to them that using them gives you a good chance of buying at or close to the bottom of a dip.

The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.

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