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Fibonacci Ratios for Trading
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Mystics, numerologists, and others looking for supernatural insight have long contemplated the significance of certain
numbers. Well, as it happens there is at least one number—or at least a mathematical derivation—that does seem to
have a nearly universal significance. That number is the Fibonacci ratio.
It is named for the Italian mathematician Leonardo Fibonacci, who is thought to have lived from roughly 1175 to 1250.
He gave us the Fibonacci sequence, which is simply a series of integers in which each number (after the first two) is
the sum of the two preceding numbers. To wit: 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on. At first glance this doesn’t look
particularly magical, but what is significant is that the adjacent terms (once you pass 2) have a ratio of roughly 1.618.
(The ratios converge very quickly to this number the higher up the sequence you go.)
Why this Fibonacci ratio of 1.618 (or 0.618 in its inverse) should be significant is baffling, but it is—so much so that it
has nicknames like the “divine proportion” and the “golden ratio.” The 1.618 figure is so prevalent, in fact, that it is
referred to by the Greek letter phi in math and science. Many aspects of plant and animal life follow the Fibonacci
sequence or ratio—from the number of petals on flowers to the arrangement of seeds and leaves to the curve of a
nautilus shell to the ratio of male to female honeybees in a hive. Even certain proportions of your own body match
this ratio.
Leaving aside the natural mysteries of the Fibonacci ratio—which you are certainly welcome to explore on your
own—it also has significance in financial markets. In this setting, three numbers are normally used: 61.8%, 38.2%
(which is merely 100% ‒ 61.8%), and 50%. Other significant ones are 24.0% and 78.6%.
When using Fibonacci ratios to predict price ranges, the normal practice is to set the 0 line at the low for the period
under consideration and 100% (or 1.00) at the high. The other percentages are then drawn in as appropriate between
the two, something most charting software will do for you. (The period used to set these ranges is normally indicated
by a sloping dotted line along the general price trend.) Thereafter, the price should tend to find support and resistance
at the various levels indicated.
Consider our chart of Alcoa (AA), which recently posted a positive earnings surprise (seen in the gap upwards in the
last two trading sessions).
Although this range was used to set the Fibonacci levels, you can already see two instances of resistance at the
78.6% level prior to the earnings announcement. Going forward, we can expect to see continued support and
resistance at these points. For example, it is quite likely that the positive earnings surprise will take the stock at the
very least back to the 78.6% (0.786 on this chart plot) line before any significant correction occurs.
These ratios can be used as part of a Fibonacci retracement in combination with an Elliott wave pattern to determine
how far a stock is likely to fall from its wave 5 peak, something we discuss in our article on distinguishing
retracements and reversals.
There are also other Fibonacci tools—specifically arcs, fans, and time zones—but those concepts are beyond the
scope of this discussion. Hopefully you now have a basic understanding of how the Fibonacci ratio applies to financial
markets, and we encourage you to read further on how to employ it as a trading guide.
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