How Fibonacci numbers can help you trade

By Dominic Frisby

Fans of The Da Vinci Code, mathematicians, technical analysts, believers in the supernatural, even some bee-keepers and rabbit-breeders – they all know their Fibonacci numbers. This is an almost-magical sequence of numbers first described in ancient Sanskrit mathematics and introduced to the West by one Leonardo of Pisa, aka Fibonacci.

What gives this sequence its perceived ‘magical’ power is that the pattern repeatedly appears throughout nature, for example in the branching of trees, the arrangement of leaves on a stem, even in the spirals of florets on a sunflower. Pine cones, pineapple fruitlets, artichoke flowers, the family trees of honeybees - all show Fibonacci patterns in their arrangement.

What’s this got to do with finance? Well, it’s claimed that this same pattern is also discernible in markets. First I’ll explain the theory – bear with me – then we’ll look at how it may apply to today’s markets.

How the Fibonacci sequence works

Each number in the Fibonacci sequence is the sum of the previous two numbers. That means the first 20 Fibonacci numbers are:

0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

Each number in the sequence is roughly 1.618 times greater than the previous number. And if you divide one number in the sequence by the number that comes after it, the ratio is consistently about 61.8%. For example, 8/13 = 0.6153, or 21/34 = 0.617.

This ratio, 61.8%, is known as ‘the golden mean’. Other key ratios are 38.2% (found by dividing a number in the series by the number two places to the right) and 23.6% (found by dividing one number in the series by the number three places to the right).

You will often find in the markets that a bullish major trend will suffer a bearish retracement to a key Fibonacci ratio, and vice versa. What does that mean? Well, for example, if an index rises 100 points from 100 to 200, it will often then retrace to a key Fibonacci level – that might be 61.8%, 38.2% or 23.6% of the move. So the index might then pull back from 200 to 161.8.

But does it really work?

Let’s take a look at this in practice. I picked two markets at random – the gold price and the Dow Jones index.

The Dow went from a low of 600 in 1975 to a high of 12,000 in 2000. That’s an 11,400 move. It then corrected. If it were to have corrected to a level that is 61.8% of that 11,400 move, it would have gone to about 7,045. In fact, it went to just below 7,200 in October 2002.

In gold’s recent great bull run, we went from a low of $250 in 1999 to a high of just below $1,030. That is a move of $780. If we look at likely Fibonacci levels to which gold would retrace from that high (i.e. possible buy-points), you get the following:

$780 x 61.8% = a correction of $482
$780 x 50% = a correction of $390 (though not a Fibonacci number, 50% is also a figure that is used, for obvious reasons)
$780 x 38.2% = a correction of $298
$780 x 23.6% = a correction of $184

A correction of 38.2% of that $780 move – in other words a reversion to a point that is 61.8% – takes us to $732 ($1030 - $298). And in fact, last week gold touched just below $740. As the May 2006 high, and also an important support level in 1980, it’s an obvious area for gold to find a low.

Now it would be easy to dismiss all of the above as mumbo jumbo, were it not for the fact that these ratios occur everywhere and with such frequency. And I would never advocate Fibonacci patterns as a sole reason for making an investment. They are, however, useful as a secondary trading tool. You may well have decided that you want to buy a stock or commodity for sound fundamental reasons, but Fibonacci numbers can help you to decide on the best time to do so.

But sometimes, of course, technical analysis goes out of the window. At one stage yesterday, by Asian trading, gold was up some $100 in a single day! It was gold’s greatest day’s trading ever.

Was this the mother of all panics? The mother of all short-covering rallies? Who knows, but it was a great day to be long. You can read more about why demand for physical gold is surging in this week’s MoneyWeek cover story, along with an update on my junior mining tips from the past year or so.

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