Both the hammer and Fibonacci are tools used in their respective fields. A hammer is used in carpentry to, among other things, frame a house. A Fibonacci - usually a Fibonacci retracement - is used in investment analysis to frame the market's recent move.

**Obligatory definitions**

Here is the section where we have to define what Fibonacci is and we'll focus on Fibonacci retracements. If you have any interest in who Mr. Fibonacci was, feel free to fire up the Google. It is irrelevant to what we are doing here.

Mr. F's claim to fame was discovering a mathematical sequence that seems to describe a lot of geometry in the real world from how petals spiral on a flower to how stars spiral in a galaxy. And from that sequence we get the "golden ratio" or "divine proportion" which somehow describes pleasing and useful relationships in art, music, architecture and design in general.

The ratio of .618 to 1 comes from a sequence of numbers where any number is the sum of the two that preceded it. Here is it in all its glory:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ...

As you can see, the numbers start to get huge. Fortunately, we rarely encounter any above 144.

And even more fortunate, the ratio of any two consecutive numbers settles on .618 fairly quickly. As follows:

0, 1, 0.5, 0.666667, 0.6, 0.625, 0.615385, 0.619048, 0.617647, 0.618182, 0.617978, 0.618056, 0.618026, 0.618037, 0.618033

First, this is the ratio calculated out to the number 610 in the sequence.

Second, and more important, you can see how the ratio oscillates higher and lower as it hones in on the .618 value. Any ratio beyond what is shown above is pretty much just rounding error away from that value.

Voila! the golden ratio!

**Fun for math nerds**

The ratio has all sorts of neet-o properties. For example, 1 / .618 = 1.618.

And 1 - .618 = .382. Guess what the square root of .382 is? That's right, .618.

.382 / .618 = .618

You have probably seen these two percentages on the charts an they are roughly equal to the simple percentages traders have used for years, namely 1/3 and 2/3 (or .333 and .667).

Guess what is

__not__a Fibonacci number. 50% or .5. Check out the sequence. It is nowhere to be found. And you cannot concoct it from math-ing 0, 1, and .618, either.

Still, traders do attach meaning to a 50% retracement or pullback and it has wormed its way into analysis using Fibonacci. Don't fight it, exploit it.

**Using this stuff**

Now is when we get to dispense with the formalities and use the name experience chart watchers use - fibos. Don't confuse this with fibbie, which is the FBI. Or fubar, which was what you may be feeling right now trying to digest all this fibo stuff.

Fire up any charting software package and under the drawing tools section you will see Fibonacci retracements and possibly Fibonacci extensions, time and arcs. They are all just different ways to look at two points on a chart - usually a high and a low - and then draw stuff off of them at specific percentages.

Take a look at this chart of the S&P 500 from 2007 to 2011. Using the basic set of fibo retracements of 38.2%, 50% and 61.8% look how nicely we could project where support and resistance might be.

Here is where you can get into trouble. These levels are likely places to find support and resistance levels but not always. And sometimes you might be tempted to add more fibo lines until you find one that fits.

My advice is to never add more percentages except for one... and it is a bizarre one. We'll get to that later.

Remember, we are only trying to frame the market, not nail all of its turns and accelerations. We'll use other tools to attack that part.

Anyway, we can see that the rally peaked at the 61.8% retracement and the ensuing correction stopped at the 38.2% retracement. Whoopee! It worked once. We can even see the market stumble in the vicinity of the 50% level.

Let's repeat this. Fibos are likely place for turns, not guarantees. But we can beef them up a bit by measuring fibos from other points and see if they overlap, or cluster. If they do, then we have a better support or resistance target.

Check out how the rally from the 2010 pullback low to the highs of 2011 is 161.8% of the pullback itself. Something usable must be going on here.

Even better, what if moving averages hit those fibos? Or normal horizontal support or resistance? Or trendlines?

Getting the drift? As with any tool, the more things that point to a price level the more likely that price level will be important.

Now for the bizarre. Some people use a 78.6% retracement level. Note how this is kind of close to 75% but that is not what makes it bizarre. It .786 is the square root of .618.

In my book, if a market can retrace this much of a previous trend, it is rather likely to retrace the whole thing.

**The other fibo stuff**

We touched on extensions, time and arcs so let's put in the quick definitions. A fibo extension is a number bigger than one and it projects where a market can go. Look for such numbers as 1.382, 1.618, 2.618, 3.618, etc.....

Draw an arc centered on the origin for each ratio (usually the original ones less than 21) to find trend targets.

And instead of measuring price, do it on the time axis. Think about looking for a 61.8% price retracement that took 61.8% of the time of the previous trend to happen. Make a fibo box out of it.

Fibos are also used in Gann and Elliott Wave analyses. For the latter, we like to see Elliott Wave 3 to be 1.618 or 2.618 the length of Wave 1. That is a whole nother can of worms so we'll end this right here.

Use fibos on your charts but please use other things along with them. They can help you frame the market but like a hammer, you will have to decide where to put the door and windows. Fibos do not dictate where you buy and sell.

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