1 Fibonacci Retracements This method will help you to to predict important retracement levels! 2 Fibonacci in Nature The golden ratio and the golden spiral. 3 5 Fibonacci Tricks More information on how to get the best out of Fibonacci levels

01.      Introduction to Fibonacci Retracements

If you've been trading for any length of time, odds are that you already know all about Fibonacci relationships.

Fibonacci was an Italian mathematician that gave us a particular series of numbers:

0   1   1   2   3   5  8   13   21 etc...

To get the next number in the series, you simply add the last  two numbers together.

0 + 1 = 1

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

3 + 5 = 8

5 + 8 = ...

etc ... You get the idea?

Eventually, you can divide two numbers in the sequence together to get the important Fibonacci ratio 1.618 or 0.618.

Interestingly, you can get this ratio from running a Fibonacci series using any two starting values. Just pick two numbers put of the air. say 76 and 3. Then start generating new numbers by adding the last two:

3   76  79  155   234   389    623   1012 etc...

623 / 1012  is 0.6156, so we're already getting close to the 0.618 with only a few iterations of the sequence.

In our trading system, we will be looking at 4 different rations:

0.618, 1.618, 0.786, and 1.27

These numbers are the same ones Larry Pesavento recommends, and have proven to be extremely important. The first two numbers in the sequence come straight from the Fibonacci series, and the second two numbers are their square roots.

For trading purposes, you simply locate an important recent high and low, find the distance between them, and mark the ratios off at the appropriate price levels.

In the chart below, you can see how the market responded when it reached important Fibonacci retracement levels:

The first retracement level (c) was calculated using the swing (a - b) and caught the high at c.

Next, the 1.27 retracement of (b - c) was exactly on the low point d.

Finally, the o.786 retracement or (c - d) forced a tripple top at point e.

This chart not only demonstrates the importance of Fibonacci retracement levels, but the importance of using the square roots of the original 0.618 and 1.618 ratios.

Now you now how to predict important retracement levels!

### By Elliott Wave International

If you've studied the financial markets, even for a short time, you've probably heard the term "Fibonacci numbers." The ratios and relationships derived from this mathematical sequence are applied to the markets to help determine targets and retracement levels.

Did you know that Fibonacci numbers are found in nature as well? In fact, we can see examples of the Fibonacci sequence all around us, from the ebb and flow of ocean tides to the shape of a seashell. Even our human bodies are examples of Fibonacci. Read more about the fascinating phenomenon of Fibonacci in nature.

Let's start with a refresher on Fibonacci numbers. If we start at 0 and then go to the next whole integer number, which is 1, and add 0 to 1, that gives us the second 1. If we then take that number 1 and add it again to the previous number, which is of course 1, we have 1 plus 1 equals 2. If we add 2 to its previous number of 1, then 1 plus 2 gives us 3, and so on. 2 plus 3 gives us 5, and we can do this all the way to infinity. This series of numbers, and the way we arrive at these numbers, is called the Fibonacci sequence. We refer to a series of numbers derived this way as Fibonacci numbers.

We can go back to the beginning and divide one number by its adjacent number - so 1÷1 is 1.0, 1÷2 is .5, 2÷3 is .667, and so on. If we keep doing that all the way to infinity, that ratio approaches the number .618. This is called the Golden Ratio, represented by the Greek letter phi (pronounced "fie"). It is an irrational number, which means that it cannot be represented by a fraction of whole integers. The inverse of .618 is 1.618. So, in other words, if we carry the series forward and take the inverse of each of these numbers, that ratio also approaches 1.618. The Golden Ratio, .618, is the only number that will also be equal to its inverse when added to 1. So, in other words, 1 plus .618 is 1.618, and the inverse of .618 is also 1.618.

This is a diagram of the Golden Spiral. The Golden Spiral is a type of logarithmic spiral that is made up of a number of Fibonacci relationships, or more specifically, a number of Golden Ratios. For example, if we take a specific arc and divide it by its diameter, that will also give us the Golden Ratio 1.618. We can take, for example, arc WY and divide it by its diameter of WY. That produces the multiple 1.618. Certain arcs are also related by the ratio of 1.618. If we take the arc XY and divide that by arc WX, we get 1.618. If we take radius 1 (r1), compare it with the next radius of an arc that's at a 90° angle with r1, which is r2, and divide r2 by r1, we also get 1.618.

 Now here are some pictures of this Golden Spiral in various aspects of nature.   For example, on the top is a whirlpool that displays the Golden Spiral and, therefore, these Fibonacci mathematical properties.   We also see the Golden Spiral in the formation of hurricanes (center) and in the chambered nautilus shell (bottom), which also happens to be a common background that Elliott Wave International uses for a number of its presentations and graphics.

The Golden Ratio is also visible in the DNA molecule. Research has shown that if you look at the height of the DNA molecule relative to its length, it is in the proportion of .618:1. If we look at the components of the DNA molecule, there is a major groove in the left section and a minor groove in the right section. The major groove is equal to .618 of the entire length of the DNA molecule, and the minor groove is equal to .382 of the entire length.

 This graphic of the human body also shows how the Golden Ratio exists in certain relationships of the human anatomy.

More on Fibonacci:

03.     FIVE FIBONACCI TRICKS

Fibonacci jumped into the technical mainstream late in the bull market. Futures traders had it all to themselves until real-time software ported it over to the equity markets. Its popularity exploded as retail traders experimented with its arcane math and discovered its many virtues.

Fibonacci ratios describe the interaction between trend and countertrend markets -- 38%, 50% and 62% retracements form the primary pullback levels. Apply these percentages after a trend in either direction to predict the extent of the countertrend swing. Stretch a grid over the most obvious up or down wave, and see how percentages cross key price levels.

Convergence between pattern and retracement can point to excellent trading opportunities. Keep in mind that retracements work poorly in a vacuum. Always examine highs, lows and moving averages to confirm the importance of a specific level.

Discord between retracement and the underlying pattern generates noise instead of profit. Move on to a new chart when nothing lines up correctly. This divergence generates most of the whipsaw in a price chart. Alternatively, strong phasing between Fibonacci and pattern exposes highly predictive reversals at narrow price levels.

Let's look at five tricks that may improve your Fibonacci skills.:

First Rise/First Failure

First Rise/First Failure marks the first 100% retracement of a trend within your time frame of interest. It provides an early reversal warning after a new high or low. The 100% retracement violates the major price direction and terminates the trend it corrects. From this level, the old trend can reestablish itself if it breaks through the old 38% level. More often, traders will use that level to enter low-risk positions against the old trend.

Parabola Hunt

Parabolic movement tends to occur between the 0%-to-38% and 62%-to-100% Fibonacci levels in all trends. This tendency offers a great tool for finding the big moves when looking for trades. Watch for congestion to form at the 38% or 62% level. Then use a simple breakout or breakdown strategy when price moves past it. The next thrust can be dramatic, with price moving like a magnet back to an old high or low. Of course, the strategy only works when you can find these levels in advance.

Continuation Gap Extensions

You can often target the exact price a rally or selloff will end at by using the continuation gap as a Fibonacci extension tool. Identify the gap by its location at the dead center of a vertical price wave. Then start a Fib grid at the beginning of the trend and extend it so the gap sits under the 50% retracement level. The grid extension points to the terminating price for the rally or selloff.

Overnight Grids

Find an active stock and start a grid from the high (or low) of a session's last hour. Stretch the grid to the opposite end of the next morning's first hour low (or high). This defines a specific price wave traders can use to uncover intraday reversals, breakouts and breakdowns. The overnight grid also offers a way to trade morning gaps. The gap will often stretch across a key retracement level and target low-risk entry on a pullback.

Second High/Low

Many traders can't figure out where to start a Fib grid. Here's a trick to help you place it where it'll do the most good. The absolute high or low in a price wave isn't the best starting point for a grid most of the time. Instead, look for a small double bottom or double top within the congestion where the trend began. Swing one end of the grid over this second high (or low), instead of the first. This will capture a specific Elliott Wave that conforms to the trend you're trying to trade.

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