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Thomas Bulkowski’s successful investment activities allowed him to retire at age 36. He is an internationally known author and trader with 30+ years of stock market experience and widely regarded as a leading expert on chart patterns. He may be reached at

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Bulkowski's Fibonacci Tutorial

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Industrials (^DJI):
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As of 10/19/2017
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Written by and copyright © 2005-2017 by Thomas N. Bulkowski. All rights reserved. Disclaimer: You alone are responsible for your investment decisions. See Privacy/Disclaimer for more information.

My book, Trading BasicsTrading Basics: Evolution of a Trader book., discusses both Fibonacci retracements (as a stop location, starting on page 50) and extensions (starting on page 84).

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Many traders use Fibonacci ratios in their trading. I have found that they work for me and perhaps they can help improve your trading, too. Let's take a closer look.

Fibonacci Turning Points

Waves in Flir Systems (FLIR) on the daily scale.

I show a chart of Flir Systems (FLIR) on the daily scale.

Points A, B, and D are major turning points. Point C is a minor reversal.

When looking for Fibonacci retraces or extensions, you will want to select turning points that are of the same magnitude. By that I mean look for large, major turning points of similar size, or focus on four smaller turning points, also of the same size.

You should probably avoid mixing small and large turning points because that may give you unreliable results (but you can try it). Many software packages will draw the Fibonacci lines on your chart for you.

Point D retraces almost 62% of the AB move. The next section explains how I used the chart to compute the retrace.

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Fibonacci Retracements

An ABCD wave to illustrate Fibonacci ratios.

The figure shows an ABCD wave. Think of each turning point as a peak or valley on the price chart, just like in the previous chart.

Assume that point A is at 10 and B is at 15. There are three main retrace values that I like to use: 38%, 50% and 62%. How we derive those values and others is not important, nor is the Fibonacci sequence.

If we take the price difference from A to B (15 - 10 = 5) and multiply it by the three Fib values, we get 5 x 38% = 1.90, 5 x 50% = 2.50, and 5 x 62% = 3.10. When you add those values to A or subtract them from B, you get three possible turning points: 13.10, 12.50, and 11.90.

The stock could turn at any of those three values as well as at other values.

If I want to buy the stock represented by the chart, I will wait for a 62% retrace and then pounce. That means placing a buy order at 11.90 in this example, or about where point C forms. Other Fibonacci retracement values are 79% and 86%.

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Fibonacci Time Extensions

To help predict when point C will arrive, you can apply the same math to the time scale. I show that with points E, F, and G. If the time between E and F is 30 calendar days then multiply it by 38% to get G: 30 x 38% = 11 calendar days. Add 11 days to F to predict turning point G. Point H might be a 162% extension of the EF move.

You can use trading days or price bars, if you wish, and maybe other extension values might work better, such as 18%, 27%, 62% and 162%. Since I don't use Fib extensions on the time scale, you will have to figure out what works best for your application.

Fibonacci Price Extensions

Let's say that you bought the stock at C. At what price will D arrive?

Since this is not a retracement but an extension of the AB move, we can apply one of the extension values. I could use 1.18 (118%), 1.27 (127%), 1.618 (162%) or 2.618 (262%). The 38% extension (1.38) is one I like. We will use that in this example.

The AB move is 5 points (10 to 15), so 38% of that is 1.90 which I add to the price of B (15) to get D (16.90). Thus, if I bought the stock at C, I would consider selling if the stock approached 17. It would not be an automatic sale, but I would search the area for overhead resistance that might cause price to stall.

The same math applies to downward price trends. Figure out the length of the first wave (use BC in this example) and calculate the retrace or extension of that move. Add the retrace value to C (for a higher target) or subtract the extension value from C to get a lower target.

-- Thomas Bulkowski

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Other Fibonacci Examples

See Also

Written by and copyright © 2005-2017 by Thomas N. Bulkowski. All rights reserved. Disclaimer: You alone are responsible for your investment decisions. See Privacy/Disclaimer for more information. Anarchy may not be the best form of government, but it's better than no government at all.