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Figure 4

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Let's now take a look at a weekly chart of Apple Inc. (AAPL) from the August low at $235.56 (point 1) to the high of $364.90 during the week of February 19 (point 2). The ensuing decline to the low at point 3 just slightly exceeded the 38.2% support at $316.30, though it held well above the 50% support at $300.

The correction took 18 weeks, and the fact that it held well above the 38.2% support for so long implied that a correction would be shallow. Those who did buy near the 38.2% support should have used a stop at least under the 50% support at $300.

AAPL hit a high of $404.50 at the end of July 2011 (point 4), therefore, the major 38.2% retracement support level, as calculated from the rally from point 1 to point 4, was at $340. The 50% support lies at $320 with the key 61.8% retracement support level now at $300.

Looking at the daily chart, we can examine more closely the rally from the June lows at $310.50 (point 3) to the recent highs (point 4). The minor 38.2%, 50%, and 61.8% support levels are identified on the chart. The low so far this week in AAPL is $353.02, which was just below the 50% retracement support at $357.20. The minor 61.8% support is now at $346.30.

By combining the major and minor levels, you can determine that an important level of support lies between $340 (major 38.2% support) and $346.33 (minor 61.8% support). The weekly uptrend is now at $324, so a stop under the major 50% retracement support at $320 could be used.

The minor 61.8% support may not be tested before AAPL turns higher, so I would be watching the $354- $347 area for new buying. A violation of the major 61.8% support at $300 would be a sign that the intermediate-term uptrend has been broken.

There are much more advanced ways that the Fibonacci number series can be applied to the financial markets, and I will discuss them in future articles. It is not necessary to have advanced software systems to do this type of Fibonacci analysis, as price history is available for free on many Web sites, and then you just need a calculator or spreadsheet program.

If you are not currently using Fibonacci analysis, I hope you will be encouraged to give it a try and determine for yourself whether it can be useful in your investing or trading.

Figure 5

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The best free online charting system that I have found that allows basic Fibonacci analysis is at FreeStockCharts.com, which is by Worden Brothers. The above chart of Freeport McMoran (FCX) is from the site and shows that FCX is just testing the 61.8% support as calculated from the July 2010 lows. Peter and Don Worden are both excellent technicians and have a wide array of more specialized analytical products as well.