phi = (sqrt5 – 1)/2
What do these numbers mean and how do they relate to trading or investing? Well it is probably easier to make an argument that they don't have any business in trading, and people who try to apply them are projecting them on the market. That would be an easy argument and it would do a major disservice to the theory and what this ratio represents. Names like Euclid, Luca Pacioli, Fibonacci and,Pythagoras probably scare some people and cause painful flashbacks of high school math for others, but they are worth looking at to see how we can apply "all that crap I learned in high school" to gain something productive today.
The ratio of segments in this 5-pointed star (pentagram)are considered sacred to Plato & Pythagoras in their mystery schools. Note that each larger (or smaller) section is related by the phi ratio, so that a power series of the golden ratio raised to successively higher (or lower) powers is automatically generated: phi, phi^2, phi^3, phi^4, phi^5, etc.
To apply this to the market, we can often become to creative(art) or too scientific in our approach. In most charting software there exists a function that will let us draw the Fibonacci extensions and retracement numbers with just the click of a button.
What we do with this tool in the chart above is to start with the lower high in 2000 and then measure to the low in 2002. The high we are using is 1530.09 and the low is 775.68. The lines that are drawn act as a type of map for the market. We should recognize when the market gets back to these levels and see how it acts. The levels act as targets, and once reached and shown to hold, then become support for the next wave up. How are these levels calculated? We take the High and subtract the low to give a value for the move down, 1530.09-775.68=754.41. 754.41 is our key number now in these calculations. We want to multiply 754.41 by 0.50 to get the 50% retracement of the move. the other two numbers at minimum that should be used are 0.382 and 0.618. The are derived from our Fibonacci numbers. If we divide any Fibonacci number by the next number in the sequence we will get approximately 0.618(21/34=0.61764). The flip side of this is of we take inverse of this, 1-0.618=0.382. These are just 2 of the basic numbers that can be used. In the above chart of the S&P 500, it is apparent that these levels show to be valid when reached. This could be for many magical reasons, or just a self fulfilling prophecy because so many people use them. Regardless of the way, it is good to have a knowledge of where these levels exist in the major indexes.
Triangle patterns are one of the most reliable chart patterns to look for. The are formed by a series of lower highs coupled by a series of higher lows. Below is an example, Williams Companies, WMB.
This shows one of the smaller breakouts this stock has had. Its breakout was accompanied by strong volume, and once the rally stalled, it formed a tight triangle on the weekly chart. The Fibonacci numbers and ratios not only gave an indication where the bottom of this triangle might form if it was a healthy breakout, but it also gave a price target for the next break out! If we went back to our example of 21 and 34, and instead divided 34/21, we would get 1.619. This is very close to the 161.8% extension number given by are chart tool. Another way to check the system is to look at the width of the triangle around the middle area. In WMB it is around 1.30,(16.50-15.20). If we then take 1.30 and multiply by the 1.618, we would get 2.10. If we then add 16.50 and 2.10, we get a secondary target that gives us a safe price target for our break out of the triangle of 18.60. This is not a huge trade, but not bad on a percentage basis, and the risk was definable. It is also a product of the size of the triangle formed. The bigger the triangle, the more potential the trade has.
Next post will continue with triangles and touch on how to find them using a computer program.
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