In a previous article, I showed how it is entirely possible to make profits in trading the financial markets, by using simple Fibonacci sections of waves that occur in all markets. This has the advantage that simple Fibonacci charts can be used, without the need for complicated technical indicators.

The Fibonacci sequence is derived from the natural growth sequence of 2, 3, 5, 8, 13, 21, 34, 55 and on to infinity. I showed how the ratio of each number is related to the one before it by the ratio of 1.618.., and to the one just ahead of it by the ratio 0.618.. Interestingly, these ratios still apply if any starting point is chosen! So that a sequence starting at, say, 15, would have the sequence 15,15,30,45,75,120,195,315, and so on. This would produce the same ratios of 1.618 and 0.618! The Golden Ratio, or Golden Mean, 1.618, is given the name *phi.*

Growth in nature (rising markets) is expressed by 1.618 and 1.618 squared ( = 2.618). Decay (falling markets) is expressed by their inverse fractions, 0.618, and 0.382. But of course, growth of all natural things takes place in spurts, followed by set-backs, and then another spurt, and so on (3 steps forward and 2 steps back). Through observing many stock charts, early technical analysts discovered that when a market makes a solid move (up or down), then the corrections often stop at Fibonacci numbers of 0.618 (61.8%) or 0.382 (38.2%) of the wave’s move. Further out, if we look at 1.618 cubed (4.236), its inverse is 0.236 (23.6).

This can work on very short-term charts and even monthly charts. A good example is that of the British Pound/Dollar. At the start of 2008, the Pound was trading around the $2.00 area, but then suffered a massive decline starting in July 2008 and bottoming in January 2009 at 1.3460 area. It then staged a strong rally, topping at 1.7050 area in August 2009. It has since then dropped to a recent low of 1.4216 on May 20th 2010. This level represents a 76.4% retracement, or 23.6% from a complete retracement. The chart looks very beautiful. I have been looking for a low-risk entry point to go long since then.

I have found that deep retracements of 61.8% and 76.4% are very common, and often give us a low-risk entry point for a trend change. If I do Fibonacci charting to find a retracement level with a complete 5- or a 3-wave Elliott pattern, together with a **divergence** in a momentum oscillator, then I have a very high potential winning trade. Choosing Fibonacci retracements allows me to place close protective stops (in case I am wrong).