# Fibonacci Wave Ratio Analysis

Introduction to Using Fibonacci Ratios in Elliott Wave Analysis

We see fibonacci relations in nature, as well as in market action. When talking about wave ratios in the market, we can be talking about relationships between the magnitude of waves, or the time relationships between waves. Here, we will discuss the relative magnitude here between waves. All the information found below can be found in Frost and Prechter’s Elliott Wave Principle, a great book to learn about the basics of Elliott Waves.

Retracements:

Deep retracements are commonly seen to correct between 50% and 61.8%. In the very liquid and volatile forex markets, we often find even sharper retracements such as 78.6%. Flat corrections usually have a smaller retracement ie. 38.2%.

Motive Waves:

While Frost and Prechter mentions retracement wave ratios, they also point out that a more reliable use of fibonacci wave relationship is in the application to alternate waves, meaning waves in the same direction. Let’s take an impulse wave, broken down into 5 waves, where either 1, 3, or 5 can be extended. Wave 1 and 5 tend to have wave equality or a .618 relationship. Wave 3 tend to have a fibonacci relationship with 1 and 5 as well, typically seen to be 1.618 ,or 2.618.

When there is a 5th wave extension, it is usually wave 4 that separates the complete motive wave into 2 fibonacci sections. For example, 1-2-3-4 : wave 5 = 1: 1.618.

When there is a 1st wave extension, it is wave 2 that separates the sections. For example, 1-2: 3-4-5 = 1: 0.618

Corrective Waves:

Zig Zag is an ABC correction against the trend. The conventional zig zag will have A and C wave equality. Also, in a double zig zag, or double 3′s, the two corrective waves are often equal.

Flat is seen as a sideways correction, so the length of A, B and C are approximately equal.

Expanded flat has B surpass the origin A, and then C surpass the origin of B. Wave C is often 1.618 of A, and also 0.618 pass the end of A as shown in the illustration below. Wave B in these expanded flats are usually 1.236 or 1.382 that of A.

Triangles typically will have wave relationship between alternate waves. So for example A:C = 1:0.618, B:D = 1:0.618, and C:E = 1:0.618.

Frost and Prechter noted that Ralph Nelson Elliott did not intend to compare only length between waves, but also the percentage growth of decline.

For example, instead of comparing the pip value of a wave A to C, he intended to look at the price decline in percent between A and C.  The difference in these two (point/pip comparison vs. % comparison) wave analysis applications can be significant when comparing long term waves, but when we deal with very short-term moves, the difference may not be a big deal.

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