It was already stated that wave theory is comprised of three aspects—wave form, ratio, and time. We've already discussed wave form, which is the most important of the three. Let's talk now about the application of the Fibonacci ratios and retracements. These relationships can apply to both price and time, although the former is considered to be the more reliable. We'll come back later to the aspect of time.
First of all, a glance back at Figures 13.1 and 13.3 shows that the basic wave form always breaks down into Fibonacci num­bers. One complete cycle comprises eight waves, five up and three down—all Fibonacci numbers. Two further subdivisions will pro­duce 34 and 144 waves—also Fibonacci numbers. The mathemat­ical basis of the wave theory on the Fibonacci sequence, however, goes beyond just wave counting. There's also the question of pro­portional relationships between the different waves. The follow­ing are among the most commonly used Fibonacci ratios:
1. One of the three impulse waves sometimes extends. The other two are equal in time and magnitude. If wave 5 extends, waves 1 and 3 should be about equal. If wave 3 extends, waves 1 and 5 tend toward equality.2. A minimum target for the top of wave 3 can be obtained by multiplying the length of wave 1 by 1.618 and adding that total to the bottom of 2.
3. The top of wave 5 can be approximated by multiplying wave 1 by 3.236 (2x1.618) and adding that value to the top or bottom of wave 1 for maximum and minimum targets.
4. Where waves 1 and 3 are about equal, and wave 5 is expect­ed to extend, a price objective can be obtained by measur­ing the distance from the bottom of wave 1 to the top of wave 3, multiplying by 1.618, and adding the result to the bottom of 4.
5. For corrective waves, in a normal 5-3-5 zig-zag correction, wave c is often about equal to the length of wave a.
6. Another way to measure the possible length of wave c is to multiply .618 by the length of wave a and subtract that result from the bottom of wave a.
7. In the case of a flat 3-3-5 correction, where the b wave reaches or exceeds the top of wave a, wave c will be about 1.618 the length of a.
8. In a symmetrical triangle, each successive wave is related to its previous wave by about .618.
Fibonacci Percentage Retracements
The preceding ratios help to determine price objectives in both impulse and corrective waves. Another way to determine price objectives is by the use of percentage retracements. The most com­monly used numbers in retracement analysis are 61.8% (usually rounded off to 62%), 38%, and 50%. Remember from Chapter 4 that markets usually retrace previous moves by certain predictable percentages—the best known ones being 33%, 50%, and 67%. The Fibonacci sequence refines those numbers a bit further. In a strong trend, a minimum retracement is usually around 38%. In a weaker trend, the maximum percentage retracement is usually 62%.It was pointed out earlier, that the Fibonacci ratios approach .618 only after the first four numbers. The first three ratios are 1/1 (100%), 1/2 (50%), and 2/3 (66%). Many students of Elliott may be unaware that the famous 50% retracement is actu­ally a Fibonacci ratio, as is the two-thirds retracement. A complete retracement (100%) of a previous bull or bear market also should mark an important support or resistance area.