Just as 1.618 and 0.618 describe the relationship between one numerical value and the next in the Fibonacci Series, so they also describe the relationship between one surge in prices and the next in the financial markets. For example, if a price moves from 5 to 8, then you can multiply 8 by 1.618 to predict that the next price surge will be to 13. Likewise if the price retraces from 13 to 8, multiplying 8 by 0.618 predicts that the next retracement will be to 5. It is assumed that a similar relationship will be found in price movement whether the direction is upward or downward. Thus, an original price change to the downside would be expected to move at a rate of 1.618, and a reversal to the upside would advance at the rate of 0.618.
Following on from there, it is found that just as the ratios between any two successive numbers in the Fibonacci Series are important, so are the ratios between a number and the third above, and also the fourth above:
Given the basic series:
1 2 3 5 8 13 21 34 55 89 144 233 377
The following table shows the basic plus additional calculated ratios which are found to be of secondary significance in computing trends:
| Fibonacci Series | Growth | Retracement | Inverse |
| 1st and 2nd numbers | 1.618 | 0.618 | 0.382 |
| 1st and 3rd numbers | 2.618 | 0.382 | 0.618 |
| 1st and 4th numbers | 4.236 | 0.236 | 0.764 |
| Other key ratios | 1.382 | 0.500 | 0.500 |
Also shown are two other numbers that are important in the Fibonacci Series: 0.5 and 1.382. The former, 0.5, is an important retracement ratio because it is halfway between 0.382 and 0.618. The mid-point is always of importantance in any growth cycle and, in the financial markets, when prices drop to the mid-point of a previous trading range, it is generally necessary form a decision as to whether price levels are likely to move back up again, or to continue downwards.
Markets move in rhythms. An impulse wave that defines a major market trend will have a corrective wave before the next impulse wave reaches new territory. This occurs in either bull market or bear market conditions. The most common approach to working with corrections is to relate the size of a correction to a percentage of a prior impulsive market move.
A retracement of 38.2% indicating continuity of the primary uptrend
Fibonacci Retracements can be visualised by first drawing a trendline between two extreme points, for example, a trough and opposing peak. A series of nine horizontal lines are drawn intersecting the trendline at the Fibonacci levels of 0.0%, 23.6%, 38.2%, 50%, 61.8%, 100%, 161.8%, 261.8%, and 423.6%.
After a significant price move either up or down, prices will often retrace
a significant portion of the original move. As prices retrace,
support and resistance levels often occur at or near the Fibonacci Retracement
levels.
Extensions appear as extreme price movements. They express themselves in runaway markets, opening gaps, limit-up and limit-down moves, and high volatility. Such situations offer excellent trading potential as long as the appropriate analysis is carried out and trading is carried out following clearly defined rules.
Reaching a level that can be calculated as the previous up-swing size x 1.618
Valleys in the down-trend identified from the original swing using Fibonacci numbers 1, 1.618 & 2.618
There is no sure way of using the time factor by itself in forecasting. Frequently, however, time relationships based on the Fibonacci sequence do fit wave spans with remarkable accuracy, giving the analyst added perspective. Elliott said that the time factor often "conforms to the pattern" and therein lies its significance.
In wave analysis, Fibonacci time periods serve to indicate possible times for a turn, especially if they coincide with price targets and wave counts. Therefore with a judicious employment of time analysis techniques, trades can be entered or exited at the price change rather then after the fact. However, the concept is dynamic and the distance between two highs or two lows is seldom exactly the same, and the projection can vary depending upon the swing dimensions of the market price pattern.
Distance between two peaks multiplied by Fibonacci ratios 1.618 and 2.618 predicts another two peaks weeks into the future
Human behavior is not only reflected in chart patterns as large swings, small swings or trend formations. Human behavior is also expressed in peak-valley formation. Fibonacci channels make use of peak and valley formations in the market and lead to conclusions on how to safely forecast major changes in trend directions.
The secret of Fibonacci channels is to identify the correct valleys and peaks to work with. Support and resistance lines can be drawn weeks and months into the future, once the appropriate tops and bottoms in the market have been detected.
Evidence of
major support
and resistance lines identified from peaks and valleys
Fibonacci ellipses identify underlying structure of price moves. Fibonacci ellipses circumvent price patterns. When a price pattern changes, the shape of the ellipse circumventing the respective market price pattern changes too. We can find long and short ellipses, fat and thin ellipses and ellipses that are flat or have a steep angle. There are very few market price moves that do not follow the pattern of a Fibonacci ellipse.
The strength of Fibonacci ellipses is that no matter how many waves or subwaves we find in a price pattern, we receive a solid overall picture of the total price pattern as long as it can be circumvented by a Fibonacci ellipse.
Fibonacci ellipse with ratio 6.854 pinpoints target price and overall pattern
The name Fibonacci fan is derived from the fan-like appearance of the three trendlines as shown in the chart below. The Fibonacci fans are drawn using typical tops or bottoms. The three Fibonacci fans project into the future with slopes at 38.2%, 50% and 61.8% (plus additional levels if required). As the daily prices pass the three fans, predictions about future price movements can be made based upon whether there appears to be support or resistance at the points of intersection. If the prices hold at the fan line, support exists; if prices pass quickly through the fan line, then support will not be encountered until the next fan line.
Support and resistance levels of an early 2003 bull rally projected into 2004
Fibonacci Fan Lines are displayed by drawing a trendline between two extreme points, for example, a trough and opposing peak. Then an "invisible" vertical line is drawn through the second extreme point. Three trendlines are then drawn from the first extreme point so they pass through the invisible vertical line at the Fibonacci levels of 38.2%, 50.0%, and 61.8%.
Fibonacci spirals provide the optimum link between price and time analysis. Each point on a spiral manifests an optimal combination of price and time. Corrections and trend changes occur at all prominent points which contact the Fibonacci spiral on its growth path through price and time. If the correct origin is chosen, Fibonacci spirals can identify turning points in the market with high accuracy.
Fibonacci spiral predicting most key peaks and valleys many months ahead
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Charts created by Fibonacci Solution Fibonacci trading software