# Our Fibonacci Ratios

Fibonacci Projections and Retracements

Retracements:

Fibonacci retracements are popular among technical traders. They are based on the key numbers identified by mathematician Leonardo Fibonacci in the 13th century. Fibonacci’s sequence of numbers is not as important as the mathematical relationships, expressed as ratios, between the numbers in the series.
In technical analysis, a Fibonacci retracement is created by taking two extreme points (usually a peak and a trough) on a stock chart and dividing the vertical distance by the key Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8%, and 100%.
Once these levels are identified, horizontal lines are drawn and used to identify possible support and resistance levels.
The following chart illustrates how a Fibonacci retracement appears. Notice how the price changes direction as it approaches the support and resistance levels.

Projections:

Fibonacci Projections, also known as Fibonacci Extensions or Expansions.

The application of Fibonacci projections differ from other studies in that two price waves are required: an initial wave and a completed wave in the counter direction. The Fibonacci price projection is then projected from the end of the counter trend move.

When using Fibonacci projections, the technical analyst waits for the market to turn and then applies the Fibonacci projection ratios on the price wave that preceded the last movement. This study is then projected from the end of the last price swing. This requires three points: a previous swing high and swing low followed by another swing high in a down trend, or a previous swing low and swing high followed by another swing low in an uptrend. The Fibonacci ratios are applied to the swing high to swing low in a down trend and projected from the next swing high, or from the swing low to swing high in an uptrend and projected from the next swing low. Horizontal lines are then drawn at these levels and are used a possible support or resistance levels.

The Golden Ratio

In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is an irrational mathematical constant, approximately 1.6180339887.

At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties.

The golden ratio is often denoted by the Greek letter Φ (phi). The figure of a golden section illustrates the geometric relationship that defines this constant.

Fibonacci Projection and Retracement Ratios calculated by Olaptrader:

Fibonacci_Project_1.270
Fibonacci_Project_1.414
Fibonacci_Project_1.618
Fibonacci_Project_2.000
Fibonacci_Project_2.240

Fibonacci_Retrace_0.382
Fibonacci_Retrace_0.500
Fibonacci_Retrace_0.618
Fibonacci_Retrace_0.707
Fibonacci_Retrace_0.786

To summarize, for retracements, a technical analyst waits for the market to turn and then divides the previous trend movement, or wave, by the Fibonacci retracement ratios, starting from the previous high to the low in an uptrend and in the opposite direction in a down trend. Horizontal lines are then drawn at these levels and are used a possible support levels if the larger trend is an uptrend, or as possible resistance levels if the larger trend is a down trend. These thus become places at which the trader could buy in a larger uptrend or sell in a larger down trend. The most significant levels are usually the 61.8% level and the 38.2% level. The 23.6% level and the 78.6% (or 76.4%) levels are not as significant.
For projections, three points are required, a previous swing high and swing low followed by another swing high in a down trend, or a previous swing low and swing high followed by another swing low in an uptrend.
Using the FMLabs toolkit, we look back at the previous trend and calculate the relevant future price targets for the various projection or retracement ratios, as seen above. See an example below from IBM. * The first row will not have a different retracement or projection price because there is no prior trend to analyze.

There are also other types of Harmonic Patterns which use Fibonacci ratios such as the Gartley, Bat, Butterfly, Crab and AB=CD patterns.

We may possibly calculate these historical values in the future.

These Fibonacci ratios and their historical accuracy – in terms of predicting price reversals – will be analyzed as part of our future OLAP application. These results will be analyzed in an OLAP cube in addition to hundreds of other technical indicators in order to give the trader a means of finding complimentary technical indicators that have historically been more accurate in terms of predicting future price movements. This is the power of multi-dimensional analysis. 