Nº 6: Application of Fibonacci Ratios in Technical Analysis

No matter which financial instrument you are trading, Fibonacci ratios serve as an important tool in technical analysis.

The Fibonacci Sequence was introduced some 800 years ago by Leonardo 'Fibonacci' Pisano in his book Liber Abacci while describing a hypothetical mathematical problem projecting rabbit population growth starting with a single pair of rabbit. The resulting number sequence was 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. This number sequence was later found to have several interesting and unique correlations, such as;

• The sum of two consecutive numbers is the next higher number in the sequence.

• From number 8 onward, the ratio of any number to the next higher number in the sequence is 0.618. Conversely, dividing any number to the next lower number yields 1.618, which is also known as the Golden Ratio that is observable all around us including human body, sunflowers, rose petals, ocean waves, hurricanes, mollusk shells, tree branches, Greek Parthenon, Leonardo da Vinci's Mona Lisa, even the spiral galaxies of outer space and the list goes on.

• With an exception of the first three numbers in the sequence, the ratio of any number to the next alternate number is approximately 0.38. For example, 8/21=0.38.

Application of Fibonacci Ratios in Technical Analysis

The technical analysis of any financial instrument chart utilizes Fibonacci sequence as a ratio relationship between various numbers in the series. Almost all major trading software available in the market today provides the option to draw Fibonacci Retracements on a chart with only two clicks - first to define the lowest price point (A) and the second to define the highest price point (B) of a major move up - or vice versa in a major move down. The result is a set of horizontal lines as shown below.

The software automatically draw these Fibonacci levels of 23.6, 38.2, 50.0, 61.8 and 100.0. These levels identify the points at which the price action is most likely to find support after a pull back that followed a major uptrend. In the example above, the price retraced back to 38.2 Fibonacci level before resuming the move higher.

As mentioned above, these levels are derived using ratios of various Fibonacci numbers;

• The 23.6% ratio is derived from dividing a number in the Fibonacci series by the number three places to the right. For example: 89/377 = 0.2360.

• The 38.2% ratio is derived from dividing a number in the Fibonacci series by the number two places to the right. For example: 89/233 = 0.3819.

• The basis of the 'golden' Fibonacci ratio of 61.8% comes from dividing a number in the Fibonacci series by the number that follows it. For example, 89/144 = 0.6180.

• The 50% retracement level is not based on Fibonacci numbers but it is widely viewed as an important potential reversal level in trading, notably recognized in the Dow Theory (which is beyond the scope of this article).
  

These levels have stood the test of time and should not be ignored when analyzing market trends.

Another key application of Fibonacci ratios in trading are Fibonacci Expansions, which are again available as an option in all trading software and are normally set at .618 and 100. However, these can be customized to add or remove levels pertinent to a particular instrument. It is always a good idea to add 50% Expansion level beyond the default option, but some historical data may give a better clue about the customization required for a particular instrument.

The Fibonacci Expansions provide an indication about the expected extent of the next move up in an uptrending market - or vice versa in a downtrend. The example below illustrates this concept where price moved higher to a Fibonacci Expansion level of 50% (D) after retracing to 38.2 Fibonacci Retracement (C).

It is important to note that Fibonacci Retracements and Fibonacci Expansions are in no way definitive analysis tools as there is no certainity about which particular levels will actually provide Support and Resistance to the current price action. Therefore, Fibonacci ratios are effective in identifying points of interest but only serve as one piece of the puzzle in trading and must be employed along with fundamental data and other technical analysis tools.