Fibonacci numbers

Fibonacci numbers can be used in numebous trading strategies. However, this is important to undertand what these Fibo numbers represent and learn more about the basics of the Fibonacci numbers.

Fibonacci numbers series and its unique properties was first written about by a mathematician named Leonardo de Pisa de Fibonacci (1170–1240). The series starts like this: 1—1—2—3—5—8—13—21—34—55—89 .. , … and goes on from there. Basically, the first two numbers are added to get the next number in the series. As you can see, this series goes on forever.

Fibonacci ratios

What is fascinating about Fibonaci numbers series is the ratio that is found when a number in the series is divided by the preceding number in the string e.g., 8/5 or 55/34). This ratio, no matter where you go in the summation series, is right around 1.618. Over the years, this Fibonacci ratio, 1.618, has been mentioned in writings, essays, and speeches by some of the greatest minds in science and mathematics. Why? Because it is found in the structure of a universal assortment of phenomena in the physical world. This includes nature, architecture, geometry, music, our DNA, and most relevant to us … the financial market.

What Fibonacci ratios are used in trading?

In technical analysis this is possible to use Fibonacci to find important support and resistance levels. But what Fibonacci numbers are used in specific calculations to make these kinds of projections? What are the best Fibonacci numbers to use? Here they are:

The basic Fibonacci ratios are 1.618 and .618.

Besides these two numbers, other derivative ratios that can be used in trading are:

.382 = .618 squared. Also, the ratio between alternate numbers in the Fibonacci sequence is 2.618 or its inverse, 0.382 .500 = divide the 2nd number by the 3rd in the Fibonacci sequence.

.786 = square root of .618

1.000 = 1.618 x .618 (also used simply for symmetry measurements)

1.272 = square root of 1.618

2.618 = 1.618 squared

There are certain specific ways and trading strategies in which these ratios are used. The important point here is to know which ratios are used and how they are derived. But now at least you should have a basic understanding of the background of Fibonacci and the ratios used in trading. If you are interested in furthering your education in the history of the Golden Mean or Fibonacci, all you need is a computer and Internet connection. There are thousands of articles and materials on the subject. Have fun!

Through the use of expansions studies, we will be calculating key areas of price support and resistance.

Price expansions are similar to projections with one small difference. Instead of measuring swing X:A and projecting it from B, we project the values from А. В is not used in this study. Basically, expansions measuring swing X:A „expand“ that swing further in the direction price is headed using the following Fibonacci ratios: .618, 1.00, and 1.618. These price levels will be labeled as (Exp) on the charts. To calculate an expansion only two points must be established (X, A). For illustration purposes, let's say X is 50 and A is 45 in Figure 4.1.

First, let's calculate what the range of X to A is:

Price @ A: $45

Price @ X: $50

Range = $5.00

Next let's multiply this range by each Fibonacci ratio:

Ratio Points

0.618 $ 3.09

1.000 $ 5.00

1.618 $ 8.09

Finally, take the number from each ratio and subtract it from A, which is $35.00. This will provide you with Fibonacci projection levels.

So, if I were to ask you for the 0.618 expansion of swing X;A, the answer would be $41.91. The price levels in the table above represent Fibonacci price support decisions. The exact same analysis can be done for Figure 4.2 to calculate projection levels acting as resistance. In Figure 4.2, X is $30, and A is $40. This time instead of subtracting from A we would add to A, to determine price resistance levels:

Expansions are a „confirming“ Fibonacci study. This simply means that the other three studies — retracements, extensions, and projections — should be the first price studies applied to a chart. Then utilize this price study to confirm a potential price support or resistance zone.