Each number in the sequence of the Italian mathematician Fibonacci is the result of the sum of the previous two numbers. The starting point in the sequence of numbers is considered to be 0 and 1. Their sum is 1 (0+1) and this is a new number in the sequence. The next number, the sum of the previous two, is 2 (1+1).

0+1=1

1+1=2

1+2=3

2+3=5

3+5=8

5+8=13

Fibonacci sequence of numbers: 1, 2, 3, 5, 8, 13, 21, 34…

Fibonacci found that each successive number is approximately 1.618 times larger than the previous one. This pattern of increase finds many manifestations in nature and science. It is known as the “golden ratio”. In finance, the levels of 61.8% (e.g., 21/34=0.618), 38.2% (e.g., 13/34=0.382), and 50% are followed with particular interest. The latter is not a direct result of the sequence of numbers but has proven to be highly significant given its median value.

These three levels are considered support or resistance, depending on the direction of the trend. If a currency pair rises from 0 to 1, a possible future decline will find support at levels of 0.618, 0.5 and 0.382 (38.2%, 50% and 61.8% retracement of the 0 to 1 movement, respectively). These are critical support points around which prices are expected to experience fluctuations, resulting in the upward trend being restored.

In the opposite direction, in a hypothetical 1 to 0 decline, we can define resistance levels at 0.382, 0.5 and 0.618 (38.2%, 50% and 61.8% retracement of the 1 to 0 decline, respectively).

When a support or resistance level is broken, the quotes are expected to move towards the next Fibonacci key level.

Chart 1: Fibonacci 38.2% Retracement. Chart: Investing.com

Chart 2: 50% and 61.8% Fibonacci Retracements. Chart: Investing.com

Chart 3: 50% Fibonacci Retracement. Chart: Investing.com

Chart 4: Entire Trend from Charts 1-3. Chart: Investing.com

Most often, traders look for opportunities to open a position in the direction of the main trend. Charts 1 – 3 show how individual retracements can be used to open a position in the main direction. Chart 4 shows the entire downtrend and its end, which occurred with the break of the trend line.

Like any support and resistance, Fibonacci levels are used as an entry point to open a position as well as to place stops and take profits.

Setting price targets is based on the same concept of the golden ratio. Once prices have realized a retracement, the main trend is expected to resume.  Price targets may be placed at Fibonacci extension levels of 138.2%, 150%, 161.8%. In Charts 5 and 6, the price target of 161.8% has been reached.

Chart 5: Fibonacci Price Target. Chart: Investing.com

Chart 6: Fibonacci Price Target. Chart: Investing.com

Some trading and risk strategies are built on the idea of retracement levels. For example, a set of rules for:

1) opening a position at a 50% retracement,

2) a price target of 150% and

3) a stop at the start of the main trend.

Such tactics would fix a risk/reward ratio of 1:2. While extremely simple, this is a strategy defining an entry, stop and target. Of course, it should be further refined to get a finished look.

Fibonacci levels are a fundamental tool in technical analysis. They are most often applied to determine supports and resistances. They are most effective in combination with other analytical techniques and tools.

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