In this article we will discuss about a widespread, well-known key element of technical analysis. Why do you think technical analysis especially some elements work so well for financial markets? Why do you think Fibonacci levels are usually strictly followed?

Because thousands and billions of traders and computer programs for trading use these elements. This way everybody acts the same at the same time…

This is why we decided to present in the category of technical analysis, the most used and well-known methods of predicting financial evolution. These methods are easy to understand and are very efficient.

We will discuss about Fibonacci levels. We will find out what Fibonacci levels are and how they are calculated. We will use them in our charts and we will see how they act. We will discover how useful Fibonacci levels are and, at the end, we will draw the conclusions. We will use Fibonacci levels daily in our analyzing and trading system.

**1. ****What are ****Fibonacci levels?**

The truth about Fibonacci levels is that they are useful (like all trading indicators). They do not work as a standalone system of trading and they are certainly not the “holy grail”, but can be a very effective component of your trading strategy.

But who is Fibonacci and how can he help you with your trading?

Leonardo Fibonacci was a great Italian mathematician who lived in the thirteenth century who first observed certain ratios of a number series that are regarded as describing the natural proportions of things in the universe, including price data. The ratios arise from the following number series: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144

This series of numbers is derived by starting with 1 followed by 2 and then adding 1 + 2 to get 3, the third number. Then, adding 2 + 3 to get 5, the fourth number, and so on.

**2. How are Fibonacci levels calculated?**

The ratios are derived by dividing any number in the series by the next higher number, after 3 the ratio is always 0.625. After 89, it is always 0.618. If you divide any Fibonacci number by the preceding number, after 2 the number is always 1.6 and after 144 the number is always 1.618. These ratios are referred to as the “golden mean.” Additional ratios were then derived to create ratio sets as follows:

The first set of ratios is used as price retracement levels and is used in trading as possible support and resistance levels. The reason we have this expectation is that traders all over the world are watching these levels and placing buy and sell orders at these levels which becomes a self-fulfilling expectation.

The second set is used as price extension levels and is used in trading as possible profit taking levels. Again, traders all over the world are watching these levels and placing buy and sell orders to take profits at these levels which becomes a self-fulfilling expectation.

Most good trading software packages include both Fibonacci Retracement Levels and Price Extension Levels. In order to apply Fibonacci levels to price charts, it is necessary to identify Swing Highs and Swing Lows. A Swing High is a short term high bar with at least two lower highs on both the left and right of the high bar. A Swing Low is a short term low bar with at least two higher lows on both the left and right of the low bar.

**Fibonacci Retracement Levels**

In an uptrend, the general idea is to go long the market on a retracement to a Fibonacci support level. The price retracement levels can be applied to the price bar chart of any market by clicking on a significant Swing Low and dragging the cursor to the most recent potential Swing High and clicking there. This will display each of the Retracement Levels showing both the ratio and corresponding price level. Let’s take a look at some examples of markets in an uptrend. The same points made by these examples are equally applicable to markets in a downtrend.

3. Chart examples for Dow and e-mini S&P 500.

1. In the first example we have an ascending trend and a Fibonacci retracement of 38%. After the price went down 38% of the entire going up value, it returned to an uptrend. The 38% retrace is the best moment to initiate long positions.

2. Here the image is reverse. We have a downtrend, a 38% pull back and then the price continued to go down.

3. The price had a 50% retrace during an ascending trend.

4. The ascending trend had a 61% pull back.

5. The last example shows a good moment to enter long after a 50% retrace

4. Conclusions

a. Correctly used and followed, Fibonacci levels along other technical analysis and astrological analysis methods can offer complex and correct information for profitable transactions.

b. Trading methods based on Fibonacci levels can be found and can work very well. These methods can be harmoniously correlated with other methods of financial analysis resulting in a complete and complex trading system approaching financial reality.

c. We often use Fibonacci levels amongst other various methods of analysis that we will describe later.