Fibonacci Retracements are technical indicators that provide information about a size of a pull-back and possibly the entry point for trade of trending security. Thus, a successful trader can identify support and resistance levels that help him to trade efficiently desired financial instruments.

Leonardo Fibonacci (Leonardo Pisano Bogollo) was an Italian mathematician from Pisa who brought Hindu-Arabic numeral system to Europe. In his book, Liber Abaci, Fibonacci introduced sequence of numbers where a sum of first two give a third number as a result: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144; As the numbers keep being divided by each other, the sequence reaches Golden Ratio (also known as Phi) – approximately 1.618. This number is seen everywhere around – there’s plenty of interesting literature about this to read if desired.

Using the above theory we can calculate Fibonacci Retracements.
First retracement is basically derived from Golden Ratio (number divided by first highest number): 89 / 144 * 100 = 61.8056 –> This gives us the most approximate value of 61.8%
Second retracement is number divided by second highest number: 55 / 144 * 100 = 38.1944 –> 38.2%
Third retracement is number divided by third highest number: 34 / 144 * 100 = 23.6111 –> 23.6%
Finally, there is also retracement of 50%, which is not anyhow calculated, it is just generally considered by traders as pull-back may often occur at a half of the previous advance.

Every trading platform includes Fibonacci Retracement tool in their packages, so it can be nicely displayed on the chart. The tool requires Java (Flash), so the charting platform must be equipped with that. Then, you just select Fibonacci Retracement from the tool and drag it from the lowest (highest) to the highest (lowest) point of the stock price.

Kaz Minerals plc.; Source: StockCharts.com

Above is a trending stock that entered bull market in July and peaked in December 2017, when stock started to pull back. Putting the Fibonacci Retracement on chart shows us the pull-back stopped at 23.6% level. Stock was stabilizing for second half of December – this is interpreted as sideways trading around the 23.6 line. Then the stock took off in the beginning of January 2017. It is likely for stock to continue its bullish trend.
The retracement was drawn by dragging the retracement from the lowest point (July 2016) to the highest point of the price (December 2016) – the points are displayed as two horizontal blue lines with two yellow dots on the sides.

It is hard to know at which level the stock retraces and thus, as always, other technical indicators must be engaged. It all depends on a strength of the trend and overall market conditions. In the stronger trend conditions, the stocks retrace at lower levels (23.6% and 38.2%); while in the weaker trend conditions, the stocks retrace at higher levels (50% and 61.8%).

Fibonacci Retracements should be used in rather liquid markets with active stocks – then an amount of traders is significant and such indicator becomes popular between the market participants and serves as very useful tool in trend trading analyses.