Leonardo Pisano, nicknamed Fibonacci, was an Italian mathematician born in Pisa in the year 1170. His daddy Guglielmo Bonaccio operated at a trading message in Bugia, now called Béjaïa, a Mediterranean port in northeastern Algeria. The young Leonardo examined mathematics in Bugia, and also during comprehensive journeys, he discovered the benefits of the Hindu-Arabic numeral system.

In 1202, after returning to Italy, Fibonacci recorded what he had discovered in the « Liber Abaci » ( » Publication of Abacus »). In doing so, he promoted using Hindu-Arabic numerals in Europe.

**The Fibonacci Number Series**

In the « Liber Abaci, » Fibonacci explained the numerical series now named after him. In the Fibonacci sequence of numbers, after 0 as well as 1, each number is the sum of the two prior numbers. Therefore, the series is as complies with: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 and so forth, extending to infinity. Each number is approximately 1.618 times above the preceding number.

**The Golden Proportion**

This figure– 1.618– is called Phi or the Golden Ratio. The inverse of 1.618 is 0.618. The Golden Ratio inexplicably appears often in the natural world, style, fine art as well as biology. As an example, the ratio has been observed in the Parthenon, Leonardo da Vinci’s Mona Lisa, sunflowers, increased petals, mollusk coverings, tree branches, human faces, old Greek vases and also the spiral nebula of deep space. (See likewise: Fibonacci as well as the Golden Proportion.).

**Fibonacci Levels Utilized in the Financial Markets.**

The levels made use of in Fibonacci retracements in the context of trading are not numbers in the sequence; instead they are stemmed from mathematical relationships in between numbers in the sequence. The basis of the « golden » Fibonacci ratio of 61.8% comes from dividing a number in the Fibonacci collection by the number that follows it.

For example, 89/144 = 0.6180. The 38.2% ratio is stemmed from splitting a number in the Fibonacci collection by the number two places to the right. For example: 89/233 = 0.3819. The 23.6% proportion is originated from separating a number in the Fibonacci collection by the number 3 locations to the right. For example: 89/377 = 0.2360. (For relevant insight, see Investopedia’s video clip: Trading With the Golden Proportion.).

Fibonacci retracement levels are shown by taking low and high points on a chart and also noting the crucial Fibonacci ratios of 23.6%, 38.2% and also 61.8% flat to produce a grid. These horizontal lines are made use of to recognize possible price reversal factors.

The 50% retracement level is generally consisted of in the grid of Fibonacci levels that can be attracted making use of charting software application. While the 50% retracement degree is not based on a Fibonacci number, it is widely deemed an essential potential reversal level, significantly acknowledged in Dow Concept as well as also in the work of W.D. Gann.

### Fibonacci Retracement Levels as Part of a Trading Strategy

Fibonacci retracements are often used as part of a trend-trading strategy. In this scenario, traders observe a retracement taking place within a trend and try to make low-risk entries in the direction of the initial trend using Fibonacci levels. Simply put, traders using this strategy anticipate that a price has a high probability of bouncing from the Fibonacci levels back in the direction of the initial trend.

For example, on the EUR/USD daily chart below, we can see that a major downtrend began in May 2014 (point A). Price then bottomed in June (point B) and retraced upward to approximately the 38.2% Fibonacci retracement level of the down move (point C).

*Figure 1: EUR/USD Daily Chart Fibonacci retracement. Chart Courtesy of TradingView.*

In this case, the 38.2% level would have been a good place to enter a short position with the goal of capitalizing on the continuation of the downtrend that started in May. There is no doubt that many traders were also watching the 50% retracement level and the 61.8% retracement level, but in this case, the market was not bullish enough to reach those points. Instead, EUR/USD turned lower, resuming the downtrend and taking out the prior low in a fairly fluid movement.

Keep in mind that the likelihood of a reversal increases if there is a confluence of technical signals when price reaches a Fibonacci level. Other popular technical indicators that are used in conjunction with Fibonacci levels include candlestickpatterns, trendlines, volume, momentum oscillators and moving averages. A greater number of confirming indicators in play equates to a more robust reversal signal.

Fibonacci retracements are used on a variety of financial instruments including stocks, commodities and foreign exchange. They are also used on multiple time frames. However, as with other technical indicators, the predictive value is proportional to the time frame used, with greater weight given to longer time frames. So, for example, a 38% retracement on a weekly chart is a far more important technical level than a 38% retracement on a five-minute chart.

### Using Fibonacci Extensions

While Fibonacci retracement levels can be used to forecast potential areas of support or resistance where traders can enter the market in hopes of catching the resumption of an initial trend, Fibonacci extensions can compliment this strategy by giving traders Fibonacci-based profit targets. Fibonacci extensions consist of levels drawn beyond the standard 100% level and can be used by traders to project areas that make good potential exits for their trades in the direction of the trend. The major Fibonacci extension levels are 161.8%, 261.8% and 423.6%.

Let’s take a look at an example here, using the same EUR/USD daily chart:

*Figure 2: EUR/USD Daily Chart with Fibonacci extension. Chart courtesy of TradingView.*

Looking at the Fibonacci extension level drawn on the EUR/USD chart above, we can see that a potential price target for a trader holding a short position from the 38% retracement described earlier lies below at the 161.8% level at 1.3195.