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Leonardo Pisano, often known as Fibonacci, was an Italian mathematician born in Pisa around 1170. Guglielmo Bonaccio’s father worked at a trade station in Bugia, now known as Béjaa, a Mediterranean port in northern Algeria. Fibonacci studied mathematics in Bugia as a young man, and throughout his extended travels, he learnt about the benefits of the Hindu-Arabic numeric system.

Key Takeaways

• After 0 and 1, each number in the Fibonacci sequence is the sum of the two preceding numbers.
• The numbers employed in Fibonacci retracements in trading are not numbers in Fibonacci’s sequence; rather, they are constructed from mathematical correlations between numbers in the series.
• Fibonacci retracement levels are shown on a chart by taking high and low points and marking the important Fibonacci ratios horizontally to create a grid; these horizontal lines are used to detect likely price reversal points.

The Golden Ratio

Fibonacci returned to Italy in 1202 and wrote what he had learnt in the “Liber Abaci” (“Book of Abacus”).Fibonacci described the number sequence that is now called after him in his book “Liber Abaci.” After 0 and 1, each number in the Fibonacci sequence is the sum of the two preceding numbers. As a result, the sequence is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, and so on indefinitely. Each number is roughly 1.618 times larger than the one before it.

This number:1.618 is known as Phi or the “Golden Ratio.” The Golden Ratio occurs strangely often throughout nature, architecture, great art, and biology. The ratio has been detected in the Parthenon, Leonardo da Vinci’s Mona Lisa painting, sunflowers, rose petals, mollusc shells, tree branches, human faces, ancient Greek vases, and even spiral galaxies in distant space.

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0.618

The golden ratio’s inverse (1.618) is 0.618, which is also often employed in Fibonacci trading.

Fibonacci Levels Used in the Financial Markets

The numbers employed in Fibonacci retracements in trading are not numbers in Fibonacci’s sequence; rather, they are constructed from mathematical correlations between numbers in the series. The “golden”Fibonacci ratio of 61.8% is calculated by dividing a number in the Fibonacci sequence by the number that follows it.

For instance, 89/144 = 0.6180. The 38.2% ratio is calculated by dividing a Fibonacci number by a number two places to the right. For instance, 89/233 = 0.3819. The 23.6% ratio is calculated by dividing a Fibonacci number by a number three places to the right. For instance, 89/377 Equals 0.2360.

Fibonacci retracement levels are shown on a chart by drawing high and low points and marking the important Fibonacci ratios of 23.6%, 38.2%, and 61.8% horizontally to create a grid. These horizontal lines are used to pinpoint potential price reversals.

The 50% retracement level is often included in the Fibonacci grid that may be produced using charting software. While the 50% retracement level is not based on a Fibonacci number, it is commonly regarded as a significant potential reversal level, as identified in Dow Theory and W.D. Gann’s work.

Fibonacci Retracement Levels as Trading Strategy

Fibonacci retracements are often employed in trend trading strategies. Traders use Fibonacci levels to create low-risk trades in the direction of the original trend when they see a retracement inside a trend. Traders that use this approach expect that a price will most likely bounce from the Fibonacci levels back in the direction of the original trend.

On the EUR/USD daily chart below, for example, we can observe that a strong slump started in May 2014. (point A).The price then bottomed in June (pointB) and retraced higher to about the 38.2% Fibonacci retracement of the down trend (point C).

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In this situation, the 38.2% mark would have been a great location to open a short trade in order to profit from the continuation of the May downturn. Many traders were undoubtedly following the 50% and 61.8% retracement levels, but the market was not strong enough to reach those levels in this occasion. Instead, the EUR/USD fell, continuing the downtrend and breaking through the preceding low in a somewhat smooth action.

If there is a convergence of technical indications when the price approaches a Fibonacci level, the chance of a reversal rises. Candlestick patterns, trendlines, volume, momentum oscillators, and moving averages are among other common technical indicators that are employed in combination with Fibonacci levels. A higher number of confirming signs in play indicates a more powerful reversal signal.

Fibonacci retracements are used to a wide range of financial products, including stocks, commodities, and currency exchanges. They are also employed in a variety of periods. However, like with other technical indications, the predictive value is related to the time range chosen, with longer timeframes receiving more weight. A 38.2% retracement on a weekly chart, for example, is a significantly more significant technical mark than a 38.2% 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 the hopes of catching the continuation of an initial trend, Fibonacci extensions can supplement this strategy by providing traders with Fibonacci-based profit targets. Fibonacci extensions are levels drawn above the typical 100% level that traders may use to predict regions that would make ideal possible exits for their trades in the direction of the trend. 161.8%, 261.8%, and 423.6% are the primary Fibonacci extension levels.

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

Looking at the Fibonacci extension level depicted on the EUR/USD chart above, we can see that the 161.8% level, at 1.3195, is a possible price objective for a trader holding a short position from the 38% retracement stated previously.

The Bottom Line

Fibonacci retracement levels often and uncannily predict reversal points. However, they are more difficult to trade than they seem in hindsight. These levels work best as a tool inside a larger plan. Ideally, this technique seeks the convergence of numerous indicators in order to discover probable reversal regions that provide low-risk, high-potential-reward trade entry.

However, Fibonacci trading tools suffer from the same issues as other universal trading systems, such as the Elliott Wave theory. Having said that, many traders have found success in employing Fibonacci ratios and retracements to make trades inside long-term market patterns.

When combined with additional indicators or technical indications, Fibonacci retracement may become even more potent. The Technical Analysis course at Investopedia Academy covers these indicators as well as how to turn patterns into meaningful trading ideas.

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