• Bocconi Students Options Club

Fibonacci Retracement

Leonardo Pisano otherwise nicknamed “Fibonacci” was an Italian mathematician from the 12th century born in Pisa. He was a mathematics student, and whilst travelling discovered the multitude of advantages of the Hindu-Arabic numerical system. When he returned to Italy in 1202, he documented what he had learned in the ‘Book of Abacus’ (“Liber Abaci”). In this book, he describes the renowned sequence that is now named after him.

The Fibonacci sequence is one of the most famous formulas in mathematics, perhaps due to its simplicity. The sequence works as follows: each number in the sequence is the sum of the two numbers prior to it.


The first 10 elements of the sequences being: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. The mathematical equation for it being: Fn = Fn-1 + Fn-2

Despite the simplicity, the Fibonacci Sequence is said to be tightly linked with what we know as “The Golden Ratio”/Phi (1.618... ).


Basically, as the sequence goes towards infinity, the ratio of the sequence approaches 1.618. What this essentially means is each number is approximately 1.618 times greater than the previous one (precision increasing as the numbers go towards infinity). This ratio is said to appear in patterns in nature for example in the growth of plants, and arrangement of leaves. In the world of art and design, it has earned a huge reputation for being involved in the works of Salvador Dalí for example. Even the Pyramids of Giza and the Mona Lisa are said to incorporate it.


Yet, perhaps the most impressive use of it, is in the man- made financial markets where the Fibonacci Sequence can help identify possible price reversal points.


In Financial Markets

The first important disclaimer is that in the context of trading, the numbers used in Fibonacci Retracements are not numbers in the Fibonacci

Sequence; they are instead derived from mathematical relationships between the numbers in the sequence.


Key Fibonacci Retracement Levels

For example, a value that is extensively used, is the inverse of the golden ratio, which is 0.618 or 61.8%. The basis of it coming from dividing a number in the Fibonacci Sequence by the following one. Mathematically: Fn-1 / Fn61.8% Another useful retracement value being that of dividing a number in the sequence by the number two places to the right. (E.g. 13/34 = 38.2%) In other words: Fn-2 / Fn38.2% As you can see, each retracement level is associated with a percentage. The percentage basically indicates how much of a prior move the price has retraced. The Fibonacci retracement levels are: 23.6%, 38.2%, 61.8%, and 78.6%, (While it isn’t a Fibonacci ratio officially, 50% is also used.)


How are Fibonacci Retracement Levels Used?

Fibonacci retracement levels are depicted by taking high and low points on a chart and marking key Fibonacci retracement levels (mentioned above) horizontally. These horizontal lines are often used to identify a possible price reversal point, which are called support and resistance levels. Support levels refers to the price level that an asset does not fall below for a period of time, the support level is created by buyers entering the market when the price of an asset falls to this lower price (Resistance being the opposite). These levels should not be relied on exclusively, it is dangerous to assume the price will reverse for sure once hitting a specific Fibonacci sequence.

Fibonacci Retracements are often used as part of trend-trading strategy. In short, trend trading is a trading style that attempts to catch gains through the analysis of an asset’s momentum in a particular direction. In this scenario, traders observe a retracement taking place within a trend and attempt to make a safe entry with the help of the Fibonacci levels. Traders using this anticipate that a price has a high probability of bouncing from the Fibonacci levels back in the direction of the general trend. Fibonacci retracements can be used in order to determine stop-loss levels, place entry orders, or price targets. For example, an investor sees a stock increasing in price. After moving up, it retraces to the 38.2% level. Then, it increases again. Since the support bounce occurred at a Fibonacci level during a trend up, the investor decides to buy in, whilst setting a stop loss at 38.2%.


Fibonacci retracement levels are static prices unlike moving averages. The static nature of the price levels makes identification faster, allowing for further accuracy in decision-making too. Helps traders and investors to anticipate and react prudently when the price levels are tested. Fibonacci levels are points of inflection where some type of price action is expected, either a reversal or a break.


Example of Using Fibonacci Retracement Levels

Below we have a chart of the EUR/USD and can see that the major down trends began on May 2014, at point A. The price then bottomed off at point B in June, and retraced to approx. 38.2% Fibonacci retracement level of the initial movement down, this being at point C.

In this situation, one expects that after hitting 38.2% that the downward trend will continue, therefore it is an excellent opportunity to enter in the short position. However, the problem with the Fibonacci Retracement Levels is that many traders were probably looking at the 50% line, or even the 61.8% one. However, in this case the trend was not bullish enough to keep increasing up to those levels.

The chance of a reversal increases if there is a combination of methods of technical analyses that concur with each other when the price reaches a Fibonacci level. The more confirming indicators, the more believable and robust the reversal signal is. Other popular technical indicators that are used in combination with Fibonacci levels include trendlines, volume, momentum oscillators, and moving averages.

Fibonacci retracements are used on most financial instruments, including stocks, commodities, and foreign currency exchanges. They can also be used on different timeframes. However, as with other technical indicators, the predictive value increases with the timeframe length.


Fibonacci Extensions

As mentioned previously, Fibonacci Retracements apply percentages to a pullback, Fibonacci Extensions are the “opposite”, they apply percentages to a move in the trending direction. Essentially, when the price reaches a Fibonacci ratio, instead of retracing, it instead follows the initial trend. Fibonacci extensions consist of levels drawn past 100% level and is used by traders to make good potential entries or exits for their trades in the same direction as the initial trend. The major Fibonacci extension levels are 161.8%, 261.8% and 423.6%.


Concluding on The Fibonacci Retracement Levels

As we recall, the retracement levels indicate the price at which it might find support or resistance, however there is no insurance that the price will actually stop there. This is why the price starting to bounce off the retracement level, is a better indicator.

Another argument against the retracement levels is that there are so many retracement levels that the chance price will reverse near one of them is very high. This leads to investors not knowing which one will be particularly useful at any given point in time.

Fibonacci retracement levels often indicate reversal points accurately. However due to the points previously mentioned, these levels are best used as a tool within a broader strategy. That said, many traders are very successful using Fibonacci retracements to place transactions within long-term price trends. Fibonacci retracement can become an even more precise tool when used in harmony with other indicators and technical signals.