Trading based on the Fibonacci method is a unique way of analysing markets. The Fibonacci hypothesis that was developed by the famous mathematician, Leonardo de Pisa, has stood the test of time.

Even to this day, traders apply the concepts of Fibonacci and the golden ratio; represented by the number 1.618, in various forms of technical analysis. Fibonacci methods, however, are most commonly applied to identify support and resistance levels.

Traders use the Fibonacci numbers in order to estimate where prices might retrace or reverse by measuring the most recent leg of an uptrend or downtrend.

Fibonacci-based trading methods work due to the fact that they’re widely practiced. So, despite the mysticism attached to this form of technical analysis, it is, in fact, a self-fulfilling prophecy. To put it in other words, given the widespread use of Fibonacci-based methods of analysis, traders tend to watch these levels and trade based on the Fibonacci levels, making them into forms of support and resistance that simply work.

Before we get into more detail on the subject of Fibonacci trading, a bit of history and context is required.

## Where did the Fibonacci numbers come from?

It is said that in the year 1202, Leonardo de Pisa, or Leonardo Pisano, who was born in Pisa, discovered the Fibonacci sequence of numbers. Although the Fibonacci sequence is largely attributed to Leonardo, his knowledge came from his travels to the Far East. Having learned about the Hindu-Arabic numeral system, Fibonacci documented his discovery in his famous work; ** "Liber Abaci",** which eventually led to his nickname as Fibonacci.

The works of Leonardo eventually gave way to the discovery of what is called *"the golden ratio." *

The golden ratio has been proven to appear, not just in the financial world of trading, but in every aspect of life; from famous pieces of Ancient Greek architecture, to nature. The most famous example of the golden ratio is the nautilus shell. The golden ratio can be seen in the nautilus shell, which expands in a logarithmic spiral. By connecting the arcs with squares, or Fibonacci tiling, the sizes of the squares follow the Fibonacci sequence of numbers.

### Understanding the Golden Ratio or Phi

The golden ratio, or phi, is the number 1.618. The inverse of this is 0.618. Phi (pronounced “fi” or “fy”) is the ratio of the length of one line segment to another, which results from dividing the original line at a certain point. For example, the distance from point A to point C in the line below is said to be 1.618 times that of the distance from point B to point C, and the distance from B to C is 0.618 times that of A to C. In mathematics, phi with an upper-case 'P' represents 1.618, while phi with a lower-case 'p' represents the inverse, which is 0.618.

The golden ratio occurs in the numerical series developed by Leonardo, also known as the Fibonacci sequence of numbers.

## What is the Fibonacci sequence of numbers?

Leonardo described his sequence of numbers in the following way:

0,1,2,3,5,8,13,21,34,55,89,144,233 and so on.

The further you progress into the sequence; you will find that each number becomes 1.618 times greater than the preceding number. For example, when you divide 89 by 144, you get 0.618, but when you divide 89 by 55, you get 1.618; the golden ratio. This is similar to the illustration given in *figure 1* with regards to points A and B in relation to point C.

Based on the Fibonacci sequence, we now know two main ratios; phi, which is 1.618 and its inverse; 0.618. Aside from the above, other ratios include 0.382. This ratio is formed when you take a number and divide it by the number two places to the right.

Thus, 89/244 = 0.3819 or 0.382 when rounded to 3 decimal places. Further variations also derive other ratios such as 0.236, which is derived from taking a number and dividing it by the number four places to the right. In the world of technical analysis, the following ratios are the most important: 0.236, 0.382, 0.618, and 1.618. Of course, you can find many other ratios, but the above four are the most important.

## How to use Fibonacci ratios in Forex trading

Traders know that prices never rise in a straight line. Prices tend to rally or decline, then retrace, and then continue in the direction of the previous trend. By using Fibonacci ratios, you can measure a wave (a rally or a decline) and then anticipate where the price might retrace when it pulls back.

The Fibonacci ratios are the key levels where you can expect the price to retrace. Thus, Fibonacci ratios are nothing more than support and resistance levels. They work because these levels are watched by a large number of traders.

Fibonacci levels can be combined with any trading strategy. For example, if you use a moving average, you can apply Fibonacci levels to measure the length of a rally and then wait for the moving averages to confirm the bullish or bearish trend when the price makes a pullback.

Of course, using Fibonacci levels requires a bit of discretion. For example, the points you choose to measure the Fibonacci level can vary from one trader to another. Likewise, some traders use only the opening and closing prices, while others use the high and low prices.

Remember that Fibonacci levels are an exact science.

### The Fibonacci retracement tool – MT4

The MetaTrader 4 (MT4) trading platform, as well as just about any other trading or charting platform, has the Fibonacci measurement tool. You can access this from MT4’s main menu: *Insert > Fibonacci > Retracement.*

There are many other Fibonacci tools; such as the Fibonacci spiral, Fibonacci arcs, and so on. But among all these tools, the retracement tool is the most widely used. In MT4 and most other charting platforms, you can also adjust the levels.

In this example, we only apply 0.618, 1.618 (which is the extension), and 0.382. You can adjust further values by double-clicking on the Fibonacci tool and entering the values yourself. An example of this is shown in figure 2 below.

## How to draw Fibonacci levels

The first step is to identify a strong movement in the market. This could be a strong rally or a strong decline. Now, starting in the opposite direction to this strong movement, click on the starting point of this rally (could be a high or low) and drag the Fibonacci tool to the end point.

A quick way to see if you’ve plotted the Fibonacci tool correctly is to simply look at the 0 and 100 values. When the Fibonacci levels are plotted, you’ll see the retracement level 0.382 followed by 0.618.

Figure 3 illustrates an example of how to draw the Fibonacci tool.

## How to trade with Fibonacci levels

Now that the Fibonacci levels are in place, the next step is to expect a reversal either at the 0.618 or 0.382 Fibonacci ratio levels. These are nothing but supports and resistances. In an uptrend, when you measure the Fibonacci ratios (as shown in figure 3 for example), the 0.618 and 0.382 (and other Fibonacci ratios) are potential support levels.

Conversely, when you measure a downtrend using Fibonacci ratios, the levels of 0.618, 0.382 etc. become potential resistance levels.

Depending on the price action at these levels (or based on signals from other technical indicators) you can expect prices to reverse (or in some cases break these levels and change direction).

In most cases, when the price retraces to 0.618 or 0.382, you can expect it to then rally towards 1.618, which is known as the Fibonacci extension level.

This principle is widely used as a trading strategy in itself as traders typically buy or sell near the Fibonacci retracement level and take profit near the Fibonacci extension level.

In the above example in figure 3, a long position would have been opened at either 0.382 or 0.618 (deep or shallow retracement) with a Take Profit set at the 1.618 extension level.

Some traders also make use of the 50% retracement level, while others prefer to round off the Fibonacci ratios to 0.40%, 0.62% and so on. It doesn’t make much of a difference; just as one trader may use highs and lows while another trader might use the opening and closing prices.

Fibonacci ratios can be applied to any market and any timeframe as long as there is a strong movement in the market. One of the most important aspects of successful trading with Fibonacci levels is to have patience and wait for a pivot high and low to be formed.

Figure 4 shows the Fibonacci ratios applied to a daily chart for Cisco Systems (CSCO).

In the above example, you can see where the high and low points were taken from and the subsequent retracement to the 38.2% Fibonacci level.

Most traders tend to plot Fibonacci levels as the price evolves. However, a trader must wait for a few sessions until the retracement is in the early stages. Another important thing to bear in mind is that just because the price retraces to a Fibonacci level, there is no guarantee that the price will continue in the direction of the trend.

There are many instances when the price bounces off the 61.8% retracement but the subsequent rally fails, with the price eventually changing trend and thus, its direction.

In conclusion, Fibonacci ratios might seem mystical but they are nothing but support and resistance levels that are widely watched by traders. The popularity of Fibonacci levels makes them a self-fulfilling prophecy; as large buy and sell orders are placed at these levels.

The fact that Fibonacci levels represent potential areas of support and resistance makes them a unique choice for trend traders.