*This is part eight of a series on technical analysis about Fibonacci Retracements. Click here for the series overview in part one. Click here for part two on the history of technical analysis. Click here for part three on an overview of candlestick charts. Click here for part four on basic candlestick patterns. Click here for part five on advanced candlestick patterns. Click here for part six on Bollinger Bands. Click here for part seven on trend lines.*

Technical analysis focuses on identifying trends and patterns in trading, and one common tool used to do this is the Fibonacci retracement. It’s based on the Fibonacci sequence, which starts out like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc. The sequence goes on infinitely, and each number in the sequence is the sum of the two numbers that came just before it.

Additionally, each number excluding the first few numbers in the sequence is about 1.618 times bigger than the number that came before it. Excluding the first numbers in the sequence, you get about 1.618 when dividing each number by the number that came before it, and you get approximately 0.618 whenever you divide each number by the next number. This 1.618 or 0.618 ratio is considered to be the Golden Ratio, and it can be observed throughout nature, in finance and everywhere else. The Golden Ratio is the basis for the Fibonacci retracement and a number of other Fibonacci-related tools used in technical analysis.

## Calculating Fibonacci retracements

While trend lines mark actual support and resistance levels on price charts, Fibonacci retracement levels are predictions about where future key levels might be. Each of the levels is tied to specific percentages. The official Fibonacci retracement levels are 23.6%, 38.2%, 61.8% and 100%. These percentages are derived from calculations made using the Fibonacci sequence. However, some technical traders also use 50% and/ or 78.6% to calculate retracements.

For example, dividing each number by the number that comes after it equals 0.618, which becomes 61.8% when written as a percentage. Dividing each number by the number that comes two numbers to the right it equals 0.382, which becomes 38.2% when written as a percentage. You get 0.236 when dividing one number by the number that comes three numbers to the right. A 100% retracement is a complete reversal of the previous move.

It’s easy to calculate Fibonacci retracements. You start by drawing trend lines at a high and low point. Then you multiply the price difference by the percentage to get the retracement numbers. For example, to get the retracement levels for a $100 high and $50 low point, you multiply the amount of the change (in this case, $50) by .236, .382 and .618 to get 23.6%, 38.2% and 61.8% of the change. Then you subtract these numbers from the original high, which was $100. You then draw lines at each of these levels to mark the retracements.

## Interpreting Fibonacci retracements

The concept is that the markets will always retrace part of a price movement and that this retracement can be predicted using the Fibonacci sequence and the Golden Ratio. Each percentage refers to how much of the previous high or low is being retraced. Each retracement line is considered to be a support or resistance line. In most cases, prices bounce off these retracement lines.

Using the example from above of a price range between $50 and $100, you get Fibonacci retracement levels of $88.20, $80.90, and $69.10. A technical trader might wait until the price drops to $69.10 and then buy the security, assuming it will bounce back up to $100. Then when it reaches $100, the trader might sell to take a profit on the moves. The expectation is that when a price has retraced part of a move, the larger trend will remain intact, meaning that the move will pick up where it left off and continue in the same direction after the partial retracement.

No technical analysis tool is perfect, and Fibonacci retracements are no exception. As with all indicators and tools used by technical traders, retracements are entirely subjective and can by used in different ways by different traders. The reason these patterns repeat themselves is unclear, so some traders may feel confused because understanding why retracement happens isn’t possible most of the time. Additionally, the levels identified by Fibonacci retracements won’t always hold true. They are more of a general guideline, so traders should never rely solely on retracements.

## Fibonacci arcs, fans and time zones

The Fibonacci retracement is only one of the tools which stems from the Fibonacci sequence. The other tools which are based on the Golden Ratio include Fibonacci arcs, Fibonacci fans and Fibonacci time zones. These other Fibonacci tools are more complicated and thus are used less often than Fibonacci retracements, but they are important, nonetheless. Charting software makes them more accessible for beginners.

Fibonacci arcs are three curved lines marking the 23.6%, 38.2%, 50% and 61.8% levels from any particular level. Before drawing the arcs, traders draw a base line connecting a significant high point with a significant low point. The arcs are then drawn off the base line. Some traders prefer to use arcs because they take into account not only the price but also the time. The arc shows how the price could move as it curves with the passing time. Charting software makes it much easier to draw Fibonacci arcs.

Fibonacci fans are even more complicated. They consist of diagonal lines emanating from a significant point on the price chart. Drawing the fan starts by selecting a base line which connects the high and low prices over a set period of time. The retracement levels are set by looking at 23.6%, 38.2%, 50% and 61.8% of the base line. Charting software makes it easier to see the retracements marked by the Fibonacci fan.

Fibonacci time zones are the only one of the retracement groups that consists of vertical lines. These retracements have a heavier focus on time rather than price. To draw time zones, traders start with a particular date, which is then designated as zero. Each time zone appears at the interval dictated by the Fibonacci sequence, which means the next zone is the very next day, while the one after that is two days later, followed by three days and then five days, all in order of the Fibonacci sequence. Some traders choose to skip over the first few numbers in the series so that the numbers are a bit more spread out.

Traders also use other tools which are based on the Fibonacci sequence, like Gartley patterns and Elliott waves. The next articles in this series will focus on some of these other tools.