Everybody knows Leonardo da Vinci and Galileo Galilei, but not their fellow countryman Leonardo Fibonacci as much. His work was on golden ratio and most importantly for traders, the set of technical analysis tools that bears his name. 

Fibonacci spent much of his youth traveling throughout the Mediterranean learning the systems of arithmetic that merchants used to conduct their business transactions. Later in life, he discovered what is known as the “Fibonacci sequence” – a series of numbers (beginning with 1) in which a given number is equal to the sum of the two preceding numbers:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, etc.

The sequence of numbers is ultimately less significant than the ratio you get from dividing any adjacent number into the other – for example, 8/13. As you move up the sequence, the ratio approaches the number 1.618, or its inverse, 0.618. This is known as the golden ratio. The golden ratio shows up in patterns throughout nature, including:

• The petals of flowers 
• The branching sequence in trees
• Concentric snail and nautilus shells
• Spiral galaxies
• Hurricanes
• DNA molecules

Once you become sensitive to the Fibonacci sequence, you can see the pattern appearing in nature, buildings, art, and even the human body. Rumor has it that if you measure from your shoulder to your fingertips, then divide that number by the distance from your fingertip to your elbow, the result will likely be close to the golden ratio.

This is relevant to trading because …..

This is all very interesting, but what does it have to do with trading?

Back in the 1970s, some investors theorized that the ebbs and flows – buying and selling – in the stock market might follow patterns similar to those of a natural ecosystem. They began applying Fibonacci numbers to their charts in the form of Fibonacci retracements. 

Fibonacci retracements are designed to locate areas of support and resistance on a price chart based on numbers from the golden ratio converted into percentages. The levels include 23.6%, 38.2%,50%, 61.8% and 78.6%.

Where did these levels come from? Well, 38.2% comes from dividing a number in the series by the number found two places to the right, and 23.6% comes from dividing a number by the number found three places to the right. The 50% level isn’t really a Fibonacci number, but many traders see it as significant. 

To view these Fibonacci retracement levels, head over to the charts tab on the Thinkorswim platform (this is available in all interactive trading platforms, ETrade, Tradestation, and so on, if not ask your broker) from TD Ameritrade and pull up a chart. Select the time frame you want to analyze and then identify a high or low point. Select Drawings > Drawing Tools > % (Fibonacci Retracements). Then place your cursor on the high or low point, click once, move to the next low or high point to the right, and click again. The tool automatically calculates the corresponding Fibonacci levels based on percentage retracements.

How to use Fibonacci Retracements

In the chart of the SPDR S&P 500 ETF (SPY) in Figure 1, notice the top level $358.65 is 100% and the bottom level $319.8 is 0%. The retracement levels in between are areas you can watch for potential technical or resistance levels. Fibonacci retracements can also be used in the opposite way – from a low point to a high point (as long as the high point is to the right of the low one).

When SPY started to move above its March low, it met slight resistance at the 23.6% level. Even though it broke above it, the close was right around that level. SPY then continued moving toward the 38.2% level, hesitated there for a few days, and broke through that level. On the second retracement plot (with a 100% high of $353.78 and a 0% low of $322.54), the resistances are at 23.6%, 50%, 78.6%. You can also see 23.6% acting as a support. As you move through the price chart, you can see how the different retracement levels acted as support and resistance levels. 

The definition of support is a price area below the current market where you will look for the possible termination of a decline and where you would consider being a buyer of whatever market you are analyzing. You might be looking to buy at or around support either to initiate a new trade on the long side or to exit a short position if you think the support may hold and the market will not decline any further.

The definition of resistance is a price area above the current market where you would look for the possible termination of a rally and consider being a seller. You might be looking to sell at or around resistance to initiate a new trade on the short side or to exit a long position if you think the resistance may hold and the market will not go any higher. 

Fibonacci retracement is just the objective tool to show you where those supports and resistances are.

You can try applying this tool to individual stocks or exchange-traded funds. You can also combine Fibonacci levels with other indicators to get more trading signals for confirmation.

Fibonacci in the Markets

You might wonder how Fibonacci numbers, which are so prevalent in nature, can have anything to do with a human system like the stock market. Is there something about the human emotions of greed and fear (which drive buying and selling) that corresponds with Fibonacci numbers? May be; maybe not. But we do know that Fibonacci retracements are accepted and used by many traders, including some who trade for large institutions and hedge funds. This can give them a self-fulfilling aspect, at least in the short term, and in the absence of other technical or fundamental data. Do they always work? Of course not. But they do provide some objective levels to watch.

Once you have become familiar with the Fibonacci sequence, you can explore some lesser-known technical tools as Fibonacci extensions and price projections.

Courtesy: TD Ameritrade, Fibonacci Trading by Carolyn Boroden