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# Fun with Math: Applying Fibonacci Retracement Brackets

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June 20, 2016

What does an Italian mathematician from the 12th century have to do with the stock market?

Leonardo Fibonacci discovered a special sequence of numbers called the Fibonacci sequence. It looks like this:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 …

Notice the pattern in these numbers? Each is the sum of the previous two numbers. For instance, the next number in the sequence is 233 (89 +144).

The Fibonacci sequence creates two interesting ratios. First, divide a number in the sequence by its previous number, and you’ll get a ratio of about 1.618. For example, 34/21 = 1.619.

This ratio, 1.618, is known as the golden ratio or golden mean. You can observe this ratio in objects like a nautilus shell, in the way trees branch out and grow, the spirals of galaxies, and in lots of art and architecture. Another Leonardo, in this case da Vinci, used the ratio 1.618 to create the Vitruvian Man.

Another special ratio from the Fibonacci sequence is found by dividing a number by its following number. For example, 13/21 = 0.619. This is the inverse of the golden ratio (1/1.618 = 0.618), and it forms the basis of the Fibonacci retracement bracket investors use today to identify support and resistance in the stock markets.

## From Pisa to Wall Street

Way back in the 1970s, some clever investors observed that trends in stock prices sometimes aligned with the Fibonacci sequence and in particular its ratios. They noticed that stocks typically don’t trend higher or lower in straight lines. Sure, stocks can trend for extended periods, but eventually, trends reverse. After reversing, stocks tend to retrace previous trends. It was in these retracements that investors observed alignment with the Fibonacci sequence.

But the connection between the Fibonacci sequence and the stock market is sometimes dubious. Proponents of Fibonacci analysis, and related types of market analysis such as Elliott Wave Theory, argue that the stock market is analogous to a natural and complex system like an ecosystem. There are many changing variables, but underneath all the chaos is order, and most importantly, repeatable patterns. Some investors try to use Fibonacci analysis to identify these patterns and help support their decision making.

Now, like most forms of technical analysis, Fibonacci analysis relies on historical data, and there’s always a risk of hindsight bias when applying historical data to decisions about the future. For this reason, Fibonacci analysis probably should not be applied as a standalone form of analysis. But it does have potential benefits, so let’s take a look at a couple of real-world examples of how some investors might apply the Fibonacci sequence.

## Finer Points of Anchoring Brackets

There are a couple of different tools that investors use to apply Fibonacci analysis. One of the most widely used is the Fibonacci retracement bracket. On the TD Ameritrade Trade Architect® platform, you can find this tool under Drawing Tools in the lower, left-hand corner of a chart. It’s called Fibo Retracement.

The Fibo Retracement tool is a bracket that extends from a low to a high in the case of an uptrend. The bracket divides the range from the low to high into different price levels based on the Fibonacci sequence. The resulting price levels can be used to identify potential support or resistance levels. Figure 1 shows a Fibo Retracement applied to a very long-term uptrend in the Biotechnology Index (\$BTK.X).

FIGURE 1: 10-YEAR FIBO RETRACEMENT OF \$BTK.X.

The Fibo Retracement is anchored at the financial crisis lows in 2008 and all-time highs in 2015. Chart source: Trade Architect® by TD Ameritrade. Not a recommendation. For illustrative purposes only. Past performance does not guarantee future results.

This is an example of how to identify potential support levels. Take note of the bracket’s anchor points, which define the move we’re measuring with the Fibo Retracement. In this example, I’ve used very long-term anchor points to measure an uptrend in the \$BTK.X starting all the way back near the depths of the financial crisis in 2008. About one year ago, the uptrend ended and the \$BTK.X began to trend lower. It was only after the \$BTK.X began to roll over and trend lower that I was able to identify where to anchor the upper end of the Fibo Retracement.

Now that we’ve looked at how to use the Fibonacci retracement brackets to determine support, let’s take a look at a market that’s trended lower and use the brackets to find resistance.

This time, I’m going to anchor the bracket from high to low on a downtrend. Figure 2 shows the Fibo Retracement applied to the Oil Service Sector (\$OSX.X). The \$OSX.X has been in a downtrend for about two years. I used an anchor point at the high from about two years ago and a second anchor point at the lows reached earlier this year.

FIGURE 2: TWO-YEAR FIBO RETRACEMENT OF \$OSX.X.

The Fibo retracement is anchored at the highs in 2014 and recent lows in early 2016. Chart source: Trade Architect® by TD Ameritrade. Not a recommendation. For illustrative purposes only. Past performance does not guarantee future results.

Here, the Fibo Retracement shows potential resistance levels for the \$OSX.X if it continues retracing its two-year downtrend. Note how the \$OSX.X stopped moving higher in late April near the first retracement level near 176.

## What’s With the Levels?

Now that you’ve seen examples of how to apply Fibonacci retracement brackets to an uptrend and downtrend, what can you do with this analysis?

Fibonacci retracements project potential future support and resistance levels. This is in contrast to support and resistance levels based solely on historical prices. (For more on the basic concepts of support and resistance, check out “Technical Analysis for Investors: Applying Support and Resistance.”)

Projecting potential future support and resistance is valuable because it can help investors determine potential entry points, define possible profit targets, and help with risk management.

Take the example of the \$BTK.X we looked at in figure 1. Suppose an investor observes the recent decline in biotech stocks and finds a few stocks in this sector with appealing valuations. How might the Fibonacci retracement bracket applied to the \$BTK.X help identify entry points? One possibility is that the retracement levels could serve as targets for entry points. For example, suppose the \$BTK.X drops to the 50% retracement level. It might find support from this level and bounce.

Fibonacci retracement levels can be used for target exit prices, too. Take the example of the \$OSX.X in figure 2. Suppose an investor decides to buy stocks in the oil services sector because of the big drop over the last two years and appealing dividend yields in the sector. She might use the retracement levels of the \$OSX.X as a general guide for price targets. For example, if the \$OSX.X rises to the 38.2% retracement level near 200, she might take profits in the stocks she owns, sell covered calls, or buy protective puts.

Another way some investors apply Fibonacci retracements is when managing risk. Let’s suppose an investor owns several biotech stocks and is worried about further losses in the sector. Going back to the example in figure 1 of the \$BTK.X, he could place a stop loss about 3% to 5% below a retracement level that aligns with his risk tolerance.

Using Fibonacci retracements to find potential entry points, target prices, and stop-loss levels are just a few of the ways the tool can be used. I encourage you to log in to your account on tdameritrade.com, launch Trade Architect®, and practice applying Fibo Retracements to stocks and markets you’re interested in. Experiment with different anchor points, measure uptrends and downtrends, and see if you can identify actionable support and resistance levels.