There is an observable pattern to the way the natural world is formed, if you know how to look. It’s a visible pattern that emerges from the growth of every tree, flower, and plant. Surprisingly, this pattern also applies to how we conduct business, including in the stock market. The pattern is called the Fibonacci sequence: a series of numbers that generates the next number by the sum of the previous two.

For example: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.

As these numbers emerge in nature, so does the ratio of 1.618—referred to as the Golden Ratio. Almost everything in nature has properties of the Golden Ratio, and as many traders have discovered, the stock market follows this pattern, too.

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Fibonacci the Mathematician

In the 1200s, a young mathematician contemplated the following question:

“If a pair of rabbits is placed in an enclosed area how many rabbits will be born there if we assume that every month a pair of rabbits produces another pair, and that rabbits begin to bear young two months after their birth?”

The question seems odd, but the answer turned out to follow the Fibonacci sequence—a naturally occurring recursive doubling sequence that leads to exponential growth. This sequence can be seen all across nature; it’s the way limbs grow from tree trunks, how leaves grow on the stems of flowers, and how green onions grow their tops.

Fibonacci in the Stock Market

Fibonacci ratios, referred to as “retracement ratios,” are used in the stock market to identify potential price reversal levels. The ratios are derived from the distance between Fibonacci numbers. For example, three popular ratios are derived from the three Fibonacci numbers: 21, 34, 55.

(34-21)/34 is a ratio of 38.2%; (34-21)/55 is a ratio of 23.6%; and (34-21)/21 is a ratio of 61.8%

These ratios are applied to price charts to see where the retracements fall. Despite the complexity of the math, it’s not reserved for complex trades. For example, you can apply these ratios to price charts for any stock, including something as basic as wheat futures. In fact, it’s often beneficial to do so. Wheat is a popular futures contract, and for good reason.

RJO Futures says Chicago SRW wheat is “the most liquid wheat futures contract in the world, trading the equivalent of more than 15 million tons each day in 2013.” Applying the Fibonacci retracement ratios to a stock you’re already successfully trading can give you an even bigger advantage to calculate risk.

According to TradingMarkets.com, “Fibonacci analysis is a way to forecast levels of support and resistance and project price targets. It can be used to set stops as well as timing entries, however, the most valuable information is what it can tell us about risk.”

Putting Fibonacci into Action

To create the retracement chart, traders take two extreme points like a peak and a trough, and divide the vertical distance by three main Fibonacci ratios: 23.6%, 38.2%, and 61.8%. Horizontal lines are then created at each level to pinpoint potential levels of resistance and support.

Identifying these points can predict the potential points at which an asset’s price might reverse.

The Fibonacci ratios are just one indicator you can use as part of your trading strategy.

Where Did These Ratios Come From?

In the 1200s, a young man in his 20s named Leonardo Pisano Bigollo became captivated by mathematical ideas from India. Part of an important trading family, he traveled through the Middle East where he was exposed to these mathematical concepts. Returning to Pisa, Bigollo published the concepts in a book called Liber Abaci, which became a phenomenon across Europe and made him the most revered mathematician of his time.

Bigollo, lovingly referred to as Fibonacci, didn’t just outline mathematical concepts in his book. He wrote a discourse on how they applied to commerce.

At the time his book was published, Western civilization was still using Roman numerals, which made complex mathematics impossible. When Fibonacci came back from his travels, he brought with him the number system we use today called Arabic notation (originally from the Hindu system). Fibonacci detailed this number system in his book.

This new number system opened up new possibilities for the Western world that transformed mathematics, science, and commerce. To put it into perspective, imagine trying to solve complex algebraic equations using the Roman numeral system—it’s virtually impossible.

In this way, the Western world was limited by its number system without knowing it, and what Fibonacci brought back expanded our understanding and our ability to expand our worldview.

How have you seen the Fibonacci sequence at work?

Comment below!

Larry Alton is a professional blogger, writer and researcher who contributes to online media outlets and news sources. A graduate of Des Moines University, he still lives in Iowa as a full-time freelance writer and avid news hound. In addition to journalism, technical writing and in-depth research, he’s also active in his community and spends weekends volunteering with a local non-profit literacy organization and rock climbing.

1. Disclosure: 90% of stock traders lose money. DON’T DO IT! Buy and hold index funds until you’re within about 7 years of retiring. Trying to use technical indicators to time the market is a FOOL’S ERRAND! And if you’re on this website then it’s because you want to learn about real estate. Don’t get derailed by trying to get rich quick with the stock market. Focus on being an expert in real estate! Fibonacci is not your key to success in the stock market.

Actually, if any of you hear your mechanic or uber driver trying to give you stock tips, let me know so I can start selling.

• Disagree. Trading the market isn’t a “get rich quick” scheme. If you go into any significant investing opportunity thinking that you’re bound to fail — including REI. I only trade options off technicals and have been quite successful doing that for several years now. In addition to real estate. I make money wherever money’s being made.

• I’m glad you’ve been successful doing it. But the last several years have also been the EASIEST time to make money in this stock market. I’m guessing you made money buying calls? Or maybe selling puts? How many times did we even see the VIX above 15 in the last 3 years?

I would highly advise against anyone trying to learn how to trade the stock market. There’s a reason less than 15% of the top 100 equity hedge funds were able to beat the benchmark SP500. And those funds are full of the smartest people in the world putting in 60 hour weeks. Buy and hold and when the crash comes, scale into it.

2. Please don’t turn Bigger Pockets into some stupid get rich quick ponzi scheme. I have heard of Fibonacci and it is relatively bogus. Of course, every bloke is a genius when the overall stock market goes up 25% a year. The Dow has quadrupled since George W left town. And I liked George W.

Next you are going to be telling us to invest in Bitcoin.

Stick to real estate investing articles. They are plenty of places for stock pickers and options folks and all the rest to trade theories and war stories. Stocks are covered in the media every day. There are multiple websites including Bigcharts.com devoted to stocks. There are entire newspapers devoted to the stock market. Yes, my wife and I own a decent amount of stock and it has done real well the past few years. We are passive buy and hold investors.

Similar to real estate, there are no secrets and no gimmicks.

There are precious few resources devoted to mom and pop real estate investing. It is considered “exotic”, “alternative” and risky by the mainstream media. I really enjoy the articles by fellow landlords, fellow flippers and even the goofy note buying guys.

BP Editors: Please keep the focus 100% on Real Estate.

3. Another good post Larry. I have been a trader for aboit 20 years ish now. A great way to make money. Not very tax friendly however. Hence, my interest in realestate.

4. No idea whatsoever how this article was supposed to educate or enrich me. Perhaps we can start putting the names of blog authors on the listing under BP blogs so we don’t waste our time on stuff like this.

• Jerry,

I agree and have found the new and improved main blog page to be one of those “looks pretty” steps backwards. I never use it. I always go here:

https://www.biggerpockets.com/renewsblog/recent-posts/

From there you can always see the author.

I use it to find the authors who I love, like Andrew Syrios and a few others, and to avoid or skim the ones I don’t, ah hem.

5. Yup, Fibonacci retracement levels are like gold and always work… except for the 50%, 60%, or more of the time that they don’t. Been doing this a day or two…

The best rules I have learned over the last 30 years is: 1. The trend is your friend, and 2. Don’t catch a falling knife.

6. Total drivel

7. I came to Bigger Pockets after consuming the information at Boggleheads and wanting more. I suggest anyone here looking for stock/bond investment advise to go there. Similar DIY approach and SOLID information.

8. A very well written article. Someone who combines old and new technologies will certainly excel. Fibonacci has provided scientists with thousands of answers and Fibonacci numbers constantly appear in nature.
Learn to include Fibonacci numbers and sequences in your work, real estate, and life and watch the results.

9. Just because something might work on a few stocks does not mean it’s a valid strategy. Buying stock because some sequence is present does not mean it’s a good idea. You should only buy based on the underlying company. The same concept is used in real estate. You buy because of the price is good, not because some sequence of appraised values have been seen. I would caution anyone looking to follow this advice to look at the fundamental logic behind this method.

10. Oh my… where to begin with these comments? I rarely post comments here, but after reading some of these responses, well…

First off, I don’t recall a single thought from the article stating that Fibonacci numbers were some sort of “get rich quick” or Ponzi scheme. Larry’s point was simply that the Fibonacci sequence is another tool for analyzing levels of “potential” support and resistance levels. Another tool in a traders toolbox, that’s all. He offered some background in where the sequence came from, and how it is observed in nature. Can it have application in the market? Perhaps. But that is the point. Just as traders use moving averages, MACD histograms, RSI, etc, the Fibonacci is simply another tool.

And for those who believe trading the market is risky, be it equities, options, futures or forex, understand that many people are successful, just as many are unsuccessful, at any and all of these. It is certainly NOT a fool’s game, except for the uneducated fool. For an educated trader who knows how to use probabilities, manage trades, and hedge as appropriate, the market is another place to make money while minimizing risk.

Like others, I have been successfully trading for years, but I had to get educated. I took classes, and continue to do so. Any of you can do the same. You’re taking the time and effort to learn about real estate aren’t you? Well you can do the same for learning to trade the market.

• Todd, we do read and think, thank you very much. This is supposed to be a real estate investment site. There are many, many, many sites, newspapers, blogs, etc. devoted to stock picking, options, futures, and the like.

If you and your friends make money picking stocks, bully for you. I know it is possible to invest in stocks and futures during the day and manage a dozen rentals on the side. Nothing wrong with that.

Many visitors to this site are real estate newbies looking for some advice and help. All the various strategies, tactics, and tools for investing in real estate, notes, real estate lease options can get confusing even for serious people.

The last thing a confused real estate newbie needs is to get distracted by stock picking advice than may or not be of dubious value.

Editors of BP: Stick to Your Knitting. Dance with What Brung Ya. Stay Focused. You are one of the best resources for real estate investors of all stripes. Don’t let yourselves get distracted. Don’t let your readers get distracted. There are many more things to cover in the real estate world.
Don’t get involved in stock picking, Bitcoin, Sugar Beet futures or anything but real estate.

• prove to me that your trading has beaten the S&P 500 over the last 7 years and I’ll admit you are right.

and i said “fool’s errand”, not a “fool’s game”. the majority of those who try and “trade” the market will ultimately either lose money or will fail to make the same return that passive investing would have given them. and that small amount of people who can beat the market will only get smaller as markets become more crowded with algorithmic trading. the retail trader is at more of a disadvantage now than ever.

11. Fibonacci sequence is great for calculating the number of seeds in a sunflower head & the number of swirls in a Nautilus shell.
As far as whether it could explain the stock market I’m agnostic, but since the stock market is emotion driven, if everyone believes the Fibonacci theory applies I suppose it could influence the market. If everyone believes in reading chicken entrails or tea leaves then chicken & tea could run the market (“Tea leaves form a crow…SELL NOW…or wait, is it a bat? Buy!”).
As others have said, if I want stock timing info I’ll research the stock market. I’d rather follow the recent changes to the tax code, or find out about online real estate tools.
As interesting as the history of Fibonacci is, real bunnies more accurately depict a form of geometric progression. They typically have 4-12 offspring per litter, & can have one litter per month. They are fertile at 6 months of age, thus their first litter could be born at 7 month.

12. Gotta say I’m pretty disappointed to see this content on BP. If you could tell the future price of a stock based on a pattern in it’s past price history then everyone would be doing it. If you are going to write about trading on technicals then post some P&Ls to prove its efficacy. Otherwise please don’t peddle this stuff on a site dedicated to real estate investing. Warning to any amateur investor thinking about doing this: the validity of trading on technicals (chart patterns) has always been questioned on Wall St. Today the viability of these strategies for the retail investor is even lower than the past. While you are using a ruler to measure retracement patterns, thousands of high frequency hedge funds have servers running the algorithms and executing orders in nano seconds.

13. I have less trust in BP as a brand because it published this article.