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Fibonacci sequence stock trading

What is Fibonacci sequence stock trading, does it work and why do traders use this method and what if anything does it have to do with the golden ratio? These are all good questions that we will look into here.

The golden ratio or golden mean

OK this is a topic I could get lost in. But fear not. I will control myself and do my utmost to stick to the point.

Golden ratio architecture

Mathematicians in ancient times, which back then meant most clever people, noticed that a particular number and ratio kept cropping up in nature. Artists and architects famously made use of this ratio between the main vertical and horizontal elements of their works as it was naturally pleasing to the human eye. This ratio was known as the golden ratio, or the golden mean and expressed in numbers is

Golden ratio

This ratio is usually represented by the Greek letter phi. The proportions of phi, the golden ratio, and its formula are shown here.

Golden ratio with shell

The Fibonacci sequence

Parking the golden ratio to one side for the moment, in the year 1202 Leonardo Fibonacci wrote a book that included a sequence of numbers, starting with zero and 1, where the next number in the series is the sum of the previous two numbers. The start of the Fibonacci sequence is as follows.

Fibonacci number sequence

The formula to generate this series is

Fibonacci sequence formuka

How the Fibonacci sequence connects with the golden ratio

If you are wondering what all of this has to do with stock trading, we’ll get to that soon.

But first, we note that if you take the ratio of each number in the Fibonacci sequence to the previous number in the sequence, the higher up you go the ratio converges to the golden ratio of 1.61803, etc. For example, the 25th number in the sequence is 46,358 and the 26th number is 75,025 and 75,025 divided by 46,358 is 1.618033989. Here is what that looks like on a graph.

Fibonacci convergence to golden ratio

So what ? you may ask.

Well without going into any more of the maths or getting into detail the implication is that the Fibonacci sequence is a natural sequence of numbers that shows up all over nature. By that, I mean in the repetitive fractal patterns found in ferns, snowflakes, and seashells just to name a few.

Fractal pattern

Fibonacci ratio percentages

We still haven’t got to trading stocks yet I know but we are nearly there.

The Fibonacci series of numbers can also generate a further series of ratios from within itself.

You take a number some way into the list, say the 50th number. You use that as a denominator then calculate the ratios of the earlier numbers in the sequence in relation to that number. We end up with a sequence of ratios that also converge to the same numbers the higher up the sequence you go. This is easier to see in a table.

Fibonacci ratios table

These are the Fibonacci percentages used in Fibonacci retracement trading. The ones most used are

100%, 61.80%, (50% added and explained later) 38.20%, 23.61%, while the smaller percentages, 14.59%, 9.02% and 5.57% are rarely used.

Why and how does this work?

Since the Fibonacci numbers are used in nature, this also applies to human psychology. And since human psychology drives supply and demand for stocks on exchanges, these ratios show up in percentage relationships between successive levels of price support and price resistance in a traded stock.

OK, I’ll admit the “why” is a little flimsy. So let’s look at the “how” instead.

I guess at some point hundreds of years ago when clever people weren’t called scientists but natural philosophers. So these natural philosophers were studying market price movements, knowing how Fibonacci numbers appear all over nature they would logically look to find evidence of Fibonacci numbers in stock price movements and particularly price reversals.

Like so much in technical analysis, word got around about some clever trader using Fibonacci numbers to predict price movements. Everyone else started to do the same and so it became a self-fulfilling prophecy.

Golden ratio stairwell

Halfway mark

The Fibonacci ratios used in trading insert a 50% mark as the third number in the sequence counting down. Natural and fractal patterns notwithstanding, if traders are looking for price breakpoints halfway has a good feel to it so everyone who uses Fibonacci ratios includes 50% in the sequence.

Fibonacci ratios in action.

To test this out we’ll use the State Street Global Advisors Standard and Poor’s 500 index-tracking ETF which goes by the symbol SPY. If we cast our minds back to around 25 March 2020. We had seen the SPY hit an all-time high in February and the SPY hit a high of $334.89 on 19 February 2020.

Since then the index had a precipitous fall to a low on 23 March and SPY closed on that day at $221.97. Watching trading volume we just saw two days of what looks like a reversal, most of the sellers have been shaken out and the market looks like it might be starting to climb back up. SPY closed on 25 March at $245.71.

Assuming we were watching this closely this is what we would have seen at this point in time.

SPY Feb to March 2020

1)Data source: Yahoo finance. All charts and graphics created by Badinvestmentsadvice.com

If we decide it is time to buy we would want to know where we think the price is headed before it is likely to hit resistance again. This is where the Fibonacci ratios can be used.

We set a horizontal line at the price low point and make this the 0% line. We set another horizontal line at the price high point and make that the 100% line. We then add horizontal lines at the Fibonacci ratio percentages. This is what our chart would look like.

SPY Feb to March 2020 w Fibonacci lines

Assuming we had decided to buy at this point, we would be looking for price resistance at the Fibonacci levels. Here is what happened next.

SPY Feb to March 2020 38.2pc resistance

Here we can see already in early April the price seems to have hit resistance at the 38.20% level. We could opt to sell and take profit at this point, or ride it further and hope. Or better watch the volume and other indicators to inform a decision.

Here is what happened next.

SPY Feb to March 2020 23.61pc support

So the price pulled back from the 38.20% line but then met support at the 23.61% line. After that let’s see what happens.

SPY Feb to March 2020 til June

The price of the SPY then went on to break through the 50% line. It traded in the range between support at the 50% line and resistance at the 61.80% line until if finally broke through the 61.80% resistance around 20 May 2020.

What Fibonacci levels mean for trading

The use of Fibonacci ratios as demonstrated here is referred to as Fibonacci retracement levels. It refers to the fact that the price is projected to meet resistance and support levels in a range where it previously traded.

Traders want to know the projected levels of resistance and support as being price points to either exit or enter long positions or enter and exit short positions respectively.

Fibonacci levels can also be used to project price resistance and support levels in previously uncharted price territory.

In an example where the price of a stock has just broken through a previous all-time high, you would look for a previous low price, measure that distance from the high and set a new high above the previous all-time high by the same amount. Then divide the space between using the same Fibonacci ratio percentages.

Fortunately, to do all of this on an online brokerage platform you shouldn’t need to fumble around with Excel or a calculator. Any decent online brokerage platform should allow you to set up Fibonacci levels automatically just by setting the start and endpoints. And if they don’t then you might want to look for another broker.

Other graphical uses of Fibonacci

Here we used the Fibonacci ratios to draw horizontal price levels which were met at some point in the future when the price moved to those levels. The same Fibonacci ratios can be used to chart in arcs around key price events and when price patterns are showing signs of convergence or divergence. This adds the factor of time into the projections.

But more on that another time.

Does Fibonacci retracement actually work?

We saw here in this example that it did work, some of the time. But there were also price corrections that happened at other price points in between the Fibonacci levels, so the method does not appear to be infallible.

The general experience among traders is that similar patterns are often seen after a major price reversal. The price tends to cross the 23.61% level and meets its first resistance at the 38.20% level. It then pulls back to the 23.61% level where it meets support and heads back to the 38.20% mark where it may breakthrough.

As I said before, a lot of this is going to be self-fulfilling prophesy because so many traders are setting market orders according to Fibonacci levels.

What strategies work with Fibonacci ratios?

Many trading strategies work with Fibonacci ratios. The Fibonacci levels are best used with other indicators such as MACD, volume, and the relative strength index. Like all indicators, they have their weaknesses and should not be relied upon without noting what is going on in the broader market.

Fibonacci levels are best used to point towards likely price corrections, trend reversals or price bounded within a range.

To learn more about Fibonacci retracement, check here.

This is a summary pdf on Fibonacci retracement percentages, and you can download it here.

Fibonacci retracement percentages PDF


I hope you found this article interesting and useful. Do leave me a comment, a question, an opinion or a suggestion and I will reply soonest. And if you are really inclined to do me a favor, scroll down a bit and click on one of the social media buttons and share it with your friends. They may just thank you for it.


Disclaimer: I am not a financial professional. All the information on this website and in this article is for information purposes only and should not be taken as investment advice, good or bad.


Affiliate Disclosure: This article contains affiliate links. If you click on a link and buy something, I may receive a commission. You will pay no more so please go ahead and feel free to make a purchase. Thank you!


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1 Data source: Yahoo finance. All charts and graphics created by Badinvestmentsadvice.com

Andy

26 Comments

  1. Wow Andy, u sure know a lot about Financial Markets. Fibonacci sequence stock trading is such a complicated thing to understand. U seem to have mastered this.  I wonder if the Fibonacci retracement actually works with the Stock market. It seems a fairly decent comparison, and one that is convincing too. I will give this a look because i trade stocks everyday. 

    Aparna

    • Hi and thanks for the comment. I was looking around for any studies to see whether anyone has done any analysis on the success rate of Fibonacci projections but I was not able to find any. I know that the general impression of many who do use it that it does work most of the time. Most brokerage platforms will provide this as a feature so you just need to set the start and the endpoints and they will do all the calculations for you. Best of luck in the markets. Kind regards, Andy

  2. Hi, we’re currently reading into investing and trading and still have a long way to go before we fully understand anything. I have however stumbled across the Fibonacci sequence trading but this article explains it beautifully in a way easily memorised, it’s concise and informative. Will use this article as reference once I’ve learnt a bit more. Thank you

    • Hi and thanks very much for your comment. You may want to check out some of the other articles here which look at technical analysis more broadly and then other price indicators more particularly. Thanks again and best regards, Andy

  3. Wow.
    This is the closest I’ve come to understanding why technical analysis works for some traders.
    I will probably have to come back to this for the latter half as I know I haven’t taken it all in- due to me needing sleep and coffee, not at all because of the content, it’s really well written and well presented.
    I will be sharing this with my cousin who has been learning to trade at the same time as me, and he has definitely been leaning more toward the formulaic side of things.

    My favourite part of this is how data and numbers tend to fall in line with the natural world and how the universe works. Makes it much easier to understand scientifically!

    Thanks for the good work!
    Tony

    • Hi Tony and thanks for the comment. As you might be able to tell I am a bit of a fanatic about finding links between ancient knowledge and the present day so I had a lot of fun putting this piece together building it from first principles and trying to walk through the steps without skipping over anything or making leaps of faith. I hope you find as much if not more from it on the second read. Thanks for the comment. I would be very interested to hear any comment suggestion or question your cousin may have. Thanks again and best regards, Andy

  4. I find it interesting how the Fibonacci sequence works in nature, like the example you gave with snowflakes. It is fascinating how this can be applied to stock trading. Although I do not understand much about stock trading, I found it explained a lot to me about stock trade patterns. I didn’t know that many traders set market orders according to Fibonacci patterns.
    Very interesting!

    • Hi and thanks for the comment. I know this phenomenon comes as a surprise to many people. On the other hand, if you remember that the psychology or what price proportions seem right to people will drive prices does seem reasonable. As regards whether many traders use Fibonacci ratios, again we have to remember that it is the large institutional investors who drive the market, so what most individual investors do doesn’t have much influence. Thanks again and I am glad you found it interesting. Best regards, Andy

  5. Very interesting read! I’ve heard and read about the Fibonacci sequence occurring in nature but never in something constructed by man, such as the stock market. You provided very clear and insightful evidence that trading at benchmarks using the sequence actually works. I will definitely have to give that a try next time I decide to invest in stocks.

    • Hi and thanks for the comment. AS with all indicators and investing and trading decisions I would take care to consider what is going on in the broader market and looks for clues from multiple indicators. Thanks again and best regards, Andy

  6. You did a great job ! I believe that this is information that can’t be found on the web easily and you decided to share it with others for free, that’s really great!

    I didn’t know much about Fibonacci stock trading but I’ve been always interested to know more about this topic and your comprehensive guide helped me a lot. I don’t know if you wrote this post 100% by yourself or got help from other sources as well, anyway, it has really brilliant information which convinced me to share it with my friends on social networks.

    I think, the Internet needs more quality posts like yours these days, especially when we see a lot of crappy ads and scams about this topic. You can’t read a post easily on a website without seeing tons popups but your site and post is an ideal example of a quality article which is not covered by annoying ads, has very useful information and lets readers enjoy reading every piece of it.

    Thank you again and I wish you continue providing such that quality information in the future which turn the Internet and blogs into a better place to surf!

    Best,
    Ali

    • Hi Ali
      Thanks for your comment and for taking such an interest in the topic. I’ve used Fibonacci ratios to look for price points for a while now on my brokerage platform and it does it automatically. For this article, I went back to basic math sources mostly on Wikipedia. All the calculations in the article I did from scratch using the formulae. I didn’t actually know how the ratios were derived from the Fibonacci sequence but I had an idea – you know one of those ideas that come to you at 2.30 am. When I woke up I tested the idea and it worked. In subsequent research, I found explanations of how the ratios were derived which confirmed my approach. Rather than use my brokerage platform to chart the movement of a stock price I found the raw data on Yahoo Finance, credited them of course, and built the candlestick chart in Excel. I didn’t actually know that the Fibonacci ratios would show levels of price support and resistance for that piece of stock price history until I tried it – and they did. So in many respects, this post was quite a genuine piece of statistical research in ways that may not be evident to the casual reader.
      Thanks again for your comment.
      Kind regards
      Andy

  7. I’m fascinated with the Golden Ratio ever since I was a little kid. I even tried adding until I get to 7 digits to see if there’s ever an end to the ratio. I didn’t know it’s relevant to stock trading until now.

    I failed miserably when I try stock trading. I used that scaling up method my professor told me back in college, and it just didn’t work when one time a couple of shares just plummeted down to zero and I lost all my money. The scaling method is only effective if the share price will rise a little after it goes down. It doesn’t work when the price goes down to the ground. 

    • Hi and thanks for your comment. That was an unfortunate first experience of stock trading. Unless we are very fortunate I think our first forays into the stock market are likely to be losers. In the example you gave it sounds like you were trying to read a pattern in stock price movements and project to what should happen going forward. And then it didn’t happen. When it comes down to it, none of us has a crystal ball. If you get another chance I would suggest trying a less risky approach and take a position in an index-linked ETF – especially if you can get in after a market correction. Good luck and thanks again for the comment. Best regards, Andy

  8. Hey! Boy do you know your stuff. So much work has gone into this article. I have dabbled in trading before but nothing major. I have never come across this sequence before but it is very interesting, especially the way you have explained it. I have definitely been educated a lot more now. Thank you for this informative piece.

    • Hi and thanks for your comment I really appreciate your positive feedback. I suppose I was a bit indulgent in getting into the details of how it all worked and where it all comes from. On the other hand, the research and working through the numbers certainly served to consolidate my understanding as well. I am very glad you found it informative and I hope useful. Kind regards, Andy 

  9. Hi Andy, what an interesting read! 

    I knew Fibonacci existed but never bothered to find out more about the sequence on how it works and what it means. I was taught to trade on a clean chart so I hardly use any indicators. 

    However, I do have to admit I am totally fascinated with the information you are sharing on how the Fibonacci method is used in trading. You did a great job by giving examples, it is easier to understand. Thank you. Marisa

    • Hi Marisa, thanks for the comment and I am glad you liked it. I am impressed – taught to trade on a clean chart. I would think you look at volume at least and are you just looking at candlestick patterns. Anyway, I must admit I learned a lot digging into the background and the arithmetic. Thanks and have a great day. Andy

  10. Hi Andy,

    Thanks so much for introducing me the Fabonacci sequence stock trading. I am interested in learning about trading because I know it becomes a trend nowadays. However, Fabonacci sequence is sure seems to be complicated for me as I have never been good at math and I am so new with trading. That said, I believe someone like you who understands how this works, combine this ratio with other trading strategies you mentioned in your post, and have been trading for a while will find this as one of a great method in studying market price movements, etc so you’ll get better results.

    Keep up on sharing cool post about trading strategies, Andy. I enjoy learning something new every time I visit your website. 🙂

    Ferra

    • Hi Ferra and thanks for the comment. I am glad you found it informative. As I noted in the article, most brokerage platforms will allow you to set up all different kinds of Fibonacci studies on charted price movements including the simple one illustrated here with just a few mouse clicks. Please do check out the other articles on this site and let me know if you have any comments, concerns, questions, or suggestions. Thanks again and best regards, Andy

  11. Hello Andy, Just went thru your article. It seems you know a lot about Financial Markets. Fibonacci sequence stock trading is such a complicated thing to understand for the layman. I think I mastered it.  I wonder if the Fibonacci retracement actually works. How does it work when compared with candlestick patterns for stock price movements? It seems a fairly decent comparison and one that is convincing too. I will give this a look because I trade stocks sometimes.

    • Hi Rajesh and thanks for your comment. I think in all honesty it isn’t entirely clear whether Fibonacci retracement and extension work for any genuine natural reason or just because so many people use the levels to set trading orders. I think the example I gave here shows that they seem to work some of the time. There are other examples on the web that demonstrate as well that they do work. To your question whether Fibonacci levels work with candlestick patterns, I think you can see some classic candlestick forms in the example I gave. But let’s remember price charting is more an art than a science. Thanks again and best regards, Andy 

  12. Thanks so much for this article especially on Fibonacci stock trading. Fibonacci ratios i.e. 61.8%, 38.2% and 23.6% often find their application on stock charts. Whenever a stock moves either upward or downward sharply, it tends to retrace its path before the next move. The Fibonacci sequence is a series of numbers, where a number is found by adding up two numbers before it. Fibonacci studies do not provide a magic solution for traders. Rather, they were created by the human mind in an attempt to dispel uncertainty. Therefore, they should not serve as the basis for trading decisions. Most often, Fibonacci studies work when no real market-driving forces are present.

    • Hi and thanks for the comment. It sounds like you have some experience of Fibonacci level, maybe some positive and some not so positive. I think that is quite common. Sometimes support and resistance at the Fibonacci levels are clear to see, other times not. As to Fibonacci being made up by the human mind, in essence, that is clearly the case. Though Pythagoras and adherents to his approach would say that mathematics and nature are intimately entwined and the Fibonacci sequence is just one expression of that closeness. Thanks for your thought-inspiring comment. Best regards, Andy

  13. Thank you so much for sharing with us an interesting and research article. The main subject of this article is the Fibonacci sequence stock trading. It is truly commendable that you have demonstrated this topic so well in your article. I have learned a lot by reading your article and gained a lot of comprehension about it. Of the points mentioned in your article, I like Fibonacci ratios in action. I’m not even a financial analyst yet I found this explanation of Fibonacci levels from the link shown in your article for which thank you very much.

    I would like to share your article in my Facebook group so that everyone can know about it.

    • Hi and thanks for your positive comment. I am glad that you found it interesting. I also learned a lot from researching this topic. Best regards, Andy

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