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.
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
This ratio is usually represented by the Greek letter phi. The proportions of phi, the golden ratio, and its formula are shown here.
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.
The formula to generate this series is
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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|↑1||Data source: Yahoo finance. All charts and graphics created by Badinvestmentsadvice.com|