**Why Fibonacci?**

Fibonacci Analysis is one of the most valuable and easy to use tools that we have as market participants. I’ve studied supply and demand behavior for over 15 years and I find myself using Fibonacci tools every single day. These tools can be applied to all timeframes, not just short-term but longer-term. In fact, contrary to popular belief, technical analysis is more useful and much more reliable the longer your time horizon. Fibonacci is no different. Here is the S&P500 going back to the peak in 2007. After breaking out in 2013, the market stopped at exactly the 161.8% extension of that entire 2007-2009 decline. That wasn’t a coincidence. I’ll do my best to explain why throughout this page.

**Many of Them Hate Fibonacci**

First of all, let’s discuss the “stigma” that surrounds Fibonacci analysis. The academic community hates it and I think the fundamental guys hate it even more. The funny part is when markets are crashing, they’re the first ones calling us technicians asking which are the next levels to watch. We hold our heads up high and just tell them, and let them keep convincing themselves they don’t need to analyze price behavior. It’s their loss, not ours.

Media-wise, they definitely hate it. On two separate occasions, on two different TV networks, I’ve been told my the producer a couple of minutes before going on live that, *“We don’t use words like Fibonacci around here, so please do not mention that”*. I kid you not.

Here I am on Bloomberg TV explaining to the lovely Trish Regan that our downside targets in Blackberry are based on off of key Fibonacci Extensions:

**History of Fibonacci**

If you are not concerned with the math behind the tool, **skip down to Execution**

We first see Fibonacci in Indian mathematics and is attributed in part due to work done in 200 BC by mathematician and author Pingala. We don’t know much about the author, but outside of India, the Fibonacci sequence first appeared in *Liber Abacci* in the year 1202, a book on arithmetic written by Leonardo of Pisa. We know him today as Leonardo Fibonacci. There is a statue of the original Big L in Pisa, Italy. It’s hard to find, but I explain how to locate the statue here for future math nerds on vacation.

In his book, Liber Abacci, Leo the Hero introduces the Fibonacci sequence to Europe and posed the following problem:

**The Problem**

Fibonacci imagines a biologically unrealistic scenario for the growth of a population.

How many pairs of rabbits placed in an enclosed area can be produced in a single year from one pair of rabbits if each pair gives birth to a new pair each month starting with the second month?

**The Solution**

The amount of Rabbits increasing as months pass by is the Fibonacci sequence. What we know is that each pair including the first pair needs 1 month to mature. Once the pair of rabbits are in production, they birth a new pair each month. Since they need a month to mature before, the number of pairs is the same at the beginning of the first and second months. That’s why the Fibonacci Sequence starts with 1,1.

In the second month, the first pair doubles so the sequence expands to 1,1,2.

*From **Robert Prechter*

Moving on, the oldest pair now gives birth to a 3rd pair so to begin the 4th month, there are now 3 pairs. The Sequence is now 1,1,2,3

Now with 3 pairs of rabbits, the oldest 2 are in production but not the youngest pair. So the older 2 reproduce making it a total of 5 pairs of rabbits. This takes the sequence rto 1,1,2,3,5. The following month, 3 pairs give birth, but not the younger 2, so it makes it 8 in total

After 12 months, there will be 144 pairs of rabbits.

**The Golden Ratio**

But it’s not the answer to the problem that is brilliant. What we want to focus on is the way in which we arrived at the solution. You see, if you add up any two adjacent numbers in the sequence you’ll arrive at the next number in the sequence. 1 plus 1 equals 2. 1 plus 2 equals 3. 2 plus 3 equals 5. 3 plus 5 equals 8 and it goes on and on….

This Fibonacci Sequence is how we calculate the Golden Ratio. After the first few numbers in the sequence, the ratio of any number to the next higher number in the sequence (adjacent to right) is approximately 0.618 to 1. Also, the ratio of any number to the next lower number (adjacent to left) is approximately 1.618 to 1. The further along you go into the sequence, the closer those ratios approach 0.618 and 1.618.

Feel free to follow along on your calculator. 34 divided by 55 gives you point 0.618. If you move along the sequence and divide 610 by 987, once again you get 0.618. Now, flip the math and divide each by the previous number in the sequence. For example, 89 divided by 55 gives you 1.618. 377 divided by 233 gives also gives you 1.618.

**Execution**

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There are two simple ways that these Fibonacci numbers can be used. Retracements, which are for counter-trend purposes, and Extensions which are used for ongoing trends. Both can be very helpful in downtrends as well as uptrends. I find Fibonacci analysis more helpful in long-term uptrends. Even if you’re a shorter-term trader, Fibonacci analysis done on your short-term time horizon is going to be more beneficial, in my experience, if it is in an asset that historically has gone up over time. To the downside, I would argue that the longer-term downside extensions rarely work. But in the shorter-term extensions absolutely do. We’ll get into the dynamics of it now, but I wanted to preface with that so you have that context as we move forward.

**Retracements**

For retracements, we’re looking for the end or at least a temporary pause after a counter-trend market move. In other words, we’re trying to find a target for a sell-off within a larger uptrend, or an end to a rally within a larger downtrend. Here is an example of the 61.8% retracement coming into play within an ongoing downtrend. This level represents approximately 61.8% of the entire decline, peak to trough:

These Fibonacci levels can be used to calculate targets regardless of the asset class. We can be looking at U.S. stocks or sector ETFs, Indexes like the S&P500, Futures Markets, Currencies, etc etc. Also, remember that the market is fractal. These levels often come into play on longer-term weekly timeframes, intermediate-term daily timeframes, and even intraday.

NOTE: when I draw these lines, I don’t calculate the exact low to the penny or exact high to the penny. Some software providers do that for you automatically but others don’t. It doesn’t matter either way. We just want to get very close. With Fibonacci, or with support and resistance and even trendlines, we want to draw these levels with crayons, not sharpened pencils. So you’ll never see my Fibonacci extensions match up to the penny. My time is better spent doing other things. Besides, the market doesn’t react to the penny either, it respects the areas. That’s the point of this. Think of supply and demand like a mattress, with a little bit of give.

Here is a chart of JP Morgan $JPM back in 2009-2011. The stock put in its epic bottom in March of 2009 along with many others at the time, and then went on to rally into the Spring of 2010. The ultimate low in 2011 came at exactly the 61.8% retracement of that entire move from low to high in 2009-2010:

This is Chevron going back to the low in 2003. If you take that historic low all the way to the epic energy stocks top in 2014, the low for $CVX in 2015 was exactly the 61.8% retracement of that entire move:

**Extensions**

Next, I want to talk about extensions. These Extensions help when we are looking for targets within an ongoing market move. In other words, we’re trying to find an upside target within an ongoing uptrend after taking out a prior high or trying to find a downside target within an ongoing downtrend after taking out a prior low. Here is an example of the 161.8% extension coming into play within an ongoing uptrend. This is the level we set once prices have exceeded the prior highs. The level in red represents approximately 161.8%

Here is a chart of the Oil & Gas Exploration and Production ETF $XOP from 2009 through 2014. You can see the peak in early 2011 followed by a swift decline in to the late 2011 lows. After finding support near those 2010 lows around $37, prices rallied all the way back to the prior highs. In 2013, prices exceeded those former highs and “broke out”, if you will. You can see starting in early 2014, prices started their next leg higher. The target becomes the 161.8% extension of that entire 2011 decline. Notice how prices stalled right and immediately started falling:

**$XOP**

Here is Tesla in 2017 getting up to the 161.8% extension of the 2014-2016 decline. This doesn’t just happen by coincidence.

**$TSLA**

The same can be seen to the downside during downtrends. Here we are looking at the Euro vs the U.S. Dollar $EURUSD in 2012. This market put in its low in early 2012 and went on to rally for a couple of months. All of this was within an ongoing downtrend. Once prices in May took out those former lows near 1.26, the next logical target was the 161.8% extension of the prior rally. This gave us a target just under 1.21 which is precisely where $EURUSD found its bottom that Summer and then went on to rally and make new highs:

**$EURUSD**

Within ongoing uptrends, once the 161.8% extension has already been hit and exceeded, we want to calculate the 261.8% extension of that same prior move. Rather than dividing the numbers along the sequence by the number directly adjacent to the left, we divide by the number 2 spaces to the left:

In these examples you can see that 144 divided by 55 (2 spaces to the left along the sequence) gives you 2.618 or 261.8%. You get the same answer if you divide 2585 by 987 and ever combination moving on gets closer and closer to exactly 2.618.

Here is a good example of the Consumer Discretionary Index Fund $XLY hit the 261.8% extension of the entire 2007-2009 decline and immediately stopped. It took 15 months of consolidation before it was able to get through this level of resistance:

Here is an example of $ASML breaking out in early 2017 above former resistance from the 2015 highs. Upon this breakout, our Fibonacci analysis gives a target just around 137 based on the high in 2015 and low in 2016. The market respected that level, consolidated, and then break out again above the 161.8% extension. This is normal for a strong uptrend. This level now becomes support with our next target above 173, which of course is based off the 261.8% extension of the 2015-2016 correction. The thought process after the breakout above 137 is that we only want to be long if we’re above that. Below that level and things get hairy:

Here is Amazon in the Fall of 2016 running into the 161.8% extension of the correction earlier in the year. After 4-5 months of consolidation, $AMZN prices were above to stay above that 834 level, where that former resistance turned into support. The next logical level was 1056 and prices reversed hard from there. Sometimes you’ll even see a slight overshoot like this that is only temporary:

Notice how the slope of the trend accelerated once the stock was finally able to get through the 161.8% extension. We can see a similar phenomenon in Kansas City Southern $KSU. As you can see below, prices stalled in late 2012 near the 161.8% extension of the 2008-2009 decline. After some consolidation, once prices were able to break out again, things really started moving fast. This should be expected.

In the case of Kansas City Southern $KSU, prices were unable to exceed the 261.8% extension after failing twice. Down we went from there. The inability for prices to get beyond this extension level is information in and of itself. From an execution standpoint, once our upside targets are hit, in this case 126, there is no reason to be long unless we are above 127. That’s the mentality here: we want to know that we’ve cleared this level before getting as aggressive again as we did once price got through 83 in late 2012.

For larger trends, we can even go beyond the 261.8% extension, in which case the 423.6% extension comes into play. This is calculated by dividing each number by the number 3 spaces over to the left. The The support and resistance principles mentioned above can also be applied here:

After that we can extend to the 685.4% extension by dividing each number by the one 4 spaces to the left:

And so on and so on:

**1.618 2.618 4.236 6.854 11.090 17.944 29.034 46.979 76.013 122.992 **

Also, these Fibonacci levels are not just resistance within uptrends, but are often levels of support during corrections within these uptrends. Here is a good example of Bitcoin, where in most cases, these levels were not just resistance, but also became support on the kickback:

Tyson foods is a good example of this. We have our Fibonacci levels up from the 2007-2009 decline, which was the most important correction in this entire chart. Notice how the 161.8% extension didn’t so much turn into resistance, but was actually important support. The exact same thing occurred with the 261.8% extension. The market can react to these important levels from both support and/or resistance:

Fibonacci needs to be used in conjunction with other tools. This isn’t some kind of holy grail. Fibonacci is only a supplement to price itself that we use in order to identify the direction of the primary trend. That’s all it is: a potential level of significance where buyers and sellers tend to gather. This example of Tyson above is a great one to add other indicators:

The moving average is used to help identify that the trend has been up and then the momentum indicator below also confirms this. So when prices are holding above a key Fibonacci extension, and momentum and the smoothing mechanism are confirming the uptrend in price, the more conviction we can have holding a long position against that level. In other words, we would keep stops below that extension level and/or only be long if we’re above it.

One thing I would like to reiterate is that only price pays. Supply and demand is based on support and resistance defined by prior levels where shares changed hands. Fibonacci, just like every tool outside of price, is only supplemental. Fibonacci works best when key levels coincide with former support or resistance. But again, all of this is just a supplement to price, just like volume, or momentum, or the use of smoothing mechanisms, or sentiment or seasonal studies. Only price pays, but Fibonacci certainly helps. In most cases, it helps a lot!