0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377…do these numbers look familiar to you? Not really, right?

If not, then you definitely need to read the following material. These numbers are the root of one of the most important techniques for determining psychological levels in life and in trading.

Behold the mighty Fibonacci ratios!

## Origin of the Fibonacci Sequence

Hundreds of years ago, an Italian mathematician named Fibonacci described a very important correlation between numbers and nature. He introduced an interesting number sequence starting from zero and one (0, 1).

Have a look below, as we build a Fibonacci sequence:

0, 1

Now we perform the following calculation, where we add to the last number to the previous number in the sequence:

0 + 1 = 1

The result we get here (one) is the next number in the sequence. Thus, we now have the following:

0, 1, 1

Now we add the last number in the sequence to the previous number as shown below:

1 + 1 = 2

Then we add 2 to our sequence:

0, 1, 1, 2

We repeat the process of adding the last number in the sequence to the previous number:

1 + 2 = 3

…and the next one:

0, 1, 1, 2, 3

……and the next one:

0, 1, 1, 2, 3, 5

……….and the next one:

0, 1, 1, 2, 3, 5, 8

………….and the next one:

0, 1, 1, 2, 3, 5, 8, 13

We repeat this process as many times as we want!

Now you know how I derived the numbers in the beginning of the article - 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.

## Key Fibonacci Ratios

But what is so interesting about these numbers? As you probably guess, the fun part begins now!

So, Fibonacci discovered the following: every number of this infinite sequence is approximately 61.8% of the next number in the sequence. If you do not believe me, let’s dive into the math for ourselves!

55 / 89 = 0.6179775280898876 = 61.8%

Wow! Let’s double check!

233 / 377 = 0.6180371352785146 = 61.8%

Do you believe me now? No? Ok then:

144 / 233 = 0.6180257510729614 = 61.8%

I think this is persuasive enough!

However, this is not the only thing, which Fibonacci introduced. He also found out that every number in this sequence is approximately 38.2% of the number after the next one in the sequence:

13 / 34 = 0.3823529411764706 = 38.2%

21 / 55 = 0.3818181818181818 = 38.2%

55 / 144 = 0.3819444444444444 = 38.2%

144 / 377 = 0.3819628647214854 = 38.2%

And also, we have another ratio! Every number in the Fibonacci sequence is 23.6% of the number after the next two numbers in the sequence:

55 / 233 = 0.2360515021459227 = 23.6%

Note that these percentages can be retrieved from each number pair, which is part of the Fibonacci sequence, continuing to eternity.

## Fibonacci Ratios Everywhere

So, this is how the famous 61.8%, 38.2% and 23.6% Fibonacci levels appear. Later, traders added another level as an addition to the Fibonacci levels.

This is the 76.4% level which is 100 – 23.6. But, what is so important about these percentages? The truth is that these ratios are all over the place in nature. Look at this shell for example:

The volume of each part of the shell matches exactly the Fibonacci numbers sequence. Thus, each part of this shell is 61.8% of the next. It works the same way with this aloe flower:

The relationship here is the same as with the shell. If we separate the aloe flower into even particles, following the natural curve of the flower, we will get the same 61.8% result.

This ratio is not only found in animals and flowers. This ratio is literally everywhere around us. It is in the whirlpool in the sink, in the tornados when looked at through satellite in space or in a water spiral.

The Fibonacci ratio is constantly right in front of us and we are subliminally used to it. Thus, the human eye considers objects based on the Fibonacci ratio as beautiful and attractive.

It works the same way even with human faces! Faces with parameters (eyes to mouth distance, eyes to nose distance, ears to eyes distance) closer to 61.8% are beautiful and attractive to the human eye.

In this manner, big corporations like Apple or Toyota have built their logos based on the Fibonacci ratio. After all, we should not forget that these are two of the most attractive and engaging logos in the world.

These ratios can also be found in human behavior and psychology.

Example: Scientists say that the average person needs a bit more than 9 hours of sleep in order to be energetic and to lead a healthy life!

So, let’s take 9 hours and 10 minutes as an average time, which humans spend sleeping every day. This means that in the other 14 hours and 50 minutes we are awake. 14h:50m = 14.83 expressed as a decimal.

Let’s now see what percentage of the day we are awake:

14.83 / 24 = 0.6179166666666667 = 61.8%

Indeed!

Another example of Fibonacci ratios in people’s behavior is when we go out clubbing with cash in our pocket. It is proven that people get depressed when they spend more than 61.8% of what they have in their wallet.

You will say “But how does all of this apply to trading?” Relax! We are almost there!

It is the same in trading!

## Fibonacci Ratios in Trading

Once an impulsive move terminates, the price of the equity is expected to decrease 38.2% and eventually 61.8%. Since it is in people’s nature to “freak out” when stocks retrace, investors tend to change their attitude when the price moves 38.2% or 61.8% in the opposite direction.

Thus, Fibonacci Retracement is a common practice to seek support and resistance in case of trend reversal. Every equity trader always double-checks his decisions with the Fibonacci trading system in order to confirm psychological levels.

Fibonacci ratios, when applied to trading stocks, correlate two trends; let's refer to them as primary and secondary. The primary trend refers to a trending move in one direction while the secondary trend will refer to counter trend moves in the opposite direction. The three most common fibonacci retracement levels are 38.2%, 50%, and 61.8% of the primary trend and most basic stock charting applications will use these as standard levels. These fibonacci retracement levels act almost as magnets once the counter trend rally takes place. These are very common, however, there are a few other fibonacci levels that can provide resistance. These are the 75%, 78.6%, 87.5%, and 88.7% retracement levels. The common rule of thumb is that when the 50% retracement level is taken out, the four levels I just mentioned become magnets to attract price. Price action must be analyzed at those levels to understand if the countertrend move will cease or whether it will continue to fully retrace the primary move.

Fibonacci retracement levels are used by many floor traders and therefore become very relevant to your **fibonacci trading** activities. These levels are so widely used now by traders, including systematic trading, that they almost become a self-fulfilling prophecy. Some advanced traders will take it a step further and add fibonacci arcs and fibonacci fans to their trading arsenal, in search of an edge.

## Defining the Primary Trend

Let's start with the characteristics of the primary trend of which we would want to play the countertrend. I found that fibonacci retracement levels are most accurate after the primary trend has been a sharp move in price accompanied by heavy volume at the end of that move. These types of moves typically exist in the story stocks of the day or the appear on the list of highest percentage gainers or losers list which complements my trading style as these are the only stocks that I will trade.

I am asked many times how to define the starting and ending points in order to calculate the length of the primary trend. I see many traders make the mistake of using the highest point and lowest point of a trending move to define the starting and ending point of the primary trend. While this may work in some cases, it is best to look for double tops or double bottoms when locating your starting and ending points. This may or may not coincide with the highs or lows of the move.

## How to Use Fibonacci Levels

I do not use fibonacci levels as a primary trading technique, however, I found that it greatly improves my odds of generating a winning trade when fibonacci retracement levels start correlating with price objectives using other patterns, such as candlestick charting formations for example. I use fibonacci levels in two ways:

1) After identifying the primary trend, use price reversal pattern recognition (through candlesticks or any other trading technique that you employ) to coincide with a fibonacci retracement level to confirm that the countertrend move has ceased. I then look for the stock to test the recent lows and double bottom or break through that level. That is where I employ the usage of tape reading to determine whether I should play the double top/bottom or whether I should play a breakout in the direction of the primary trend.

2) Many times, a stock will spike down on high volume and that will signal capitulation and put a floor in the market. Usually, an automatic rally will ensue and fail when the dip buyers lose their buying pressure. Oddly enough, this coincides with fibonacci retracement levels (usually 38.2% or 50%). Once that rally kicks in, a retest of the recent lows will be attempted and a trading range can be created between the lows that were put in with spike volume and the highs of the automatic rally. This trading range carries on for a bit of time before a breakout up through the range occurs. This breakout can be bought with good tape action and then the tape action must be hawked as well as keeping an eye on fibonacci levels which could act as resistance. If I see buying pressure fizzling out at one of the key fibonacci levels mentioned above, I get out of the trade immediately.

As you can see, fibonacci trading is a secondary part of my game but a pivotal one. You can really hit the sweet spot in trading if you can combine a few key trading elements together and design your own trading system where you put the odds in your favor. The bottom line, you probably shouldn't leave fibonacci retracement levels out of that mix.

Congratulations! You are now familiar with Fibonacci retracement levels!

Yet, that’s not all folks! Let’s now go through some other tools which include Fibonacci trading techniques.

## Fibonacci Speed Resistance Arcs

Fibonacci Arcs are used to analyze the speed and strength of reversals or corrective movements. In order to install arcs on your chart you should first discover a trend.

Then you measure the bottom and the top of the trend with the arcs tool. The arcs appear as half circles under your trend, which are the levels of the arcs distance from the top of the trend with 23.6%, 38.2%, 50.0%, and 61.8% respectively.

Each of the Fibonacci arcs is a psychological level where the price might find support or resistance.

Look at the image below, which shows Fibonacci arcs in action:

This is the 30-minute chart of Apple for the period Oct 26 – Nov 3, 2015.

I have placed Fibonacci arcs on a bullish trend of Apple. The arc we are interested in is portrays 38.2% distance from the highest point of the trend.

As you see, when the price starts a reversal, it goes all the way to the 38.2% arc, where it finds support. This is the moment where we should go long.

I recommend placing a stop right below the bottom created on the arc in case the price does not break the highest point of the trend. As you see, Apple starts an increase with a strong hesitation around the trend’s high.

Then the price breaks in a bullish direction and we enjoy a winning long position. This trade had us in a long position during a price increase of $3.19 per share.

## Fibonacci Time Zones

Fibonacci time zones tool is an interesting instrument, which refers not to price movement, but to time volume. In other words, the time zones based on Fibonacci suggest when a price movement could occur. The tool does this by underlining specific time frames based on Fibonacci levels. The example below will show you how the Fibonacci time zones work:

This is the 60-minute chart of Apple for the period Jul 22 – Aug 10, 2015. The trend we have indicated is the place where we stretch the Fibonacci time zones. This is actually our zero period.

Then the other periods are automatically adjusted. Notice that in this case, Apple’s price undertakes a move based on the Fibonacci numbers (0, 1, 2, 3, 5, 8) expressed in time frames.

Do you remember when we said that Fibonacci ratios also refer to human psychology? Exactly! This also applies to time.

When investors hold a stock for a “Fibonacci” period of time, they tend to change their attitude after this period elapses.

## Two Simple Fibonacci Trading Strategies

Next we are going to cover a few Fibonacci trading strategies you can incorporate into your existing trading methodologies. This is meant to be a fun process, so use what makes sense for your investment approach.

### Fibonacci Retracement + MACD

This Fibonacci trading strategy includes the assistance of the well-known MACD. Here we will try to match the moments when the price interacts with important Fibonacci levels in conjunction with MACD crosses.

When we discover this correlation between Fibonacci retracement and MACD, we open a position in the respective direction.

We hold the stock until we receive a contrary crossover from the MACD. The image below will give you a clearer picture of how this Fibonacci strategy works:

This is the 60-minute chart of Yahoo for the period Sep 25 – Nov 3, 2015. The indicated trend is the place where we adjust our Fibonacci retracement.

The two green circles on the chart highlight the moments when the price bounces from the 23.6% and 38.2% Fibonacci levels.

At the same time, the green circles on the MACD show the confirmation we need in these exact moments.

Thus, we go long every time we match a price bounce with a bullish MACD crossover.

The red circles show the close signals we receive from the MACD.

We open two long positions with Yahoo and we generate a profit of $5.12 per share. This is definitely an attractive gain for a period of about 10 trading days.

### Fibonacci Retracement + Stochastic Oscillator + Bill Williams Alligator

In this Fibonacci trading system, we will try to match bounces of the price with overbought/oversold signals of the stochastic. When we get these two signals, we will open positions.

If the price starts trending in our favor, we stay in the market as long as the alligator is “eating” and its lines are far from each other. When the alligator lines overlap, the alligator falls asleep and we exit our position. The next image will show you this Fibonacci trading strategy:

This is the 30-minute chart of TD Bank for the period Sep 29 – Oct 14, 2015. As you see, we place our Fibonacci retracement levels on the existing trend on the left side of the image.

The price drops to the 61.8% Fibonacci level and starts hesitating in the green circle. Meanwhile, the stochastic gives an oversold signal as shown in the other green circle.

This is exactly what we need when the price hits 61.8% and we go long! A few hours later, the price starts moving in our favor. At the same time, the alligator begins eating!

Isn’t that lovely?

We hold our position until the alligator stops eating. This happens in the red circle on the chart and we exit our long position. This trade brought us a total profit of $2.22 per share.

## Conclusion

- The Fibonacci sequence starts from 0; 1; and every number thereafter is built by the sum of the previous two.
- Every number in the Fibonacci sequence is 61.8% of the next number.
- Every number in the Fibonacci sequence is 38.2% of the number after the next in the sequence.
- Every number in the Fibonacci sequence is 23.6% of the number after the next two numbers in the sequence.
- Additional level on the Fibonacci tools can be found at 76.4%, which is simply 100 -23.6.
- Fibonacci levels are critical in equity trading, because they represent a trader’s behavior and psychological reaction to price changes.
- The most common Fibonacci trading instrument is the Fibonacci retracement, which is a crucial part of the equity’s technical analysis.
- Other Fibonacci trading tools are the Fibonacci speed resistance arcs and Fibonacci time zones
- Successful Fibonacci trading strategies are:
- Fibonacci Retracement + MACD
- Fibonacci Retracement + Stochastic + Alligator
- Fibonacci ratios are the highest form of understanding trading psychology in equity markets!

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