# Understanding Fibonacci Numbers And Retracements In The Stock Market

It's never too late to learn!

We had a look at the moving averages working in our last blog post. In this post, we will see how we can use widely followed Fibonacci numbers and ratios as overlay indicators on our stock market charts.

You don’t have to calculate anything. Just select the Fibonacci indicator from your trading software/site and place it on the observed price range, it will automatically reflect the retracement levels with percent levels.

Fibonacci retracement levels in stock market trading offer support and resistance levels. Also signals if the trend is going to be intact. Let’s jump on it.

A simple mathematical expression that describes a Fibonacci series is given as follows:

Fn+1 = Fn + Fn−1

where Fn represents the current number, Fn−1 the previous number, and Fn+1 the next number in the Fibonacci series.

Hence, Fn = Fn-1 + Fn-2

Whatever the mathematical formula suggests, every number in the Fibonacci sequence is the sum of its last two previous whole numbers.

Fibonacci series of number looks like below:

FIBONACCI NUMBER SERIES: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, . . .

0+1=1

1+1=2

And so on...

Fibonacci numbers and ratios are used as a means of determining potential support and resistance levels during:

1. Price Retracements
2. Price Extensions
3. Price Projections
4. Price Expansions
We will mainly concentrate on price retracements and extensions.

## FIBONACCI RETRACEMENTS

A retracement in a price is a decline or correction from a significant peak or a rally from a significant trough

The amount of retracement is usually measured as a percentage of the observed price range, measured from the peak to a previous significant trough, or from a trough up to a previous significant peak. IN UPTREND ITS DOWNSIDE RETRACEMENT; IN DOWNTREND IT'S UPSIDE RETRACEMENT

**38.2 percent, 50 percent, and 61.8 percent levels are considered very significant in Fibonacci numbers.

Let's have a look at what upside retracement and downside retracements look like.

Upside Retracement(in a pre-existing downtrend) within observed price range in below drawing:

Downside Retracement(in a pre-existing uptrend) within observed price range in below drawing:

## Fibonacci Retracement Levels Analysis

Upside retracement will occur in a pre-existing downtrend. Please have a look at the below illustration:

CALCULATING UPSIDE RETRACEMENT % LEVELS:

Assume PEAK A is at  78 and TROUGH B is at 48. The formula for calculating upside retracement levels within a given price range is:

Trough (Price + Range X Retracement Ratio)

In our example, the observed price range AB is:

Price Range = Peak - Trough

= A - B

= 78 - 48

= 30

(NOTE: We always subtract the trough from the peak, regardless of whether it is for a downside or upside retracement calculation, as the price range must always be a positive value.)

The 38.2% upside retracement level is:

= Trough + Price Range × Retracement Ratio

= 48 + 30 × 0.236

= 59.46

Using above formula for 50% & 618% levels:

The 50% upside retracement level = 63 and 61.8% upside retracement level = 66.54

Downside retracement will occur in a pre-existing uptrend. Please have a look at the below illustration:

CALCULATING DOWNSIDE RETRACEMENT % LEVELS:

Assume TROUGH A is at 59 AND PEAK B is at 99. The formula for calculating downside retracement levels within a given price range is:

Peak - (Price Range × Retracement Ratio)

In our example, the observed price range AB is:

Price Range = Peak - Trough

= A - B

= 99 - 59

= 40

The 23.6% downside retracement level is:

= Peak - (Price Range × Retracement Ratio)

= 99 - 40 X 0.236

= 89.56

Using above formula for 50% & 618% levels:

The 50% downside retracement level = ₹79 and 61.8%  downside retracement

level = ₹74

Above retracement can be called one-leg retracement meaning one leg of the wave.

## Price Extensions

A downside extension is any downside retracement that is greater than 100 percent. That means, in an uptrend, the downside retracement crosses the previous trough then it will be called a downside extension which means it gone beyond the observed price range.

Similarly, an upside extension is any upside retracement that is greater than 100 percent. That means it crosses the previous peak, it will be called an upside extension. Please see the below example:

Now we will now look at the two-leg retracement of the wave.

## Two Leg Retracement

The below figure illustrates a two‐leg retracement range:

1. The area of observation covers from point A to the current price. Applying the rule for drawing retracements, we start from the leftmost range AB, which fails to fulfill the general rule of engulfing all subsequent ranges within the area of observation.

2. The next range under consideration would be that of BC, which also fails to fulfill the general rule.

3. Hence, no Fibonacci retracements are drawn for these last two ranges.

4. Conversely, the range CD satisfies the general rule of engulfing all subsequent ranges, as long as the price remains within the range CD

5. Similarly, the range AD also satisfies the general rule of engulfing all subsequent ranges, as long as the price remains within the range AD

6. Therefore, Fibonacci retracements are only drawn for ranges AD and CD, after which we may start finding significant Fibonacci clusters within the two‐leg formation.

NOTE:  We are not drawing retracement ranges as AB and BC, as it does not engulf all the subsequent ranges and/or it will be only one leg retracement.

The same process will take place in downside retracement but in opposite direction.

## Retracement Range Invalidation

RETRACEMENT RANGE INVALIDATED(GOING BEYOND POINT D)

The below figure(addition to the above figure) illustrates the scenario of retracement getting invalidated:

The largest range AD is exceeded, thereby invalidating all previously drawn Fibonacci retracement levels. Note that invalidation also applies to price ranges within the largest range.

Exceeding the largest range within the area of observation will be invalidated at all Fibonacci retracement levels within it, but exceeding smaller ranges within it will only invalidate the retracement levels of those smaller ranges that have been exceeded.

## FIBONACCI FAN LINES(RISING & DECLINING)

Fibonacci fan lines track the amount and degree of reversal in price. They work the same as trendlines and hence are a barrier to price action(S/R).

Let's have a look at the below  illustration and how to draw it:

Steps To Draw:

1. Identify a significant peak and trough from which to plot the fan lines.
2. Draw a vertical line from the peak to the price level at point A, the base.
3. Calculate 3 retracement‐ratio values for the range AB, and then mark off the points of intersection between vertical measuring line and 3 retracement levels(points 1, 2, & 3).
4. Plot three trendlines connecting the base to each intersecting point.
5. Price finding support at the first and third fan lines & resistance at the second fan line at point X in the above figure.

FIBONACCI FAN LINES INVALIDATION

Let's have a look at the below illustration where the price range in consideration is A to C:

1. Price finds support at the first declining fan line at point D, which lies around a previous support level.

2. Price reverses rapidly to the upside once tested 1st fan line which should be with any kind of bullish or bearish support like here prior support & volume peak at D.

3. All earlier tests of the fan lines are irrelevant and may well be regarded as coincidental once price passes point C.

4. As price has crossed point C, fan lines will be treated as invalidating. Now we need to redraw fan lines again from base A to peak E.

The second scenario whereby fan lines need to be redrawn occurs when the price has moved significantly away from the original base and peak in declining fan lines or base and trough in rising fan lines.

## Probability Of Continuation In Retracement

Below illustration shows the possibility of the trend being intact at each percentage level:

You can see the importance of significant Fibonacci percentage levels in the above drawing as price action is taking support of these levels.

All the above content will help in the analysis of Fibonacci retracements levels. Of course, this is not a detailed analysis but should be fine for stock market trading purposes, if used.

-BY CAROLYN BORODEN

TIP: You can make use of Kindle to read the books at less cost or free if you use a trial period offer with Amazon if not having Prime membership. If you are a prime member you can read selected books for free.