Important numbers

The whole topic of numerology is vast and complicated, and is far beyond an in-depth study here, so, if you are interested in this area, I do suggest that you do some further reading and study yourselves. All I would like to do in this chapter is to cover the numbers that are used in MTPredictor and discuss why they are important.

The first major source of these numbers in market analysis can be traced back to R. N. Elliott and W.D. Gann, and possibly much earlier. There have also been many fine analysts in more recent years who have taken on the subject of numerology and applied it to Price and Time analysis with great success.

If you head even further back in history, several leading mathematicians feature, such as Pythagoras and Fibonacci. Fibonacci however, was the key source for most of the ratios now used in the financial markets.

Leonardo Fibonacci was reputed to be one of the greatest mathematicians of the Middle Ages, publishing a number of papers in the years 1200 - 1220, and is best-known for his Fibonacci number series, the implications of which I'll go into in greater detail soon.

The Fibonacci number series is the answer to this type of question: if you had two rabbits and let them breed, how many rabbits would you have at some defined point in the future? This seems a bizarre start to one of the most important number series in the financial markets.

The number sequence starts at 1, and then adds the previous two numbers together to produce the next number in the series:

And so the number series goes on:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 etc.

Okay, so far we have a set of numbers that is important for performing static counts in the markets, particularly in Time analysis (more on this later). This is the Fibonacci number series. However, this number series is unique, in that if you take any two adjacent numbers and divide the bigger by the smaller they come closer and closer to 1.618. 1.618 is one of the most important numbers governing the natural world.

The significance of 1.618, and its reciprocal 0.618, is astonishing because this ratio can be found throughout all aspects of nature, from how shellfish grow to ratios between different elements of the human body. This ratio can even be found within the Great Pyramid of Giza in Egypt, or even in the ratios of subjects in masterpieces of art. I encourage you to look into this ratio in more detail for yourself, however for the purposes of this book, all you need to know is that the ratios of 1.618 and 0.618 are the fundamental building blocks from which swings in financial markets appear to unfold.

Let me show you a few examples, starting with a simple retracement of a prior swing on the SPY (the US stock that tracks the S&P index):

Rle: (SPY) Standard & Poors Dep R Day Date: 16/06/2002 O: 103.74 H: 105.03 L: 103.63 C: 104.97 ©

Rle: (SPY) Standard & Poors Dep R Day Date: 16/06/2002 O: 103.74 H: 105.03 L: 103.63 C: 104.97 ©

08/03/2001 25/04/2001 12/00/2001 30/07/2001 20/09/2001 0S/11 /2001 24/12/2001 12/02/2002 02/04/2002 17/05/2002 04/07/2002

Here you can see how the market declined off the May 22 high into the September 21 low in 2001. The market then rallied back up, however, as you can see from the chart above, this rally stopped right at the 0.618 level. In fact, the market made three attempts to break his level, but it could not, before it declined sharply.

If you now move a little further forward in time to look at the decline off this high on January 7 2002, you can see how the market found support at the 0.618 expansion of the September 21 to January 7 rally:

Rle: (SPY) Standard & Poors Dep R Day Date: 17/10/2002 0:66.87 H: 69.30 L: 67.85 C: 66.27 ©

Rle: (SPY) Standard & Poors Dep R Day Date: 17/10/2002 0:66.87 H: 69.30 L: 67.85 C: 66.27 ©

31/08/2001 2S/10/2001 17/12/2001 07/02/2002 01/04/2002 20/05/2002 10/07/2002 28/08/2002 17/10/2002 05/12/2002 23/01/2003

I know many of you will already be familiar with price retracements, however some of you may not have seen (or indeed heard of) price expansions. A price expansion is simply taking the value of a swing, multiplying that value by a certain ratio (in this case 0.618) and then either adding onto the higher value (to expand upwards), or subtracting from the lower value (to expand downwards).

Here you can see how the double bottom at the July/October lows in 2002 fell right at this 0.618 expansion level of the prior swing.

Price retracements and expansions are not the only price calculations performed on swings in the markets; you can also use price projections. A price projection is where you take the length of one swing in the market then project it from a third point, with the original length multiplied by certain ratios. I'll cover this in more detail in later sections, however a good example of this is the chart on the next page.

Here I have taken the length of the price swing from the December 2 high into the December 31 low in 2002, then multiplied this value by 1.618 and then subtracted it from the January 30 2003 high. In effect, what this is doing is taking 1.618 times the December 2 to December 31 swing and then projecting that from the Jan 30 high.

As you can see in the chart above, the March 13 low felt exactly at this 1.618 projection.

I did not have to look very far, or actually very far back in time, to find some excellent examples of how the stock market made major turns just using the 1.618 and 0.618 ratios of prior swings in the market.

I hope this has shown how important the Fibonacci ratios of 1.618 and 0.618 are, and how they can be used as multipliers in conjunction with prior swings in the markets to help project future levels where support or resistance may unfold.

These ratios are not the only ratios to use. There are two more important ratios derived from the primary 0.618 ratio: 0.786 and 0.382. 0.786 is the square root of 0.618, and 0.382 is the square of 0.618.

In addition, two more important ratios are derived from the important 1.618 ratio: 2.618 and 4.236. 2.618 is the square of 1.618, and 4.236 is the cube of 1.618.

As a result, the main Fibonacci ratios that I consider most important are 0.382, 0.618, 0.786, 1.618, 2.618 and 4.236.

There is also one more ratio that I use: 1.272, which is the square root of 1.618.

As you can see, at first sight this may seem slightly complicated, but all you need to realise is that all these ratios are derived from the bedrock 0.618 and 1.618 Fibonacci ratios. All that is needed to produce these numbers is some simple maths. However, when performing normal analysis you do not need to worry about this, as the MTPredictor software program takes care of all these numbers for you.

If you would like to take your study of numerology further, then you can start to look at additional ratios that are derived from the square, circle, triangle and rectangle. From these arise such ratios as 1.414, which is the square root of 2, which is the value of the hypoteneuses from the square of equal sides of 1. The square root of 5, which is 2.236, is another important number.

As you may have gathered, the main use of the these ratios is in taking the price length of a prior swing in the market, then multiplying it by one of these ratios, then projecting it from another point. This then projects into the future support or resistance levels where the market may well make a turn. This is called dynamic analysis, where prior ratios are multiplied and then projected into the future.

Another way to use these numbers is in static analysis, simply adding the value of these numbers to prior points. However, this is most relevant to Time analysis, so I will leave an in-depth study of this for the chapter dealing with Time analysis.

I will go into more detail on which ratios and which swings are used in the next chapter on WPTs, but my concern in this chapter is to introduce the ratios that are used in MTPredictor: mainly based on the Fibonacci ratios of 0.382, 0.618, 0.786, 1.272, 1.618, 2.618 and 4.236.

R. N. Elliott made extensive use of the Fibonacci ratios and number sequence in his work developing the Elliott wave theory in the 1930s. You will see more of his work once I cover static Time counts in later chapters.

However, the Fibonacci numbers are not the only ones that are important in the markets. As I touched on a few paragraphs ago, there are also important numbers derived from the most basic mathematical relationships of 100% and 50%. The main reason for these ratios' importance is that they are very obvious places on a chart for support and resistance to be seen. W. D. Gann based much of his work on these numbers.

Let me show you a few examples.

The 50% value is best used as a retracement level. If you look at the chart below, you can see how Diamonds Trust (DIA), the US stock that tracks the Dow Jones Industrials index, made a rally off the July 24 2002 low that retraced half (or 0.50) of the March 19 to July 24 decline:

Once the market had reached the 50% (0.50) retracement level, it turned, made a high and continued to decline from there.

Very often a counter trend swing will retrace 50% of the prior move before making either a high a low. This is a very obvious level, of which most technical traders are aware.

The second ratio of 100% is best used as either a price expansion or a price projection.

This second chart on the DIA shows how very often a turn in the market will be made after a move has continued 100% (1.00) of the prior swing:

Hie: (DIA) Diamonds Trust Day Date: 30/04/2003 0:04.93 H: 05.41 L: 04.44 C: 04.00 ©

Hie: (DIA) Diamonds Trust Day Date: 30/04/2003 0:04.93 H: 05.41 L: 04.44 C: 04.00 ©

22/07/2002 21/03/2002 23/D9/2002 23/10/2002 22/11/2002 26/12/2002 29/01/2003 03/03/2003 02/04/2003 05/05/2003 04/00/2003

Here the price difference between the December 2 2002 high and the December 31 2002 low was expanded below the December 31 low by 1.00. As you can see, the ultimate low of March 12 felt right at this 100% expansion level.

You would be amazed how many times this price relationship works in the markets, particularly as it is a relationship that is not very well known. Many you will be familiar with price retracements, but I guess that few of you will have seen price expansions before and, particularly, the way a 100% expansion of a prior swing will very often produce a turn in the market.

The third method of price calculation is the price projection. I will take a look at an example of this on the next page.

Continued on the next page

Here is a chart of the SPY, the US stock that tracks the S&P 500 index:

Here is a chart of the SPY, the US stock that tracks the S&P 500 index:

As you can see from the chart above the August 23 high felt right at the 100% (1.00) projection of the July 24 low into the July 30 high projected from the August 5 low.

This is a very important relationship, because it is a three swing correction where the third and first swings are equal in price. Or put another way, this can be labelled an ABC correction where wave A is equal in price to Wave C. I hope this sounds very familiar from what you have read earlier in this course.

W.D Gann was probably the most famous market technician to make extensive use of ratios derived from 1. In particular, the 50% retracement can be directly attributed to him. Most of the analysis in this book is related to the Elliott wave theory and the Fibonacci number series, so the ratios based on 1.618 and 0.618 are considered more important, although the 0.50 and 1.00 ratios do have their place.

As such, you should add 1.00 and 0.50 into the current list of important numbers.

At first sight this may seem very complicated, however you do not need to spend too much time on the chapter or worry about what ratios to use, how to use them, or what swings to use them from, because MTPredictor can perform all this work for you. As a result, this chapter should be treated more as information only rather than an in-depth study.


There are two sets of numbers that are important for performing mathematical analysis in the markets.

• The first of these is the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 etc, where these numbers are normally used for static Time counts.

• The second is 0.382, 0.5, 0.618, 0.786, 1.00, 1.272, 1.618, 2.618 and 4.236, where most of these numbers are derived from the important 1.618 (and 0.618) ratios that derive from the first series, and are mainly used for dynamic analysis, with the length of a prior swing being multiplied by these ratios.

As you have seen in this chapter, very often financial markets make reversals at, or very near to, price retracements, expansions or projections of prior market swings which are then multiplied by these particular ratios.

In other words, you can use these ratios to help anticipate future support and resistance areas where markets are likely to make a reversal so they should be considered leading indicators because they can help project in advance potential future support and resistance areas.

Again, this chapter is by no means a full and complete look at the topic of numerology, there are many additional sources you may want to consider if you wish to take your study of numerology further. There are also additional ratios and additional techniques that can be used to anticipate future support and resistance areas. This chapter contains only the ratios and techniques that I have found useful based on my own experience in the markets.

However, I do suggest that if you are interested, you do take your own study and research further, not only because it can lead to additional ratios and techniques to use, but also because the topic is absolutely fascinating! It is a real eye-opener to see how often these important ratios unfold in everyday life. It will certainly change the way you look at many elements from nature from now on.

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