**Well, well, after some break let’s take a look in our education program - we have passed through some technical issues – support/resistance, trends and candlestick patterns. The time has come to turn in a bit other side and shift to something really superb – Fibonacci numbers and ratios.**

Commander in Pips:Commander in Pips:

**And who is it - some famous Italian fashion designer?**

*Pipruit:*

**Almost, but not of clothes. He is a famous Italian mathematician, who discovered a number consequence with tremendous features that is highly applicable to financial markets including Forex – but let’s move step by step. The first step is a bit of history, the second – a bit of math and then – how it could be used on Forex.**

*Commander in Pips:***Oh, History and math – again…**

*Pipruit:*

**Don’t worry son, it will be very shallow information and you will not need to solve any tasks – just to understand what a Fibonacci consequence is.**

*Commander in Pips:***Thank you, Sir. I think I can take it then.**

*Pipruit:*

**Ok, we will not move too deep in history, because the ratio that we will talk about was known even in Pythagoras’ times (580-500 B.C.E), we will directly move to 12th century in Pisa, Italy where Leonardo of Pisa (1170-1240) was born.**

*Commander in Pips:***His father’s name was Bonacci, so Leonardo was “Figlio Bonacci” which means “son of Bonacci” and then it was contracted to FiBonacci. He was a genius mathematician and discovered the next consequence of numbers, when he had trying to solve the task “How many rabbits would be produced in one year’s time, beginning with two rabbits”. The answer is what we know today as the Fibonacci summation series:**

*Commander in Pips:***1; 1; 2; 3; 5; 8; 13; 21; 34; 55; 89; 144; 233; 377; 610; 987; 1597; 2584; 4181; 6765; 10946 etc.**

The major feature of this consequence is that each number equals to the sum of two previous ones:

2=1+1;

3=2+1;

5=2+3;

……..

377=233+144

10946=6765+4181

………

3=2+1;

5=2+3;

……..

377=233+144

10946=6765+4181

………

And you can prolong this consequence to infinity. But we dare not interesting much in these numbers themselves, but in some ratios that could be obtained from any pair of these numbers. Particularly these ratios are extremely useful in trading and strongly applied by many market participants:

1. If you divide any number (after the initial 5 numbers) into the next standing one you will get 0.618. For instance – 233/377 =

**0.618**, or 6,765/10,946 = 0.618

2. If you divide any number (after initial 5 numbers) into the previous standing one you will get 1.618. For instance – 377/233 =

**1.618**, or 144/89 = 1.618

3. If you divide any number (after initial 5 numbers) to next nearest one you will get 0.382. For instance – 144/377 = 0.382. or 4,181/10,946 = 0.382. Also this ratio could be obtained as 1-0.618 =

**0.382**

From these three major numbers 0.382, 0.618 and 1.618 we will get some derivative numbers that are highly applied in trading:

1.

**0.786**– square root from 0.618;

2.

**1.000**;

3.

**1.272**– square root from 1.618;

4.

**0.500**;

5.

**0.886**– square root from 0.786;

6.

**2.000**;

7.

**2.618**.

So, here is a full series of ratios that you should learn and remember better, than your parents’ names:

So, here is a full series of ratios that you should learn and remember better, than your parents’ names:

**0.382; 0.5; 0.618; 0.786; 0.886; 1.0; 1.272; 1.618; 2.0; 2.618**

**It sounds more interesting, that I’ve assumed. And why is it so big deal with all these numbers? Why do they work?**

*Pipruit:***1.618 ratio calls as “Divine proportion” or “Golden mean”. Because of this number describes almost any natural proportion in universe and great wonders of human being. For instance, The Great Pyramid in Giza is structured with this proportion. Other examples include works of great artists, such as Leonardo da Vinci, Rembrandt and others. You can meet this ratio in nature with numerous cases – in flowers (sunflower, roses, daisies), seashells, pineapples, and even in human faces and body. Say, measure the distance from your elbow to the tips of your fingers, then between your fingertip to your wrist and finally, from wrist to elbow – you will get 1.618 ratio:**

Commander in Pips:Commander in Pips:

**(Elbow-Fingertip)/ (Elbow - Wrist) = (Elbow - Wrist)/ (Wrist-Fingertip) = ~1.618**

**Wow! Cool! But why do these ratios work on financial markets?**

*Pipruit:***There is no definite and clear answer on this question, and as you understand this answer will never appear. But, as this ratio the one that is building in nature of all being on the Earth, the basic thought about it is as follows. The price is driven by human senses – fear and greed. And the prevailing one or another comes to the market in a way of price movement. Since human feelings and emotions are also natural substance, the way how they becomes stronger and weaker are also a natural subject and, hence the subject of 1.618 ratio.**

Commander in Pips:Commander in Pips:

**Hm…**

Pipruit:Pipruit:

**Finally this is not so important. I just can tell you, that these numbers work and must be used in trading.**

Commander in Pips:Commander in Pips:

**So and how we will use them?**

Pipruit:Pipruit:

**Currently for simplicity let’s say that numbers that equal or less than 1.0 are used for calculation of**

Commander in Pips:Commander in Pips:

**retracement**. Those are, that equal or above 0.618 – for extensions. So, tell me, what numbers we will use for retracement and which one for

**extensions**. So, tell me, what numbers we will use for retracement and which one for extensions

**Let’s see. For retracement they will be -**

Pipruit:Pipruit:

**0.382; 0.5; 0.618; 0.786; 0.886; 1.0**. For extensions are –

**0.618; 1.0; 1.272; 1.618; 2.0; 2.618**.

**Yes, that’s it.**

Commander in Pips:Commander in Pips:

**But, Commander, why we use 1.0 as for retracement as for extensions. And, in general, why we couldn’t use, say 0.5, for extension?**

Pipruit:Pipruit:

**Well, the major difference here is in direction of using these numbers. Retracement is an opposite move to previous one; extension is a continuation of previous move after some retracement. So, Fibonacci retracement levels are treated as support or resistance and used by traders for entering or exiting from trades or placing stop orders. There are so many traders using these levels, so they become a self-fulfilling prophecy.**

Commander in Pips:Commander in Pips:

The Fibonacci extension levels most time are used as profit objectives - profit taking levels.

**Ok, I’ve got it. And how to build these levels on the chart?**

*Pipruit:***Most forex trading software already includes tools for building retracement and extensions, so you will not have to do it manually. Furthermore, you will be able even adjust them, so to choose what levels you want to use and which one you don’t.**

*Commander in Pips:*To calculate and draw any level you will need to identify

**swing high**and swing low levels.

So, we will treat as swing high a candlestick/bar that has at least two lower highs on both sides of itself – from left and from right.

**Swing Low**a candlestick/bar that has at least two higher lows on both sides of itself – from left and from right.

**Well, currently it sounds too confusing and sophisticated. Can you show me some picture?**

*Pipruit:***Yep. Here it is:**

Commander in Pips:Commander in Pips:

Chart #1 EUR/USD Daily. RetracementChart #1 EUR/USD Daily. Retracement

See, our initial move – AB swing. “A” is swing low and “B” is swing high. Fibonacci retracement levels always stand inside initial AB move, so here they act as support levels. I’ve marked all levels that we’ve talked about.
**Wow, 0.382 level really has supported the market. You’re right, Commander, they work!**

Pipruit:Pipruit:

**Here you can see also, why is using some levels exceeding 1.0 has no sense. Because if market will show retracement, say equal to 1.0 of AB initial swing – it will totally erase it! So, in fact this will be not just a retracement already. The word “retracement” assumes some pull back inside initial AB move usually to 0.382-0.786 level but not deeper that 1.0. The direction of Retracement move is always opposite to initial AB move.**

Commander in Pips:Commander in Pips:

**So, AB is initial move, and BC looks like a retracement, does it?**

Pipruit:Pipruit:

**Yes. That’s right.**

Commander in Pips:Commander in Pips:

**Well and how extensions do look like?**

Pipruit:Pipruit:

**Look at Chart #2. It shows extensions from the same AB up swing:**

*Commander in Pips:*

Chart #2 EUR/USD Daily. Extensions.Chart #2 EUR/USD Daily. Extensions.

**See – extension, is a continuation of initial swing after retracement. In our case this is an up swing AB. Then market has shown BC retracement, that we’ve just discussed, and continued its move up further from point C. Take a look – it has hit 0.618 expansion from AB swing, that has started from C point at 1.4033 almost pips to pips and turn to retracement. The next expansion target is 1.0 at 1.4410.**

*Commander in Pips:***Ok, so, to build an extension we need:**

*Pipruit:*1. Initial swing AB;

2. Some retracement from it – BC.

**Yes. That’s right.**

*Commander in Pips:***And how to correctly build them, to choose A, B and C points and…**

*Pipruit:***Ho-ho! Hold your horses, son. Don’t worry - we will get all the necessary details for using these tools in this Chapter in later lessons. But for now will be enough that you have learned today:**

*Commander in Pips:*1. Ratios - 0.382; 0.5; 0.618; 0.786; 0.886; 1.0; 1.272; 1.618; 2.0; 2.618.

2. What retracement is and possible ratios for retracement - 0.382; 0.5; 0.618; 0.786; 0.886; 1.0. Also we’ve studied how it looks like;

3. What extension is and ratios for it – 0.618; 1.0; 1.272; 1.618; 2.0; 2.618 and how it looks like on the chart.

If I understand corectly the definition of the swing, then the following chart is NOT a good example of ABC pattern. The problem is poit B that has no 2 higher lows on the right side.

Thank you!