# Fibonacci basic tutorial

My experience makes me a believer in the adage that there is a natural order in the markets that has more geometric symmetry than most traders realize or want to believe. This is a fact, not subjective, because almost all market turning points adhere to a certain numerical sequence that you can prove to yourself by looking at historical charts. This sequence applies to both price and time. The primary tool used for this trade analysis is Fibonacci relationships. They include Fibonacci retracements and extensions, as well as time measurement, pivot dates by ratio and numerical sequence.
There is no need to go into the history of Fibonacci, other than to know it is the force that rules the movement of about anything you can imagine, including the financial markets.
The Fibonacci series is a numerical sequence that expands by adding the previous numbers together as shown here:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, etc.
Fibonacci
The most interesting property of this numerical sequence is that as the series proceeds, any number is 1.618 times the preceding number, and 0.618 of the next number.
Example:
1.618 x 34 = 55 x 1.618 = 89 x 1.618 = 144.
.618 x 55 = 34, .618 x 89 = 55, .618 x 144 = 89.
The .618 and 1.618 numbers are what they call the Golden Numbers. You will also see the sequence root of .618, which is .786, and 1.272, the square root of 1.618, occur frequently in your trading.
Suffice to say, the Golden Numbers are dominant in math, nature and science. Planets revolve around the Golden Number, as does your heartbeat on an EKG, and even the index finger on your hand. Each section of your index finger, from the tip to the base of the wrist, is larger than the preceding one by about the Fibonacci ratio of 1.618. And lastly, they tell us that the Egyptian pyramids are based on the Golden Ratio/Numbers.
Key Point:  My source for all of this trivia is goldennumber.net, but you can just go to Google.com and find any number of sites that give you this background in volume. If you believe it, I can teach you how to use it in a pragmatic way trading and investing in the markets.
Key Point:  In spite of all the financial, economic and geopolitical events that affect the markets, you will see beyond any doubt that the up and down price fluctuations in all major markets are governed by the Fibonacci Golden Ratio.
Fibonacci is a sequence tool that is excellent by itself and that becomes very powerful when combined with volatility bands and standard deviation, let alone any of the other tools.
Fibonacci Retracement
I use the following Fib retracement ratios:
• .236
• .382
• .50
• .618
• .786
• 1.00
The minor ratio that will come into play sometimes is the .707 Fib retracement (square root of .50).

Retracements depict the potential reversal levels, support and resistance.
To calculate a retracement in an uptrend, which is when a stock rallies and then pulls back to some percentage ratio of the previous swing point low, you would do the following:
• High - Low x Fib Ratio, then subtract it from the High.

• Calculation of .618RT level

60 - 40 = 20 x .618RT = 12.36
60 - 12.36 = 47.64 (.618RT level)
• Complete the other ratios for practice.
• To calculate a retracement in a downtrend, which is when a stock declines and then pulls back to some percentage ratio of the previous swing point high, you would do the following:
• High - Low x Fib Ratio, then add it to the Low.
• Calculation of .382 level

50 - 30 = 20 x .382 = 7.64
30 + 7.64 = 37.64 (.382RT level)

mplete other ratios for practice

• Fibonacci Extensions
I use the following Fib extensions ratios:
• 1.272
• 1.618
• 2.00
• 2.24
• 2.618
• 3.14 (Pi -- Key ratio)
• 4.236
These extensions occur after price exceeds the 1.00 level and makes new lows or new highs beyond the last leg.
A minor extensions ratio that will come into play sometimes is the 1.414.
To calculate a Fib extension after price exceeds the low or high of the last leg, you would:
Extension down
• High - Low x Ratio, then subtract from the High.
Calculation of 1.272 extension down

90 - 80 = 10 x 1.272 = 12.72
90 - 12.72 = 77.28
Extension Up
• High - Low x Ratio, then add to Low.
• Calculation of 1.618 extension up

90 - 80 = 10 x 1.618 = 16.18
80 + 16.18 = 96.18

• We have given you some Fibonacci background, and the basics of calculating the retracements and extensions, in addition to the ratios that I suggest you use. Now we will build on that.
Key Point:  When you look at retracements and extensions in terms of price, you should also look for symmetry of time using the same ratios. It is not mandatory that you have both, but it is much better symmetry when you do, which builds your case for higher probability.
Key Point:  Once you have identified a high-probability zone, it is the price action at that zone that determines what you will do.
The following SPX charts will demonstrate retracement, extension, time and price action at different zones.
• This SPX weekly chart frames the Fibonacci retracement levels between the 1553 top and 769 bottom. You can see that the .236RT to 1553 of 954 was a major obstacle. The first rally from 776 reached 965, but didn't close above it.
From 965, the SPX declined to the 769 bottom (A) and then rallied to 954, right at the .236RT level, but failed to close above 954. The next leg down (BC) made a 789 low, then reversed to the upside and approached the .236RT level for the third time.
Key Point:  The more price trades at resistance or support, the weaker the line is and the probability of penetration increases.
Price breaks above 954 and trades to the 1015 level. The 1.272 Fib extension of the BC leg is 999, and for 12 weeks, the SPX traded sideways with a high close of 998.
Key Point:  If price breaks out of a range at a Fib level, the highest probability is that it will seek the next level.
• The .382RT to 1553 is 1068, and that is exactly where the SPX traded and went sideways for four weeks (more detail on next chart) before breaking out and trading to the next Fib zone, which is the .50RT to 1553 of 1161. Notice also that there is a confluence with the 2.24 Fib extension of the BC leg at 1159. At the completion of this course on Jan. 29, 2004, 1155 is the rally high on Jan. 27, the SPX had traded down to 1122.38.
This chart demonstrates the natural order that the SPX has traded just using Fib retracements, extensions and time, which you will see better on the next chart. You have anticipated the key zones in advance.
• On this chart, we will start with the time symmetry that is present in this move.
• The BC leg from 954 - 789 was 14 weeks to the low and 13 weeks (Fib number) to the low close. Any reversal bar setup right there had to be taken. The 789 low week was a reversal bar (Hammer) with a high of 841.39. Sequence traders took entry.
Now it gets more interesting. Once price broke out above 954, you had anticipated the 1.272 zone, but on this chart, you also see that the last low in that zone was week 21 following the 789 low week. 21 is the 1.618 Fib extension of 13. Price then rallied, breaking out of the 1.272 zone range.
Key Point:  When looking for time symmetry, you can use the low close or low, and measure it with a high close or high. That will all be considered symmetry.
• After the 1.272 breakout, the SPX traded right up to the .382RT zone at 1088. The first weekly bar in that range was the 34th week, and price went sideways for four to five weeks with a high of 1064. Once again, there was price and time symmetry, as 34 (Fib number) is the 2.618 Fib extension of 13.
The advance above the .782RT level means anticipation of the next Fib RT zone, which would be the .50RT to 1553 at 1160. There is also a .50RT to the 1530 secondary high of 1150, and then the 2.24 Fib extension of the BC leg at 1159. The 1530 high was the 1,2,3 lower top to the 1553 all-time high after the initial decline to below 1350 from 1553. That would make it a significant high to measure a retracement.
From a time perspective, the 1155 high is Week 46 and the high close is Week 45. The 3.14 Fib extension of 14 is 44.
Review these two charts several times so you gain a good idea of the structured way a market trades most of the time and enables you to anticipate high-probability zones where you will take some kind of action, either buy or sell, but it is never nothing.