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Monday, May 30, 2011

The Gann square of nine

W.D. Gann's square of nine - If ever there was a bit of trading mumbo-jumbo that I counted as not worth thinking about, it was W.D. Gann's square of nine. How could I bother with century-old jargon about prices vibrating off each other, square-outs of time, prices related to degrees of a circle, producing a mystical numerology that purports to give exact dates on which particular prices must be reached?
Nonetheless, I decided to make another attempt to understand it when Jeff Cooper, a trader whom I (otherwise) respect, described his use of the Gann square in a RealMoney.com article. Something in the article jogged my memory, and it was then that I realized Gann's square of nine is in fact known to mathematicians in a context totally unrelated to the stock market. To mathematicians, the square of nine is known as Ulam's Prime Number Spiral, and displays some of the properties of the greatest unsolved mystery in mathematics the distribution of the prime numbers.

SIGNIFICANCE OF PRIME NUMBERS

What could these two fields trading the stock market and prime number theory possibly have in common? Puzzled, I could not find a writer, trader or mathematician, who had mentioned the equivalence of the spirals of Ulam and Gann; Jeff Cooper confirmed to me that he had never heard of this connection. If it has been noticed before, it is at least not well known. Is it possible there is some hidden relationship here that could profit a trader? Could prime numbers be turned into prime cash? I decided to track down the connection.
Gann's square of nine consists of the integers arranged in the form of a square spiral. One can construct it using a spreadsheet or graph paper. Place the number 1 in a central cell; to its left place the number 2; above that is 3, and move around clockwise, adding one each time: to the right of 3 is 4 and 5, then below 5 is 6 and then 7. To the left of 7 is 8 and then 9, which completes the first square. To the left of 9 place 10 to start a new square out, and above 10 place 11, and so on, around and around as large as one likes (Figure 1). Gann believed this arrangement captured a hidden law that the markets inexorably followed.


Figure 1: The Gann square of nine. The mathematician Stanislaw Ulam discovered that the prime numbers shown in blue sometimes fall unexpectedly along lines in the square, such as in the diagonal ray extending from the center to the northeast corner.
In trading, the numbers are interpreted as prices, and their circular arrangement represents the passage of time; a full turn around the spiral takes one to the next larger square and represents a single period, such as a year. Of particular significance are lines of numbers that fall along the eight cardinal directions of a compass: the four rays emanating from the center in the directions of north, east, south and west identify the alignment of prices that occur at certain times of the year, as do the set of diagonals running from the center to northwest, northeast, southwest and southeast.
Gann traders look for prices at significant highs and lows then check along these significant rays to find other prices at which future highs and lows are expected to occur. Traders can also find price relationships by looking at angles of 90 degrees, 180 degrees, and so forth, that are formed with respect to a significant price. For example, in the first square, 9 is related to 3 by a 90-degree turn, and 7 is related to 3 by 180 degrees. With these tools, Gann traders make forecasts of the size of price oscillations and the timing of significant turning points in the markets. Gann himself apparently used these methods to predict wheat prices in 1909 that established his fame.
The figure known to mathematicians as "Ulam's prime number spiral" is constructed in exactly the same fashion as the square of nine, but its use is quite different. It was discovered by mathematician Stanislaw Ulam in 1963. While listening to a "long and very boring paper" at a science conference, Ulam drew a square grid, thinking he might set up a chess problem; instead, he began numbering the intersections of the grid by spiraling out from the center. Then he idly began to circle the prime numbers the only integers that cannot be calculated by multiplying together other integers. He was astounded to find that sets of prime numbers arranged themselves along diagonal lines in the diagram. See Figure 1, where the primes are in the shaded cells; note the sequences such as 7, 23, 47, and 79, or 5, 19, 41, 71, 109.
Subsequently programming a Maniac II computer to generate a picture of the distribution confirmed that prime numbers appeared along diagonal lines throughout the largest square spirals that could be made. For example, Gann's 45-degree line, the northeast ray, holds the primes 5, 17, 37, 101, 197, 257, 401, and so on: 70% of the numbers out to the 10th square are primes, even though only about 20% of the integers up to 401 are prime.
Prime numbers are important because they act as the "elementary particles" of the numbers: all integers can be uniquely calculated by multiplying together only primes. The distribution of the prime numbers among the other integers is considered by many to be the greatest unsolved mathematical mystery.
The patterns that leapt to the eye in Ulam's spiral indicate some underlying order to the distribution of the primes that has yet to be fully understood. Some people regard the mystery of the prime numbers with an awe that rivals Gann's mystical search for the hidden laws of the stock market. But what brings these two mysteries together into the square spiral?

NATURAL SQUARES CALCULATOR

The answer to this question, although only a partial one, is that Gann's square of nine is a parabola calculator. Gann referred to it as the "natural squares calculator" and may have derived it from ancient techniques for computing squares of numbers. Note that the natural squares 22 = 4, 3= 9, 5= 25 and so on fall along the southwest diagonal of the square. In fact, each of the cardinal rays extending from the center is described by a quadratic equation, which on a time-price chart forms a parabolic curve.
Let us label the ever-larger concentric squares with integers n. The center square, with just the number 1, we will label as n = 0; the next square out, with three unit cells on a side and largest number 9, will be labeled n =1, the next, with five cells on a side and largest number 25, is n = 2, and so on, so that the nth square has sides of length 2n+1 cells.
The area of the nth square is then (2n+1) 2 = 4n2 + 4n + 1, and this is also the largest number in each square (equal to the number of cells in the square). These largest numbers per square are lined up along the ray extending from the center to the southwest. Thus, the southwest ray corresponds to the quadratic expression 4n2 + 4n + 1.
All eight rays important to Gann theory are described by quadratic expressions of the form 4n2 + an + 1, where the choice of the coefficient a determines the angle of the ray. Gann called the ray pointing to the east the "zero degree ray," and so each of the others correspond to successive increments of 45 degrees; using this identification, the coefficient a that generates the parabola corresponding to the ray at angle w is given by a = 1 - w/45, where w takes on the values between 180 degrees and minus 180 degrees.
On a stock chart of price versus time, formulas of the form 4n2 + an + 1 produce a parabola, where the parameter n represents time and the expression evaluates to the corresponding price. Gann's contention that prices along the same ray "vibrate" against each other is actually a way of saying that sometimes critical prices fall along a parabola, which is a fact of trading life: blowoff tops occur when price goes parabolic. Thrusts increase in length and pullbacks decrease; parabolas can also describe the slowing down and turning of a trend as thrusts become smaller and pullbacks greater.
When Gann describes price moving between rays of different angles he is describing the motion of the stock price between members of a fanlike family of parabolas, effectively describing a parabolic trend channel. To good approximation, all linear trend channels eventually become parabolic trend channels as markets turn. Gann's square of nine and his use of esoteric language disguise genuine phenomena that traders can find useful.

APPLYING TO TRADING

What does this have to do with primes? In Ulam's spiral, the curious alignments of prime numbers is also related to the spiral's function as a parabola calculator. In the 18th century, mathematicians Legendre and Euler discovered that some sequences of primes can be generated by quadratic expressions. A particularly famous expression is x2 + x + 41, published by Euler in 1772, which has 40 consecutive primes. These prime-generating quadratic polynomials appear as lines in the square of nine.
Although most of these lines do not pass through the center, with suitable labeling of the squares they can be described by parabolas of the form 4n2 + an + b. In the case of the sequence of primes 5, 19, 41, 71, the parabola has coefficients a = 10 and b = 5, and primes are generated for n = 0, 1, 2, 3, as well as various higher n. For the sequence 7, 23, 47, 79 the corresponding coefficients are a = 7 and b = -1 for n starting at 1.
Not every number along these lines is a prime, but an unusually high proportion are. According to the prime number theorem, the chance that any randomly selected integer x is a prime is roughly one over the natural log of x; the frequency of primes along some of the lines in the Ulam spiral far exceed that random distribution.
Ulam and his coworkers showed that along some diagonals, almost half the numbers less than 10,000,000 are prime. Just why this is so is still a mystery of mathematics. There are partial explanations. For example; some diagonals across the spiral can contain no primes on them because their quadratic expressions can be factored into the product of two linear expressions, and as a consequence there must be clusters of primes elsewhere; but it's not clear this explains the consistency of the distribution.
A Gann square of nine in which any given line of primes passes through the center and falls along the Gann cardinal directions can be formed by suitable adjustment of the central and incremental numbers that generate the square. By starting with -1 in the center of the square rather than 1, the 5, 19, 41. . . sequence becomes the southeast ray while the 7, 23, 47. . . sequence becomes the southwest ray.
Adjusting the center element can generate other prime rays; placing 17 or 41 in the center square generates spirals in which every number along a diagonal is a prime out to the 16th and 40th squares, respectively. These rays correspond to two of the most famous prime-generating quadratic expressions.
A Gann trader with an eye for primes could look for market price oscillations among prime-number parabolic channels. For example, in Figure 2, the Standard & Poor's 500 from 1994 to 2000 was supported by the parabola that corresponds to the northeast ray of the standard square of nine, which happens to be the ray with the most prime numbers of the cardinal directions. The upper curve of the parabolic channel corresponded to the ray 180 degrees opposite, the southwest ray, which happens to have absolutely no primes.

Figure 2: A Gann parabolic channel for the S&P 500 from 1994 to 2000. The upper parabola corresponds to the southwest ray in the square of nine, starting at the 10th square; the lower parabola is the northeast ray, starting at the ninth square. Time is scaled so that one complete turn of the square is equal to nine months.

Personally, I find it difficult to believe that prime numbers can be particularly useful in trading unless they have a psychological effect: traders of any methodology might instinctively see prime numbers as special or offbeat (as they do not appear as results in multiplication tables learned in school), and thus provide a more attractive place for entry and exit stops than the more obvious numbers ending in zero or the simple fractions of 10.
A better lesson to be drawn is that both Ulam and Gann were able to use this unusual arrangement of numbers to visually detect patterns that otherwise might be difficult to find. This is a technique that any seeker of hidden relationships can put to use. Whatever its meaning, I can't help but believe Gann would have been pleased to find his square of nine vibrating with a deeply hidden order of mathematics.

Gann numbers

Gann numbers - There is no simplistic explanation for Gann numbers, but it basically charts a relationship between price movements and time. Although it is increasingly used in stock trading, there is every chance you could find a reference to it in forex trading too. As you can see from the chart below, Gann numbers are calculated by using angles in charts. This helps in determining the support and resistance areas and could be used to predict the timing of future trend changes.
can-numbers

Fibonacci numbers

Fibonacci numbers! Doesn't that sound a lot like an enormous chapter in high school mathematics' book? If that's what you think then you are absolutely right. We are indeed talking about those kinds of numbers. Fibonacci numbers are a sequence of numbers formed as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… etc
The sequence begins with 0 and 1.  Then keep adding the last two numbers to get the next. Meaning that:
0+1=1
1+1=2
1+2=3
2+3=5
3+5=8
5+8=13
well, you have got the picture now!
Why this sequence is called Fibonacci? The sequence of numbers was discovered by Leonardo de Pisa, also known as Fibonacci. He lived in 12th century and was lucky enough to be the one to discover this amazing mathematical sequence. Off the topic Fibonacci numbers can be found EVERYWHERE! Scary enough these numbers represent the natural proportions of things in our enormous universe. And since forex is a part of the universe – Fibonacci numbers are applied here as well in search of a simple proportional solution for trading profits!
Speaking of trading, lets get to the main issue here – forex. You don't have to learn how to calculate any of this by yourself. The forex broker of your choice will provide you with software that calculates everything for you. 
Now here is the mystery – with major ratios calculated from Fibonacci numbers forex traders can actually predict a behavior of trend and countertrend movements in forex market. Spooky!!! 
Here is a set of numbers to remember: 38%, 50% and 62%  
If you take these percentages and apply them to the trending price you will notice not only a certain amount ofretracement, but also where new high and low could go. These marks are very important to forex traders since they are support and resistance areas where the price will either hesitate for a while or will reverse. 
Before grabbing the charts there is one more thing you have to know. The primary trends move all together in 5 waves. First there are 3 forward waves, and then there are 2 backward waves. Now countertrends move differently – 3 waves at a time. First there are 2 forward waves, followed by 1 backward wave.  
Now you are officially eligible to get some charts to "play" with and test your knowledge. Once you figure out how to place the marks correctly (every trading platform is different), you will definitely notice Fibonacci ratios in the price movements as it changes the position from support to resistance and back to support. Then you will realize that looking at certain time frames the trends tend to have similar proportionality. Wow!!

Whether on a hourly or a daily chart the Fibonacci lines that you draw are relevant until the price action has either confirmed or rejected them. Lets say if the price retraces to 38% line and then suddenly reverses again back to its original path crossing over the 0% line then you can for sure say that the cycle is over.    

Wednesday, May 25, 2011

Standard Deviation Channel

Standard Deviation Channel is built on base of Linear Regression Trend representing a ussual trendline built between two points on the price chart using the method of least squares. As a result, this line proves to be the exact median line of the changing price. It can be considered as an equilibrium price line, and any deflection up or down indicates the superactivity of buyers or sellers respectively.

Standard Deviation Channel consists of two parallel lines, equidistant up and down from the Linear Regression Trend. The distance between frame of the channel and regression line equals to the value of standard close price deviation from the regression line. All price changes take place within Standard Deviation Channel, where the lower frame works as support line, and the upper one does as resistance line. Prices usually exceed the channel frames for a short time. If they keep outside of the channel frames for a longer time than usually, it forecasts the possibility of trend turn.

Equidistant Channel


Equidistant Channel represents two parallel trend lines connecting extreme maximum and minimum close prices. Market price jumps, draws peaks and troughs forming the channel in the trend direction. Early identification of the channel can give a valuable information including that about changes in the trend direction what allows to estimate possible profits and losses. It is necessary to give the direction of the channel and its width to build the instrument.

Linear Regression Channel


The linear regression channel, similar to the Bollinger Bands, is a technical analysis tool that can be used to trade the binary options market.  The linear regression channel is a statistical technical analysis tool that captures the recent ranges and creates a statistical boundary where prices are likely to trade over a specific period of time.
Linear regression is a statistical approach to determining (via modeling) the relationship between one or more variables, where the model depends linearly on the unknown parameters to be estimated from the data.   The conditional mean of the given values (say prices of a financial instrument) are a function of that particular instrument or another instrument.  In essence, one specific variable is dependent, to a degree, on another specific variable.  The degree of dependence is called the R (squared), which is denoted in a percent format.
The linear regression channel is a channel that is created using a specific amount of data points where a regression line is created using the R (squared).  Parallel lines are then drawn that are one or two standard deviations away from the mean line.  The channel incorporates a larger percentage of the recent range of prices and theoretically will be bound where most of the price action over a future period of time.  This is accomplished by increasing or decreasing the standard deviation.  The larger the standard deviation, the more price and potentially future prices will be incorporated into the bands.  The linear regression channel can be used as a mean reverting indicator, where the bands on each end are support and resistance for price action.  In the hourly chart of USD/JPY, the linear regression channel incorporates the majority of price actions during a 20 period range.
  
The linear regression channel can be used successfully to trade hit or miss options, range options, one-touch options or above or below options.  For above or below options, an investor can use the high end of the linear regression channel to buy below options, and the low end of the linear regression channel to purchase above options.  For range trading, the channel should be an excellent strategy.  Placing a trade, this pays off if price action trades in a range in the future should be statistically significant.  This strategy is based on the idea that the current range will continue to perpetuate in the future is not other news is added to the market.  A two standard deviation range will incorporate 95% of the current prices, which should act as a very strong guide for future trading.  For example, a range box can be placed in front of the price action with a length that is similar to the trend channel.  
These strategies using the linear regression channels have a lot of statistical merit and should be tested using numerous financial instruments to find the binary option and instrument that match an investor’s risk profile.

Channel


There are line studies being largely used in technical analysis and helping to define channels and trend changes. These instruments are:

Gann Grid


Gann Grid represents trends built at the angle of 45 degrees (Gann Lines). According to Gann’s concepts, a line having a slope of forty-five degrees represents a long-term trendline (ascending or descending). While prices are above the ascending line, the market holds bull direction. If prices hold below descending line, the market is characterized as a bear one. Intersection of the a Gann Line usually signals of breaking the basic trend. When prices go down to this line during an ascending trend, time and price become fully balanced. The further intersection of Gann Lines is an evidence of breaking of this balance and possible change of the trend.

To build a Gann Grid, it is necessary to define two points determining sizes of cells.

Gann Line


Gann Line represents a line drawn at the angle of 45 degrees. This line is also called "one to one" (1x1) what means one change of the price within one unit of time.

According to Gann’s concept, the line having the slope of forty-five degrees represents a long-term trendline (ascending or descending). While prices are above the ascending line, the market holds bull directions. If prices hold below the descending line, the market is characterized as a bear one. Intersection of Gann Line usually signals of the basic trend break. When prices go down to this line during an ascending trend, time and price become fully balanced. The further intersection of Gann Line is the evidence of breaking of this balance and possible changing the trend.

It is necessary to define two points for building a Gann Line.

Tuesday, May 24, 2011

Gann Fan


Lines of Gann Fan are built at different angles from an important base or peak at the price chart. The trend line of 1Ñ…1 was considered by Gann the most important. If the price curve is located above this line, it is the indication of the bull market, if it is below this line it is that of the bear market. Gann thought that the ray of 1x1 is a powerful support line when the trend is ascending, and he considered the breaking this line as an important turn signal. Gann emphasized the following nine basic angles, the angle of 1x1 being the most important of all:
  • 1Ñ…8 — 82.5 degree
  • 1Ñ…4 — 75 degree
  • 1Ñ…3 — 71.25 degree
  • 1Ñ…2 — 63.75 degree
  • 1Ñ…1 — 45 degree
  • 2Ñ…1 — 26.25 degree
  • 3Ñ…1 — 18.75 degree
  • 4Ñ…1 — 15 degree
  • 8Ñ…1 — 7.5 degree

The considered ratios of price and time increments to have corresponding angles of slope in degrees, X and Y axes must have the same scales. It means that a unit interval on X axis (i.e., hour, day, week, month) must correspond with the unit interval on Y axis. The simplest method of chart calibration consists in checking the angle of slope of the ray of 1Ñ…1: it must make 45 degrees.
Gann noted that each of the above-listed rays can serve as support or resistance depending on the price trend direction. For example, ray of 1x1 is usually the most important support line when the trend is ascending. If prices fall below 1Ñ…1 line, it means the trend turns. According to Gann, prices should then sink down to the next trend line (in this case, it is the ray of 2Ñ…1). In other words, if one of rays is broken, the price consolidation should be expected to occur near the next ray.

Gann Tools


W.D. Gann (1878-1955) developed a number of unique methods of price chart analysis. He paid the most attention to geometrical angles reflecting the interrelation between the time and the price. Gann believed that certain geometrical figures and angles have specific features to be used for forecasting price dynamics.

Gann considered that there was an ideal ratio between time and price if the price grew or fell at an angle of forty-five degrees to the time axis. This angle is designated as "1Ñ…1" and corresponds with unit price increase for each unit time interval.

Fibonacci Spiral

 The Fibonacci Spiral is a geometric spiral whose growth is regulated by the Fibonacci Series. Its sudden, almost exponential growth parallels the rapid growth of the series itself.
 The spiral itself is a series of connected quarter-circles drawn inside an array of squares with Fibonacci numbers for dimensions. This is illustrated below.

Fibonacci Channel


Fibonacci Channels are built using several parallel trend lines. To build this instrument, the channel having the width taken as a unit width is used. Then, parallel lines are drawn at the values equal to the Fibonacci Numbers, beginning with 0.618-fold size of the channel, then 1.000-fold, 1.618-fold, 2.618-fold, 4.236-fold, etc. As soon as the fifth wave finishes, correction in the direction opposite to the trend can be expected.

It is necessary to remember for a correct Fibonacci Channel building: base line limits the upper part of the channel when trend is ascending, and the lower part of it when trend is descending.

Fibonacci Time Zones

Fibonacci Time Zones are a series of vertical lines. They are spaced at the Fibonacci intervals of 1, 2, 3, 5, 8, 13, 21, 34, etc. The interpretation of Fibonacci Time Zones involves looking for significant changes in price near the vertical lines. In the following example, Fibonacci Time Zones were drawn on the Dow Jones Industrials beginning at the market bottom in 1970.
You can see that significant changes in the Industrials occurred on or near the Time Zone lines.

Fibonacci Time Goal Analysis

For construction of this tool, the user sets position of two extreme points. The Fibonacci Time Goal Analysis uses relations of 0, 618, 1,000 and 1,618 for an exact prediction of day, time and the price accordingly at which reaching the trend will change a direction.

Fibonacci Price Projection


Fibonacci Price Projections Traders often get excited when they believe they can use an indicator or tool to ‘project’ prices into the future, but in reality, price projections just give us a possible target that the market may or may not achieve.
Traders use Fibonacci Price Projections (also called “Extensions”) in a similar manner as Fibonacci Retracements, but they are looking to project where price will travel upwards to hit resistance (in an uptrend) rather than find where price will find support via retracements.
While traders often use Fibonacci ratios 38.2%, 50.0%, and 61.8% for retracements, it is quite common to use 61.8%, 100.0%, 132.8%, and 161.8% for Price Projections and Extensions.
What exactly does this mean?
To draw a Fibonacci Projection grid, we’ll need to identify a swing low, swing high, and price retracement against the swing high (for uptrends – reverse the definition for projecting price in a down-trend).  Let’s see an ideal example:
Fibonacci Price Projection Example
This example is done in the context of an uptrend.  We start our projection grid off a Swing Low and then draw the first line to the next Swing High.
1.  In an up-trend, Identify a Swing Low (retracement)
2.  Use your Fibonacci Projection Tool to move from the Swing Low to the next Swing High for the ‘base.’
3.  Draw the Second Line from the Swing High to a Retracement (Swing) Low
The first line (from Swing Low to Swing High) serves as the “Measurement Swing” by which we will soon create Fibonacci Projections.  The “Retracement” Swing provides the base from which to project Fibonacci relationships of the first swing.
For example, if the original swing is $10 and our retracement is $5 down, we would take the Fibonacci ratios of the $10 swing (61.8%, 100%, etc) and then add those values to the Retracement Low.  Luckily, most software programs do all this for us with three clicks – you just need to know where to point your mouse to click.
Now, unlike the Fibonacci Retracement tool where we are looking to find support, we are now looking to find points above price where the market is likely to experience Overhead Resistance.  These will now serve as Profit Targets to help us establish risk/reward relationships.

Fibonacci Retracement

The Fibonacci Retracement is probably the most heavily used Fibonacci tool in the toolset. You will find Fibonacci Retracements as a solid tool in identifying key support and resistance areas.
If prices have fallen from a recent swing high down to a swing low, the expectation is that price should retrace distance, high to low, by a ratio of the Fibonacci sequence. .
You can use Fibonacci retracements and extension from a tick chart through a daily, monthly and weekly.  Literally any time frame
It is important to note, the larger price move from swing high to swing low, the more accurate the retracement projections. Identification and selection of the correct swing points are keys to success.

While there are many variations of the ratio set, simple is better, lets focus on four major retracement levels.
  • 23.6% -- The shallowest of the retracements. In very strong trending markets price typically quickly bounces in the area of this ratio.
  • 38.2% --- This is the first line of defense of the current trend. Breaking this level starts to erode the underlying trend. 
  • 50% -- The neutral point of any retracement. This is the critical tipping point.
  • 61.8% -- retracing to this typically signals a breakdown in the trend.
  • 100% -- Matching the move
In this section we will also show examples of how potential opportunities form when price retraces beyond 100% by following another set of Fibonacci ratios:
  • 138.2%
  • 161.8%
  • 200%
Notice in each case we have simply added 100% to the standard ratio set. I use this set of retracements on a daily basis, from 23.6% all the way to 200% and sometimes 300% For my style of trading I find 38.2%, 50% and 61.8% quite reliable.I use the other primarily as confirmation levels.

So lets take a look at some examples of Fibonacci Retracements in use. 
Example 1:
Take the example below. The EUR/USD had risen from 1.3360 to 1.4278. The next day the EURUSD failed to make a new high and the potential swing point was in place. So I using swing points I placed a Fibonacci retracement on my chart.
Fibonacci retracements
The trend was obviously very strong and the first retracement to the 23.6% level was met with a violent change in direction. You can see the dip below the 23.6% level and the sudden reversal. While there are multiple entry methods, the most conservative would be to wait until the level is penetrated and price establishes itself above that level and enter on the open of the next bar as shown.
Fibonacci retracement
With the right money management, you can see in this example this could have been a serious winner.
Fibonacci retracement entry
Once you understand the method you can find countless examples. Every market, FOREX, Equities and Futures each exhibit these patterns to some degree. 

Example 2:
Lets look at another example using the USDCAD. You can see in this example there are multiple entry points for both trend and countertrend trades.
Fibonacci retracement stopped and entry
Fibonacci retracements zoom
Lets zoom in and look at the area highlighted in blue. Fibonacci Ratios work on virtually any size price swing.
The chart below shows the Fibonacci Retracement applied to the smaller price swing.
Fibonacci retracement short
The blue ellipses show the high potential entry points. Notice, in each of these cases you could have entered the market with a relatively tight stop loss with high reward potential.

Ok, we have shown some examples of well behaved price action. What happens if price retraces 100%?  How far can it go beyond this point? Fibonacci ratios provide some clues to answering this question and finding low risk entry points.

Example 3:
The example below shows the GBPUSD making a bottom and bouncing back. And multiple entry points from the same set Fibonacci  Retracement levels.
Fibonacci retracement short set-up
Of note are the high potential entry points at 38.2%, 50% and 61.8%. Each of these could have been entry points with solid profit potential. However, notice after the initial breakout above 100%, there were other opportunities to get in the trade. Ultimately price jumped to the 138% point before backtracking.

This example shows yet another way to use Fibonacci Retracements. This example shows why it is valuable to identify potential levels above and beyond the initial 100% retracement.

Retracements are the cornerstone of Fibonacci theory as it applies to the financial markets. Hopefully these examples have provided guidance from which to draw your own retracements and expand your trading toolset.

To recap, while there are other retracement values, my defaults Fibonacci Retracements always include:
23.6%100%
38.2%138.2%
50%161.8%
61.8%200%
You can never tell when price action it going blow well beyond the 100% level.

Fibonacci Fans

Fibonacci Fans

Having had a look at speed resistance lines in forex charts – their purpose as an indicator being to provide information on possible levels of support/resistance in a retracement following a trend and also the rate of retracement – we probably ought to check out Fibonacci fans, similar method, looking to supply a similar answer, given an initial trend….
A picture being worth a 1000 words etc. here’s the deal on a real chart.
fibonacci-fans.gif

Having found a trend line, the (here) 2 outer fan lines are drawn from the origin to intersect the perpendicular of the peak at the 2 Fibonacci retracement levels, 0.382 and 0.618, or 38.2%, 61.8% on the chart. (If you’re not up on Fibonacci calculations the background is here – Fibonacci retracement). There’s a 3rd fanline (here, black) at the secondary Fibonacci root 0.500.
The interpretation is simple – a price finds (trailing) support/resistance at the fan lines. It should/may bounce between these 2 containments for as long as the trend continues.
Naturally, the use of Fibonacci fans rest heavily on the principles of Fibonacci retracement in general – if you don’t entirely buy into this as a viable forex technique when taken out of the classroom – as I for one, do not – their use is, well, dubious… but, there’s room in this world – you’re always encouraged to think differently…

Fibonacci Arc


To build a Fibonacci Arc, the position of two extreme points must be set. This is done by drawing a trend line between the two points. This line can be drawn from the lowest cavity or gap, to the highest peak on the chart. Then three arches are created with the center arch falling at the second extreme point. The arches should be drawn at the Fibonacci levels of 38.2%, 50% and 61.8%.
Fibonacci Arc is considered to demonstrate the potential levels for support and resistance. Generally, Fibonacci Arcs and Fans are both drawn on the chart at the same time. This allows the levels of support and resistance to be defined by the points where these lines cross. It should be understood, that the points crossing the arches from a price curve can vary depending on the scale size of the chart. But, because the arch is a part of a circle, its form is always constant.



Simply put, Fibonacci Arcs are constructed by first drawing a trend line between the two most extreme points on the chart. For example, the trend line should be drawn from the lowest gap to the highest opposing peak. Then, three arches are drawn with the second arch centered around the second extreme point.
The radius' of these arches represent the distances along the trend line in proportion to it's length and are equivalent to the Fibonacci levels of 38.2%, 50.0%, and 61.8% on the chart. By interpreting the Fibonacci Arcs, you are able to anticipate the support and resistance as prices approach the arcs.
The following chart will illustrate just how the arcs can supply information on support and resistance. The most common technique is to display both the Fibonacci Arcs and Fan lines together in order to anticipate the support and resistance at the points where the lines intersect. Remember that because the arcs are circular in relation to the chart axis, the points at which they cross the price date will vary depending on the scale size of the chart