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Sticky Scope and Basis for Fibonacci & Pivots
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JimDean
Posted 9/20/2010 10:07 AM (#943)
Subject: Scope and Basis for Fibonacci & Pivots



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Fibonacci numbers are fascinating to many people, and have found many uses in trading. Some are fairly simple, and very common (retracement rules), while others can get very complex mathematically (spirals), or even take on a "mystical" flavor (Elliott Waves).

This Room is dedicated to general discussion about Fib's and their derivatives (plus Pivots). Please do NOT post OLang code here for indicators or systems or stops - rather, put the code in the OLang Sections with URL-links here to them.

Please make sure your posts have SOMETHING to do with either Fibonacci or Pivots. The following posts in this (frozen) thread give a some simple general tutorial on the Fibonacci series and ratios, and also on Pivot theory and construction.

Please note: "Pivots", here, refer to peaks and valleys ... not to "floor pivots" which are simple levels based on ratios against a prior bar. Floor Pivot discussions should go elsewhere.
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JimDean
Posted 9/20/2010 10:30 AM (#944 - in reply to #943)
Subject: Scope and Basis for Fibonacci & Pivots



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Brief, brief primer on Fibonacci concepts:


A. The Fibonacci Series is: 0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987, etc to infinity … each new term is the sum of the prior two terms. This series can be used for bar-count Fibonacci validations, for instance. Many people use it to define parameters for moving averages, etc.


B. The "golden ratio" (GR) is approx 1.61803… - it's the quotient of a number in the Fib series divided by the prior number in the series (610/377, 377/233, 233/144, etc - less accurate for the first few terms in the series … the GR "converges" as the numbers get bigger. It's an irrational number which is a "universal constant", like pi or e. Derivatives of the GR are the basis for almost all Fib trading applications and most leg-based Wave theory.


C. The INVERSE of the golden ratio (IGR) has an interesting property also - it equals the golden ratio minus one: 0.61803... If anything, the IGR is better known than the GR, since it's always a part of popular "Fib Retracement" tools and rules.


D. Other "Fibonacci Ratios" (FR) are powers and roots of the GR(1.618) and IGR(.618) ... the most common are the square root(.786) and cube root(.852) of IGR, the square(.382) and cube(.236) of IGR, and finally, the square(2.618), cube(4.236) and square root(1.272) of GR. Since the series starts with 1,1,2 … those ratios (1/1=1.00 and 2/1=2.00 and 1/2=0.500) are also considered part of the "magic ratio list" (my term). A "sequential list" of these popular ratios is therefore (less-popular values are italicized):
.236, .382, .50, .618, .786, .852, 1.0, 1.272, 1.618, 2.618, 4.236


E. The Fib series, and the Fib ratios derived from the GR, appear in nature in countless amazing ways - the shape of a leaf, petals of a flower, chambers in a nautilus shell, dispersion of smoke, etc. Truly, truly cool. Personally, I believe this is just one of millions of other things in the observable universe that testifies to the amazing and glorious handiwork of Creator God. But that's a bit off-topic :-)


F. Many people over the past decades have observed that "moves" in the market seem to fall VERY often into patterns related to these "magic ratios" and to the Fib series. This has given rise to many complex "market theories" - most notably Elliott Waves - which IMO are interesting but which I also think are too force-fit (and complex) to be useful in practice, in their full-bore implementation. However, I do consider the rudimentary conceptual building-block concepts of those theories to be useful (such as 5-leg waves and ABC patterns ...)


For those of you who never encountered this information before, it probably sounds like a bunch of interesting (or boring) math ... but don't discount it too quickly. This is NOT in the same camp as astrological studies, Maria's musings, or Joe Kramer's wildman "predictions". The evidence of Fib effects in real-life stock charts over many decades is just too pervasive to discount.
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JimDean
Posted 9/20/2010 2:36 PM (#945 - in reply to #943)
Subject: Scope and Basis for Fibonacci & Pivots



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Brief primer on Pivot construction (remember, no code in this Room, please):


The most common (simple) definition of a Pivot is a bar that is both preceded and followed by two lower highs (peak or high pivot) or two higher lows (trough or valley or low pivot).

Pivots are the basis for many "chart patterns" such as double tops/bottoms, head-and-shoulders, and of course almost all leg-based Wave theory. They often denote price-resistence and price-support areas ... VITAL concepts for a trader to understand.


There are many alternative means for identifying Pivots, as well as using them. This "primer" speaks mainly of how they can be identified ... many following discussions will deal with their use.

The most important thing to know about a Pivot is that you don't know you've got one until it's a few bars in the past. The basic Pivot-ID rule says that a High pivot must be preceded and FOLLOWED by two bars with lower-highs (and no intervening bars with higher highs). This means that a you cannot know a bar is a Pivot until at least two bars AFTER it have completed.

This is important since when Pivots are used as a part of Trading Strategies ... for Indicators, Systems, or Stops, it can be easy to fall into the trap of looking over historical simulations and presuming that you can "get in" or "get out" AT the Pivot. You cannot. Period. There is always, always a "delay".

A goodly number of Nirvana's tools incorporate "pivot logic" ... and Nirvana does caution users about this ... but since many people don't "read the instructions" they don't realize it till they've lost money and asked questions and suffered some frustration. Hopefully this post and related threads will help eliminate that problem!

Recently, Nirvana has added a feature to the Strategy Builder screen where red borders appear around Blocks in the strategy that contain selections which are referred variously as "non-mechanized" or "optimized". These terms IMO are OK but can be misleading in that they are not complete nor precise. Suffice it to say that most (not all) strategies that use Pivots in them somewhere will have a red border on one or more boxes. A lot more could be said about this, but it would take us off-topic ;~)


There's a LOT MORE to Pivot-identification than just the surrounding-two-bar rule. The rest of this post will discuss various means of more robust "Pivot-trapping". I'll explain them in terms of a hypothetical (ie for-a-fee ;~) Indicator or System or Stop that has a variety of user-controlled input-parameters to toggle and tune the rules. Please note that although some of these are used in the industry, most of them are "home grown" ideas:

1. Typically pivots are defined on the basis of a bar's High or Low price - but sometimes those prices can be sort of crazy. So, parameter-driven alternatives worthy of consideration might be:
Extremes: high or low
Tails: wick or shadow (wick = halfway point of top tail, shadow = halfway point of bottom tail)
Body: open or close (depending on which comes first)
Range: single-point, average of high and low
Typical: average of high, low and close
Guts: (my favorite) weighted average of OHLC = (H+L+O+O+C+C)/6
Close: a stable single point, but not as representative of the full bar as some other combo's

2. The "two-bar" rule is arbitrary ... it could be modified to call for 3 bars on each side ... or maybe 4 ... or even just 1. Lower numbers increase the number of pivot-candidates, higher numbers make pivots more "picky".

3. The surrounding-bars classically can be in any sequence. That is, if the sequence of Highs is 5,4,6,2,3 then it would define the 6-bar as the high pivot, as would 4,5,6,3,2. However, the second "successively lower highs" sequence defines a more consistent "arrow" point, so, though it's less common, the points ID'd that way might be more "legitimate". Note that this "successive" rule just ignores intermediate bars, so a two-bar-successive rule would ID the 6-bar as a pivot in the following sequence: 3, 5, 4, 1, 6, 3, 4, 2 ... where the ones in that group which matter are: 3,4,6,3,2. Please note that this rule, while finding fewer and "cleaner" pivots, can introduce more lag.


Once a Pivot has been "identified" (by the rules above), some methods call for it to be further VALIDATED by prior or subsequent horizontal (time) &/or vertical (price) differences. Again, this can be done in many ways, that should be selected based on the application the Pivot is being used for. Some of these methods are implemented by standard tools like OT and MetaStock ... but many of them are "home grown" alternatives:

4. A minimum Price-change between Pivots is sometimes used to validate a pivot ... that is, if a new pivot is not "far enough away" from the prior one (vertically, in dollars), then it might not be considered legitimate. This required-minimum change can be usefully expressed either as Percent of Close, or as an ATR multiple (or the max or of both).

5. A minimum number of bars between Pivots is the "horizontal/time" alternative (or companion) to the vertical/price rule above. If a new pivot comes "hard on the heels" of the prior pivot, maybe it's not a legitimate pivot ... maybe it's just a volatily consolidation zone. Min-bar-spreads can help in some cases to avoid false pivot-ID's.

6. A minimum DIAGONAL distance between Pivots might be used for validation ... ie a combination of price and time rules. The units of that distance would be either "bar-percent" or "bar-ATR's" ... bar being the time component and percent or ATR being the price component. The good old Pythagorean theorem is used to calc the diagonal distance: time^2 + price^2 = timeprice^2 ... you input the value for "timeprice" and the code compares that to the combo of time and price differences.


The bottom line is that there are many mathematical and logical twists and turns that you can use to formulate how to find a Pivot ... the goal of course is to find something that usually matches what your eye and brain are telling you - and what you think OTHER traders are "seeing".


All of this can be done in OLang - for those of you who already know how to program pivots, this should give you some nifty new ideas - for those of you who don't want to try to program them, but would like to make use of this in your personal trading strategies, contact me via email for a price-estimate.
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JimDean
Posted 9/20/2010 3:02 PM (#946 - in reply to #943)
Subject: Scope and Basis for Fibonacci & Pivots



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What happens when you COMBINE Fibonacci thinking with Pivot-identification? Well ... you gain even MORE ways to "validate" a potential Pivot. You need to read the two preceding posts before diving into this one, btw.

The core idea of pivot-to-pivot "Wave" theory is that the length of a wave often is related to the length of the wave (or waves) that came just before it. The theory is that the ratio of those lengths is commonly very close to one of the Fibonacci Ratios, or is related to the Fibonacci series (both discussed earlier).

This "length" is usually expressed and evaluated as ratio of price-differences (vertical travel), but theoretically it's just as valid to consider the number of bars (horizontal travel) instead, or to combine them into a diagonal measurement. These ideas are the basis for the construction of well-known Fibonacci Retracement ladders, Fibonacci Fans, and (if done properly, which is rare) Fibonacci Arcs. Also, it's behind the Fibonacci Spiral ... a really elegant construct, but not well know due to the difficulty of calculating and plotting it correctly.

Keeping things (relatively) simple, you might choose to "validate" Pivots by whether or not they come close to known Fibonacci Ratios or Fib Sequence spacings. It's of course unlikely that it will hit the ratio "spot on" ... so a "fuzzy equivalence factor" needs to be part of the analysis.


1. An input is required for FuzzYquality ... typically a percent of Close or an ATR multiple. Using either (or a combo of both) of these keeps the analysis normalized for use with a broad collection of symbols with different prices and degrees of volatility. It is assumed that this FuzzYquality approach is used for all decisions in the following options.

2. The ratio of the distance from the candidate Pivot back to the prior pivot, divided by the distance from the Prior pivot to the one before that, can be used as a qualifier. That is, you'll be comparing a down-leg to a prior up-leg (or vice versa). This is what's called a "retracement". Since it's unlikely to be a particular ratio always, this option might simply compare that ratio to a list of Fib Ratios ... possibly you would input a minimum and a maximum ratio to constrain the list.

3. Similar to #2, but comparing the new-vs-prior-pivot distance to the leg that PRECEDED that ... you compare a new up-leg to the most recent prior up-leg, for instance. This has no common name, but could be thought of as an "extension" or "advancement" ratio.

4. Either or both #2 and #3 could be evaluated vertically, horizontally, or diagonally (as discussed above). You'd need a "toggle" to indicate which method you wanted to use.


These "rules", while sometimes useful for "pivot-validation", become more commonly useful as a part of System signal-generation logic. For example, you might have a system that requires a retracement of the most recent leg to be at least 38% of the leg before that, but not more than 78%, to allow an entry in the same direction as the prior leg to be signaled. There are many, many ideas and approaches floating around out there ... and ones that you come up with may be better than ANY of them! The nice thing about it is that OT has the ability to backtest and confirm or debunk the methods, before you put real money on them. :~)
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JimDean
Posted 9/20/2010 3:07 PM (#947 - in reply to #943)
Subject: Scope and Basis for Fibonacci & Pivots



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Posts: 3925
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USA: GA, Lawrenceville
A useful book, not too fancy and not too simplistic, with both theory and practical methods:
"Fibonacci for the Active Trader" by Derek S. Hobbs

For those who are interested in more advanced Fibonacci concepts without digging TOO much in to the wild and wooly world of Elliott Waves,

two books by Robert Fischer:
"The New Fibonacci Trader - Tools & Strategies for Trading Success"

and his more technical book, covering Spirals and other wonders:
"Fibonacci Applications and Strategies for Traders"
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