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Joined: 10/7/2004
Posts: 799
Location: Duluth, GA
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Divergences are based on the slope of two lines going in opposite directions (one up, one down). The *sign* of the slope matters and is useful, but the steepness is a much trickier thing to evaluate legitimately and usefully.
Creating a percentage out of price and/or a percentage out of an indicator's value might help you relate/rank that price percentages to other PRICE percentages of different symbols, or relate/rank that indicator percentage to other (similar) INDICATOR percentages of different symbols. However, PRICE percentages vs INDICATOR percentages are still apples and oranges, and should not be directly mixed in formulae of any sort, IMHO. It *can* be done, but the results are usually deceptive in their usefulness.
The main reason for this is that either one or both of the two are UNBOUNDED functions (no fixed max and min) ... price definitely is, and many other indicators are as well. Even BOUNDED indicators, such as Stoch and RSI, are not generally "safe" for this, since the BASELINE against which those indicators is normalized (to get a percentage) is (usually) different for the two. Overlaying a chart of Stoch on top of a chart of RSI, even though the y-axis values appear similar, does not offer useful "crossover" points, for instance.
Another problem with divergence steepness eval's, related to visual inspection of the slope of manual or best-fit lines, is that the charting packages (notably TC) assign differing "optimized" y-axis scales to the price and the indicator chart. That is, those scales differ depending on 1) the ZOOM factor you are using at any given time, 2) the actual historic time PERIOD being looked at, and 3) the barlength in use (daily/weekly) ... the scales are determined from min and max values currently visible in the display. You can, if you wish, lock in #1 and #3, but "time stops for no man" - #2 will always getcha.
Enough negatives ... let me offer some useful positive solutions to help refine divergence analysis. This is based on the assumption that you are using the best-fit-line method to determine slopes, rather than manual peak-peak or valley-valley line construction (each method is legit, but only the former one is readily automated in TC).
The "basic" eval of a divergence has one of two legit states:
Indic UP and Price flat/DOWN = bullish/positive
Indic DOWN and Price flat/UP = bearish/negative
Any other combinations or nuances are not reliable, since they would require the SCALES to be the same. That is, these two combinations should NOT be used to flag a divergence:
Indic UP steeply and Price UP gradually (compared to one another)
Indic DN steeply and Price DN gradually (compared to one another)
If you would like to have more "nuances" to use to help "rank the strength" of divergences, let me offer two relatively easy-to-implement suggestions. I cannot cite references for this, since I came up with the concepts on my own ... so don't be surprised if you have not heard of this before. Nonetheless, it is both legit mathematically and useful, IMHO.
It *is* legitimate to compare the slope of a best-fit (linear regression) line of a given width (i.e. a 10-day span) anchored to today, to that same width line anchored, say, 5 days ago ... either mathematically or visually. The units of the two lines are the same: rise/run = delta-price/width-days. This comparison can legitimately be done for the price slope vs its prior instance, and also for the indicator slope vs its prior instance, but NOT of the price slope vs the indicator slope.
By including these "votes" in the "divergence ranking" paradigm, again just asking a "binary" question as to whether the slope is steeper or shallower than it was X days ago, we now have four new possible divergence conditions that might be telling us something useful (this table lines up properly if displayed in Courier New font, btw):
A. Indic Slope-direction Today ... Down ... .UP. ... Down ... .UP.
B. Price Slope-direction Today ... .UP. ... Down ... .UP. ... Down
C. Indic Slope versus 5daysAgo ... More ... More ... Less ... Less
D. Price Slope versus 5daysAgo ... Less ... Less ... More ... More
That is, Col#1 indicates a downsloping indicator LinRegLine today, which is MORE downsloping than it was five days ago. Col#1's upsloping price LinRegLine today is LESS upsloping than it was five days ago. Another way of thinking of this is the direction of rotation of the line since five days ago ... CW (clockwise) is a bias to the downside (less Up, more Down), and CCW is the opposite.
Col.#1 might be thought of as a STRONG bearish divergence
Col.#2 might be thought of as a STRONG bullish divergence
Col.#3 might be thought of as a WEAK bearish divergence
Col.#4 might be thought of as a WEAK bullish divergence
This is in addition to the NORMAL bull and bear divergences, which considers only rows A and B. That is, cases where rows C and D have the SAME word in them are ones in which the additional nuance is not useful, since we can't legitimately compare the "less-ness" of the price slope to the "less-ness" of the indicator slope (discussed above).
OK ... now we have SIX gradations of divergence ... you can use the same general Less/More approach to add further nuances if you want, and still keep the apples and oranges in their proper bins.
This time, instead of comparing the Indicator 10-day width slope today to a 10-day width line from five days ago, let's compare a 10-day width line today to a 20-day width line today. That is, the anchor point (today) is the same, but the historical period included is different. Therefore we can add two more rows to our table:
E. Indic Slope vs Wider Window (More or Less)
F. Price Slope vs Wider Window (More or Less)
When we include this nuance with the others, we end up with MANY possible states, where D=down, U=up, M=more, L=less, N=nodiff (i.e. the price and slope rotations are both the same letter):
A. Indic Slope-direction Today .. D .. U .. D .. U .. D .. U .. D .. U
B. Price Slope-direction Today .. U .. D .. U .. D .. U .. D .. U .. D
C. Indic Slope versus 5daysAgo .. M .. M .. L .. L .. M .. M .. L .. L
D. Price Slope versus 5daysAgo .. L .. L .. M .. M .. L .. L .. M .. M
E. Indic Slope vs Wider Window .. M .. M .. M .. M .. L .. L .. L .. L
F. Price Slope vs Wider Window .. L .. L .. L .. L .. M .. M .. M .. M
... the table continues ...
A. Indic Slope-direction Today .. D .. U .. D .. U .. D .. U .. D .. U
B. Price Slope-direction Today .. U .. D .. U .. D .. U .. D .. U .. D
C. Indic Slope versus 5daysAgo .. N .. N .. L .. L .. M .. M .. N .. N
D. Price Slope versus 5daysAgo .. N .. N .. M .. M .. L .. L .. N .. N
E. Indic Slope vs Wider Window .. M .. M .. N .. N .. N .. N .. L .. L
F. Price Slope vs Wider Window .. L .. L .. N .. N .. N .. N .. M .. M
... and the simple cases ...
A. Indic Slope-direction Today .. D .. U
B. Price Slope-direction Today .. U .. D
C. Indic Slope versus 5daysAgo .. N .. N
D. Price Slope versus 5daysAgo .. N .. N
E. Indic Slope vs Wider Window .. N .. N
F. Price Slope vs Wider Window .. N .. N
... and maybe these also ...
A. Indic Slope-direction Today .. N .. N .. N .. N .. N .. N .. N .. N
B. Price Slope-direction Today .. N .. N .. N .. N .. N .. N .. N .. N
C. Indic Slope versus 5daysAgo .. M .. L .. M .. L .. N .. L .. N .. M
D. Price Slope versus 5daysAgo .. L .. M .. L .. M .. N .. M .. N .. L
E. Indic Slope vs Wider Window .. M .. M .. L .. L .. M .. N .. L .. N
F. Price Slope vs Wider Window .. L .. L .. M .. M .. L .. N .. M .. N
... and don't forget the NNNNNN case also! ...
So, we get a total of 25 variations, all based on binary results (up/down, more/less), without violating our apples/oranges scale-mixing caveat. IMHO, this offers PLENTY of "resolution" for ranking purposes when it comes to the "strength" of divergences.
If you have a strong opininon about the RELATIVE IMPORTANCE of these three measures (rowsAB, rowsCD and rowsEF), you could choose to assign WEIGHTS to each of the distinctions. For instance, it's pretty clear that the AB state is the most important, so you might assign that a value of plus or minus 4. Let's presume that for some reason you consider the CD state to be more significant than the EF state ... in that case, maybe assign CD status as plus or minus 2, and EF as plus or minus 1. Of course the "N" cases would have values of zero.
All of this can be done either visually (a RPITA if you try to use all six rows), or quite nicely using Linear Regression PCF's (or custom indicators) which determine the DIRECTION of the slope as up/down, and the CHANGE in the slope as more/less. A full implementation of the scoring, etc is not for the weak of heart, but is yields very interesting results that, IMHO, take divergence analysis just about as far as it can be usefully extended (or further ;~)
I don't expect that many people would want to try to implement this entire array of rankings, but hopefully some of the ideas presented here will spur your thinking and offer fertile ground for analysis tools that you can feel comfortable with.
Jim Dean
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