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yes, Mike is right. The 50% retracement level is not really a Fibonacci ratio, but it is used because of the overwhelming tendency for an asset to continue in a certain direction once it completes a 50% retracement.
You get the various Fibonacci ratios by calculating ratios between various members of the sequence.
For example, if you divide each member of the sequence by the one just ahead of it, for example, 1/1, 1/2, 2/3, 3/5, 5/8, 8/13, 13/21, 21/34, etc., you get a set of ratios that converges to the famous .618:
It gets closer and closer to .618 as you do more divisions.
Note that .50 is one of the ratios in this series -- although it's basically an approximation of .618, which is what the series is tending toward. Relationships like this are how all the "Fib numbers" are derived.
(Dividing each member of the original sequence by the one two steps ahead -- such as 34 by 89 -- gives a series that converges to .382 after a few steps.)
So, it sort of is a "Fib number" and sort of isn't. But being in one of these series of ratios derived from the original sequence is the only reason anything is called a Fib ratio, or number.
Is this anything more than number games? Hard to say.
But that's sort of the general question about Fibonacci's, isn't it? Depends on how you look at it, I guess.
Bob.
When one door closes, another opens.
-- Cervantes, Don Quixote
This ratio "converges" to 1.618 as the numbers get higher and the reverse ratio becomes 0.618 (1/1.618 = 0.618), thus the golden ratio (elementary). Any other number out there like:
square root of 1.618 = 1.27
square root of 0.618 = 0.786
power 2 of 0.618 = 0.382
power 2 of 1.618 = 2.618, etc.
are a manipulation of the ratio. One can make any combination or a product number he wants using the golden ratio but it is not a Fib ratio.
That said, people tend to forget that the series starts with a 0 and an extra 1. Thus, the reason that the numbers Infinity, 1, and 2 (A/B) or their inverse 0, 1, and 0.5 (B/A) (thus 50%) can be considered Fib ratios at the low end of the series.
Regardless, the golden ratio is a "convergence" number and not an absolute number. It will have different values for different numbers inside the series depending on the numbers of decimals considered. Therefore, any ratio or (inverse ratio) from any two consecutive numbers including 0.5 or 50% can be considered a Fib ratio knowing that it will converge to or 0.618......... at high series numbers.
As far as the validity of the Fib levels and any other levels or patterns like trend lines, ice lines, creek lines, SOT, or break out of channels, patterns etc. applied in trading, are simply areas where traders have traditionally accepted as price levels where there will be a crowd psychological reaction for managing an existing trade, not necessarily entering a new trade.
So, we can sarcastically bash one vs the others as much as we want, But the fact is that some traders knowingly use these levels very successfully. The point here is that one needs to learn how to use certain tools and if they work, keep using them until they don't work or a better tool is discovered.
Cheers!
Edit: 11:46
@bobwest, I posted this a few minutes before I saw you post. Obviously, we share some views on this subject.
Because if you actually, honestly, really look at every single one of those lines you will see that sometimes prices crosses it upwards, sometimes downwards, sometimes it reverses and sometimes it pokes and reverses. Just like every other line/band/area/region/indy/divergence/plod/phod/or/wor/fib/etc/etc/etc that we use. I've yet to see any chart of anything posted where this isn't true, I mean Crumbs, it's even true of vwap and it's merry bands. Holy mackerel batman.
One man's discretion is another man's science, art or skill.
