Post by TradingForGod on Aug 13, 2004 13:02:17 GMT -5
Happy Friday the 13th everyone. Today, I thought we’d talk about one of the coolest things I have found in trading. It’s cool because it ties trading into the natural world and the creative order of things. It’s the Fibonacci series in mathematics. This mathematical series was popularized by a 13th century Italian mathematician named Leonardo Fibonacci. Thus the name…<br>
The series is very easy to construct. Start with the first two number…1 and 2. Add them together to get 3. So far the series is 1, 2, 3. Now add the last two numbers in the series so far, 2 and 3. The series becomes 1, 2, 3, 5. Repeat. 3 + 5 = 8. And so on and so on. The series becomes 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. Pretty simple, huh? Okay here comes the interesting part.
This series can go on forever, and as the number get larger the ration of the second to last number (n-1) to the last number (n) of the series converges to a non repeating decimal fraction approximated by 0.618. The ratio of the third to last number (n-2) to the last number (n) converges to a non-repeating decimal fraction approximated by 0.382. If you add these two numbers together you get exactly 1.0. Okay, that’s really not so interesting because the series is constructed by adding the last two numbers together to get the next number in the series. So by definition (n-2)/n + (n-1)/n = n/n = 1. That’s just simple algebra, BUT………<br>
If you square 0.618 you get 0.382, the other ratio in the series that adds together to get exactly 1.0. There is no other mathematical series like that. And, if you take the reciprocal of this number, n/(n-1), you get 1.618…out to infinity. If you subtract 0.618…out to infinity from its reciprocal, 1.618…out to infinity, you get EXACTLY 1.0000000000000…..out to infinity. There is no other number like that! This is truly amazing.
The ratio of n/(n-1), 1.618…, is called the Golden Ratio. What is amazing it, and the Fibonacci series, is that they show up in nature all over the place. The petals of lots of flowers arrange themselves in Fibonacci numbers. The angle of the spirals of a pine cone, and a conical sea shell, and a hurricane, and the arms of spiral galaxies are in the golden ratio. The ratio of the lengths of the bones in a human finger and hand are the Fibonacci series. This ratio is a thread that runs throughout creation. It’s all around us, and yet, we usually don’t see it.
There are lots of resources on the web if you want to read more about it, but here is one link to look at for examples of Fibonacci series, and the Golden Ratio, in nature:
www.world-mysteries.com/sci_17.htm
Okay, so what does all this have to do with trading? Well, as I mentioned yesterday in the discussion about Elliott Wave, frequently when markets retrace they pull back in relation to the Fibonacci series. Let’s look at the same MSFT chart we looked at yesterday. (By the way, I just pick this at random, so this is not a “well-picked” example”).
You can see that the rally from late March to late April pulled back into mid-May. They light blue dashed lines are a “Fibonacci retracement tool” on my technical analysis package. The dashed lines represent the 38.2% {(n-2)/n}, 50%, 61.8% {(n-1)/n}, and 78.6% {square root of (n-1)/n} retracements of the rally. Note that the pull back went to EXACTLY the 62% retracement! The advance from mid-May to July 1st pulled back into mid-July. This time, the pull-back just slightly exceeded the 38% retracement (red dashed lines). This doesn’t always work quite so “perfectly”, but I have seen it work more often than it doesn’t.
So how would you use this in trading? I’ll just give one example. Let’s say that you were bullish MSFT after the explosive gap higher in late April. But you really don’t want to buy such great strength because you’re afraid of a big pull-back. You might buy only 10% of your expected position on the break-out. That way if prices do rally, at least you participate. But you wait on the balance and scale into the rest of your longs between the 38% and 62% retracements. That would have worked great in the May dip. But in the July dip you would have only gotten a small piece of the position on since the dip went only to the 38% retracement. How will you know when the pull-back is over and it’s time to buy your whole position? Ah, that’s a topic for another column!
Two more things about Fibonacci ratios and trading. First, many times I have uses failures to hold retracement targets as an EXIT signal for a position. For instance, if you were long MSFT at the top and prices slipped below the 62% retracement of the rally from the mid-July low to the high on 7/21, that would be an exit signal for at least some length. It doesn’t mean that whole rally is done, though it might be, but it does mean that there is a deeper retracement coming that will give a better buying opportunity.
Finally, I mentioned yesterday that the “3” wave usually extends in an impulsive move, exceeding the length of the “1” wave. Well, guess what? Many times that extension is the 1.618 of the “1” wave. Yeah, that’s right. It extends by the Golden Ratio. It doesn’t happen all the time, but it’s a great place to look to take profits if the market is going your way.
I hope you are finding these columns helpful. I’ll pick it back up next Monday as we start a discussion of the various math-based indicators I look at. With the advent of cheap computing power, what was once impossibly difficult analysis has become easy. The problem is that it is SO easy that you can look at so many things it just confuses the issue. We’ll talk about five math-based indicators that I use to try to characterize the market. When combined with trendlines, Elliott Wave pattern recognition, and Fibonacci analysis, these tools are all I use. See, technical analysis isn’t so hard!
Have a blessed week-end.
TFG (TradingForGod)
The series is very easy to construct. Start with the first two number…1 and 2. Add them together to get 3. So far the series is 1, 2, 3. Now add the last two numbers in the series so far, 2 and 3. The series becomes 1, 2, 3, 5. Repeat. 3 + 5 = 8. And so on and so on. The series becomes 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. Pretty simple, huh? Okay here comes the interesting part.
This series can go on forever, and as the number get larger the ration of the second to last number (n-1) to the last number (n) of the series converges to a non repeating decimal fraction approximated by 0.618. The ratio of the third to last number (n-2) to the last number (n) converges to a non-repeating decimal fraction approximated by 0.382. If you add these two numbers together you get exactly 1.0. Okay, that’s really not so interesting because the series is constructed by adding the last two numbers together to get the next number in the series. So by definition (n-2)/n + (n-1)/n = n/n = 1. That’s just simple algebra, BUT………<br>
If you square 0.618 you get 0.382, the other ratio in the series that adds together to get exactly 1.0. There is no other mathematical series like that. And, if you take the reciprocal of this number, n/(n-1), you get 1.618…out to infinity. If you subtract 0.618…out to infinity from its reciprocal, 1.618…out to infinity, you get EXACTLY 1.0000000000000…..out to infinity. There is no other number like that! This is truly amazing.
The ratio of n/(n-1), 1.618…, is called the Golden Ratio. What is amazing it, and the Fibonacci series, is that they show up in nature all over the place. The petals of lots of flowers arrange themselves in Fibonacci numbers. The angle of the spirals of a pine cone, and a conical sea shell, and a hurricane, and the arms of spiral galaxies are in the golden ratio. The ratio of the lengths of the bones in a human finger and hand are the Fibonacci series. This ratio is a thread that runs throughout creation. It’s all around us, and yet, we usually don’t see it.
There are lots of resources on the web if you want to read more about it, but here is one link to look at for examples of Fibonacci series, and the Golden Ratio, in nature:
www.world-mysteries.com/sci_17.htm
Okay, so what does all this have to do with trading? Well, as I mentioned yesterday in the discussion about Elliott Wave, frequently when markets retrace they pull back in relation to the Fibonacci series. Let’s look at the same MSFT chart we looked at yesterday. (By the way, I just pick this at random, so this is not a “well-picked” example”).
You can see that the rally from late March to late April pulled back into mid-May. They light blue dashed lines are a “Fibonacci retracement tool” on my technical analysis package. The dashed lines represent the 38.2% {(n-2)/n}, 50%, 61.8% {(n-1)/n}, and 78.6% {square root of (n-1)/n} retracements of the rally. Note that the pull back went to EXACTLY the 62% retracement! The advance from mid-May to July 1st pulled back into mid-July. This time, the pull-back just slightly exceeded the 38% retracement (red dashed lines). This doesn’t always work quite so “perfectly”, but I have seen it work more often than it doesn’t.
So how would you use this in trading? I’ll just give one example. Let’s say that you were bullish MSFT after the explosive gap higher in late April. But you really don’t want to buy such great strength because you’re afraid of a big pull-back. You might buy only 10% of your expected position on the break-out. That way if prices do rally, at least you participate. But you wait on the balance and scale into the rest of your longs between the 38% and 62% retracements. That would have worked great in the May dip. But in the July dip you would have only gotten a small piece of the position on since the dip went only to the 38% retracement. How will you know when the pull-back is over and it’s time to buy your whole position? Ah, that’s a topic for another column!
Two more things about Fibonacci ratios and trading. First, many times I have uses failures to hold retracement targets as an EXIT signal for a position. For instance, if you were long MSFT at the top and prices slipped below the 62% retracement of the rally from the mid-July low to the high on 7/21, that would be an exit signal for at least some length. It doesn’t mean that whole rally is done, though it might be, but it does mean that there is a deeper retracement coming that will give a better buying opportunity.
Finally, I mentioned yesterday that the “3” wave usually extends in an impulsive move, exceeding the length of the “1” wave. Well, guess what? Many times that extension is the 1.618 of the “1” wave. Yeah, that’s right. It extends by the Golden Ratio. It doesn’t happen all the time, but it’s a great place to look to take profits if the market is going your way.
I hope you are finding these columns helpful. I’ll pick it back up next Monday as we start a discussion of the various math-based indicators I look at. With the advent of cheap computing power, what was once impossibly difficult analysis has become easy. The problem is that it is SO easy that you can look at so many things it just confuses the issue. We’ll talk about five math-based indicators that I use to try to characterize the market. When combined with trendlines, Elliott Wave pattern recognition, and Fibonacci analysis, these tools are all I use. See, technical analysis isn’t so hard!
Have a blessed week-end.
TFG (TradingForGod)
