I’m sorry, but maybe my brain is cramping up. I still have no idea what point is being made by the charts nor why I should care if it looks one way or the other.
Let’s keep this simple.
The classic growth rate formula is (a/b)-1; I presume we all agree on this.
If both numbers are positive, no questions arise. For example, from my S&P acceleration screen:
Ticker EPS%ChPYQ EPS%ChgTTM Acceleration
AFL 16.94% 10.47% 62%
AMZN 142.86% 680% -79%
Etc. That’s pretty easy.
If we use (a-b)/abs(b), the results for AFL and AMZN would be the same, as they should be.
Things can get crazy when we introduce negative numbers. Suppose the numerator is negative and the denominator is positive. We can live with that.
Ticker EPS%ChPYQ EPS%ChgTTM Acceleration
AMP -18.33% 39.01% -147%
Again, the answer is the same whether we use (a/b)-1 or (a-b)/abs(b).
But it makes a huge difference if we have negative numbers in both the numerator and denominator.
Ticker EPS%ChPYQ EPS%ChgTTM (a/b)-1 (a-b)/abs(b)
APC -482.5% -66.88% 621.44% -621%
We know immediately that (a/b)-1 provides an unusable number. The pace of growth has deteriorated horrendously, but the basic formula gives us a powerfully positive acceleration number because it must, given that we have negative signs in both parts of the fraction.
Here’s an example where the numerator is positive and the denominator is negative.
Ticker EPS%ChPYQ EPS%ChgTTM (a/b)-1 (a-b)/abs(b)
APD 3.08% -2.65% -216.23% 216%
We observe a marked improvement in the rate of growth. We have to be showing a positive acceleration figure. And that’s what we see for (a-b)/abs(b). But for the classic formula, (a/b)-1, we see the right absolute figure but the wrong sign; we see deceleration rather than the acceleration we know is taking place.
Now, let’s look at negative numbers in both the numerator and denominator.
Ticker EPS%ChPYQ EPS%ChgTTM (a/b)-1 (a-b)/abs(b)
AMT -26.47% -13.75% 92.51% -93
Again with the classic formula, we’re being forced into an unreasonable and unusable result because the two negatives force a positive answer. Yet we can easily see the acceleration has to be negative. The (a-b)/abs(b) formulation accomplishes this.
Moving on to the formula you propose, (2^a)/(2^b), I right away see an unreasonable result for AMT. I’m not sure whether you mean (2^-26.47)/(2^-13.75) or (2^-.2647) or (2^-.1375) but neither version works. The acceleration rates I’m getting are zero (approx.) or 0.91 respectively both of which are clearly unsuitable; common sense tells us we need to be seeing a significant negative acceleration rate.
We haven’t addressed the approaching zero issue yet, but unless my brain is completely out of whack (maybe it is), it seems your (2^a)/(2^b) cannot be the basis of a p123 factor since it fails to produce a proper answer in a basic situation. If I’m missing something, please show me by calculating acceleration rates under your formulation for each of the situations illustrated here. (I don’t understand your charts and hence can’t discuss them; specific examples such as those presented here are a language I can speak.)
Now, as to the question of approaching zero, there’s a huge difference between what p123 can offer as a standard factor, versus creative solutions individual users might develop if they wish to handle the massive onslaught of oddball situations, which happen pretty much all the time in countless contexts. And we all have our own ways of dealing with oddities we encounter (at least I hope everyone does). If your ratio is better suited for near zero situations, then by all means use it, with whatever accompanying logic (possibly involving the EVAL function) you need. And if you’d like to share your solution, then again, go for it; that’s why we have forums and the ability to set models for community or group visibility. But unless I’m really spacing out, here, it looks like we can’t use it to replace (a-b)/abs(b).