I prefaced my comments with the assumption that the data was linear (and said nonlinear data is different).
I am not sure we disagree on the calculations.
I was just focusing on one particular situation, where things were pretty linear, while highlighting that it did not address all of the situations. I guess it was implicit that one might not be using a line if things were nonlinear enough.
Perhaps the biggest problem with the slope of a regression—as any textbook will tell you— is outliers. And the worst place an outlier can be is at either extreme end. And in my experience the biggest outlier is usually the top bucket with the bottom bucket being the second worse outlier. Walter has an example of that and there are other examples in the public ranking systems. But I suspect you only have to look at your own systems for verification.
As it is, we at P123, generally have the worst situation possible for using slope. This is not separate from the problem of nonlinearity and of skew.
I think the outlier problem is about as serious as it gets. One may still want use slope but you have to be in denial to not be concerned.
When the outliers are severe enough you are getting VERY close to taking the top bucket minus the bottom bucket anyway. I will not try to quantify that here but anyone can see that the other buckets lose their impact on the slope if the outliers are significant enough.
Are we in agreement that we do not want to forget the middle buckets and we might at least look at a metric that actually measures these buckets when outliers are a bad problem? I do not mean to imply that they are always a bad problem—I do not have prefect insight into this.
In my case I would just as soon dispense with the fantasy of the slope being a line that fits anything and take the top minus the bottom from the outset. After all, slope is even a little bit off on how the top and bottom buckets are doing. What it tells me is highly dependent on the specifics of the skew and outliers. And it could literally be telling me nothing I want to know.
And again, I do not have perfect insight or knowledge regarding numbers on this but that does not make me love slope. Instead, it makes me dislike it.
I recommend you keep slope nonetheless.
I am not recommending removing anything and you do not need my input for that.
Spearman’s Rank Correlation can pick up some of the slack regarding how rank is affecting those middle buckets for those who do not like slope or think their particular ranking systems has outliers that are too extreme. AND IT COULD SERVE AS CONFIRMATION THAT THE SLOPE IS A USEFUL METRIC FOR SOME SYSTEMS. That the parametric methods are not too far off from what the nonparametric measures are telling you, in other words. I almost always look at both, myself.
What we are doing is ordering and ranking stocks. If that corresponds to an ordering of returns that is a VERY, VERY good thing. I would argue that is what we are about. But for sure, it is worth knowing how we are doing in that regard.
Anyway, good discussion. Your points are good ones. I am learning something even if we are boring Nisser. Nisser, no worries I am working on a presentation on my iPad now. You can print it out and put it on the refrigerator.
The good discussion is more important than what finally happens regarding the metric.
-Jim