One of the commonest grave errors in reasoning about numbers is to concentrate on the best or the worst, the tails, and not the entire distribution. That's why we use measures like the standard deviation or absolute deviation as a measure of spread rather than then range. It's also why we should never look at the characteristics of the best-managed or best-performing companies, and see what variables are associated with same, and then conclude that those variables, such as a focus on market leadership, have a positive impact on results.

We also see this mistake when we concentrate on the last 10 recessions, and look to see what characteristics they had in common, or the companies that perform best during a year. It's quite likely that the best and the worst companies share the same inordinate tendencies in the same direction. Furthermore, it's possible that the same variable that has an important differential impact on the likelihood of creating an extreme, has a very small overall impact on expected results.

There are numerous examples of this mistake, for example focusing on the variables that inordinately were associated with recessions in the past, e.g. the differential in the yield curve, so it would be good if you review your own favorite studies, including those of the Jim Collins variety of the 50 best-managed companies, to see the fallacious conclusions that concentration on the extremes alone can cause.

In a study I reported yesterday, I concentrated on extreme moves of 10 or more points in S&P, and I threw out all other moves. It left out much valuable information. To refresh, we were looking at one day moves and considering whether they swing from +10 to -10 or -10 to +10 to an inordinate degree. I pointed out that this was very different from the question of whether a move of + 10 was bullish or bearish, or whether a move of -10 is bullish or bearish.

I left out what happened in the vast majority of all cases when the one day move is less than 10 in absolute value, i.e. it's a small decline of less than 10, or a small rise of less than 10. The complete 3 by 3 table:

3x3 StudyWhat is clear from the table is that there is a inordinate tendency for move of less than -10 the previous day to be associated with large changes the next day. Indeed, there are almost as many changes of +10 or -10 the next day following changes of -10 the previous day as there are changes between -10 and +10. For the moves of less than 10 in absolute value, however, there are about twice as many small changes between -10 and +10 the next day, as there are big changes. The same is true for moves greater than 10 the previous day. For the individual cells in the table, you can compute a standard error of approximately 20. Thus, the entries in the first row are approximately two standard errors away from expectation.

This table shows clearly how concentrating on the extremes obfuscated much valuable information.


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