## Wednesday, October 2, 2013

### A geometric approach to materiality (Part I)

I think my friend Carl Bacon will be proud of me for this post (no, I haven't been completely won over; I just see some merit in this limited case!).

Talk is cheap: show me the numbers!

The subject of materiality came up during this week's monthly Think Tank webinar, and it caused me to reflect upon it a bit more than I have in the past.

We often opine on different approaches to defining materiality, but until you actually look at real numbers, it is difficult to judge one approach versus another. And, as for approaches to defining materiality, I believe that there are basically two in use today:
• Arithmetic Absolute: where you simply subtract the corrected return from the original, and if the absolute value is greater than some threshold (e.g., 50 basis points), you classify the error as being "material."
• Arithmetic Relative: where you take the absolute difference and determine the percentage change it represents relative to the originally reported return (e.g., if the arithmetic absolute is 0.50%, and the original return is 15.00%, divide 0.50 by 15.00 to get 3.33%).
I tend to prefer relative, because it is my belief that absolute differences mean more when returns are small as opposed to when they're large. For example, let's consider age. Our younger grandson, Caden, is one year old. Actually, he'll be two on November 21, so he's roughly one year and ten months old. We normally state ages this way for young children, yes? Why? Because to only use years will mislead, as there is a big difference between a one year old and an almost two year old.

I will be 63 on November 11. If I were asked my age, would I say that I'm 62 and ten months old? Only if I were truly anal, and then probably be even more granular.

Caden's brother turned four on August 1. If I mistakenly told you he was three (and at my age, senior moments occur more frequently), I'd be off by one year. Given that there is a pretty big difference in maturity between a three and four year old, we'd probably agree that this was a "material" error. However, if I mistakenly (?) told you I was 61, would that one year error be material? Probably not, since I haven't matured very much since I was 61.

And so, perhaps absolute differences aren't the best approach. What about relative? I think this is clearly superior, because there would be a 33% error in the case of my mistake with Brady, and a significantly smaller number when incorrectly reporting on my age.

But then after our monthly call it occurred to me: what about geometric?

Well, this post is already a bit too long, so I will save that discussion until tomorrow!