Tripping Over Skew

Apologies for the late post today but I have been on coding duty over the weekend into today, as I wanted to put together a few more weekly statistical charts for you guys. While hacking away I realized that I had actually made a mistake in labeling the weeks, and that means we are currently in week #35 and not #36. Which incidentally makes quite a bit of difference.

But before we get to the weekly goods let’s cover a related topic which is SKEW. We covered it here before and this may be obvious to some of you guys. But nevertheless it is something I tripped over today and attempting to ‘fix it’ cost me several hours of utterly wasted time (hence the late post today) and reduced time at the gym (even worse!). Look at the mean monthly skew for the S&P 500 shown above. Does this look accurate to you? It actually is but I’m pretty certain some of you guys are wondering why the S&P has negative skew almost all year.

And this is why, it all comes down to the definition of SKEW which basically defines ‘positive skew’ as left leaning and negative skew as right leaning. No political jokes or Trump bashing please 😉

Now let’s look at week #35 which actually has a decent positive mean weekly return since 1957.

And the SKEW for this week is -0.5. I actually pulled out all the values for just week #35 and plotted the date range just to make sure. It has a negative skew of -0.5 and understanding how skew is calculated is very helpful when observing the actual histogram:

Which of course simply plots the correlation between returns and their probability. And here we are of course seeing a concentration of bars in the positive range. Which now makes a lot more sense, doesn’t it? 

Most likely I will however wind up flipping the axis of all the skew charts as to not confuse people (or myself – ahem). Figuring that one out will most likely cost me another patch of hair, but in the end it’ll probably pay off as won’t have the explain the topic every single time.

More juicy stats for this week below the fold:

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