Trying out the T-distribution for fatter tails

In past posts I used a Gaussian mix to replicate fat tailed distributions. I liked that because it highlights that there may be more than one thing going on in the return "engine:" a normal narrow thing and a wilder wider unknown thing. Then I tried the same thing with a chaotic process hitting a net wealth process, like earthquake and forest fire magnitudes, which is probably closer to what is going on. BUT, both of those are a hassle to parameterize.

 I was reading in a paper by Sanjiv Das that he likes to use the T-distribution with 5 degrees of freedom as a way of modeling returns with fatter tails. I thought I'd take a look because it is way easier to set up.  The downside is that it is symmetrical with fat tails on right and left where real life returns are a little more asymmetrical. Whatever. My goal here is less hassle rather than hard fidelity.  Also I usually discretize in years rather than months and that shakes out a lot of the non-normality, or at least it does as far as an amateur like me can tell.

Here is a quick eyeball check with r = .04, sd =.12, df = 5 and N=100,000. Normal is red, t is blue.

Yeah, I guess that works.  Easy.  
 

h/t Alex Castaldo