Another game with non-normal returns (CTA index)

When I met with Professor Milevsly, one of his comments was that my code -- the code that replicates the Kolmogorov equation for the lifetime risk of ruin by a brute force application of the core probability principle -- has at least some advantages over the PDE because I can model non-normal returns. This, like the last post, is another turn in that game just to see how it goes.  His example at the table was a collared portfolio but one can just as easily demonstrate the principle with any distribution that leans away from Gauss. Here I am going to look at the CTA index and add it to a blended portfolio, a little like I did in 2010 in real life with some private placements.  According to the last paper I read on momentum I might be able to do this with a continuous distribution using chi squared math since that seems to have some affinities with trend following returns.  But that is some other day...


This run is a little sketchy because the data is pretty thin.  The best I could do with free data is use the Barclays CTA index data from 1980+ (hey, my senior year in college!). Since that is annual only, I had to sync that up with annual data for the SnP and for Tbills as well.  That means the data is a little sparse (ok a lot), a little too modern, and maybe overstates returns a bit.  It also assumes that the index is directly invest-able.  Caveats like that always make things a little less reasonable but I'm not a pro or academic, just an amateur hack so I think I can get away with it if I don't make too many grand conclusions.  This is still a playable game, I think.  It might be better if we had continuous distributions rather than discrete/empirical but we'll just view these as hypothetical could-be returns that kinda represent the general idea behind what we are trying to do.

Here is what we are comparing today:

1. Barclays CTA index for a trend following methodology
2. A 50/50 continuously reallocated blend of the S&P and 10year total return Tbills
3. A 70/30 blend of #2 and #1

Because the returns are a little high due to the sparse and modern data I'll unfairly manipulate the data and hit it with higher inflation and fees than I have before.  Lets call it 4% inflation and 1.5% fees and taxes.  This, as you can see, shows that I am not a credible data scientist.

Now we'll take our 60 year old with a 4% spend and longevity somewhere out in the 90s using Gompertz math and we will have him or  her run the portfolio in our portfolio longevity process that we did in the last several posts.  First, though, here are the density curves for the three return strategies. How's that red line for not normal?

Strategy		r	sd	skew	ruin est
red	cta	0.0642	0.1458	2.34	0.11890
blue	50/50	0.0644	0.0937	0.30	0.04623
green	70/30 blue/red	0.0643	0.0808	0.57	0.02091

Then here are the three distributions used in our net wealth process to see how it interacts with the portfolio longevity.  This is what that looks like. Ruin estimates are in the table in front of this paragraph. I did a little change-up on colors by the way.  Red is CTA only. Solid green is the 50/50 portfolio.  Dotted green is the one with 70% 50/50 and 30% CTA.

Obviously the green dotted "wins" the game but we can't really make many conclusions since this was not very rigorous or systematic. I haven't even discussed correlations which is important here. Mostly I just wanted to see what the results looked like and try to throw another non-normal distribution at my new tool for exercise.   That we have achieved.  Now I know that if I want I have a way to systematically test, with respect to lifetime ruin, just like I can in a regular simulator, odd-duck distributions and allocations.  So while this post has no big things to say in particular, the outcome is that I know I probably have what I need if and when I need it and I've taken Professor M's feedback and turned it on in a preliminary way.  That's enough for tonight.


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postscript -- I thought I'd add the cta vs a normal r=.08, sd=.1 distribution just for the visual... CTA in red.