Validating the T-distribution for use in my retirement blog

In the last post I mentioned that I saw in a Sanjiv Das paper that he used the T-distribution to model returns. This had intuitive appeal because it forces fat tails and is easy to code. This is easier than trying to figure out how to parameterize a gaussian mix or a chaos hit on net wealth. For those I need to figure out how to do them every time I fire up my R-console..again.  (t) has the disadvantage of being too symmetrical in the tails where the S&P, say, has mostly a fat left tail and it's fatter in monthly series than annual.  But I liked the hassle free nature of using a simple random t function. The only question was "does it matter enough?"

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.

Sense-making in Retirement via Triangulation

I had a chat with a worthy man on Twitter the other day. The idea within the chat was that early retirees, facing up to 50 years of life and a suppressed 10 year prospective-return expectation (he was using Research Associates [RA] capital market assumptions in this case for large cap stocks of some kind that had ~ 2.4% nominal return with a 2% inflation expectation) are in kind of a bind.  In order to attain a very high (we talked about the pros and cons of using 99%) chance of success, one might have to spend as little as 0.25% to succeed according to the conversation.  Since that is effectively a zero spend rate I thought I'd take a look at this question by triangulating my way to an understanding of how I might look at it in different ways using the various tools I have worked with over the past seven years or so.  

Multi-period efficient frontier contextualized on a surface

 A few posts back I created a geometric return surface based on combinations of arithmetic return (x), standard deviation (y) and realized long horizon geometric return (z).  That was a relatively empty exercise since there is no context as in "why wouldn't we just pick the highest z?" Well, because you can't. You are limited to what is investable along the effects of diversification that are implied in the efficient frontier.

10,000 years of a geometric return series done 1000 times

I keep saying I'm done here on RH but that does not eliminate my curiosity. I was wondering what 10,000 years of simulated geometric returns would look like. That's way way outside any reasonable lifetime but it is closer to infinity than not in practical terms. Let's see what it looks like...  

I took the (arbitrary) annualized return for N(.07,.25) and ran it through this:

On the alliance between fail rates and household balance sheets

In a previous post I riffed, among other things, on my shift, over 10 years, from simulated fail rates to the household balance sheet. The latter comment implies, but did not make explicit, that my move was from an accounting balance sheet to an actuarial one, and from a deterministic or point estimate of spending as part of the A/L calc to a 'distribution' of spending via a stochastic present value calculation.  

Evolution of RHedge over a decade in one table

This is the evolution of my sensibilities over a good long while of doing this. I keep saying I am approaching the end, and that may still be true, yet here I still am. I was at a secret covid-bar having lunch and a drink and this is what I was thinking about as I was working on such important things as my sandwich and wine:

 

Riff on time averages and geometric means

I've done posts on this before but it was on my mind again. The analysis of single period finance usually relies on arithmetic returns but real people live in time so it looks different on a realized, multiplicative (geometric mean) basis. Even Markowitz (2016) made this point on his own methods.