[revised] On the alliance between fail rates and household balance sheets - Part 2

I thought I'd take this past post [On the alliance between fail rates and household balance sheets] a little further.  The post-theme here, in case you want to bail out now, is on the affinity between MC simulation and stochastic present values in some quant terms. My goal here is not really to explain anything to anyone but more to try to consolidate something I didn't understand very well. This self-consolidation may nor may not interest anyone but me. 

Random Thoughts on Portfolio Choice and its Discontents

This has never been a teaching blog but rather a reportage-of-my-learning blog. Two different things. That means a lot of my stuff comes out like any work-product of autodidacts: spotty, holes, not 100% coherent across topics, un-tutored in others, etc. On the other hand that allows me to roll with whatever - which is what I'll do here.  I don't really have a tight theme or thesis just some thoughts from some recent spreadsheeting last week. 

Benford and Retirement Simulation

 I was watching a show on Netflix last night on Benford's Law and wondered if it would hold in the "fake worlds" I create in simulation.  This is a quick drive-by only.  The basic idea of "the Law" is something I extracted (selectively and exclusively) from Wikipedia:  

Adding incremental uncertainty to a consumption utility model

I once joked on Twitter that extreme "risk aversion" (in terms of the coefficient and the convex CRRA model iteself) was less of an "economic" topic and more one of psychotherapy. Heh. I got some pushback on that from a retirement quant but I think in the far-extreme it makes sense.  If one were to be so risk averse in the non-financial sense that one couldn't leave the house, that is not the domain of models and math but of getting mental health help to reduce the aversion.  

Asset Classes, Efficient Frontiers and Time

This post falls, like others in the past, into the category of "I wonder what it looks like?" There is no agenda here and all of the input parameters are absolutely 100% arbitrary and are not shaken against any other parameters to see anything else other than just "what happens with the first set?" I hate to say it and my gf would shake her head but this is just a joy ride. The main question here is:

What happens to an efficient frontier when going from a 2 asset portfolio to a 5 asset portfolio but especially when the EF for both is re-rendered using a "realized geometric return at infinity" adjustment?

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.  

Being In The "Zone"

"The optimal strategy might be executing a suboptimal plan at a fast pace. Strategy evolves as lessons are learned—and the person who moves faster, learns faster. Learning is a marathon and perfection is a weighted vest. - James Clear

“It is better to be roughly right than precisely wrong.“ — Carveth Read*

10 years ago I believed, more than I do now, in the grace of specific numbers and precision. Today, not so much. That's because even if I were to have a perfect, optimal retirement model, and if I had successfully tuned it to the infinity of possibilities of whatever reality we know, as of yesterday let's say, then: 1) you and I would still have results different enough today that it would be hard to explain, and 2) for both of us, the output today could be entirely stale as early as tomorrow morning. Agony, right? I used to think so. Instead, I have been thinking how it matters only generally what we spend and how we invest but not necessarily specifically or precisely. Getting into a "close enough zone" and being willing to adapt are stronger and less burdensome concepts than getting it exactly right. At least I am telling myself that so I don't pull out what's left of my hair.

The Cost of Retirement Certainty

This post is a little bit of a reprise of a post I did a couple years ago. That one, as is this one, is dependent on past conversations and correspondence with others. First, this post here is a riff on an article by Gordon Irlam on the "cost of safety,"  of which this is derivative...although he was working in utility terms and I am working in Life Probability of Ruin terms (LPR). Second, this post is the result of thinking about some conversations with David Cantor on the topic of hedging tail risk (retirement portfolios, not necessarily accumulation portfolios) by way of either technique (options hedging, trend following, risk parity, etc.) or redundancy (surplus capital, more on which later in another post). Fwiw, David has been almost my only interlocutor over the last 5 years and has been a very productive influence. The vast majority of the papers I read now come from his enthusiastic referrals.

3D Lorenz attractor fun on a Friday

I got bored this afternoon. I had been reading two books lately: Ubiquity (how catastrophes happen) and Chaos, a book on the history of the topic.  I was 2/3 through the latter and I was curious if I could pull off a self-rolled version of some of the theory. In this case I picked one of the earliest examples, a Lorenz attractor. This was originally designed to model atmospheric convection.  The point turned out to be that chaotic processes can come from deterministic models and that initial conditions matter (butterfly effect). Here is the intro in Wikipedia:

Some posts I've had fun with over the years (i.e., my favorites)

I'm not completely sure if my blogging days are coming to a close or not but I certainly feel a pull in other directions these days. I've no doubt covered a lot of ground since around 2014 (2012 if we include what I was trying to do on LinkedIn). This post is a compendium of some notable "post topics" where I challenged myself a bit and had a little fun on the way.  These are the projects I'll remember the most when I look back over the past 6-8 years. Recall again, before we start, that I am a student in these posts, not a teacher; the purpose was to learn and consolidate not preach anything.  In no particular order:

Comparing my naive complexity model to earthquakes

In my last post (My baby steps into "critical states" in a decumulation model) I cooked up a simulation that would hit a retirement plan with some chaotic negative strikes -- like the ones we see in the physical world: earthquakes, forest fires, and sand pile avalanches (in terms of how often and how big).  It was a first pass effort so I was winging it for fun and not paying attention to anything real because there is no real underlying stressor-process in retirement that is coherent. That I know of. Yet.

Then, after the post in question, I started to wonder: "huh, I wonder if this machine I cooked up is even close to any real world complexity-dynamic...in at least the way it looks and in terms of prevalence?" In this case I also said "let's try earthquakes first."

My baby steps into "critical states" in a decumulation model

I have only the most superficial, paper thin, and relatively naive understanding of statistics. I know even less about chaos theory and critical states. So, I am uniquely qualified to not write this post. How's that for sand bagging?  But I just finished "Ubiquity - Why Catastrophes Happen" by Mark Buchanan which gave me an idea for how to model hits to a retirement plan that occur like avalanches in a sand pile -- or earthquakes or forest fires -- where there are few if any normal distributions or any kind of predictability around damage magnitude.  Also, I just finished an actuarial paper on "Extreme Value Theory" so my interest was engaged.

First whack at cost of stochastic inflation in decumulation

-----
note: some errors have been corrected since initial post
-----

Ok, let's sandbag right away. I don't know if I got this in the right groove but let's roll anyway.

Using a life consumption utility model, and a simple model for auto-regressive inflation based on historical data, I ran a few new models today:

1. a baseline with deterministic inflation set to the mean of the random distribution I'll use for #2

2. a simulation using stochastic inflation that is bootstrapped from history (1914-2018) with a coefficient of auto-regression over 1 period of .64. (see the link above on inflation)

3. This scenario is the same as #2 except that the initial wealth is stepped up a bit (+25%) to get the life consumption utility up back towards #1 levels (not done analytically. Pretty much just eyeballed it). This is more or less like evaluating "certainty equivalent wealth" but I'm not totally sure about that so I won't precisely make that claim.

The goal was to determine how much extra wealth might be necessary at retirement-start to make the life consumption utility roughly the same as the baseline i.e., that is, either: a) we implicitly spend less...I realize that I have not really shown that here, or b) we have some amount of "redundant" (higher) wealth (vs the baseline) that is held in reserve in a way. Either way, same thing. I might have to expand on this because I know it's a little fuzzy.