Ok, so I've been doing this RH thing for maybe 2 years and
thinking about retirement issues for at least 10. What's the hardest thing I've dealt with so
far? Take a guess. And it's not backward induction via stochastic dynamic
programming or learning to code R or evaluating stochastic present value or
modeling longevity processes or joining stochastic lifetime process probability
math with perfect withdrawal rates or portfolio longevity processes. No, it is trying to answer my 21 year old
daughter's question about her future retirement. One would think I'd be
equipped to respond to something like this but one would be wrong. This is all harder than I thought. I've never
really had to give advice before to someone that does not speak the same
language I've been working with here at RH. Actually I have not, to my
recollection, given retirement advice to anyone other than myself. Except for
the blog I guess. But that's not advice, just an online diary of sorts.
The proximal question was something roughly like this: "dad, do
you know of any good way to estimate how much I'll have saved by
retirement?" That's more or less unanswerable
in any simple, satisfying way so I was baffled.
This, as I understood it, is really a question about the compound growth
of a net-wealth process with (hopefully) a positive savings program. That can be modeled easy enough in simple
ways given some limiting assumptions (below) but what do you throw at a 21 year old,
even one at Stanford studying econ. A
simulation? Equations? Randomized Excel model? Maybe not. So I was baffled both because I wanted to
give something really simple and mostly true (and I couldn't) and also because what I have been working on at
RH is focused more on the complexities of decumulation than it is on reduced lessons about pre-retirement accumulation. That's not my "wheelhouse" as the annoying and increasingly trite expression goes.
Two things came out of this interaction:
1) What I told her.
What I told here was more or less that the trick is not in knowing what you'll have but rather what you'll have it for. That is a recipe for: a) projecting "lifestyle" (spending) to a retirement age, then b) projecting it again from retirement into the unknowable future, and then c) guessing the PV of that post-retirement spending at the point of retirement; that seems to be the bogey to save for, right?. What is available to deal with "the bogey" at the retirement point comes from the interaction of income and spending over time with the latter hopefully being less than the former. We all hope it is enough when the time comes.
2) What I did but haven't told her yet.
I of course had ditched the discussion of stochastic present value stuff and random variables. I had bypassed dynamic asset allocation and geometric return analysis. I had not use any equations or models. I did, however, after I got back to the RH laboratory, for my own edification and for curiosity's sake, endeavor to model a very very very simple and highly reductive lifecycle process for a 25 year old that tries to look at a net wealth process across both income earning and retirement time. I might share that with her at some point but only if she wants to receive it. Others have done this kind of thing better than me; I've seen them. I just wanted to see if I could come up with something that plausibly illustrates the concept and that can show how the assumptions affect the outcome. While reductive I think I came up with something that does not totally lie about how the lifetime processes work. Except for volatility. And taxes. And longevity. And...well I guess I'm missing some stuff.
Here is the basic idea for #2
If I got the tech right, you can try it here (this is the retirement game with longevity, game rules and capital market assumptions. I added this page/version after what I initially posted which is shown in the graphic above) and tell me if I have missed the boat or lost my mind. The basic idea is this:
1. Income -- this inflates from an initial state at an inflated rate plus some additional trend that can be attributed to what I want to call human capital plus a dose of ambition. This stops at an age when you tell it to stop. This I guess is after tax.
2. Spending -- This inflates from an initial state at an inflation rate plus an additional trend that I want to call lifestyle creep. The creep stops and sticks to inflation at the retirement age. That is a bold assumption. This can be bumped down at retirement by x%.
3. Net wealth -- This starts with an initial wealth level, say zero. Then the process is: current period wealth is last period wealth times a net nominal return plus or minus net savings. Return is split into inflation and real incremental return. Vol is not modeled but vol, taxes and fees might be considered to have an impact on the total nominal return via the incremental real return plugged in there.
4. The "sustainability check" is basically a test at retirement to see if what has been achieved in terms of the wealth/spend rate compares favorably to the wealth unit multiple from a rule of thumb (the recommended multiple). In this case I use my own age-adjusted rule of thumb that is vaguely linked to a constant-risk 95% success rate at a given age. It is generally pretty good at protecting from superannuation risk, in my opinion. The ROT is 1/RH where RH is an age specific spend rate suggestion = [Age / (40 - age/3)] /100. This is debatable of course.
5. Longevity -- this charts an approximate mortality PDF. The red one is based on the SOA annuitant mortality info and the grey one is a gompertz equation where the mode and dispersion can be changed to see what happens to lower or higher expectations for mortality relative to the SOA table data.
When she gets her PhD I'll show her some stuff from Milevsky or G. Irlam. For today this kind of thing is probably a step too far for the chat we had. Maybe I'll show a little bit more tomorrow.
Let me know what you think.
post script...
Oh, and "the game?" It reminds me of the time I was once in a Northwest Airlines 747 simulator. The goal is not to crash and kill everyone on board (I crashed coming into Hong Kong). Likewise, the goal here is not to crash using reasonable assumptions. Check out sensitivity to spending. Retirement age is interesting too. If I'd had this at 25 I would have never ever considered retiring at 50. So maybe the game is flawed from a live-your-life-free-and-expansively-and-without-fear perspective. Whatever. It's good to be aware anyway. Actually I do wish I had a little known more at least 20 years ago...
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