Some thoughts on constant spending in my spend-game context

I wasn't originally going to do a constant-spend (cs) chapter of my spend game. I think that cs is mostly an academic abstraction that is not how most people behave when push comes to shove. Either that or it is for those that fetishize constant smooth spending or don't want to look at or think about retirement math or (counter-intuitively, really, when you look at it) are extremely risk averse.  But since the 4% rule of thumb is part of so many retirement conversations and because I work with advisors that avow personally knowing people who have been severely hurt by the 4% rule, it's worth another look.  This post here is pretty thin and maybe even naive and certainly others have covered this better and deeper than I have, but I thought it was worth a look if for no other reason than to contextualize the previous games I was was working on.  I will not do any utility math or certainty equivalents here because a lower constant spend rate, as far as I can tell, will always have lower utility than higher constant spend.  That is, I suppose, unless we open utility calcs to the idea that people have "utility" for other things like constant risk or growing net worth or something else like that.


In this pseudo-game we have three players: 4% constant spend, 3.5% constant spend, and 3% constant spend.  We also have two context-referees: a 10% constant-risk variable spend rate and a 20% constant-risk variable spend rate.  The "rules" are more or less the same: follow a simple non-stochastic process with $1M at year zero and then each year spend the spend, grow the remainder and move on to the next year with a new spend (in this case inflated at a fixed 3%). Each year/step/move recalculate the following: 1) the effective spend rate on then-current wealth, and 2) the new fail rate estimate[1] based on the new level of wealth and spending and age. Since this is a pseudo-game there will be no  tests to determine a winner. We will just step back and contemplate what happens when we run the players thru the rules.

The Game As it Played Out.

1. Effective Spend Rates.  As in previous games we look at what the "effective" spend rate is in terms of the period spend divided into the beginning endowment.  In this and following charts the grey area is supposed to represent lower probability survival ages. In this case I arbitrarily picked 95 and older.  Remember that this is not simulation, just a simple table of results.  These constant spend rates have been the bread and butter of an awful lot of retirement research that takes it much farther than you see here...and for more reasons than me having a fixed return and inflation assumption.  But this is my game so I get to play it this way. Also remember that the dotted lines can mostly be ignored; they are the effective spend rates for calculating a spend each year that represents a constant fail rate of x%.

2. The Present Value of Consumption.  This is the representation of what the above spend rates look like when applied to a process that systematically spends down $1M.  It is the spend in PV terms discounted at 3%.  It should be no surprise that if one inflates at 3% and discounts at 3% the result is a flat line.  For a little context, the dotted lines, as in #1, are the PV of spend rates for a 10 and 20% constant risk of fail. Note that 4% is abridged because it fails.  Also as above, the lower probability ages for survival are in the grey zone. The vertical line is the age 80 "should probably annuitize" line.

3. The Present Value of Residual Wealth.  This is the trace of residual wealth left behind by the various spend paths.  Same comments as above for dotted lines and grey zone.  As in previous post, the black line is my attempt at estimating the cost of annuitizing the then-current inflated value of a "4% constant spend" in that year.  I have my doubts about how I did this but I will continue to let it stand here. Check prior posts for how I tried to use aacalc.com to do this. Vertical line as above.

4. The Forward Fail Rate Estimates.  This takes each game step and estimates the "current" fail rate risk given new age, portfolio value, and inflated spend.  Since it is constant spend we know that risk will vary.  An analytic fail estimate is used[1] instead of MC sim to speed things up.  Vertical line as above.

 The Outcome and Some Thoughts.

• Since spend rates are constant we know that risk must vary and lo and behold it does.

• Since a lower constant-spend (for same level of capital) calculated at the beginning is more or less the same as having more capital at the beginning (for the same level of spending) and vice versa, this reminds me of the "cost of safety" post I did that reflected on Gordon Irlam's Cost of Safety page and article.  It is really clear here that for incrementally higher capital (or lower spending) there is not only a gain in risk reduction but also a demonstrably diminishing amount of "return" in terms of fail risk the further you go.  Conversely, for lower capital (higher spending) we get rapidly increasing exposure to risk. Risk-sensitivity to higher spending (lower capital) gets super high. 

• In the various games I've done, even though they are just a wee bit simple, it is clear that the absolute amount that is spent relative to the endowment has a much higher impact than in exactly how it is spent.  I should probably expand on that but that's the general conclusion I have.  

• We haven't even gotten to random returns, random inflation, or sequence of returns risk, or legacy goals for that matter.  But when we do, those will put even more stress on the game in its various dimensions. 

• The lower spend rates clearly buy safety (and rapidly so in fail rate risk terms) at the cost of lifestyle but with no gains in any kind of consumption-utility value.  On the other hand this is a little bit of a head fake based on personal experience.  I cut my own lifestyle by 50% between 2010 and 2012.  Yes, that sucked quite a bit at the time. But I regret almost none of it now. A little but mostly not. Most of what was "reduced" was wasteful, inefficient, and probably planet-destroying anyway.  There was no real loss in utility. And for what it's worth, I never had much time for thinking about the big houses, yachts, or lear jets of others.  We also have to assume that half of those folks will be insolvent in 10 years.  If running out of money has infinite disutility as they say, then perpetual freedom has infinite utility and if that comes at the cost of a slightly lower "lifestyle" then that's the way it will be.  The real story here is not about constant spending or even about dynamic spending, it's about adaptation. But that's another post.  

-----------------------------------------------------
[1] In this case I am not doing MC sim, I am using Kolmogorov eq from Milevsky's 7 equations because a) it's faster and MC sim is tedious and b) the math tracks a MC sim really well imho.  Conservative longevity, though, with modal age of mortality =90 and dispersion of 9. real return is 3% and vol is 10%.