1. Effective Spend Rates. This is what the effective spend looks like for the three constant risk paths. The two dotted lines were for reference, the higher of the two uses the excel PMT function (SSA 95th percentile dynamically estimated distribution periods) and the lower is RH40. We can ignore those two for now. Remember that 4% constant went decisively parabolic and flamed out around age 96 if I recall.
2. Lifestyle Trade-offs. This is the present value of the consumption implied by the three spending paths (10, 20 and 30% constant risk of failure). The grey area is a zone that represents an arbitrarily selected 50% reduction of the original preferred lifestyle[1]. This, rather than running out of money entirely, can be presumed to also be a form of failure. A 4% constant spend, which failed in past games, is thrown in for context as is a vertical line for age 80 as the presumed "annuitize by" age mentioned in a past post.
3. Residual Wealth Path Created by Lifestyle Choice. This shows the pv of wealth for each of the spending paths. The grey dotted lines, as above, were contextual (for me) other spend paths (excel pmt function and my RH40 rule of thumb) which can be ignored. A vertical line for the presumed "annuitize by" age of 80 is there for context. The purple line shows an attempt at estimating the cost of purchasing the 4% constant lifestyle via annuitization at each age. That line is debatable for a bunch of reasons. I cooked it up using aacalc.com just to have something there but it is probably not unreasonable even though it assumes today's assumptions will hold for some bizarre reason. That and the assumptions that underlie the aacalc method may not cohere with my overly simplistic approach.
Some Shoot-from-the-hip Thoughts...
- Constant risk means variable spend. For someone that fetishizes constant smooth spending that might be bad. But then constant risk has it's virtues as well within boundaries.
- If there is an optimal path, an argument not made here, it will be likely off the constant risk path, and again may mean non-smooth spending. This is probably where a lot of the spending rules that I never read come into play. Someday I'll check them out.
- It is relatively easy to see the trade-offs in the "retirement pie" idea especially in figure 2 (if we think of this reductive model as legit and representative which would be a stretch perhaps). One can take from the future or give to the future but it is hard to create out of thin air new value or to lower risk across the board entirely. The only ways I can think of to do that is to create new income streams though something like work or to make -- since we stipulated that a 4% constant spend at t0 was the preferred lifestyle -- a possibly permanent change (lower) in lifestyle expectations. That last may be a future post.
- The 30% constant risk path, if we assume I got the annuity valuation line correct, fails the "keep enough money around to annuitize the 4% path" for most of the way. For that reason and because it drops below the 50% lifestyle mark at a relatively early age means it fails in my book. And that is before we throw random returns, sequences of returns, or random inflation in there.
- If, at age 80, given only what I had in these charts, I had to decide whether to annuitize for a lifetime income that represents my preferred lifestyle at t0 -- and this is without getting into the hard math -- it seems self evident that I would do it. "Self insuring" longevity here, given these limited assumptions, without pooling risk looks like it means some serious diminution in purchasing power later in life that could have otherwise been locked in earlier. Maybe the markets will save us if we throw random returns in there, but then again, maybe not.
- I didn't want to turn this into a certainty-equivalent utility game but if I were to play it then the winners across every game I've played over the last month, including methods not represented here, look like this for a gamma (coefficient of risk aversion) of 4 and no annuitization (i.e., self insured):
age 65-85: 30% constant risk
age 65-95: 20% constant risk
age 65-105: RH40 - which looks like a really close proxy for 10% constant risk
Which I guess means that if one were to self-insure and if one were to have a really really long planning horizon and retire at age 58, then it might not be totally be irrational to be a little bit of a tightwad early in the game and to keep an eye on forward risk estimates. Or the alternative lesson is to perhaps spend more but still keep an eye on risk and then make sure you don't miss the annuity train when it starts to leave the station.
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[1] 5.7% growth 3% discount/inflation. Starting age 58. 4% spend in year zero is presumed to be the baseline preferred lifestyle.
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