Summary
- This is probably pretty obvious, but having lifetime income sources matters to consumption utility and seems to matter more and more as the lifetime income approaches the level of a consumption plan in a process that assumes some form of recalculation of spend rates.
- If one recalculates preferred spend rates based on a lifecycle utility model, the answer will change as wealth changes depending on the level of pensionized income and likely change at a different rate than changes in wealth. But that is only if one were to be inclined to recalculate...
The Output of the First Pass
On a first pass this is what I got doing a simulation and calculating the value function E[V(c)] on a lifetime consumption plan "c" for different c and levels of wealth given the assumptions in the notes:
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| EDULC for different levels of wealth Each line is a different initial endowment (.5M->1M) |
Analysis
At first I thought this was confusing. Yes, for lower levels of wealth with their lower (absolute) spend rates, lifetime consumption utility is going to be lower. That is not too confusing. But the optimal level for a spend rate coming out of the model slides up a bit with decreasing wealth. That seemed counterintuitive at first glance. But then I realized that the lower absolute levels of spending as wealth goes down got much closer to the level of SS income available in the model. That means that the step or "snap" of consumption to available income when wealth depletes goes down less in relative terms with lower wealth/spend and since the utility model is concave, the "penalty" from the concavity is not as severe. I have not tested it but it looks like the spend rate optimum might tend towards "undefined" at low levels of wealth which I guess might make sense too. Then, too, at some point, one has no wealth and just social security income and no spend "rate" at all in a conventional sense.
Conclusion?
One way to look at this is to say that pensionizing wealth matters, in a constructive way, to lifetime consumption utility (but that is banal; we know this). This post is just backing into that idea by lowering wealth and thus raising the relative importance and impact of lifetime income to the consumption plan via the utility math.
The other way to look at this is to consider that this might have some meaning if one were to happen to re-calculate consumption utility optima periodically as external conditions change. For example, if there is a recession and the market value of my portfolio goes down and I have pensionized income, then my optimal spend rate (using this model, anyway) as a "%" would change (if I recalculate) at a different rate than the absolute changes in wealth. In other words, in the presence of annuitization, I don't have to cut spending as fast as downward changes in wealth in order to maintain some level of "optimal" consumption (optimal only really makes sense, I guess, in a steady state???)[2]. So, in this case, with these assumptions, when the wealth changes -50%, the spend rate critical point moves around -30% in absolute dollar terms...again, only if it is recalculated.
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[1] - Assumptions are generally the following and are mostly, though not exactly, the same as this post. This is a quick and dirty run so the exact assumptions aren't as important as just doing it. I'll try to point out any differences. The basics: age 60, $1M endowment, SS of 11k at age 70, spend rates are varied in the test but are otherwise in a constant process (that assumption weakly defended here). Risk aversion set to a coefficient of 3. I'm working with a 50/50 allocation in the model for now with an 8%/3.5% return profile and -.10 correlation (all of this may be unrealistic in 2018). Random returns are normally distributed in this run. No annuities. The SS assumptions seem low but I am taking a low level of benefits and discounting further to reflect benefit risk, if any. It's a fairly arbitrary modeling choice. As in the past, note that I have not yet modeled for taxes and fees among other things though those two could be reflected in reduced return assumptions perhaps.
[2] ...recognizing as well a perhaps obvious point that in the original sim run at time zero, that run would have already anticipated changes in wealth in the simulation. So maybe this recalc is unnecessary. But here we are saying something else, like: "if wealth were to drop and stay there, and then if I were inclined to recalculate a spend rate using RiversHedge's model, what would happen to the spend rate suggestion?" Like I said, this may be unnecessary but it is part of my personal wariness approach that advocates for a continuous evaluation of things as the future rolls into the present.
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