The point should be that I thought for a second that I had mis-coded the software and that I might have to recant the last several posts. How embarrassing that would be.
The real point was to see if, based on the last post where a 50 or 60 percent allocation of initial wealth to lifetime income (SPIA) worked "best," whether a deferral of the allocation via DIAs would produce any incremental benefits, like it did when we deferred a 10% allocation where the answer was yes.
The short answer here was a very quick "no," so my goal pivoted to see: (a) if I had made coding or conceptual design errors, or (b) what went wrong or what explained the abrupt loss of lifetime consumption utility when it had worked so well in the allocate-10%-of-wealth-to-an-SPIA post. Originally I was going to see, since the 50 and 60% allocation to SPIAs were neck and neck in utility terms, whether deferring either would create any separation between the two. But basically, I just gave up after the first three scenarios because it was so obvious that this wasn't going anywhere.
A look-back at the deferral of a 10% allocation
In simple terms the chart in the past post looked like this where there were some gains in econ utility related to deferral. Note that the spend rates are relative to liquid wealth rather than the actuarial balance sheet:
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| Figure 1 from prior post - 10% alloc to SPIA and DIAs |
A - is the SPIA purch with 10% of initial wealth
B - Defer to age 70
C - Defer to age 75
D - Defer to age 80
E - Defer to age 85
Here, however, is the first three deferrals of a 50% allocation
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| Figure 2. Allocating 50% of W to SPIA or DIA(age 70, 75, 80) |
X is the spend rate normalized to the actuarial balance sheet. Y is the expected lifetime consumption utility optima selected in an unseen step for each scenario.
- The blue line is 50% into an SPIA while red is 60%.
- Purple is 50% put into a DIA deferred to age 70,
- Grey is deferred to age 75 and
- Green is deferred to 80.
- The circle is the set-up we'll examine to see what is going on. It was right about here that I thought was going to have to think about recanting or deleting posts.
Examining a longer deferral(80), large allocation to DIA(50%), and high spend rate (8%*)
*before normalization, 4% after
Since the entire point of this exercise is tied to applying a consumption utility formula to real consumption, that means to try to deconstruct what is going on in there, we should look at what is happening to consumption in real terms. When we do that by downloading all 10000 iterations for all 60 periods, this is what we get:
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| Figure 3 - Consumption paths in the 50% scenario with 8% consumption from Liq wealth |
A. this is the inital spend of 4% of the balance sheet or 8% of the monetized portion of wealth.
B. These are iterations that run out of wealth before SS or the DIA and fall to zero. Technically a zero spend is undefined in utility terms or can be thought of as infinitely negative. In the program I give zero spend some token utility for food stamps, some church handouts, food from a neighbor, and some grudgingly offered cash from your ex-wife's brother every once in a while.
C. Social Security kicks in
D. DIA kicks in for those with no money.
E. Some of the portfolios within the 10,000 iterations still have money. Spend goes out, income from dividends, SS, and DIA replenish until wealth runs out and spending snaps to income which would be....
F. longer surviving portfolios that now start to run out of money and crash to income (the DIA that is losing to inflation).
If we look at a broader context in terms of the medians of (a) spend [blue] and (b) wealth [black dotted], it'd look like this:
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| Figure 4. |
Discussion
1. Different software design and functional policy choices might fix this a bit but why paper over what is going after the fact. These are reasonable outcomes in the way things work at least in the way I designed it. I'll think about it, though. For example the "social floor" for utility in cases of no money could be set higher. But that is a judgement/policy choice. Or, rather than letting the original spend rate chug along if it's working maybe I should force every iteration's spending to the DIA, if the DIA is higher when it starts than the local consumption path. That, however, sounds like a recipe for unintended consequences if I'm not careful. Also it would affect all 10,000 iterations the same so it'd be a weird impact. TBD
2. The nature of the CRRA math is -- over 10,000 iterations, with enough individial scenarios that crash before SS or DIA start -- going to severely punish the lifetime consumption utility for those iterations. When averaged over 10,000 cycles it is going to weigh the whole thing down. Therefore high spend and high risk allocations (actually all allocations for those high spends) are asking for trouble. In real life it would probably work out differently but within the confines of a utility simulator it is bad news.
3. Also, note that those early crashes are a) not protected by a SPIA, b) they are closer in time so have less of a subjective discount, and c) happen at younger ages so have a higher rather than lower weighting from the survival probabilities. i.e., the close ones hurt more than the late age crashes.
4. The liquid portfolio here is 1/2 what it was before the annuity purchase (compared to 90% with the 10%-allocation to annuities in a prior post) and must survive 20 years and can't do it under all versions of all alternative universes served up by the sim. The real spend rate against cash is around 8%. With a volatile portfolio, that is flying way too close to the sun and one would have to, in real life, know how at 75 to bridge 5 years of no money (or only SS). For low wealth it might not be much of an adjustment to SS. For high wealth the adjustment is going to be a wake up call.
5. The DIA cash flow has lost ground relative to inflation over the years. Whether at 80 it's enough is a crap-shoot.
6. I don't really think real life would play out like this particular math game but if we were to limit the universe to the math of the sim then I would pick none of the deferrals above and here I am assuming a deferral to 85 would be worse still and an allocation of 60% of wealth to a DIA would compound problems. I'll check some other day on that.
7. It's still possible that I mis-coded something so my vigilance radar is on high.
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