Annuity Allocation and Immediate vs. Deferral in a Lifetime Consumption Utility Context

The Point of the Post

In two previous posts, using my rigid and personally particular parameters and a custom coded lifetime-consumption-utility simulator (i.e., you need to have a certain amount of skepticism present in your brain starting now) I determined two things among several attempts to try to see this:

1. At a 10% allocation to a nominal SPIA for a 61 year old using current interest regime assumptions, that allocation delivered demonstrably better lifetime utility than no use of a risk pool,

2. At a 0% allocation to a nominal SPIA for a 61 year old deferring to no later than age 80 produced higher econ. lifetime utility than the SPIA,

3. When trying to allocate to an SPIA between 10% and 80% of initial wealth, a 60% allocation to an SPIA seemed to work the best, and

4. Deferring the 60% allocation did not seem to do much good, utility wise.

So, the question today is whether some combination of allocation between 10 and 60% and some degree of deferral produces a utility-driven outcome that is better than either #2 (10% allocation, defer to age 80) or #3 (allocate 60% to an SPIA).

I'll look at the following allocations to annuities to try to answer the question above:

• 10% - 50% in 10% increments
• Deferral to 0(spia), 70, 75, and 80. 85 proved in a past post to be a non-starter for me.

First of Several Disclaimers

- Read the prior posts and then be skeptial,
- The combo of my particular parameters and my custom code means there's no universalizing this. This is more of an in-post mind game,
- There is an attempt to link to the theory and some of its discontents in link #9 below.

Background and Assumptions

The past posts, so far, are:

1. Self-Evaluation of My Own Lifetime Consumption Utility
2. Self-Evaluation of My Own Lifetime Consumption Utility, Part 2
3. Having Some Fun with Portfolio Choice vs. Lifetime Consumption Utility
4. Lifetime Consumption Utility with addition of trend following-like behavior
5. An attempt at a stylized lifetime consumption utility "frontier"
6. Lifetime Consumption Utility "Frontier" with both Trend-following (fake) and Partial Annuitization (also fake)
7. Adding a DIA to the last post that was looking at a consumption utility "frontier"
8. Lifetime Consumption Utility "Frontier" and DIAs - With Different Deferral Periods
9. Annuitizing Larger Portions of Initial Wealth in a Lifetime Consumption Utility Simulator
10. Deferring the optimal SPIA from the last post with DIAs to look for an even better set-up

with #8 offering probably the best set-up of the core assumptions though all of them set the stage so I will not recapitulate everything here again.


Catching up with Previous Charts

1. The Max Value function for allocations to SPIAs.
This is the "spend" perspective rather than the "equity allocation to risk." Spend is normalized to initial actuarial balance sheet context. 60% allocation was the winner here within the SPIAs but was neck and neck with 50%.

Figure 1

2. Deferral of the 50% (60% by proxy) allocation "winner" generated no additional utility gains.
50 and 60 percent allocations to SPIA were neck and neck on this one. testing the 60% would have had similar or worse results. I don't have a legend but 60% SPIA is red, 50% SPIA is blue. Purple is deferral of 50% to 70, grey to 75 and green to 80. 85 was not run.

Figure 2

3. The 10% allocation to SPIA had some advantages when deferred to age 80 which is the "D" scenario in figure 3, "A" is the SPIA, E is deferral to age 85, C is to 75, and B is to 70. Note: this chart was from before I started normalizing spend to the initial actuarial balance sheet.

Figure 3

Creating our token boundaries for testing future combos. 

This is a synthesis of lines from figure 2 and 3. This takes the green line in figure 3 (10% allocation to annuity deferred to age 80; this was point #2 in "point of the post" at the top) and the top blue line in figure 1 (50% allocation to an SPIA; this was point # 3 in "point of the post" though here 50 is standing in for the supposedly higher 60% red line) and proposes those two as an evaluation range. We are from here forward looking for either higher lifetime utility and/or higher capacity for spending optimally.

Figure 4

Taking a look at the scenarios for 20 - 40% allocations to annuities and their deferrals.

We've already seen 10% (figure 3) and 50% allocations (figure 2) where, for the SPIA anyway, 50 and 60% look interchangeable for now over the interval of interest ... and the presumption is that deferral for 60% will be worse than that for 50% i.e., the reason that I am letting 50 stand in for 60 is so that I don't have to run 60 even though 60 was technically the "winner."   We have the top/max scenario for 10 and 50 in Figure 4.

On the other hand, here are the scenarios run for 20, 30 and 40 so we'll have the full range from 10 to 50 down on paper:

Figure 5

In these and the previous figures, it looks like the following are "winners" in their allocation categories:

1 - 10% allocation* --> defer to 80  * to annuities within the decumulation portfolio
2 - 20% allocation   --> defer to 75
3 - 30% allocation   --> defer to 75
4 - 40% allocation   --> defer to 70
5 - 50% allocation   --> don't defer

6 - (60% allocation   --> 50% is proxy for 60 in this post)
7 - (> 60% were deemed less optimal than 60% so were not modeled)

Looking for a winner

Since we have a preliminary evaluation baseline in figure 4 that already shows the winners for 1 and 5 in the last section, we just need to add 2, 3 and 4, like this below, where the intervals are not all the same due to variability in the manual set-ups of the runs but the spend rates are normalized: 

Figure 6

Figure 6 gives us a "sort-of" winner. Before we go further, though, some more caveats...

First you have to buy into utility theory. Then you have to understand the rigid parameterization I used for myself, not the reader. Then you have to find the lifetime consumption utility differences meaningful which I really don't. Then you have to trust my software in which I have found a couple errors in the last week.

Have I shaken you off yet?  If you are still here then I can try to call an allocation of 30% of initial wealth to a DIA, deferred to age 75, the "winner" with a proviso that the 60% alloc to an SPIA and the 20% allocation with a deferral to 75 (and, for that matter, if you look closely at figure 3, the 10% allocation with deferral to 75 as well) are much friendlier to higher non-optimal spend rates.  That might be a big consideration if spending is not stable over time, but that is another story.


-------- personal notes

I realize this post was awkwardly told but it was a victim of what I had already done in a past post or two which forced me to set it up like this.

I'm surprised that the optimal spend rates weren't higher. I'm going to re-read my own disclaimers and think about this and then decide if I have a risk of having to retract all of this at some point.

fwiw, each line in, say, figure 5 is a combined run of 11 allocations and up to 9-12 increments of spend rates. 10,000 iterations per datapoint would mean  > 1M iterations per line. There are a lot of lines in this post and many of the lines are max lines that are made up of 5 or 6 or 7 other sub-lines.  I have no idea how many iterations have been done for this post, including mistake runs, but we might be in the 100s of millions over the last three weeks.  I think I'm done.