Starting with $1,000,000, a feeling that a 4% lifestyle in that first year seems about right, and an assumption of ~5.7% returns [1] and 3% inflation I'll use the following spends:
1. 4% constant inflation-adjusted spend
2. PMT function using the Society of Actuaries data (from aacalc.com) for the 95th percentile for a male. This is an aggressively conservative assumption using a healthy self-selecting sub population.
3. PMT function using the SS Administration life table data for the 95th percentile for a male. This is a normal, quite conservative assumption using a general population.
4. An RMD style function (Wealth / remaining years) using the SOA 95th percentile. Blanchett likes this type of calc but mostly at later ages where there is 15 or less years remaining in the plan. AAcalc.com (Irlam) suggests something like this as a simple rule of thumb but then again I am dumbing down what is otherwise a pretty smart ruleofthumb. You'll have to read on your own.
5. An RMD style function (Wealth / remaining years) using the SSA 95th percentile.
6. A 4% constant spend except this time with a 1/2 % downtrend in spending. These downtrends have been documented by researchers like Blanchett and others as a realistic behavioral expectation although they actually estimate the trend at -1% or more.
7. The RH40 spending formula because, well because it's my blog and I want to throw it in there. [2]
Then I'll see how it plays out in terms of spending that is discounted at the same rate as inflation (3%) and the present value of the wealth level using the same discounting assumption. I will totally ignore more complex math, multi-period models, simulation, and anything else that is too hard for me to deal with today. I'll evaluate this non-scientific pile of "spends" in even more non-scientific ways. I'll use some fuzzy criteria that the RiversHedge retirement plan might use, such as:
A. Higher spending at earlier ages is better than later especially at higher probability ages before about 85 or 95.
B. Notwithstanding A, setting aside small reserves in early retirement years (58-?, maybe 75?) for uncertain risks that are mostly unrelated to longevity risk like spending shocks, an unfortunate series of returns, unexpected inflation, etc. is probably wise. On an actuarial balance sheet these might be specifically budgeted but here we'll leave it as fuzz...
C. Depleting wealth is preferred here to leaving a legacy balance that could have otherwise been spent
D. The sweet spot for higher spending, notwithstanding B, is maybe somewhere between 65 and 85 or maybe 65-80.
E. Lifestyle compromises or destruction more than about 25% before age 85 is bad. This is a cheat for a bunch of reasons not least because for me, I sucked up a 50% reduction in lifestyle my first year of retirement. Unfun.
F. Running out of money before an arbitrarily selected age 100 is bad.
G. The utility (or the certainty equivalent) of the PV of spending, if not the sum of total spending, over two different age ranges (65-85 and 65-95) should be higher rather than lower. [3]
Given all that, and note I baked in a little too much redundancy in the criteria, we'll see who wins! Here's what it looks like on a chart
That's kind of a mess. I hope you can read it and differentiate colors because I am not writing up the legend.
In starting to look at this I'll take two spend strategies off the table: 1) the 4% constant because it fails before 100 which was criterion F, and 2) the RMD based on the SOA 95th percentile because it requires a greater than 25% hit to lifestyle before age 85 or criterion E. That's a little arbitrary I guess but those were my rules.
Here is a rank ordering of the remaining plans two ways: a) the sum of the PV of income over 2 age ranges 65-85 and 65-95, and b) the certainty equivalent [3] of income over the 2 ranges:
I am not totally sure how to interpret this but I was gratified that my RH40 rule was a strong contender and was a winner at the full age range and hyper-conservative risk aversion levels. Now let's do a more subjective analysis that would withstand no scrutiny by anyone other than me. We'll use the criteria described above against the spend plans described above. Then we'll do a very unscientific score for each intersection of plan and criteria.
Conclusions?
Well, first of all let's be clear that this is rigged. The judge is paid off. This is like an Olympic diving competition in the late 70s judged by an all east German panel. The deck was stacked if for no other reason the criteria were redundant and leaned in my favor. You had to know that RH40 would win. But then again this is not a total fake. The second thing is that there are about a million other spending plans that in this deterministic world I could have used. Knowing the rules I could have gamed this a bit. For example I could have arranged a constant spend through the (by the rules here) important years of 65-85 and then done an assertive step down thereafter or shortly before the end of the range. I could have also combined plans like the 4% constant spend with a second function like PMT using SSA95 at some threshold age or wealth or spend. In the end it probably doesn't matter because the resources are one pie and there are only so many ways the pieces can be pushed around. Others have played this game and come up with different answers. Me? I was just having fun showing that my spending rule can hang in there when looking at it seriously. In the end I guess my take away is that all these plans have pros and cons. The PMT functions are blind to non-longevity risks early in their arc, the RMDs on the other hand look too risk averse early and too generous late, and 4%-constant seems as always a little cavalier with capital over the long haul. My guess is that the RH40 rule is ok but maybe I could loosen up a bit 58-70, damp it down 75-85 and then play a different game thereafter, a game we might call annuitization.
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[1] the return is more or less arbitrary. It was selected because it solved the PMT() function using the SOA annuity life table at the 95th percentile for 4% spending in the first year. It felt like it was easier to make comparisons doing it this way but who knows?
[2] spend rate = [age / (40 - age/3)] / 100
[3] I'm not even sure if this is legit analysis in this context but I'm going to try it anyway...because big boys play with utility functions even if most real retirees don't.
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