As an introduction, the proximal reason for doing this post is the trigger I got from reading a 2012 paper by Larry Frank, John Mitchell, and David Blanchett (FMB) titled "Transition to Old Age (Superannuation) in a 3-D, Age Based, Dynamic, Serially Connected and Annually Recalculated Retirement Distribution Model." This is an unfortunately opaque paper and will appeal to few, if any, retirees and precious few practitioners. I say unfortunately because the basic concept is good: adapt plans each year in a sequential process for a lot of reasons but in particular because longevity expectations shift out a bit each year that you survive and if you happen to be one of those people that makes it to really late ages you really have to be careful. Here are some snippets from the paper:
- Dynamic, serially connected, and annually recalculated, cash flows based on age and longevity percentiles provide insights into retirement distribution tradeoffs.
- This paper extends the 3D Distribution Model developed in the work of Frank, Mitchell, and Blanchett (hereinafter FMB) (2011 and 2012) by demonstrating the adjustment of Withdrawal Rates to reduce the risk of ruin caused by superannuation (continuing to survive and live into very old ages).
- Past research and thought has been based on static distribution periods that have not been connected to each other. Results have thus been bundled together into “safe withdrawal rates” with some researchers considering the impact of probabilities (possibility) of failure rates. The question has become, “What is research trying to measure, and how to measure it?” The authors suggest, through development of the three-dimensional model, that there are many aspects to measure and factors that can be adjusted; factors the authors will label here “levers.” [e.g., superannuation, sequence risk, distribution period, volatility]
- More interesting is the fact that the retirement resource is essentially fixed and by taking increased withdrawals early, resulted in reduced cash flows later since portfolio values were excessively depleted during early years such that higher cash flows could not be sustained from resulting lower portfolio values during later years.
- Framing the distribution problem based on current age of the retiree, versus generic distribution periods, as well as serially connecting withdrawal dollar amounts and portfolio balances through annual recalculations provides deeper insights into the effects of higher distributions early on.
- Essentially, the retirement pot of money can only support so much and that balancing cash flows during early retirement years provided sustained cash flows into later retirement years should the retiree continue to survive. Much like a candle. A candle can only give out so much light based on the amount of wax and wick. Burn it brightly early and you get less light later, and vice versa
The paper (and all these points) is a front for a huge pile of research and analytics by Frank et al. and the conclusions and recommended processes appear to be based on what I'll call an expectation of dynamic simulation as one goes along. That's generally pretty hard, though. Certainly it was a hard read. Fortunately, the main conclusions -- that superannuation risk can be managed by: a) sequencing dynamic withdrawals that factor in age and longevity expectations, and b) not letting dynamic formulas (say ARVA or RMD or others) go freakishly exponential at late ages[1] -- don't have to necessarily be so deeply analytical or complex. Frank lets slip that a simple regression formula can capture most of "a" and "b" without all the mess. Or, in his words: "Figure 3 shows a derived possible regression formula: y = 0.0014x + 0.0316 or Withdrawal Rate = 0.0316 + .0014(Current Age – 61)." Aha, this is rule of thumb territory! Let's try it out. Let's play the spending game.
But first lets assemble some players. There are many. Since I don't want to do a comprehensive survey let's look at a few I've been toying with lately: 1) me [RH40, search for that on the blog, there are plenty of links], 2) Blanchett' simple formula [I've used and referenced this in the past because it is simple, sort of, and is also based on a huge pile of sims], 3) Early retirement now [I use the math that he uses as I describe here], and 4) the "FMB" regression formula as stated above.
I totally agree with Frank that serially connected age-based (and adaptive, but that is not really the game here[3]) withdrawal plans are the right way to go. The 4% rule is so 1990s. The Bogleheads, by the way, also figured this out with their variable percentage withdrawal (VPW), which is really playing the same game as below.
The Players:
1. RH40 - this is a simple, easy to remember, VPW that -- if only very indirectly -- factors in return expectations, changing longevity expectations, and varying risk aversion. It looks like this: Age / (40-Age/3) /100. I have written more than enough on this elsewhere. Search the blog. It started as an inside joke with myself but it seems to work pretty darn well every time I take it for a test drive. Why RH40? Hey, it's my blog, why not?
2. Blanchett's simple rule. I've linked to this before about a million times. Know that I have applied this here by assuming: 60% equity allocation, an 85% probability of success, -.5% fees, and (importantly) that duration is based on current age and the SSA life table 95th percentile expectation for longevity. This is a type of simplified rule of thumb that avoids (by encapsulating) other, deeper simulation work.
3. Early Retirement Now. I use his formula that I linked above but I make it hard on myself by using stochastic returns (explanation is linked elsewhere, I'll have to look it up later). That means that the withdrawal rates (WR) that will work end up as a "distribution" rather than an answer. So, I look at both the 25th percentile WR and the 50th but will end up using the 50th for the game. If that is confusing, email me. The returns are very conservative real returns. I also define the number of periods in his math as: distribution period = (SSA 95th percentile expectation - current age). All this means is that I have way way over-conservatised what I think he intended but so be it. I have also made it more complex for myself by doing random returns and expected values and pseudo-simulation but that is my way, I guess. As a side note, I'll mention that in work not shown here, ERN (with super conservative assumptions) and the formula Gordon Irlam uses at AAcalc.com for a simple rule of thumb based on fitting some Merton math are almost exactly parallel in their curve. That doesn't surprise me I guess. On the other hand neither the ERN math or the aacalc ROT, as Frank suggests we should do, looks like they respect the very very late age risk of overspending as longevity keeps pushing out. But on the other hand that is annuity territory, something that aacalc is also very good at dealing with. More on that later.
4. The Frank regression formula (or Frank/Mitchell/Blanchett, FMB). I use this just like RH40 where age is the only input.
Note: I ignore ALL other formulas and spend plans, and there are a lot of them. That is because today's game is just about a few that I have been working on lately. I am comfortable doing this because I know that in general many of the other methods are playing the same game and that the retirement pie over time can only be sliced so many ways. In the bullet points at the beginning of this post, see the fourth one and the last one. Note as well that I am NOT being very scrupulous about making sure that all the assumptions cohere. In anything other than an "amateur hack" situation like mine that might be fatal. Maybe it's fatal here, too.
The Game:
Before we start the game, goal number one is to see what these spend-players look like in withdrawal rate terms by age on a chart -- in the sense that if one started retirement at any of these ages or if one were so inclined to recalculate spending at any of these ages, something I recommend what would it look like? It would look like this. Ignore the annutization zone for now, though that might be important later. As a side note, I'll mention that when one uses a fixed terminal age (say 95) for the Blanchett rule it tracks the same path, more or less, as RH40 and ERN on this chart:
Figure 1. Spend rate for four spending methods
So far so good. I did something like this before for other methods here. The difference is that the chart here goes to really late ages which sends some formulas into crazy land. See note [1]. For ages before superannuation starts to kick in -- let's call it 80 or 85 -- all of these formulas seem to be playing the same game. Note that the "Frank regression method" was offered by the author as something that would stay relatively reasonable at very late ages (if you are doing your own spend rule and not annuitizing, that is) and would be simpler than advanced simulation.
But the chart above is not the game. That just shows that the contenders have similar profiles. The real game is about lifestyle and risk. And since this is an amateur hack blog and not science we'll keep it really really simple. First, there shall be no simulation or hard core optimization, mostly because it's too hard and time consuming right now...if I could even do it. There will be only a simple deterministic process for the game rules:
The game winners are those that: 1) deliver the most terminal wealth to age 85 when we are probably at the outer bounds of optimal annuitization[2] if not at a run-of-the-mill longevity expectation, and 2) support the highest lifestyle between age 65 and 85 in utility terms (CRRA, certainty equivalent, risk aversion coefficient = 4 ). Metrics like probability of failure, though interesting and probably meaningful and useful along the age-wise path, are ignored.
First, let's look at some charts to visualize this. This first chart below (figure 2) is the present value of the spend for the contestants. This will represent the lifestyle part of the game. The bold colors are the rules we are playing with. The grey lines are a bunch of other rules that are not in this game that I have played with before. The grey area is what I'll call the "annuitization zone" where it might be reasonable to get oneself fully annuitized[2]. Notice that this chart kinda shows that the retirement pie is finite and that early consumption disadvantages later consumption and vice versa. A point made in some retirement research papers is that the choice will depend on preference for early consumption in the go-go years as well as one's risk aversion to extreme longevity scenarios.
And here (figure 3) is the related chart that shows what residual wealth is left behind by the rules at a given age for the game we are playing. Same color key. Again the grey area is the annuitization zone and the grey lines are other spend methods not played here.
The Game Results:
1. Terminal wealth. Just by looking at the chart we can see that ERN loses here[4] and the others are more or less a draw but we'll give the win to Blanchett. At least RH40 wasn't last. These are the terminal wealth values at age 85. Remember we have a fixed return assumption here, not stochastic. I think it was around 5%:
But the chart above is not the game. That just shows that the contenders have similar profiles. The real game is about lifestyle and risk. And since this is an amateur hack blog and not science we'll keep it really really simple. First, there shall be no simulation or hard core optimization, mostly because it's too hard and time consuming right now...if I could even do it. There will be only a simple deterministic process for the game rules:
- start with $1M
- each year (starting at age 58) consume part of portfolio using each rule
- assume some rate of return to grow the portfolio (details and rationale in a past post, I'll try to remember to find and link it). This is a weak link in the game
- update the rule each year and repeat
- render each year's consumption and residual wealth in PV terms (.03 discount)
The game winners are those that: 1) deliver the most terminal wealth to age 85 when we are probably at the outer bounds of optimal annuitization[2] if not at a run-of-the-mill longevity expectation, and 2) support the highest lifestyle between age 65 and 85 in utility terms (CRRA, certainty equivalent, risk aversion coefficient = 4 ). Metrics like probability of failure, though interesting and probably meaningful and useful along the age-wise path, are ignored.
First, let's look at some charts to visualize this. This first chart below (figure 2) is the present value of the spend for the contestants. This will represent the lifestyle part of the game. The bold colors are the rules we are playing with. The grey lines are a bunch of other rules that are not in this game that I have played with before. The grey area is what I'll call the "annuitization zone" where it might be reasonable to get oneself fully annuitized[2]. Notice that this chart kinda shows that the retirement pie is finite and that early consumption disadvantages later consumption and vice versa. A point made in some retirement research papers is that the choice will depend on preference for early consumption in the go-go years as well as one's risk aversion to extreme longevity scenarios.
Figure 2. present value of consumption
And here (figure 3) is the related chart that shows what residual wealth is left behind by the rules at a given age for the game we are playing. Same color key. Again the grey area is the annuitization zone and the grey lines are other spend methods not played here.
Figure 3. Present value of residual wealth
The Game Results:
1. Terminal wealth. Just by looking at the chart we can see that ERN loses here[4] and the others are more or less a draw but we'll give the win to Blanchett. At least RH40 wasn't last. These are the terminal wealth values at age 85. Remember we have a fixed return assumption here, not stochastic. I think it was around 5%:
| RH40 | 556,850 |
| FMB | 558,802 |
| Blanchett | 563,589 |
| ERN | 493,929 |
2. Utility (certainty equivalent) of consumption from age 65-85. There could be a whole bunch of different outcomes here for different permutations of age ranges and risk aversion parameters. In fact, if we were to use age ranges that go to 105 where "self-management without annuitization" was the game, the results would be very starkly different. We'll stick with 65-85 and gamma (risk aversion coeff) of 4 and end-game before annuitization at 85. Below is the calculated annual certainty equivalent over the age range. Utility is calculated using CRRA [consumption^(1-gamma)/(1-gamma) ] and averaged and then the CE is backed into by inverting the formula. I hope I did this right otherwise this might be an embarrassing post. Good thing I have few readers. Gamma = 4 was selected because that's what other papers sometimes posit as a behaviorally tested "average" value but who knows? The winner here is ERN with RH40 a close second.
| RH40 | 39,150 |
| FMB | 38,807 |
| Blanchett | 38,730 |
| ERN | 39,632 |
Conclusion. This may be unsatisfying but I don't really see any big differences here. As they say in central Wisconson, it's a horse a piece. These are all pretty close and it's probably a matter of preference for how much sacrifice one is willing to make early for delivering a pile of cash to the doorstep of the annuity choice. I guess the real winner is the blogger for methodically going through the analysis process to better understand how some of this might work in real life. But that was the point all along, wasn't it?
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[1] "The final consideration is to begin using the 1/n adjustment to the distribution period to mute the exponential nature of growing withdrawal rates due to ever shorter distribution periods." ... "The result is a more linear graph, with a muted exponential character, to reduce the withdrawal rate, thus extending portfolio values into the future which mitigates the risk of superannuation." ... "The exponential nature of distributions in older years should be constrained to a more linear nature or, better said, the exponential nature should be muted. "[2] For incredibly sophisticated and trustworthy analysis see Irlam here or here and elsewhere at aacalc.com. The short version of what he says is that annuitization is recommended in chunks starting earlier in life with full annuitization at something like no later than 80 for reasons offered in the links. I use full annutization at 85 as a simple end-game here for illustration plus I had already invested heavily in the age 65-85 thing for reasons related to past spreadsheet work mostly unrelated to this post. Here is an excerpt from the second Irlam link showing an optimal (binary, all or nothing) annuitization choice by age and level of wealth.
[3] We are, of course, a little adaptive here by responding to age changes and different longevity expectations but we are not adapting in the real life sense that if we got a bad health diagnosis we might radically change the longevity assumptions all along the way, etc.
[4] This is an artifact of how we applied ERN: 1) the spend rates were derived using conservative assumptions, and 2) since I randomized returns to get the spend rates, the outcome was a distribution. I used the 50th percentile in the game. I'd be curious how the 25th would perform. My expectation is that it wouldn't win the certainty equivalent part of the game but would show well in terminal wealth. Just a different way to slice the retirement pie.
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