Note: as in the previous essays, this is a draft as I hone some of this content. Also, since I view these essays as consolidating and integrating what I've learned about ret-fin so far, I will continue to add to and update this provisional latticework over time in response to new findings or errors.
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This essay is a continuation of:
Process 2 – Stochastic Consumption Processes
“Once we start viewing money as wealth, as a stock of money and not necessarily as a flow, then we seem to get less happiness out of spending it than we do from money that’s automatically turned into a flow,” M. Finke
Spending is easy, right? I mean that “easy” in two ways. First, I mean it conventionally, as in money going out the door seems an easier thing than the money that might or might not come in the door, or at least it seems that way in my household. I also mean it in the sense that I often see in the academic and practitioner literature: “…you have an endowment of $1M and you then spend 40K in constant inflation adjusted terms for 30 years…” That constant assumption rolls off the pen so easily.
But it’s not easy or constant in real life. It is easy, and constant, usually only in two contexts: 1) it is a financial modelling convenience: constant real consumption is really easy to manipulate in both open-ended simulation as well as in any related analytic expressions, and 2) given some proper assumptions, a constant spend is an expression of what is assumed to be rational behavior by way of risk aversion and consumption smoothing (i.e., constant real spend) in the economics of retirement. Risk aversion and smoothing can be connected to each other, by the way:
So, ultimately, risk aversion is identical to consumption smoothing. They are the same property! At times we’ll talk about how people’s risk aversion affects their path of consumption even when there is no uncertainty. That is because by measuring the degree of risk aversion, we are also measuring people’s desire to smooth consumption.” Vollrath (2007)
But for a constant spend (say the 4% rule) to work it requires some hard assumptions regarding discount rates and longevity. Milevsky (2011):
“In the language of economics, when the subjective discount rate (SDR) in an LCM [life cycle model] is set equal to the constant and risk-free interest rate, a rational consumer will spend his total (human plus financial) capital evenly and in equal amounts over time. In other words, in a model with no horizon uncertainty, consumption rates and spending amounts are, in fact, constant, regardless of the consumer’s elasticity of intertemporal substitution (EIS). The question is, what happens when lifetimes are stochastic?”So, smoothing, in the end, is just an abstraction that requires some unrealistic assumptions. Milevsky (2011) goes on to remind us
“Counseling retirees to set initial spending from investable wealth at a constant inflation-adjusted rate (e.g., the widely popular 4 percent rule) is consistent with life-cycle consumption smoothing only under a very limited set of implausible preference parameters—that is, there is no universally optimal or safe retirement spending rate. Rather, the optimal forward-looking behavior in the face of personal longevity risk is to consume in proportion to survival probabilities—adjusted upward for pension income and downward for longevity risk aversion—as opposed to blindly withdrawing constant income for life.”Or, more pithily, regarding the use of something like the fixed 4% rule to the exclusion of all other considerations:
“We are not the first to point out that this “start by spending x percent” strategy has no basis in economic theory.”But here I am already in trouble because we are entering the world of economics, utility, risk aversion, and intertemporal substitution. I would only embarrass myself going too far down that path since I know so little economics. Instead, I will merely attempt, before we get to portfolio considerations, interactions with returns, or thoughts of ruin or sustainability or utility, to describe spending as a process on its own terms as well as to consider some ways to measure and evaluate the process as a whole. It might seem silly or dumb to do it like this but my sense, after reading a pretty big pile of academic and practitioner research is that spending is often glossed over and overly simplified. Rarely is it looked in the face for too long. The usual practice is to assume a constant spend or maybe some ad-hoc rules and then instantly integrate it with portfolio longevity, ruin risk, or feasibility. That is the right thing to do in the end, but I wanted to take a look at spending on its own before I try to connect spending with those other topics later. To this end, it might be helpful to the reader to make sure that I am clear about what I am NOT doing here.
- Connecting spending to returns or portfolio longevity (where possible), that’s later
- Articulating specific spending rules, ad-hoc or otherwise
- Providing a deep dive into detailed retirement spending categories
- Coming up with “set and forget” frameworks
- Articulating connections between spending and income, yet…
- Describing optimal or prescriptive frameworks for individual plans for spending
- Analysis of bequests or long-term care since those can often be separated out
- “Catastrophic” spend shocks (I think these can alternatively be modeled as wealth shocks)
- Short or long term gains taxes or fees though these can be modeled as a form of consumption
- Spending as a simple time-based process
- How spending has a shape
- Some sense of how spending might drift
- Some sense of how there might, or might not, be some diffusion over one or more periods
- Habit formation in spending over more than one period
- Possible psychological states coming from a constant spend
- Spending Evaluation via present value, stochastic or otherwise
- Spending Evaluation via rudimentary life-cycle utility
- Spending Evaluation via Perfect Withdrawal Rate distributions
- Notes on sequence risk and statistical process control
A. Spending as a Simple Process
Let’s skip past the economics for a minute – in other words, we'll ignore things like utility or marginal rates of substitution or any discussion of wealth or longevity (or borrowing) constraints – and just focus on spending as a simple process over time. We can do this because: a) I don’t know the econ, b) we will get to some of the economics in a later essay, and c) if we throw our own constraints into the mix, say that we model the spending process only over the intervals where
- For all periods "t" evaluated, wealth > 0 (for now)
- Time period “t” is less than or = a random terminal longevity or arbitrary fixed horizon T*
- Spending is (for now) uninfluenced by minimum spending floors or availability of lifetime income
- We at least entertain the idea of random spending variance and/or habit formation
1. Constant spend: c(1) = c(2) = c(3) = … c(n). We’ll ignore here -- given our constraints – longevity (human or portfolio) or wealth depletion risk. This constant pattern is supposed to be associated with risk aversion and consumption smoothing even though we saw from Milevsky’s comment that it is likely to be a rare thing: “[it] is consistent with life-cycle consumption smoothing only under a very limited set of implausible preference parameters.”
2. Shaped Spend: c(p) = vector[c(1),c(2),c(3)…c(n)] where the vector of c’s are a custom or arbitrary plan which might or might not be optimal. This shaped path can be arbitrary based on unavoidable personal circumstances or expectations or due to life’s many contingencies. It can also be something deliberate that comes out of some kind of optimization effort or from specific family needs over important intervals in the life plan. Either way, view it as something ex-ante deterministic for now. This below is generally similar to how I do my own plan but with some adjustments.
This idea of “shape” may seem, at first glance, trivial or an aside meant to fill out a list. But the idea of shape may be one of the more important and under-appreciated concepts in retirement finance. Certainly, it is (important) if the plan is somehow optimal. But even if it isn’t, as Robinson (2007) concludes, “the spending pattern itself, [even] without a stochastic factor, causes the most significant effects in changing the probability of shortfall.” This is the same conclusion I made to myself after three years of looking at this subject which is why I dote on spending as a process. Robinson identifies several shapes or patterns for investigation – high then declining (the socialite), declining (the gardener), rising (the uninsured), rising then falling (the explorer), and any pattern with a debilitating shock along the way (the unhappy) – but there could be in practice an infinity of shapes, only one of which, at any given time, might be optimal.
5. Dynamic spend: This can maybe be articulated as c(t) = f(w(t), a(t), c(h), λ, i, π, γ, other) where f can be any function or rule, w(t) is wealth at time t, a(t) is age at time t, c(h) is the history of past spending choices up to and including the prior period, λ is a mortality hazard rate for the then current age, i is an updated inflation expectation, π is pension annuity income available at time t, and γ is a risk aversion parameter. The custom or dynamic spend can maybe be characterized as a spend rate that rigorously recalculated or re-optimized over time or alternatively as some type of ad-hoc or heuristic “spending rule [see point 5b below].” c(t) can’t be known in advance in this case for evaluation but it would be a relatively trivial exercise to embed the rules or recalc into a simulation.
This type of spend has not been illustrated here but to visualize this, think of things like
- Guyton and Klinger spend rules
- “Snake in a tunnel” methods of adjustment
- Percentage of net worth adaptation*
- ARVA (annually recalculated virtual annuity) rules
- Age based heuristic rules like “divide age by 20” or even my own RH40 rule
- “Constant risk” adaptations of spending based on projected future risk
- Optimized spend paths coming out of some machine that knows the LCM, updated as needed
- Generic parmetric formulas [12]
*5a. Active destruction: This point is tongue in cheek and is technically covered under dynamic spend above if we were to contrive a "perverse" rule for ourselves. The reason I want to draw this out here is that many retirement commentators will describe retirement spending choice as existing on a spectrum somewhere between constant and “percent of portfolio.” This is wrong for at least two reasons: (a) there is no “spectrum” and spending can take on any shape that is rational or irrational, random or planned, and that may or may not be in the list offered in this essay, and (b) if there were to be a spectrum then they (the spectrum proposers) forget the other side of the spectrum where instead of spending correlating up and down with return (portfolio) experience, it instead goes in opposition to returns. Why do I bring this up? First because “they” always forget the other side and I’m here to remind them. Second, because I personally lived this type of active destruction during the GFC. One needs to be aware of at least the possibility that this can happen over some intervals. To visualize it, it might look like this:
5b. Spend Rules. You'll notice, if you read on, that nowhere do I discuss or evaluate spend rules since they have become so common in the literature and others cover it better than I do. But, I will say that if we went with the idea of a (false) spectrum of spending choices that extend beyond "constant" that I presented in 5a, then the ultimate rule might be spending a percentage of a portfolio's current value. This could, under a pretty limited number of parameters, offer a perpetuity. But probably not. It would also introduce a ton of lifestyle volatility and, no doubt, a degradation of utility. While we can debate whether a constant spend is or isn't the same as risk aversion, we can maybe at least agree that spending that could go up or down 50% a year would be kind of annoying. Short of using the "percent method," there are an infinite number of other ad-hoc rules, some less annoying than others and only a few of which might have some economic rationality. Some might also offer real extensions to portfolio longevity or boosts to lifetime consumption utility while others might have less of a payoff. But most rules, in my judgement -- other than the rule of just being more conservative in the first place or hedging out spending with lifetime income or aggressively and dynamically updating over time -- are (without reference to any quantitative proof here) a pretty thin branch to hold on to. Here is earlyretirementnow.com, whose judgement I trust, on spend rules in the context of early retirement:
"Of course, critics would argue that most early retirees will use flexibility to save their early retirement way before they risk running out of money. But as I showed in some of the recent SWR Series posts (see Part 23, 24 and 25), this form of flexibility is not without pitfalls either. It’s certainly not as simple as some people want to make it! Everyone can tighten the belt by 30% or 40% or even 50% and consume less (or go back to work part-time) but my simulations in those previous posts show that the duration of your flexibility can be really unpleasant. In some of the cases, flexibility involved going back to part-time work not for years but two decades. Not really a workable solution for me!" [emphasis added]or, here, less dramatically, is Robinson (2007):
"Making stochastic consumption partially correlated with investment return [i.e., a rule] reduces the risk of shortfall, but not by a great deal."So, no rules.
6. Optimal spend paths: Ok, so I can’t totally ignore the fact that the economic literature has at least some closed-form frameworks for determining (usually solved by way of dynamic optimization methods or related linear approximations[3]) optimal consumption in the lifecycle model (LCM). Here I am thinking mostly only of the work I’ve seen myself, say from Yaari (1965), Leung, Milevsky (2011 Appendix A p 36), LaChance (2010. p31), etc. I’m sure there are others. But for the remainder of the essay I will try to pretend that this literature does not exist. This is because: a) I have a hard time reading the math and I don’t know the topic, b) I forswore in this essay making any direct connection (yet) between spending, wealth, income, longevity, etc. which would be required for constructing or explaining optimal paths, and c) I’ll hazard a guess that no retiree in history, and probably all but one or two economists (and maybe not even them), has ever really lived their real retirement on (or even looked at) a continuously optimal spend path based on closed-form calculus. It also seems, from personal experience, that it might be rare for an advisor to know what I am talking about here…if they’ve ever even seen it. So, we can ignore this optimality topic, at least for now, but a standard visualization of optimal consumption in the LCM would look like this:
Regarding 6(b) on spending and wealth, the common intuition, which feels correct, is that one usually makes a strong connection between wealth, age (longevity expectation) and spending. LaChance (2010): “these results reinforce the notion that consumption behavior is explained by wealth and that consumption increases with wealth…consumption tracks income when wealth is low…, increases with wealth afterwards, and at time zero the individual saves only if his wealth is below a certain target…” but “…for the case where […wealth = 0…] , equation 10 shows that [optimal consumption] can be expressed without any direct reference to wealth.” That last quote may seem counterintuitive but she goes on to describe the optimal consumption path, whether wealth is zero or not, as dominated by other things: “in a model with certainty, an individual who accumulates his optimal level of wealth W*(t) at time t does not need to consider this level of wealth directly when establishing how much to consume.” and “While the previous literature has often focused on wealth as a determinant of consumption…our solution indicates that the evolution of this behavior over the life-cycle is explained by the function λ(t). This function captures the combined effect of income profiles, risk aversion, time preferences, investment return, and mortality.” Milevsky (2011) concurs in taking us away from an over-focus on wealth: “The main point of our study can be summarized in one sentence: The optimal portfolio withdrawal rate depends on longevity risk aversion and the level of pre-existing pension income. The larger the amount of the pre-existing pension income, the greater the optimal consumption rate and the greater the [portfolio withdrawal rate].” i.e., this is really a topic for a different essay… My reservations about looking at LCM and lifetime utility at this stage of my essays notwithstanding, it will be difficult to not dip our toes into it a at least a little bit for evaluative purposes. More on that later.
7. Other Spend Processes: Spend paths and rules could take on an infinity of rational or irrational forms not described here. These above are just a few designed and enumerated in order to nudge us off a constant spend assumption. One could also view “other” here as some combination of what has already been listed in items 1 through 5, say something like: a custom fixed shape (#2) with some modest variance period to period (#3) with some low degree of habit formation (#4) along with periodic dynamic recalculations (#5). That one sounds like me.
B. Is Spending Constant in Real Life or does it Drift?
Is spending constant? Most certainly not, not least because of price inflation. But we are interested in real rather than nominal spending in this essay. But before we leave inflation behind too quickly, I should at least acknowledge that the basket of goods consumed in retirement, especially late retirement when health related consumption goes up, is different than that which we might purchase in mid-adulthood when things like transportation or entertainment are more dominant. I had always referenced my own plan to CPI-U, a basket for urban consumers. Blanchett (2016), on the other hand, suggests instead CPI-E, a basket for the elderly where the weights are adjusted up for medical care and down for education, transportation, and apparel. I didn’t even know there was a CPI-E. The point here is that the decision to dismiss inflation and think only in real terms is not a benign choice if we don’t know what kind of inflation we are talking about.
The other thing I will leave behind is the idea of “replacement rates” since I am mostly interested in the post-retirement spending process[4] rather than in the shift from the pre-to-post human capital stages of life. While there is most likely a discontinuity in spending when moving from work to retirement it might not be exactly the "standard" 70-80% often mentioned. In fact, according to Blanchett (2016) the scope of the discontinuity is sensitive to income, taxation and expense relative to income and can range from 54 to 87% or more. A close read of the tables in his paper would likely be rewarded if one were to be interested.Now to the question of whether spending drifts in real terms over the course of a retirement. At least as far back as Yaari (1965 – case C) the general sense has been that, in the presence of complete insurance markets (ignore whether we should explore the question of completeness when it comes to "real" annuities, but it is less complete than I used to think), no bequest motive, and an appropriate life-cycle utility evaluation, it would optimal to annuitize all wealth (except that we are ignoring wealth for now). This would imply a constant spend (or income, anyway; assume that spending and income are the same for a moment in this world) over a lifetime. But is this what we really see? Look up “annuity paradox” and you see that people are not exactly running to annuities in droves. What happens to spending when we are not either helped or constrained by lifetime constant income?
For real, observed spending in the world, two credible resources, Banerjee (2014) and Blanchett (2016) both provide some compelling evidence that spending drifts. Both of them paint, for the most part though one has to be careful here, a picture of spending that declines into late age where medical spending starts to overwhelm if one lives long enough. Banerjee, depending on how you interpret him, makes a case for spending declines of somewhere between 1.7 to 2.5% a year to about age 90[5]. Blanchett says something similar but qualifies his results by level of income
Households with lower levels of consumption and higher funding ratios tend to have real increases in spending through retirement, while households with higher levels of consumption and lower funding ratios tend to see significant decreases. The implication is that households that are not consuming retirement funds optimally will tend to adjust them during the retirement period, i.e., spending is not constant in real terms.and suggests that there is a decline of something like 1% per year in spending during the retirement interval after the initial drop (replacement ratio) at retirement’s start. Given the data he is using and skipping over the various qualifiers on income and fundedness, Blanchett supplies us with the formula for a regression he did on the data to provide a short-hand description of retirement spending:
DAS
= .00008(Age^2) – (.015*Age) - .0066 ln(ExpTar) + 54.6%
Is this really what happens? It is if you believe the cross-sectional data applies to individual people. Me? My own data has fallen so far over the last nine years but that was for reasons all my own. Ongoing? I've already cut pretty deep. I'm not sure how much further I could go without a major crisis to motivate me. This, for fun, is my recent history. I wouldn't underestimate the challenges implied by those first three years:
The question here is not what exactly happened but "did it drift in real terms?" which it did. Some of of this was intentional, some not. Going forward, I believe my own capacity and desire to spend will more likely rise now than it will fall as life shortens, uncertainty fades, travel and bequest beckons, and risk aversion abates. On the other hand my actual current plan that is in place now assumes a reduction at 70 of about 16% and at 85 as much as 30% if that cut is necessary as a minimum floor above which I can spend more if things work out. This three phase plan is more or less in line with the other lines on the Blanchett-Banerjee chart, just less continuous. But note that I’m also currently reserving (saving) against longevity uncertainty because I don't have lifetime income. This reserve is a type of hidden "spend" or intertemporal substitution so my combined spend+reserve may in fact fall if we call the reserve a type of current consumption while real period-consumption might rise. We’ll see what happens, won’t we? In the end, maybe we can at least agree with Blanchett that maybe I am (and we are) not always on an optimal path and so “spending [will not be] constant in real terms.”
C. Does Spending Diffuse Over Time? Part I – Single Period
I have to admit right away that I do not have the data or research to answer this question in its “big” form (is the phenomenon of spending diffusion seen empirically in the world?) [6]. Most of the following will be personal, anecdotal, or guesswork. Also, I know of very few retirees who can truly test the idea of diffusion by repeating their retirement many times over under the exact same conditions to see what happens differently each time.
Before we get to diffusion, though, I wanted to at least get to the idea of intra-period (single period) variability. While spending may not be exactly a random process over the long run – Dirk Cotton, in private correspondence told me that “consumption has several components, but it can be broken down into “habitual” spending and spending shocks. Habitual consumption is not random in the sense that it can be pretty well predicted from one month to the next.” – there is no doubt variability in a single period sense. I don’t even need to read obscure research papers to know that. I have almost 9 years of my own monthly post-retirement spending data to prove it. And, not only is there variance in the data, it is skewed and skewed (fat tailed) sharply to the right. This is what it looks like with the data scrubbed of my personal spending amounts:
Dirk Cotton went as far in his blog (theretirementcafe.com) as to bring in the math of chaos theory, as opposed to more normal probabilistic process, for its explanatory power over that less habitual "other" spend. I won’t go that far but I do like the way he presented it and I think it looks applicable. Recall that we saw something like the mix of two different distributions/processes before when we were modeling non-normal return distributions in "Process 1 - Return Generation." We learned there that a fat tailed distribution can be modeled as a combination of two or more normal distributions. That means for spending we might say we have: (1) a lower dollar and common/repetitive process with a narrow distribution, and (2) higher dollar and less common process with a wide (or basically not very predictable) distribution. So, while the #2 process here may not be a real probabilistic process in real life[8] we can at least pretend to do it like that it if this was just for fun or if, perhaps, we needed, for whatever reason, to programmatically simulate spending in some tractable way in software. We’ll see later that this might be important if we are tuned into the issue of modeling sequence of spending risk.
To do this kind of thing we would take the data driving the frequency distribution above (say my own monthly data) and derive a density from it and then also run an expectations maximization function (in R in this case but one could do it manually in a spreadsheet if pressed) to decompose the underlying distribution into at least two separate components. We could then use the two separate processes to reconstruct an artificial mixed distribution that more or less describes spending in a way that I can automate for research. When I do this in practice, this is again scrubbed again of my personal info, it looks like this where the black line is a density proxy for the frequency distribution I charted above for my monthly spend and the red line is the artificially reconstructed density from the fake mix of the two artificial distributions (blue dotted):
The basic point here is that if I needed to, I could model randomized period spending in a piece of software by either bootstrapping off my own data or by mixing two normal probability distributions where one represents recurring habit and the other represents “other” spending or spending shocks – keeping in mind that the magic of the Central Limit Theorem will wash out some of this fat tailed-ness in real life over longer aggregation periods like one or five years.
C. Does Spending Diffuse Over Time? Part II – Multiple Periods.
So, is spending random and diffuse over multi-period time like we tried to describe in a small way in section A.3 above or in the sense of a random walk (GBM) that we would use for stock prices? Highly doubtful even though it is fun and sometimes useful to model it that way. First of all, I have no literature (yet) that tells me that an open-ended random walk in spending is either likely[6] or observed. Second, unlike markets or stock prices which we can’t control, there would be expected to be (based on personal, anecdotal experience) a fairly quick behavioral intervention on a random spending process if for no other reason than to force spending to a budget, or at least the idea of a budget, because we can. Third, even for those people that don’t have a grad degree in macroeconomics, and for un-degreed amateurs like me, there is probably somewhere in the back of the mind at least the idea that spending has both a sustainability component to it and a lifestyle [utility] component to it so that, like with budgeting, the implicit but unspoken concept of “ruin-fear[9] and/or utility loss” will keep spending self-correcting to some extent even without advanced analysis. Before we get into other parts of this essay, or future essays, that touch on lifetime consumption utility or portfolio longevity we might assert that the raw intuition on spending randomness might look like this where B is a selected constant spend, A is a rising spend and C is a declining spend:
In the back of our head we might guess that A will run out of money sooner rather than later and in the event sooner than B. B might or might not last our lifetime depending on how long we think life is but we've assumed this plan fits. C might last forever but will be less fun than B. Given the non-linearity of utility math (even the amateur, naïve kind I’m thinking about here) and the infinite disutility associated with a spending crash to zero, most people probably get the idea that a spend process like C would be less fun than B though it lasts longer and B will always be preferred to A (in this setup, depending on when T*, the death or planning horizon, occurs). Simplistic, yes, but maybe this intuition is enough to keep spending from being entirely a random walk in practice through the forces related to fear or habit or willfulness. Note here that the spending crash idea is not exactly ruin in real life. The "crash" is only to available income which either comes from exogenous institutional support (social policy or family or a pension) or endogenous sources (say, reallocation of assets to lifetime income if we still have the resources to reallocate). We’ll have more to say on that income flooring concept later. The point here is that our intuition might lead to the conclusion that diffusion over multiple periods is unlikely if behavior is naively self-correcting.
The closest I've come to seeing the idea of (lack of) diffusion is in the work of Banerjee (2014) though he usefully reminds us that this is from longitudinal data that does not follow individuals over a life path. This is his version of the distribution of spending by age group:
So, since spending is clearly random in single periods but doesn’t feel all that diffuse over many periods, the only thing I can say about spending and randomness is that a spending process looks to me more like an industrial production process than it looks like a random walk of a stock price -- even though modeling it that way can provide some insights. To capture this idea, imagine manufacturing widgets on an assembly line. The process is mostly constant but there will always be some random variation in size or other production errors where excess variation costs us real money in lost sales and product returns and there is always the risk of "error equilibrium drift" or major production shocks. So, in the interest in profitability we’d want to first baseline the process, then improve the process in iterative steps, and then finally optimize the process -- all based on some type of cost/benefit rationalization. Then we'd keep it under as much control as makes sense economically with low variation and minimum or optimal error rates.[10]
In our spending case, for which the manufacturing example is an analogy, we would be motivated by the intra-period utility gain and loss coming from “control” (since low spending has a non-linear utility penalty and high spending has an accretive effect on sequence risk) as well as any full life-cycle additive-utility gains or losses (since spend crashes at wealth depletion have a pretty big impact on lifetime consumption utility) as proxies for "profitability" or "success" in the manufacturing analogy. The main things industrial ops managers watch for in the assembly line example are typically pure chaotic shock, about which they can do relatively little and which may bankrupt them, and creeping changes in the equilibrium process stats -- which we'd maybe call lifestyle creep or habit formation in the spending example -- about which they can and should do a lot. Just ask a Japanese auto manufacturer. We won’t get any further into industrial control, Deming cycles, six sigma or continuous improvement here, even though that is the model I want to articulate, but maybe we can at least say a little bit about habit formation which will be my proxy for an industrial process under control.
About “habit formation,” which might stand in for a control process here or a process that is at or near equilibrium, the least we can say is that we know how to create a naïve model for technical retirement analysis purposes in the form we described in A.4 and where the extreme form of control (do we still call it risk aversion? see the next section) would be the constant spend. The advantage here for us as analysts is that the formula for lifestyle-habit is simple, can be dialed continuously, by way of the parameters, from a constant spend to a pure random spend, and, together with consumption it can be plugged straight into an adapted form of Yaari’s Fisher-style utility function if necessary. Even the full-on dialed-to-random-and-unconstrained setting is ok because, while unrealistic, it can give us a type of boundary on spending that is useful for inspection and analysis. More on that later.
D. The Dirty Little Secret of Constant Spend is that it is an Active Risk-taking Posture.
While shaped spend paths or random spend paths, with or without habit formation, look riskier than constant, "risk-averse," and under-control consumption and while most ret-fin literature will correlate constant consumption and risk aversion (“risk aversion is identical to consumption smoothing” from the grad macro textbook I am using), a constant spend is not entirely benign in terms of the subjective experience of risk. Note that I say subjective here because we have not gotten yet to the evaluation of lifetime consumption utility with the possibility of wealth depletion, which would help us. With that tool, one would be able to easily see the potential cost of a constant spend during a random lifetime. But even if one did not evaluate utility or ruin probabilities at the start of some interval in question, the risk would become apparent soon enough in real life if one were to evaluate risk dynamically over time. The question is not so much whether ruin or utility is or isn't a good or meaningful way to evaluate spending plans (there are pros and cons) but rather what psychological state would you really have as life unfolds if you knew just enough to be dangerous? Let’s look at it this way: take a 60-year-old with $1M in 1965, allocate a portfolio to 50% equity and 50% bonds, and spend 3.5% constant (inflation adjusted) thereafter, a rate that by most measures should be eminently sustainable. Then ask yourself each year “what is my ‘effective’ spend rate and what is my new lifetime ruin probability” given the then-current state info like: new portfolio value, the evolved spend, and current conditional survival probability. The effective spend, by the way, is the then-current inflated constant spend rate divided into the then current portfolio. The LPR, if you need to know, I calculate like this
where g is a representation of a mini-sim for the
probability of portfolio longevity (fail) at time t and tPx the conditional
survival probability using Gompertz math. Discussing LPR here jumps the gun a bit on my “Process 3 – Portfolio longevity” and “Process 4 – Human Mortality” but since
we are talking about spending, I wanted to briefly throw it in now to try to disabuse us of
the notion that a constant spend is either easy or low risk. Rolling these kinds of assumptions through
the 1970s, it would look like this:
The "effective spend rate," given the baseline assumptions and the fun of the 1970s, goes above 5% at age 69 and then stays there forever. The dynamically re-estimated LPR climbs above an entirely arbitrary threshold [11] of 10% for a total 18 years, which happened to be 70% of the years between 60 and 85, 16 of those years being contiguous. This may have “worked” or been sustainable in the end (think of something like the arbitrary 4% rule that “worked” in Bengen), but I would have been miserable for almost that whole time given what I now know about retirement finance. And they say consumption smoothing is identical with risk aversion!? Not in the ‘70s. Not if you look at risk dynamically. Spend rules might have helped a bit but probably not by much. See A.5 above.
E. Spending Evaluation – Part I: Intro to Balance Sheets
It is difficult to separate the idea of a spending process from the idea of feasibility (i.e., will this plan even work?) and one would have a hard time evaluating feasibility without a discussion of the balance sheet because assets (and/or income…a separate discussion) are “required” to fund the spending plan, which is a liability, over a lifetime or at least some planning horizon. This is pretty rudimentary, but the balance sheet is nothing more than a net worth calc: NW = Assets – Liabilities. The trick here is that there is a bit of a leap for most retail retirees in that they'd have to calculate, for example, (if they even keep a balance sheet at all) the present value of flow items like spending (liability), human capital (asset before retirement), Social Security (asset), and pensions or annuities (assets) to do this properly. Having lept that fence, which is pretty high for most retail retirees, then the net worth evaluation becomes some form of a discussion around the “required assets” (RA) necessary to fund the liability and here "RA-liability" has to be >= 0. The advantage of evaluating feasibility in terms of RA is that RA is a currently observable “fact” where forward simulation of spending and wealth, via some form of Monte Carlo simulation, towards some hypothetical terminal wealth distribution is a little bit more of a fiction (as are “fail rates” by the way) and a bit of a black box -- though the two approaches are neither dissimilar nor entirely unrelated.
The spend liability as a present value (PV) can be evaluated either simply and deterministically with a yes or no at the end of the process on whether the plan is feasible using a single number, or it can be a more complex process evaluated by using random variables for the spend plan and/or the discount rates (the implied cumulative return processes) and/or inflation. Going down this path would make the spend liability what is called a stochastic present value (SPV) and the required assets analysis would then become a management “process” of evaluating a distribution of potential liabilities with some degree of certainty or uncertainty of the ability to fund them with available resources. How far one goes down this path depends on the sophistication and the needs of the retiree and the skills and interest of any advisor involved. I’ve taken it pretty far myself in order to learn but in practice I keep it pretty simple. I am not running a pension fund or pricing annuity products so a simple probability-weighted deterministic calc is usually sufficient for me and I rarely do even that.
E. Spending Evaluation – Part II: Simple Deterministic Present Value
Take any spending plan of any shape C(p) = [c(1), c(2), …c(n)] from time t = 1 to t = T where T is some planning horizon (say 30 years or to age 95) and d is some discount rate representing some assumption about risk or return processes (beyond the scope here but maybe: Mindlin (2014), Ross(1995), Turner (2015), etc.) and it is simple enough to calculate the present value of the spend plan in order to evaluate required assets and simple feasibility. This is more or less from page one of any coherent finance book:
Since we don’t know how the world will play out it might pay dividends for us to consider some or all of the variables in the previously described PV calc as random. This infusion of randomness could apply to parameters for inflation, consumption in real terms with or without habit formation or drift, the cumulative return processes implied in the discount rate, and, for that matter (and not least), lifetime. This is effectively the same kind of thing we do in Monte Carlo simulation except here it is done in reverse. We do this in reverse in order to allow ourselves to compare the spend liability (distribution) to the currently observable assets on the balance sheet. Randomization of the spend liability parameters gives us a stochastic present value (SPV) which is another way of saying we get a distribution of possible PVs of spending (rather than a single number) from which we then have to carefully consider what we really need to evaluate in our balance sheet analysis.
Where T is random time of death, C is the consumption path and R is the cumulative return process (i.e., discount rate) and 1, on the right-side form, is the binary that is "on" if alive and "off" if one is dead past time T. Me? I might modify the right-side version to look more like this which in its discrete form is more tractable and stable in an amateur simulation:
No retirees I know, and few advisors for that matter, use continuous form math, so if one were to want to jump to an implementable, discrete version of this, this is how I did it in simulation mode in 2017, a form I borrowed from both personal intuition and Mindlin (2009):
c(t) is consumption in period t as part of any plan of any form that is random or discrete, shaped or flat; d is the randomized discount or implied cumulative return process for which I can offer little advice right now, N is the end of the planning horizon or it could be transformed to random lifetime via random draws or maybe by way of a probability vector on C, and “i” is the number of simulated iterations. c can be randomized via inflation or in real terms via the drift and diffusion of GBM. It can be modeled with or without habit formation or rules or it can be constant/deterministic, either shaped or flat. Any way you do c and the other variables, the result will be a spending distribution in present value terms with the only difference, when choosing what to loosen up as random, being how wide or skewed the variation is. The sim form above E[pv(c)] is an expected value which is of limited use to me since the distribution is likely to not be normal. More useful, then, in central tendency terms is the median or mode. More useful still is integrating the distribution to the Pth percentile, say .95 (where P is an arbitrary policy choice no matter what the statisticians tell you). Either median or Pth percentile would then become the SPV that one would use with the balance sheet to evaluate the likelihood of RA to be sufficient for funding the spend liability. This is basically how (some) pension analysts do it. Note that you’d have to do this again next year, too, if we are being really honest with a "process" methodology.
To see what SPV looks like visually as a distribution, here is a chart from an early 2018 post on SPV that I did with different and arbitrary flavors of randomness that I added to both the numerator and denominator. [https://rivershedge.blogspot.com/2018/01/how-big-of-deal-is-it-to-randomize.html] This was set up for a 100k (initial) cash flow at time zero over either N periods or random life. This was not a formal analysis, I was just trying to shake out the idea and the purpose here was visualization rather than accuracy or realism. The cases were:
0 - the deterministic, probability weighted present value i.e., the "single number"
A- the baseline sim with nothing varied except inflation.
B- the sim with the denominator discount rate randomized
C- the denominator discount rate is randomized and spending in numerator is randomized
D-only the numerator spending variance (and inflation) are randomized
E. Spending Evaluation – Part IV: Lifetime Consumption Utility
I have not studied economics but I get, at an amateur level, the basic point of consumption utility and its concavity. If I am starving, having an extra dollar to spend on a second piece of bread has higher marginal utility to me than consuming my second Lear jet (I hope). This gives the utility of consumption its shape and power:
So, considering utiles, which I don’t particularly like to do most days, rather than dollars seems particularly effective in evaluating competing consumption plans and it’s essential when looking for optimality if optimality can even be found. It is nearly impossible to separate the idea of consumption utility evaluation, by the way, from the effects of time on wealth, returns, wealth depletion, and random lifetime but we will try to separate for now then and come back to the broader topic later. Also, we will focus more on additive lifetime consumption rather than single period since it is the entire life of consumption we are trying to evaluate. The most common reference in this area, from what little I know, is Yaari (1965) and what Prof Milevsky insisted I refer to, if I want to be precise, as the “expected discounted utility of lifetime consumption” (which I’ll refer to as EDULC). In continuous form it’d look like this (eq 13 p 142 Yaari 1965, Case A only):
Here, for example, is another version of habit oriented consumption utility from Bilsen (2018) where he transforms a dynamic problem to a static variation:
Me? I don’t really live in a continuous or optimal world and I know nothing in practice about habit formation so in my own simulation in past blog posts, when I calculate the expected value of discounted lifetime consumption it looks like this where I make no attempt whatsoever to find a max or optimal V and I don’t think much about bequest or habits:
And here, I use a vector of conditional survival probabilities rather than draw random lifetime directly. For the interested, this happens to make the EV more stable faster with fewer simulated iterations. k is the subjective discount, S is the number of iterations, and g is CRRA utility in the “-1” form because I have a hard time getting my head around discounting utiles with a negative sign. That's me as an amateur speaking.
This effort to evaluate a consumption plan or plans C(p) = [c(1), c(2), … c(n)] via discounted lifetime utility is only mildly interesting even though it is a constructive addition to the evaluation of spending plans. It gets radically more interesting when we add a net wealth process that can deplete wealth and crash spending to available income before a random lifetime ends and it also gets way more interesting when we add, at some unknown time when we can still afford to do so, an endogenous reallocation of still remaining resources to lifetime income. These are considerations we won’t discuss here in this essay but this is the kind of thing where the utility approach shines even though I say I dislike utility. So, for the purposes of this essay, ignore those issues for now. While we are at it, also ignore that risk aversion is really subjective if not entirely arbitrary, constant relative risk may not precisely describe human behavior very well, and that the abstractions of utility are hard to interpret in retiree-common-sense terms. Just note that we now have a powerful tool available to us for evaluating a lifetime "spending process” which is why those wily economists came up with it in the first place.
- MC is usually highly integrative – I say highly integrative in the sense that MC tries really hard to tie everything together at once before we know the underlying processes well: return generation, net wealth, dynamic rules, stochastic spending, inflation, etc etc. Me? I am trying to focus on spending only, so I think a discussion of MC would distract us a bit.
- MC is opaque – Most people, many advisors included, don’t really know how the internal engine of an MC sim works and have a hard time explaining what is going on and therefore sometimes mis-use the conclusions. I can offer personal experience with a large national brand financial services enterprise if you are interested. Untangling spending as an independent stochastic process in that context is thus that much harder. Also, I have lost count of the types of sims I have built on different platforms for different reasons. All of them were deficient in some way and I am less sanguine on their use than I used to be though they are fun to play with.
- MC sometimes answers questions we didn't ask and misdirects us – A focus on fail rates is sometimes an answer to questions that are not really being asked. In addition, a focus on fail rates misses, even when modeled well, some of the issues around random life, failure magnitudes, and the irrationality of thresholds, if any are given, among other things. There have been quite a few papers and posts out there that cover these issues with MC sims, including work by Dirk Cotton, Wade Pfau, Michael Kitces, and others including me. Best to know the cons of MC sim before we get to the pros.
- Like Dorothy and the ruby slippers, we already had the power to go where MC goes and we’ve had the power all along. We just didn’t know it.
That last point probably requires some explanation. Many financial tools like MC sims, SPV, PWRs, and even closed form analytic expressions are, in essence, the same thing in that they are all working with the same underlying processes. They just come at it from different directions and they speak different dialects to different people. For example, many knowledgeable commentators make a useful distinction that I like between the "sustainability" over time that is analyzed via MC sims and an initial feasibility calc that requires a balance sheet and present values: it’s hard to sustain something that was never feasible in the first place so maybe one should look at feasibility before running off to a simulator. But the two concepts share a ton of common ground. I saw this in a paper I read recently – Robinson (2007) – where with some calculus ninja tricks they reversed the wealth process that underlies MC sim and showed that it is also, in effect, an SPV feasibility calc. Like this… from their Appendix on page 12:
Assume the Brownian Motion processes from Robinson that we saw in "C - part III" above
That means that wealth at time t can be described, in Robinson though this is common elsewhere, by
Whether you like it or not, I’ll call this the heart of MC simulation. It is a net wealth process which is what MC gets at through brute force. The C term for spending, by the way, means that this process, unlike that for a stock price, can break through zero (i.e., fail, hence fail rates). Maybe this assertion is a stretch for the point I am making but using A.2, Robinson goes on…
E. Spending Evaluation – Part VI: Perfect Withdrawal Amounts
Evaluating spending programs via SPV or lifetime utility is useful and important. But these approaches also require a bottom up or stipulated or admitted or dynamically optimized or designed approach to specific spending programs which are then either evaluated for feasibility against current assets or are evaluated by way of their relative optimality against the other proposed spending plans. Another way to look at a spending process is to come at it from another direction altogether. We can do this in terms of what would have been possible to spend over an interval given perfect foresight on returns (or hindsight if we are at end of life). This perfect foresight creates a type of limit for what can be spent over a lifetime/interval given a bequest motive >=0. We were going to avoid returns and wealth in this essay but this analytic method using returns creates a type of outer boundary for spending, an evaluation technique which I think might be useful later.
The formula in Suarez (2007) for the perfect withdrawal rate – which is an inverted and adjusted form of the math for a variable rate loan except that here we are receiving payments rather than paying and shows what could be spent with perfect foresight of a forthcoming return sequence – looks like this where Ks is the starting endowment and Ke is the ending endowment or bequest, r is the random return which can be modeled as a normal distribution or other shapes as needed.
1) PWR given a fixed planning horizon of 30 years, and
2) PWR with a random planning horizon following a Gompertz distribution with life mode = 90 and a dispersion of 8.5 given a start age of 60.
Note that the at the 5th percentile, where only 5% of the withdrawal rates would have represented a lower lifestyle over the interval of interest (call it a fail, maybe), we are very close to the 4% rule. That’s because the underlying processes in PWR are playing the same game Bengen and every other retirement researcher has played over the years; the underlying processes haven’t changed since 1994 nor will they change in the future. Note also that we don’t really care so much about the right side of the distribution where things would have been good; that would be an elegant problem to have. The left side where consumption would be compromised in the tough scenarios is more interesting. We can see there, on the left side, that random lifetime (in this example) has very little impact. The right side stretches out pretty far for the red distribution because in random life we have at least some cases where we live 1 year and spend 100% of wealth "perfectly" but on the left we have relatively few years where we lived radically beyond 30 years combined at the same time with terrible returns.
This PWR distribution, then, if you believe the stable and independent draw on a random “r,” is the entire universe of what we could theoretically spend in an ongoing spend process which is why I think it is useful in contemplating “Process 2 - Stochastic Consumption Processes” even though it is typically framed as a return driven process. I have not shown sensitivity of the distribution to changes in the parameters like volatility but that is easily done.
F Spending and Sequence of Returns
It may seem strange to end an over-long essay on spending with another discussion of returns. But, as we saw in our look at PWRs, the limit of spending is our returns. If we have perfect foreknowledge, our spending is our returns. And not just our returns matter but the exact “orientation,” or what we call sequence, of returns
“the sequencing issue is precisely what makes the optimal withdrawal problem unique. In most financial analysis discussions, an understanding of the total accrued return will suffice, but here it is of the essence to know not just how much but when this much. In retirement, it makes a huge difference if “good” financial results come first and “bad” ones later, instead of the other way around, because in this stage of the life cycle the rates of return apply sequentially to an ever-dwindling capital base – the retiree is constantly drawing down her savings to support herself…we think Sn is an expression that should be investigated further since it is a measure of orientation (return rates going up, going down, up a little then down a lot, etc.), and this is the crucial element that the adjustment factor should capture.” Suarez (2015)Suarez goes to great length to, successfully I think, to show how the math itself provides the intuition on the role orientation plays in spending (“We note that, for any given (unordered) set of rates, this expression decreases if “big” rates show up at the beginning of the retirement period and “small” rates show up at the end, because the last rates appear more times than the first rates in the summation.”). We can help Suarez along a bit by making a graphical enhancement to the formula like this:
One can see in this that the capacity to spend (i.e., PWR) is entirely a function of returns and how they "stack" in sequence. Just looking mechanically, there are more “r”s at the end (look "vertically." This is Suarez’s point.) so that low returns early and high late makes a big number which would make the PWR lower. It may also be helpful to think of early spending as an opportunity cost of compounding capital (if I have it right. Look "horizontally." Suarez also makes this point in the quote above.) that hurts us because we could have captured some of the late high returns with money that was otherwise spent early. Me? As a retiree I will clearly be hurt or helped by sequence but there is nothing much I can do about it except to be cautious in my early spending or hedge it out with lifetime income by way of an annuity.
But now here is a subtle point about sequence risk that Dirk Cotton indirectly helped me make in a recent post of his. Sequence risk is not strictly a "partitioned" risk that only attaches itself to some specific and artificial early-retirement interval after which life is good. Given unknown longevity, one’s retirement is in fact always in a continuous state of becoming (let's call it a process, then) so that technically one is always in the early part of retirement which means that one is always exposed to sequence risk. Yes, with two years to go the impact is not as severe as it would be with thirty, but then the risk is not entirely gone either at that point.
Dimitri Mindlin (2016), for his part, was not overly impressed with sequence risk in his 2016 article: “The concept ‘sequential risk’ is just an observation. Moreover, this observation is not terribly insightful – it merely informs us that asset prices may decline substantially at the most inopportune times. An investment strategy that is solely based on this observation may be sub-optimal and should be taken with a healthy dose of skepticism.” But I think his caution is constructive here. Let’s enumerate some of his main points:
- "The manager’s job is to prevent crashes, period.” Sequence risk should not be managed in isolation to the detriment of reaching the main goal.
- “the retiree should not rely on an inadequate deterministic model. In the world of risky assets, one should be exceedingly skeptical of the results of deterministic calculators.”
- “the “sequential risk” observation is just a useful illustration to an already well-known occurrence.”
- “The problem is “sequential risk” neither constitutes a proper quantitative definition of risk nor produces well-defined arguments.”
These kinds of points are neither fatal nor unhelpful to the discussion of sequence as an important retirement topic though I will say it does augment the point I made that there is not much I can do about it except spend less or hedge it out somehow. i.e., the outcome should be the focus rather than choosing strategies that mitigate sequence risk to the detriment of the end goal.
But before we get too complacent on sequence risk, here is some material from a post by earlyretirementnow.com (2017). ERN is a PhD in econ that writes a nifty retirement-quant blog, plus he retired early and has stepped away from his W2 income and, one would assume, a significant chunk of his human capital. As far as I can tell Mindlin is not retired. I have a small inclination to listen carefully to ERN first. Here are some of his main points on sequence risk:
- “I can’t stress enough how important Sequence of Return Risk is for retirement savers. if someone asked me for the top three reasons a retirement withdrawal strategy fails, I’d go with: 1. Sequence of Return Risk, 2. Sequence of Return Risk, 3. and let’s not forget that pesky Sequence of Return Risk!”
- “...close to 96% of the variation in the SWR [save withdrawal rate] are explained by the average returns in the 6 [five year] windows.”
- The average return for years 0 to 5 explains about 29% of SWR variance and the average return for years 5 to 10 explains another 19%. [from a post by Dirk Cotton on the ERN post]
- “SRR [sequence risk] matters more than average returns: 31% of the fit is explained by the average return, an additional 64% is explained by the sequence of returns!”
- “you can’t hide from SRR. If you try to equalize the final portfolio value through VPW [a spend rule] then SRR hits you through the withdrawal amounts!”
In the following table I ran a number of different scenarios:
· High early returns, flat spending
· Low early returns flat spending
· High early returns, high early spending
· High early returns, low early spending
· Low early return, high early spending
· Low early returns, low early spending
...plus a few others. I ran it deterministically and only looked at the terminal wealth at period 10. Then, because the interaction of spending and returns does not really necessarily always depend on the ordinal sequence early to late, I also ran the scenarios as a type of interference wave: spend peak meets return trough, and spend trough meets spend return peak in intermittent waves over the 10 periods rather than in an early vs late structure. When I play with all of this, this is what I get:
Scenario 3 is what is typically referred to as sequence risk in the literature. Scenario 6 I’ve only seen, so far, in ERN and Dirk Cotton’s work plus a few others. Scenarios 10 and 11 are totally untouched as far as I can tell. In section C, part II above, I referred to random spending as less of a Brownian motion machine and more of an industrial process control problem. This spending sequence issue here was why I made that claim; out of control spending can hurt if it has a wave effect. I have been accused from time to time of being a little anal on my personal spending control but that doesn't bother me because I am, in fact, a little anal sometimes. That's because I can see that an out of control process that has wide and/or erratic variance can have a negative impact on outcomes. Not dealing with it would be a little like assessing a tax on myself for a lack of self-awareness or a tax on refusing to see the obvious. These are taxes I am reluctant to pay. In a later essay on management and monitoring processes I’ll try to get back to this topic of spending as a statistical process control or continuous improvement project to see if it is still meaningful.
Concluding Thoughts
You may have noticed that there is not only (almost) no retirement advice in this essay, the essay feels like it is also almost unusable for traditional planning purposes. That is by design. My main purpose was not to plan or advise, it was to work with what I consider to be one of the five main retirement processes in order to visualize it as a flow, a process. Originally this purpose was not even for the reader, it was for me to be able to see the flow more clearly for myself. I’ll also note that the flow of both return generation (Process 1) and stochastic consumption over time (Process 2) need to be seen well on their own terms before we start to integrate them later in “Process 3 – Portfolio longevity.” The other reason for this essay is the reason I mentioned at the beginning: for us to realize that spending as “easy and constant” is often an academic paper-writing fiction, a convenience assumption that is easily made and lightly skipped over. Think about it the next time you see a constant spend assumption somewhere. So, I hope this has been helpful. While a little bit long, and even though I’d guess that it barely scratches the surface of a more formal discussion, it at least represents a little bit of what I have read and internalized over the last two or three years.
- Advisor fees and taxes are part of the consumption process but otherwise unmentioned. They should be. Often these costs are modeled in net returns which is an ok shorthand but might be better modeled explicitly, if possible in a consumption model. Think of it this way. Say you are an early retiree where a safe withdrawal for your age might be closer to 3% than it is 4. If you spend 2% on your advisor fees off the top, then well....
- One thing I’ve learned in life is that the more I write in terms of pure volume of words the clearer it is to me that I do not really understand the thing I am writing about well enough to be concise. This is a very long post. Make your own inferences.
Notes
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[1] Yaari (1965) famously puts it thusly: “The specific form in which the utility function V is written (equation (1)) means that an implicit assumption has been made to the effect that the consumer’s preferences are independent over time. This is not a very happy assumption but unfortunately some strong assumption of this sort must be made in order to make the problem manageable.” Diamond (2000) and Davidoff (2005) attempt to loosen this up a bit.
[2] Alternatively in Bilsen (2018): d log h(t) = (β log c(t) – α log h(t)) dt, log h(0) = 0 where h is the habit or lifestyle, c is consumption, alpha is “rate at which the log habit level exponentially depreciates” and beta “models the relative importance between the initial habit level and the individual’s past consumption choices.” The implication of this is that the log habit level is “a weighted sum of the individual’s log past consumption choices”: log h(t) = β
Bilsen points to work by Kozicki and Tinsley (2002) and Corrado and Holly (2011) but does not mention Mirrlees.[3] Bilsen (2018) describes one approach to linear approximations of the budget constraint.
[4] Pre retirement drift is called lifestyle creep and speaking from anecdotal or personal experience I can affirm that it does exist when income rises. Not so sure about everyone else.
[5] Banerjee emphasizes that he is using cross-sectional data not following individual families.
[6] I like the humility of this quote in Robinson (2007): “One particularly useful piece of empirical research remains undone to support our conclusions. There is lots of information on long run investment returns and so we can support our choices of those parameter values. However, our choices of α, β and ρ [spend parameters] are instinctive, not evidence-based. They are not simple statistics that are immediately observable from information that is widely known. What we need to find is data on spending patterns that provides longitudinal evidence of how people change their total spending in their retirement years.” [emphasis added] Robinson (2007)
[7] In fact, in my own data there is a little bit of a "small numbers problem.” The number of observations that contribute to the 2nd distribution is probably less than 10-20. We’ll model it probabilistically anyway just to do it.
[8] See Taleb on black swans. Nice to know that retirees are exposed to two black swans: one for returns and one for spending.
[9] Ruin is probably an over-played concept in retirement finance. First, people adapt, self correct, and go back to work. They cut spending. In the end one is likely rarely ruined. Rather spending falls at some point to available income which in terms of social institutions means at a minimum social security and tangible and intangible transfer payments to the less well off. Income, to which spending "snaps" when wealth depletes, can also be pre-purchased via lifetime income by way annuities as long as some wealth remains. Spending probably does not go to zero with its infinite disutility. It just goes to something lower than before.
[10] I spent a ton of time doing this in a past life with software production in a continuous process. It was very, very expensive to make mistakes so we engaged in the equivalent of a six-sigma process to wring errors out of the process balances against the cost of the human capital required to get it to work. I assert, without much support, that the same principles apply to spending processes.
[11] “What do we consider to be an acceptable risk of shortfall? That is a decision for every retiree or planner to think about, but our choice is 10% [I've also seen 30%]. We think that many people would choose 5%, but we know of no formal evidence on this question. [emphasis added]. Robinson (2007)
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re: "Is Spending Constant in Real Life or does it Drift?"
ReplyDeleteOne thing I've been wondering more about recently is whether inflation is the wrong thing to even care about. I first started thinking about this when reading Robert Gordon's Rise & Fall of American Growth -- the whole point of "growth" is that things -- quality of life, material possessions, etc -- go up FASTER than inflation. Otherwise we'd all still have the same quality of life as 1890s America and no one would be complaining about stagnant real wages.
I think of it as a reframing, instead of "how do I keep up with inflation" it is "how do I keep up with improving socio-economic conditions". In other words, if you retire as solidly middle class, are you still solidly middle class 30 years later?
Admittedly, this is more of a problem for early retirees who may easily have 50 years ahead of them. And, if you believe Robert Gordon and his "end of American growth" thesis, maybe it is less of an issue going forward.
As an example of how inflation alone doesn't capture this aspect:
In 1901 the average hourly wage in manufacturing was $0.23 an hour. If you “kept up with inflation” then you’d be making $0.62 an hour. Except by 1950 wages in manufacturing were actually $1.59 an hour. If your real income was constant over that time period you went from a decent working class family to virtually destitute.
If you shift perspective from inflation to "maintain socio-economic status" then historical simulations have very different results. Instead of 4% and the late 1960s/early 1970s being the worst time periods, instead it becomes 2.5-3% and the 1940s/1950s with their tremendous increases in standards of living as the things we consider "modern life" -- electrification, television, cars, washing machines, telephones, etc -- became universal.
I'm an early retiree, so this is admittedly more relevant for me than for the bulk of retirees, which is probably why I spend so much time thinking about it.
I hear you. I retired in early 50s and the prospect of what? 40 or 50 years(?) to manage was daunting. Also the idea of "just" keeping up with inflation clashed with what was still a growth and/or accumulation mindset. I've seen some first-hand ruination from inflation so that's bad enough. Keeping up with society (my kids, maybe?) is a different problem. Sobering even now that I'm 60 where I'm still playing a long game. I'll take a look at Gordon. At a minimum it looks like you're describing is what I wan't to call a macro level lifestyle creep (drift) which, in the Robinson and Tahani paper, is the more destructive of the several spending "shapes" they set up.
DeleteAlso, your sidenote on "The Dirty Little Secret of Constant Spend" prompted me to write something on that topic. I agree that people who only look at the end state ("retiree was a success!") ignore all the states along the way. Investing is a process, after all.
ReplyDeleteI argue that ignoring the "unsafe withdrawal rates" that you are forced into along the way is a misleading description of a "safe withdrawal rate".
https://medium.com/@justusjp/the-myopia-of-failure-rates-846f35a1c8eb
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