"Theories and models are attempts to eliminate time and its consequences, to make the world invariant, so that present and future become one. We need models and theories because of time…You can only be disappointed if you had hoped and desired. To have hoped means to have had preconceptions – models, in short – for how the world should evolve. To have had preconceptions means to have expected a particular future. To be disappointed therefore requires time, desire and a model…You can count yourself lucky if your model of yourself survives its collision with time."
– Emmanuel Derman, Models. Behaving. Badly. 
Everything changes and nothing stands still…You could not step twice into the same river.
What little I’ve learned about retirement finance so far since 2015, the year I started my blog, tells me that there seems to be no real, perfect spending rule that will save me, except maybe with hindsight, and no such thing (serious academic papers notwithstanding) as a fixed optimal retirement solution, at least not a permanent one anyway. There is only, in the end, what I’ll call “flow.” By flow I mean that retirement is not an object or a thing or a solution or a "number." It is a process, a continuous unfolding-in-the-present of new and unstable circumstances, challenges and changes to which we need to respond anew in each one of those present moments.
This concept of flow means, to me, that constant vigilance (along with initial feasibility assessments; more on these two things later)  becomes paramount in entering and then managing “the flow” of retirement. This essay and the ones to follow, in order to examine the need for vigilance, will take a close look at retirement finance as a process, or, rather, what I consider to be the five main processes that influence decision making about an ongoing retirement flow over time, decisions that hopefully will drive positive outcomes all the way to the end of life. The skin-in-the-game consequences to a retiree for getting it right or wrong demand a close look at all of this.
Just to be clear, I am not an academic, practitioner or actuary. I am a retiree. I am certified in nothing…other than me informally attesting to you that I have skin in my own game. But even as a retiree, I will have little to say here on what I want to call last-mile considerations -- social security claiming strategies, estate planning, budgeting, which accounts to draw down first, portfolio design, or tax strategies – that are typically of great interest to the retail retiree and common in the literature. These topics happen to be where the financial services industry earns its keep and I will not intrude. Neither will I have much advanced insight into academic, optimal solutions which are often opaque or unavailable to me. Rather, these essays will be a representation of my current, evolving, and personal understanding of how the deeper general flow of retirement works as I see it through my own early-retiree quant-ish lens, a lens that sees nothing but a river of uncertainty all the way to the horizon. This word uncertainty is important here because while risk can be managed or hedged or insured, uncertainty can’t so it needs to be monitored and managed over time.
The key element in all of this to follow will be time. It is time that creates flow and flow changes things, like when we try to step into the same river twice and find not only a different person but also a different river. I’ll take a look in this series at five retirement processes and how they are influenced by time or are at least necessary to deal with changes that come with time. The five processes I see that are essential to this discussion include the following:
1. Return generation in multi-period time
2. Consumption processes over time, especially in the presence of randomness and uncertainty
3. Portfolio longevity, a combination process made of both return generation and consumption
4. Human mortality and conditional survival probability
5. Continuous monitoring, management, and improvement processes in retirement finance.
Graphically we might present the five like this:
The essays to follow will examine the five processes and some of the interrelationships between them that matter the most to a retirement flow. While these interrelationships are important it is also important to recognize that to a great extent they are all really independent of each other. While mortality might at some point be influenced by running out of money, as would spending, those can be extreme considerations. For the most part, the underlying processes do not really know each other very well. This is why stable optimal solutions are hard to come by in this business. We’ll take a look at each in their turn to see what they mean and how they interact. I don’t consider any of this to be particularly unknown in the industry, this is just my personal attempt, for my own purposes, to integrate what I have learned into a single, coherent view that makes sense to me.
The basic outline of forthcoming essays will look like this, by process, if I can pull it off:
1. Return generation in multi-period time. This means taking a look at the implications of what happens to returns within a multiplicative process that evolves over time. In this world, arithmetic expected (forthcoming) average returns can mis-set expectations since they will overstate expected geometric mean rebalanced returns, the ones that one would expect to be realized in real life, which will, in turn, be a little higher than a common rule of thumb used to estimate the geometric mean, a rule of thumb which will itself be higher than the (incorrect) weighted average of individual geometric return estimates of the individual components. The final exact real outcome of any individual’s “returns path” through time will match none of these, of course, but the idea is to get a sense for the process and have a general idea of its potential influence on things like terminal wealth, portfolio choice and efficient frontiers, effects over short horizons, strategy dominance, and relative likelihoods at the chosen horizon. That’s a tall order, and I won’t get too deeply into the science, but we’ll at least try to visualize some of it in order to get a feel for the "flow" of a return generation process.
2. Spending. Spending always seems to get glossed over like it is simple or constant or perfectly well understood. Which it’s not. It is, rather, random (with a skewed distribution), prone to shocks, subject to trends (up, down, steps), and often unpredictable in unpredictable ways. It also, in my opinion, profoundly dominates other inputs (perhaps, say [gasp] asset allocation?) when looking at net wealth processes and portfolio longevity. Spending, especially in its stochastic present value form in the context of a household balance sheet, is the core factor in feasibility analysis both before and during retirement. Spending is also the means by which economic utility of different retirement strategies can be evaluated with or without considerations related to portfolio longevity (next process). If we were to assume immortality, by the way, spending would seem to be the only process guaranteed to last forever. It is worthy of a look.
3. Portfolio Longevity. Portfolio Longevity (PL) is an abstract, derivative construct made up of the combination of processes “1” and “2” above (it’s a net-wealth process at that point) but when these two are combined the resulting net process has its own separate properties and distributions that are worth understanding and contemplating. For example, I think that when a retiree asks a question about “sustainability” and is given an answer that only focuses on “fail rate percentages” at “30 years,” that answer feels a little like a non sequitur. What they really are asking is about time and the probabilities of wealth+spend lasting “long enough” which is a slightly different but not entirely unrelated question. This other question can perhaps be evaluated in several ways: (1) simply and analytically (say divide endowment by spending which yields a broad-stroke estimate of years) or (2) by more complex deterministic formulas for PL or (3) via a simple mini-simulation that (notably) has no real time or life boundary and generates a distribution for the years that a portfolio will last over an interval that could include eternity. That last approach can provide us an interesting portfolio longevity distribution that does answer the retiree’s question though in a way that may be a little complex for many retail retirees. Then, to take it even a step further, this PL distribution, an object coming out of the unbound mini-sim, when it is combined with random lifetime survival probabilities (next section), provides the “lifetime probability of ruin (LPR)” that happens to also satisfy the 1930s era Kolmogorov differential equation for LPR. LPR, by the way, is more or less what would also come out of a traditional Monte Carlo simulation if the sim were to have random life (usually in the hands of a skilled modeler). Personally, I think that this concept of LPR -- as a place where returns, volatility, spending, portfolio longevity and random life all converge – is an interesting and important thing to understand especially since it is an essential part of the continuous vigilance project when we are thinking about evaluating sustainability.
4. Random Lifetime. A big reason that a lot of retirement analysis is a challenge is that lifetime is random which can make the math pretty complicated pretty quickly. This randomness gets lost or ignored in a lot of analysis, however, and is almost entirely opaque to retail investors because random longevity is hard to grasp when using fixed planning horizons (30 years) or a simple mean longevity expectation (say 85) or some conservative estimate (to age 95). Also, the fact that longevity expectations move conditionally with advancing age is apparent mostly only to actuaries and usable information in only rare circumstance. My guess is that most retail investors don’t need to know the details of all this but awareness of the impact of longevity uncertainty is important especially on the far (superannuation) right end of the distribution. I mean, really, what would you do if you are the one that lives to 105. And even at 105, there would still be some (small) residual conditional survival probability. The main goal here might be merely shift a reader’s point of view from “30 years” or “to 95” to thinking in terms of distributions.
a) Family Financial Statements. This includes a balance sheet, income statement, and cash flow all as ongoing projects rather than as a one-time effort. The balance sheet would include the present value of flow items like spending, pensions and Social Security,
b) Feasibility analysis. This extends the balance sheet discussion by describing feasibility in terms of present value “solvency” using current observables on the balance sheet. Most retail retirees would probably be lost at present value analysis but I’d take a shot at discussing even more complexity like stochastic present value and a distribution of spend rates on the liability side in order to evaluate the robustness of the solvency equation.
c) Forecasting, Sustainability and Risk Assessment. Discussion here would be on things like the use or mis-use of simulation and fail or ruin estimates, portfolio longevity, perfect withdrawal rates, etc. Emphasis will be on dynamic, continuous evaluation in the presence of state changes as well as the importance of continuous monitoring of feasibility.
d) Household "Ops Research." Discussion here might be on various monitoring-analytics such as viewing spending in a statistical process control and continuous improvement process context. Also, additional elements of the balance sheet would be explored. The idea of a simple annuity boundary and its role in monitoring processes would be introduced. Additional topics might include ideas for thresholds for fail rates or the idea of spending retrenchment as well as the limits of retrenchment.
e) Incremental Portfolio Optimization. You’ll notice the word “incremental” in the heading. That’s because the general topic of, and literature on, portfolio design and optimization is an ocean that is both very deep and very wide and I will not touch it. That’s for you and your advisor. Also, the general topic probably properly belongs to a discussion that would hopefully pre-date “process 1” above. But this initial-pre-design idea does not absolve a process-focused manager from being aware of (and reactive to) things like: tactical reallocation opportunities as they arise, changes in the forthcoming scenarios for inflation or interest rates, new products or market opportunities that appear (say Tontines become available or maybe more efficient annuities), or constructive additions come over the horizon related to what we know about modern portfolio theory and its corollaries (say factor tilts, style premia, liquid alts, new research on asset allocation in the presence of annuities, etc.). This is a pretty open-ended proposition, I'll warrant, so I will likely focus only on one example: the impact of adding trend following to a retirement portfolio…since there is some literature on that topic that I can use. That idea in particular can be highly accretive to the concept of portfolio longevity. The other thing to note here is that even though this "incremental" topic may look obscure or peripheral given the way I’ve placed it in the discussion, it really isn’t. It is, counterintuitively, a highly integrative and essential subject since it requires a comprehensive understanding of how the 5 processes interrelate as well as a decent knowledge of financial theory and the evolving solution landscape. My guess is that this could be an entirely separate paper/post/book but we will start with one illustrative example and take it from there.
This is an introduction to a 5-part series. For the rest I plan to follow this outline though it may change:
1. Return Generation in multi-period time
2. Stochastic spending processes
3. Portfolio longevity using process 1 and 2
4. Human Mortality and conditional survival probability
5. Managing and monitoring processes in retirement