What is the most sensitive factor in the computation of retirement income? **Time!** *It is the one input that is largely ignored.* Time … or better said, aging … has succumbed through the common use of a fixed age such as 95 or 100.

You may click on the graph to enlarge it (hold shift key and click for a separate window).

Retirement is not a static timeframe, a view that comes from calculations or simulations over fixed *ending *periods; in other words, the ending age doesn’t change, OR the time period is fixed. No. Retirement is a series of *rolling time periods* where you age a year, and your expected longevity goes up a little too. Researchers often use rolling time periods when they evaluate the markets, but don’t use rolling time periods when they evaluate retirement. [You Should Expect to Get Older, As you Get Older with visuals for how longevity graphs change with age. It’s tempting to jump to the conclusion of age 95 when you view the graphs, and that’s the bias effect mentioned below – few actually reach it; which comes at a cost for the many.]

Even if you use the same, fixed, ending age for calculations or simulations, you’ve aged a year. It becomes very difficult to evaluate progress when you’re, say 12 years, into the retirement spending plan, i.e., your simulation, you developed 12 years ago. No – now you’re 12 years older, or any number of years more or less than 12 years (we’re all different) … so what does the plan suggest success should look like now?

Setting a fixed old age is a form of survivorship bias … you see those living into their late 90’s, or early 100’s, and this leads to the conclusion that you also need to plan to that age. Adviser’s tend to set *everyone* surviving to such an age with their retirement income calculations. Such practice perpetuates this bias.

Why is it important to understand time and its’ use in retirement calculations? **Because using an age (as is common today), which is unlikely you may outlive, you’re penalizing your present-day income … just in case you’re among the very small percentage who may outlive that fixed older age.** This means it is likely you’re unknowingly leaving a bequest on the table that is larger than intended, simply by constraining spending when you’re actually alive to spend!

The usage of those fixed, older, set ending ages unintentionally came from the transition between deterministic calculations (the old way in the 80’s for example) and stochastic calculations, and the fact that some time period needs to be chosen over which the calculation needs to take place.* The problem is that a *calculation* is simply the answer TODAY. You derive a solution that is only good today for the specific time period chosen, and of course other inputs; however, *time* has a larger effect on the answer than those other inputs do.

Each and every age has *its’ own ending age, resulting in its’ own time period, *that is slightly different in length than those ages near it. These slight differences result is cash flow differences, resulting in differences in capital balances when compared to fixed periods or fixed ending ages.

Another issue is that Monte Carlo stochastic simulations [of which I’m a proponent of – just one simulation series at a time for each age to seek the solution though] also generate multiple iterations, that taken together, have been interpreted as a model … Because, at the end of each iteration is a range of possible values. *However, these are simply visible parts of the derivation of the solution and the terminal values are remainder values of the derivation of the solution*. Please see the comparison diagram between long division and single period simulations that illustrates this point.

**Restating the not so obvious:** Can you see the *single solution* that ALL Monte Carlo simulations solve for? Look again at the bottom simulation of the graphic above. Can you find the solution? The solution that the simulation was solving for? See it – it’s the single left-most point on the graph. What confuses most is that you can increase, or decrease, the spending rate, and thus change where that solution point lands. This is because a common factor used in simulations – the percent of iterations allowed to fail – is also allowed to change . *Something* needs to be fixed (NOT ending age), or at least better understood, in order to derive a solution that can be interpreted properly to compare apples to apples of the other variables allowed to change. That *something* is the percentage of simulations that fail … another commonly overlooked factor.

You may click on the graph to enlarge it (hold shift key and click for a separate window).

**What is the different between a calculation or simulation, and a model?** The graphic at the very beginning represents a model since ALL points graphed are specific solutions (derivation of those solutions are not illustrated). The Monte Carlo simulation shown in the second graphic above is simply one solution (the far left point).

Yes – the *single* answer of the calculations and simulations are usually correct – but only given the inputs, and only over that SINGLE TIME PERIOD used. **If one thing is certain about retirement, it is that time periods are anything but fixed! **There is *only* one solution to calculations or simulations as software is configured today … the far left point of the simulation! All the other points depicted helped derive that single solution.

**And if time periods are not fixed, AND time is the most sensitive factor when determining retirement income,*** then calculations need to be redone each and every year in retirement*. And rather than reserve income for years you’re *un*likely to be alive to spend that reserved income, as is common practice today using a single set ending age, why not perform a calculation each year that is reserving money to fund the years you’re *most* likely to be alive? I call this reserving “personal mortality credits.”

In other words, retirees should be encouraged to spend money while they’re most likely to be alive to spend it, with an eye on reserving money for the future years they’re probably going to be alive with future spending needs. A model provides insight into how to balance the present and future.

How can you determine the probable time you’ll have for spending? By using period life tables. The Actuaries Longevity Illustrator is one place to get this information. Social Security Life Tables is another source. Couple should determine the joint time period (which is more easily determined from the actuary illustrator). Monte Carlo simulations are useful in that you can standardize the simulations each year by using the same failure rate for simulations, e.g., 10% of the simulations fail. This means that 90% of the simulations reserve money, i.e., the personal mortality credit, for spending beyond the number of years you’ve used for the simulation time period (that comes from the 50^{th} percentile, expected longevity, age from the tables minus your present age). When you model “multi-casting” each year, you get a diagram like that at the very top of this post … not like the second diagram.

The generic rule of thumb, e.g., 4%, doesn’t factor anything about your specific portfolio characteristics, nor does it factor in specific ages (the time element). There is also no defined transition between time periods (the natural process of aging), and thus no defined transition between spending adjustments. Yes, there are another set of rules of thumbs called decision rules. But, these are rules of thumbs applied to the 4% rule of thumb.**

I think some in the profession has gone away from doing specific calculations using specific data inputs from actual portfolio characteristics (projected or historical returns and standard deviations from the actual portfolio).(µ) The profession has also gotten away from using actual time periods. Both of these factors are important and are quite different from one person to the next, one portfolio to the next, and change over time during retirement.

Unfortunately, calculators and software, available to people or planners, is based on a single fixed period calculations (either the ending age is fixed, e.g., 95, or the period of time evaluated is fixed, such as the common 30 year usage) that research shows contain *accumulating *cash flow and future balance errors … in other words, research shows these are single, today-only solutions, and not models of the future. An important consideration then is that research that is solution based, such a Monte Carlo simulations today, should also look at *other ages (time periods)** as part of the research, to see how age affects results. If one wishes to see solutions for all ages, then results should be depicted much like the graphic at the very beginning … based on *ages, *and NOT “time since retirement.”

**Software today does not say as much about the future as is presently believed or perceived. **

Software needs to be programmed (the programming doesn’t exist today)** that incorporates redoing calculations for each age of retirement, and uses its’ specific time period for each age in order to be truly called a retirement income model. I refer to the model approach as “multi-casting” where each year has a new simulation, or calculation, cast using updated time frames. In other words, programming has not kept pace with the technological ability to perform more complex calculations.

**In the meantime**, until software is programmed*** to be closer to a model, people and planners **should do an annual recalculation**. Ken Steiner, a retired actuary, argues the same – only using a deterministic approach rather than a stochastic approach. A deterministic approach for modeling is more difficult because of the problem of tracking possible ranges of portfolio values into the future; which is why I’m a proponent of the stochastic approach. Ken’s approach is also not a model approach (it is a single calculation each year in the present, rather than calculating every year in the future too) … which goes to my argument that software programming needs to be updated across the board to represent a closer approach to modeling the range of potential future outcomes. This said, Ken’s approach in summary: 1) Do the specific calculation, and 2) Do the calculation each year. Any approach that recalculates prudent and feasible spending each year is more refined than applying general rules of thumbs from research that is often unrelated to your actual facts and circumstances.

**The advantages of multi-cast, rolling time period, modeling over single period calculations/simulations are many:**

- You can see the results for years well into older ages, into the 100’s if desired. With simulations, if you change the age you wish to see results to
; because, the time period has been changed over which the calculation/simulation is done.**it changes the solution for the present age****Multi-casting doesn’t change prior solutions**by changing the age you wish to see results depicted to, or from. In other words, if you wish to see how things may look at different ages, the answer should be “revealed” (solution has already been calculated in the**model paradigm**). As calculations are done now, when you change that end age, or staring age, you are interested in, the*answer for today*also changes, because of the**calculation paradigm**. - Future solutions are affected by prior spending decisions. This is where it becomes obvious that
**future spending requirements are directly related to spending decisions in prior years**. Spend more today leads directly to spending less tomorrow – you can’t spend dollars, or growth lost on those spent dollars, more than once! A model approach to diagramming this illustrates this relationship directly – try to raise the left side of the spending model, and the right side drops; and vice versa. - The range of future values and spending are more refined where the wide dispersion of ending values, FOR EACH YEAR,
**become more focused within a narrower range of possible future values**(compare the simulation fan effect to the model’s tear drop effect between the two diagrams above … and more in point #5). This too leads to more direct observation of how future desires are affected by prior spending. - The
**bequest**# nature that is built into the process and modeling becomes clearer. Since a person who is still alive has a probable number of years still to live, those probable years have resources reserved to support spending over that time period. What I’ve referred to above as “personal mortality credits.”**People don’t need to set aside as much as they think****for bequests**, because of this built-in bequest nature. Logically, if one spends any bequest while alive, there are no funds to support income after that point. **A key difference at this point:**A single period, single-cast, simulation*has the*A model using multi-casting,**same spending**across ALL percentiles each year, either constant across all years, or dynamically changing between one year and the next.*has*Higher capital balance percentiles (95th in diagram above) have greater spending because more money allows for more spending. Lower capital balance percentiles (5th in diagram above) have lower relative spending because less money would require lower spending. All 1,000 percentiles have a different spending amount because all 1,000 percentiles have different capital balances, which is true for each and every year. Research cited in our paper suggests people will spend more, or less, depending on what their capital balance is.**different spending**across ALL percentiles each year.- A model reflects real life expectations. If you expect an inflexible minimum required spending,
*no less than,*from the portfolio (in addition to Social Security and/or a pension you already receive), the model shows more spending failures (scenarios running out of money) at older ages. Alternatively, if you cap your spending from the portfolio to*no more than*, the model shows portfolio balances growing faster under good market conditions, because you’re not spending it down. Thus, model outcomes are as expected. Prior, single cast simulation, research demonstrates this too. The difference though is those iterations show an ever widening range of possible outcomes, while the model narrows those ranges to more real life expectations based on all the other reasons discussed above. - Use of Period Life Tables to set
*rolling time periods*solves the profession’s dilemma as to “when does the client transition between time periods, and how do they transition?” Annual recalculations automatically, and slowly, make the transitions. A model approach incorporates these transitions as seen in the top graphic to this post. - Modeling each age’s range of spending and capital balances helps to visually connect the interaction between spending more, or less, now to the range of possible spending and capital balances at any given future age.
- The current prevalent use of Monte Carlo simulations is to cast and compare Terminal Portfolio Values (TPV). This becomes problematic when changing variables
*within*that single period simulation. Our research (linked to below) showed that there are accumulating errors of both cash flow and capital balances due to distortions caused by not recasting time periods. In other words, the last year of a 30 year single cast simulation is only*one year*in length. However, for those still alive at that age (whatever age that may be), statistics from life tables (especially adjusting for greater coefficient of variation) suggest the time period should be anything but one year! Unless of course the retiree has reached very old ages. These distortions are especially problematic for what is called “Glidepath” evaluations, because the time-effect element has not been separated from the allocation-effect element in these studies. Trying to “chop up” the research into different “time buckets” (single cast simulations over different time periods) may be a first level solution. However, the transition between single cast simulations for spending and capital balances across the simulation percentile spectrum isn’t factored into this approach. Multi-casting corrects for these distortions better.

**Combining all of these points together lead to modeling income each year on BOTH the amount of capital available to spend (thus, the income amount), AND the probable time period over which to spend it! Each iteration, each year, has a different capital balance, income, and time period.**

**Moral of the story:** So, why is TIME important? Because each age has a different time frame for how long money probably needs to last. The older you get, the less time you have, and thus the less money you need. The answers from most retirement income calculations are generally good. However, ONLY for this year, i.e., for THIS single calculation that is done THIS year. The calculations say little about the future other than it could be different, over an ever growing wider uncertainty (see bottom graphic in the second illustration above). More importantly, these single period calculations say little about what to expect for bequests (remember, because you’re always alive when doing the calculation, what 90% success rate means is that there is a remaining value for future income needs, and ultimately that means a bequest too). A model approach provides a more refined look at what those future values may be through evaluation of future balances AFTER future spending based on those possible balances during aging time frames (the first graphic above).

Advisers like myself have clients of many different ages. All their time frames are different, with no two being the same, therefore their solution for retirement income this year are different too (let alone, different portfolio allocation characteristics, spending and bequests desires too). I encourage prudent client spending for *any client, regardless of age, while they’re alive to do so. *In order to do this, you need to pay attention to time.

*Only through software programming and paradigm upgrades* will it be possible to peer deeper into the **modeling of aging, and see the differences that age, and aging,** has on the science of retirement income, to explore with more granularity and **gain more refined insights that the time function has on the effect of rolling cash flows and capital balances.** Once this is done, even more questions for further refinement will come, and the boundaries of retirement income knowledge will expand once again even further. The profession should accept nothing less than better programming

There is a difference between rolling time period models, vs “moving through time” within a single period calculation/simulation.

The above insights come from published research work by Shawn Brayman and I called “Combining Stochastic Simulations and Actuarial Withdrawals into One Model.” Burns, a financial journalist, wrote a short article on the paper found here.

Further discussion on this work may be found at Just where does the fear of outliving our money come from? Part I and, Just where does the fear of outliving our money come from? Part II.

*How does one measure the time period in question? Do you count the years *from* the initiation of retirement (as is the common paradigm now)? Or do you count the years *remaining* in retirement? The prior leads to “Retirement Duration”, “Years in Retirement”, “Retirement Period”, etc. terms. The latter is an actuarial form of measurement of the relevant period to measure. The prior leads to the question: “Does it matter to a retiree how long they’ve been retired, or how much they can spend now *based on their age now *regardless of long they’ve been retired?” Perhaps the paradox of so many methods trying to determine spending strategies (Pfau JFP 2015) may be resolved by multi-casting rolling time periods. More discussion on the time perspectives may be found “Summary: Two schools of thought on retirement income,” based on “Is ALL of your portfolio at risk of loss?” In other words, the current paradigm counts the years incorrectly starting from a *past point in time.* **The actuarial paradigm counts the years ***to a future point in time … and that future point continues to roll slowly ahead – it is not fixed.*

**I have the utmost respect for academically rigorous research and those doing such work. Without earlier research insights, the profession would not be able to expand the boundaries of knowledge by building on prior research and recognizing areas that may be expanded by further research. What I refer to above is how research based on narrower factors, e.g., 60% equity allocation, should not, in practice, be applied across the board to all allocations, nor to a retiree whose allocation is other than 60% equity. This broad application, of more narrower work, is what I refer to as rule of thumbs. Similarly, a 30-year time period should only apply to a narrow group of retiree’s whose ages fall within that time frame from period life tables. My arguments are based primarily on those numbered above. I think researchers should emphasize how their insights apply (or emphasize it only applies to the limited situations their research looked at), to avoid it being misapplied to all situations. **Use of rolling time periods**** will end the debate in the profession as to how long a time period advisers should use for retirement income. The answer is plain and simple and right in front of them all along … use the period life tables!**

(µ) The landscapes that plot out 3-D vary given different time frames, portfolio characteristics, and withdrawal rates measured by the same POF (percentage of failing simulations). Thus, specific retiree characteristics will derive different answers. (Figure 1, Frank, Mitchell, Blanchett JFP 2011).

*****Software programming**: I’m not holding my breath on this since adviser driven solutions tend to get overcome by the inertia of status quo of software developers and programmers. Michael Kitces has thoughts on this “How The Advisory Industry Has Stifled FinTech Innovation.” There are many who criticize Monte Carlo simulations without realizing that the calculation is sound, but the interpretation of the calculation as a lifelong model is the real underlying issue. Rather, programming should advance to take advantage of the software capability to do more complex calculations that are interconnected over rolling time periods. Software needs to model the aging process first because of the large influence of time, and then research can look into cash flows, capital balances, effects of portfolio characteristics, etc. in a more detailed manner in relationship to aging through retirement.

#Bequests: Our eyes are naturally drawn to the far right of diagrams and mentally interpret THAT as the bequest value. However, if you think about the diagram at the very top of this post, a possible bequest value could be as soon as tomorrow, next year, or any year along the diagrammed solutions! **Every point in a model is a possible bequest value.**

PS. Our research work in 2012 change only the **time period** over which income was spent during each year’s separate simulation. Our most recent research in 2016 changed **both the time period AND the amount spent** *within* each year’s simulation; which more closely reflects what other researchers (discussed in paper’s literature review) have found to be spending patterns of people when their capital amounts change over time.

PPS. This is *almost* similar to Kitces “Dynamic Programming” where “…dynamic programming analysis is actually to start in the last year of John’s life and then work backward.” …. The key difference with multi-casting rolling time periods is …that “*the last year of John’s life” *slowly changes* … *it updates slowly as one progresses through the period life tables. Unless this nuance is also taken into account, then once again, cumulative cash flow and capital balances errors become the issue for those later/older ages because the time frame is over a single period in dynamic programming too, rather than modeling rolling time periods that aging entails.

Note 1: The above is not something I explain in any detail to clients. This post is meant for the more sophisticated reader and those in the profession and academia. We need to think deeper about programming and the interpretation of results. Software, programming and hardware capabilities allow for more advanced modeling, modeling that should be embraced by researchers, programmers and the profession to better represent the process of aging through the time differences each age represents – not only during retirement, but also during accumulation years.

Note 2: Some have suggested using Gompertz equations. These are good first order determinations of the length of time a retiree at any age. Gompertz Law could be utilized to estimate the expected longevity, but doesn’t have the ability to refine time frames by setting computations over ever-changing percentiles of mortality by age to compensate for the uncertainty effect measured by the Coefficient of Variation [life tables don’t have the same shape for different ages … as one ages, the tables grow shorter and wider], as discussed by Mitchell (2010, Table 1). Period life tables allow for this granularity by being able to calculate other-than-50th percentile and move towards the right side of the table to adjust for more capital preservation for those older potential years. You see, if the table says expected longevity is 4 years long, then you’d spend 25% of the capital. However, the spread between table early possible demise, and later possible demise may be longer than 4 years. Prudence suggests spending based on the longer expectation – of course, health depending – which means shifting the time frame towards the right side of the tables (right side referring to percentiles within standard deviation curves).

Note 3: Some have suggested using the IRS Required Minimum Distribution (RMD) tables. These tables have more of a taxation agenda built into them rather than capital retention agenda retirees require. There is also a distortion coming from ever decreasing time frames leading to an exponential growth in spending. We found that this distortion can be managed through applying an adjustment 1-1/n, where n is the time frame coming from the life tables (with time also adjusted for Note 2 above … i.e., BOTH adjustments are necessary).

Graphics source: Better Financial Education.

Nobel Laureate Gene Fama on what models do … they help you interpret data better

https://www.dimensional.com/video/?v=0_306fi31l&p=bc30b90a-6b6f-4131-a09d-c89ec8f12942&f=false&d=true&t=A%20Philosophy%20of%20Empirical%20Work&c=&z=https://cdnapisec.kaltura.com/p/1581781/thumbnail/entry_id/0_306fi31l/width/900/height/506

“Does Monte Carlo Analysis Actually Overstate Tail Risk In Retirement Projections?” by Kitces

“The most common criticism of using Monte Carlo analysis for retirement planning projections is that it may not fully account for occasional bouts of extreme market volatility, and that it understates the risk of “fat tails” that can derail a retirement plan. As a result, many advisors still advocate using rolling historical time periods to evaluate the health of a prospective retirement plan, or rely on actual-historical-return-based research like safe withdrawal rates, or simply eschew Monte Carlo analysis altogether and project conservative straight-line returns instead.

In this guest post, Derek Tharp – our Research Associate at Kitces.com, and a Ph.D. candidate in the financial planning program at Kansas State University – analyzes Monte Carlo projection scenarios relative to actual historical scenarios, to compare which does a better job of evaluating sequence of return risk and the potential for an “unexpected” bear market… and finds that in reality, Monte Carlo projections of a long-term retirement plan using typical return and standard deviation assumptions are actually far more extreme than real-world historical market scenarios have ever been!”

My comment on this great work is that indeed, this would also suggest that the upside of the simulations (when you look at what I call “remainder values” above) are overstating results as well. This strengthens my argument above that annual recalculations are necessary in order to derive THAT YEAR’S SOLUTION for any given age.

Today, annual recalculations are done each year. I suggest above that modeling needs to incorporate this approach to avoid the misinterpretation of single period simulations as representing the model for future year potential.

https://www.kitces.com/blog/monte-carlo-analysis-risk-fat-tails-vs-safe-withdrawal-rates-rolling-historical-returns/