Friday, May 1, 2015

Spending Rules That Fit the Patterns of Retirement, and Some That Don't

I noted in a recent blog post that Spending Typically Declines with Age after we retire. In a follow-up post, Retirement Spending Assumptions and Net Worth, I explored two recent papers on retirement expenditures that suggest how much spending might decline for you based on how much you plan to spend annually on non-discretionary expenses and your net worth.

I also pointed out that spending rules typically assume that spending will be flat throughout retirement, contrary to what Blanchett, Banerjee and several other researchers have found in studies of data for actual reported retirement spending.

The question most of these spending rules answer is, "how much can I safely spend from savings this year assuming I will spend that same amount every remaining year of retirement?", when the question retirees actually mean to ask is "how much can I safely spend from savings this year given what I assume I will need to spend in the future?"

The difference can be substantial. Quoting Blanchett from Estimating the True Cost of Retirement (PDF), 
"When combined, these findings have important implications for retirees, especially when estimating the amount that must be saved to fund retirement. While many retirement income models use a fixed time period (e.g., 30 years) to estimate the duration of retirement, modeling the cost over the expected lifetime of the household, along with incorporating the actual spending curve, result in a required account balance at retirement that can be 20% less than the amount required using traditional models."
Sustainable withdrawal rate models make this flat-spending assumption, though it isn't difficult to change the models to fit a different spending assumption. I ran my own Monte Carlo model assuming a 50% equity allocation with constant spending and estimated a 95th-percentile safe withdrawal rate of 4.1%. Then I modified the model to spend 1.5% less in real dollars for each year of ten thousand 30-year scenarios. The second model estimated a 95th-percentile safe withdrawal rate of 5%. That's 22% more annual spending, or $9,000 a year more "sustainable" spending than the SWR model suggests for a $1M initial portfolio balance.

Looked at from the wealth accumulation perspective, a retiree would need to save 18% less to generate the same annual spending if she expected expenditures to decrease 1.5% a year on average rather than assuming expenses would remain flat throughout retirement as most spending rules assume.

The ARVA (PDF) spending strategy model, or annually recalculated virtual annuity, is more problematic. ARVA assumes that the correct sustainable amount to spend in the current year is the amount that an inflation-protected life annuity purchased in the current year would pay out. The retiree doesn't actually need to buy the annuity, she can simply base spending on what would happen if she did. An inflation-protected annuity will pay out the same amount throughout retirement and it isn't clear to me how ARVA could be adapted to predicted declines in spending needs as we age.

This problem extends to life annuity strategies, in general. Inflation-protected life annuities will pay out a flat rate throughout your lifetime in real dollars that will not match declining expenditures. From that perspective, nominal life annuities may not be quite as bad as they seem, since inflation will eat away at the real annual payouts, but expenditures will probably decline, too. The problem is that even "normal" inflation of 2% to 3% is greater than the estimates of expenditure declines, so this is a poor way to match income and expenses. Runaway inflation could be devastating.

Moshe Milevsky's formula for calculating sustainable withdrawal rates without simulation also seems problematic, as it, too, assumes the sustainable spending that it calculates will continue to be spent throughout retirement. It isn't clear to me that regularly rising or declining spending could be incorporated into his probability models, let alone irregular net spending, but his math is well above my pay grade. Milevsky's formula doesn't accommodate the loss of a first spouse except under the assumption that spending doesn't decline. Based on his responses to similar questions in the past, I would guess he would tell us that these scenarios would have to be calculated individually with numerical analysis if we want to avoid simulation.

As I mentioned in Retirement Spending Assumptions and Net Worth, it is probably more common for a retiring household to experience irregular spending throughout retirement, and the SWR model can easily be modified to accommodate that expenditure, as well. I repeat that chart here for your convenience. The red columns show irregular spending. Your spending in retirement is much more likely to resemble this than a straight line.

Bond ladders work well with any spending pattern including irregular ones. It is simple enough to match bond purchases to different amounts of future spending.

If spending increases as we age in retirement, most spending rules will overestimate the safe amount to spend in the current year. It is more likely that your spending will decline over time, in which case these models will provide current-year safe spending amounts that are too conservative. With irregular spending, it's hard to know where to begin with most spending rules.

My last three posts have followed a theme. First, spending is more likely to decline as we age than to remain flat.

Second, by looking at our own non-discretionary spending and net worth, we may be able to determine a more accurate assumption for our own retirement expenditures.

And, third, most spending rules aren't based on a realistic financial model of actual retirement. They assume flat spending, fixed lifetimes (e.g., 30 years), constant risk aversion, and average market returns and they make other spherical cow assumptions that simplify the math but can lead to inefficient saving and spending.

I suggest modeling your expected expenses and income to consider expected market returns, life expectancy and expected expenditures. They are all "stochastic variables", which means they have a random probability distribution that can be analyzed statistically, but can't be predicted precisely.


  1. Dirk, thanks for this analysis. I always wondered about the impact that declining real spending would have since most models I had seen assumed constant real spending. This gives me a ballpark idea of the margin embedded in models assuming constant real spending. Brad

  2. A great series of posts on the topic Dirk. Blanchett and I, along with Dr Mitchell, looked at measuring spending choices in our JFP Paper (Mar 2012). We called it the “Consumption-Oriented Retiree” which can be found by looking for that section heading in the paper. The model approached the question of what is the effect on lifetime spending early by pulling spending into the early years as well as how to measure and monitor doing just that.

    Yes, one could spend more today as you point out in this post (5.0% versus 4.1% spending rate in your example above). However, this FORCES spending reduction later which is common sense as well. Thus, once could PLAN on reducing spending later in life … then life happens as the saying goes … but, switching to higher consumption later wouldn’t normally be possible (potentially possible if markets provided abnormally consistent higher returns; i.e., higher than median returns).

    The value of the work from the paper is that one can compare the higher withdrawal rate (your 5.0%) to the distribution period implied under the “flat consumption” assumption and then see what the likelihood of outliving that shorter time period is looking at a period life table (hint: more people would outlive shorter time periods). This is another way to evaluate the risk of the spending plan – the risk of outliving your money. The only way to reduce the risk of outliving it, is to reduce the spending – thus forced into the reduced spending plan. I only bring it up to be sure readers are aware of the impact of their choices to avoid unintentional consequences.

    You see, when the markets misbehave as they occasionally do, then the reduced portfolio value means reduced spending – or an even higher likelihood of outliving their money. Measuring both the success rate (you chose 95%) AND likelihood of outliving time periods provides a more sensitive measure about impacts from spending choices.

    So in summary, even though models may be based on “flat” lifetime spending, this builds in a pad for the spending decisions from market misbehavior. The portfolio value difference implied between your 5.0% and 4.1% may be thought of as the reserve portfolio amount that provides the buffer for not needing to reduce spending as much, or at all, during market misbehavior; as well as the reserve for the possibility of outliving the modeled time period (you didn’t state what that was in your example). Doing the extra calculations for likelihood of outliving time periods as well as implied portfolio value differences is important so one understands the effect of combined risks from markets, longevity and spending choices better.

    Your last paragraph suggests the above … but I thought it important to highlight the stochastic nature of everything. Recalculating each year and updating expected longevity based on present age is critical. Calculations specific to each situation rather than rules of thumb are important. Establishing a decision rule when to adjust spending based on market curveballs, good or bad, during the current year is important as well.

    You may assume future spending patterns – and then life happens.

    Note the opposite effect can also be measured and monitored for those who have some retirement spending wishes along with a bequest motive by “pushing” spending into later years … called the “Inheritance-Oriented Retiree” in the joint paper with Blanchett and Mitchell. And yes, there are people with such desires too.

    Great series of posts Dirk!

    1. Great stuff. Thanks, Larry.

      The only point I think I see differently than you is "building in a pad", in this case by assuming flat spending. If we "build in a pad" by assuming flat spending, that both spouses live to 95 or 100, that our market returns are 5th-percentile, etc., we soon end up with a worst-case cost of retirement that no one could afford.

      I prefer to model retirement as accurately as possible, without "padding", and then to plan for the worst case separately. I want my reserves to be planned, not built in as margin. Otherwise, you end up with a strategy that says, "save as much as you can, spend as little as you can, and hope you don't live a long time." Ultimately, none of this is guaranteed.

      By updating dynamically, we should be able to "smooth" our way into slow changes in our finances, but changes aren't always slow. We have to plan for that, too.

      I can highly recommend the aforementioned papers for readers who want to delve deeper.


  3. I would agree in general with your "pad" comment. However, Dynamic Updating by revisiting the calculations each year with updated date does not ASSUME "... that both spouses live to 95 or 100, that our market returns are 5th-percentile ..." Such assumptions are padding by definition to be conservative.

    The differences are using life expectancy, joint or single, at all times, which on its own tends to shorten the time period to an end age earlier than 95 until the late 70’s, early 80’s depending on which life table one uses; and then slowly extends the end age past age 95. Market returns should be 50th percentile. I prefer to use the facts for 50th percentile, markets and longevity, and then evaluate how changing those for slightly better or worse, affects the outcome. These two differences alone tend to increase spending early on compared to static and flat spending simulations.

    You see, the money spent between 5.0% and 4.1% comes from somewhere … and that comes from future ability to spend all else equal regardless of model or assumptions (because higher spending reduces portfolio balances – all else equal). My point simply is that the markets also MAY take away future ability to spend by having an extended period of misbehavior. That uncertainty has greater consequences that are UNPLANNED. So the old saying about having x-months in reserve still applies to retirement. The difference now is the question about how to calculate that reserve. It’s as simple as spending decisions based on the implied portfolio values between what you could spend and what you decide to spend. Going in consciously knowing this is important so one is aware of consequences – eyes wide open as they say.

    Yes, past generations have reduced spending in general with differences being between income relative to assets (your 2nd post in the series). No one is sure yet what newly retired and future generations will decide to do – and medicine advances may be the curve ball on decisions.

    So yes, in agreement as we are most of the time, with differences between where to start using what data and what the specific retiree’s goal may be. Great conversation Dirk!

    1. Or, you could say that the money you don't spend between 4.1% and 5% comes from a possible need to spend more when you're older, which would be a change from 2000-2010 data, and may occur when you're no longer around.

      That's why you need a backup strategy that might be reserves, or could be insurance, or delayed Social Security benefits. Reserves are expensive (Scott, Watson, Sharpe).

      I wasn't suggesting that Dynamic Updating makes these overly-cautious assumptions, just railing against the idea of building a plan based on assuming the worst case of everything. I believe in modeling the most likely future, revising that model every year, and always actively planning (as opposed to padding) for a really bad outcome, while understanding that some outcomes can be worse than those foreseeable.

      Future spending may not mimic the study of 2000-2010, and the the market may not mimic the past 200 years. But I think both are a good Bayesian priors.

      You seem to be saying "don't spend money now because you might need it later." I'm saying that the best information available is that spending will decline as we age. Plan on spending more now, have a plan in case you're wrong, and adjust as you go.

    2. Actually I agree more with your last sentence as well (and the rest too); and not so much with what you thought I was saying (putting words in my mouth) in the last paragraph. Just to be clearer …

      I'm simply pointing out that it is possible to calculate and compare the options so that each retiree goes into their plan more informed than simply planning on spending more now and reduce later. And, to do this every year - which removes some of the past uncertainty from last year's calculations through the use of updated data.

      The moral of the story is ... although we don't know in advance what the total amount may be, because of market uncertainty (whether risk is retained or transferred) and all things equal, we have an ultimate given total amount that one can spend - the choice for each retiree is how much to spend today versus spend in the unknown future. In other words, be careful how one plans because they may be forced to live it!

      Some people I've talked with have the perception that they can spend what they'd like (more today) and the markets will make up for that spending by giving them more to spend in the future too (i.e., money illusion). Simply pointing out that the research suggests spending generally being a "smile" pattern. However, our research suggests that prudently spending more today through use of life-table-established time periods each year does allow for higher relative spending today. Using shorter time periods through the use of life table percentiles (where a higher percentage of cohorts outlive the time period) moves the spending ability even higher. It does force spending reduction later though. A crocked smile, without an anticipated uptick at the end.

      Simply stating that doing what you are suggesting, spend more now, is possible, and can be measured by comparison of time periods to life tables. For example from Annuity life tables, a 65 year old couple has an expected longevity of 28 years where 50% by definition (50th percentile) outlive 28 years and 50% don’t. By the way, the table suggests 41% of 65 year old couples outlive a 30 year period. You could calculate the suggested withdrawal rate on that time period using the other criteria you specified (5% simulation failure rate). Let’s say that gives us your 4.1% rate. Then one could look at how much they would like to spend, i.e., 5.0% from your example and determine how long a time period that spending level may last, and compare that time period to the table percentiles to see what percentage of cohorts outlive that time period – say 63rd percentile outlive that time period based on that spending rate. The ripple effect is a forced requirement to reduce spending later in order to not outlive that time period and have reduced portfolio values to support spending after that age – because one has put themselves into a higher likelihood of outliving the time period in question. It is simply each retiree’s choice and decision whether that’s what they want to do. But now, they are more informed of the implications of their spending plan – whatever that may be.

      So I don’t disagree at all with the research or your presentation of it. Simply pointing out that some additional computations should be made to fully understand implications of any prudent spending decisions, and that those calculations should be redone each year with a more complete understanding of the consequences of spending decisions.

      Great stuff Dirk!

    3. Larry, we seem to be finding less and less to disagree on, but since I hate to take "yes" for an answer and kill a fun discussion, let me make what I believe is an important point.

      I'm not suggesting that we transfer wealth from later in retirement to earlier because we know late retirement will be cheaper. I'm only saying that the amount of money we can "safely" spend in the current year should be calculated based on expected future spending and that expectation may not be of constant real expenditures. This should be recalculated periodically, so whether or not such a wealth transfer occurs will depend on the evolution of key model parameters. Bad market behavior would have a nearly immediate impact on spending. If costs don't decline with time, that information is factored into the new calculation. And if a transfer does occur, it would be smoothed by annual recalculations.

      (I think this is nearly identical to what you say in your final paragraph.)

    4. Amen! To a fun conversation and to your summary!

      PS. Enjoy the fight coming up soon!

  4. Genuinely very interesting. It is not something that I had thought of before. However, it is something we sort of know from experience. My grandfather stated himself that he experienced a consistent and fairly steep decline in his expenses over time during retirement. Nothing he consciously did. It just happened.

    Thanks for putting this together.

    1. It is something we experience. And even when households experience high end-of-life expenses, they are often lower, in real dollars, than the cost of early retirement.

      I have watched my father-in-law become less and less active and spend less, accordingly, though he does the things he wants to do and buys the things he wants to buy. At 97, and living at home, he spends almost nothing.

      Thanks for writing!

  5. A note to my readers:

    After my discussion with Larry Frank (above), I want to make clear that I am not suggesting that a retiree should spend more early in retirement because expenses will decline later in retirement. They probably will, but they may not.

    I am recommending that a retiree re-evaluate spending annually (see Dominated Strategies and Dynamic Spending) to determine the sustainable amount to spend for that year and, further, that the best assumption for that calculation will depend on the retiree's individual expectations for future spending. A good initial assumption, I believe, is declining spending, but an individual may have reason to believe her spending will be flat or even increase.

    That expectation may even change by the next review cycle, as other factors may change, as we gain another year's new information. Perhaps next year we will have information that leads us to believe our spending will more likely be flat and that will change the sustainable spending estimate going forward.

    That doesn't mean I am recommending that we spend more in early retirement, though this approach will produce a larger number than assuming flat spending. If our spending turns out to be flat or increasing, or we see poor market returns, or we have reason to adjust our life expectancy, that new information will affect the spending calculation for next year. This may or may not lead to spending more in early retirement.

    It is simply a strategy of making the best decision under currently known conditions every step of the way. Perhaps that is a subtle point, but it is a critical one.