# It is Optimal for Retirees to Plan for Reduced Spending with Age

Recently, I reviewed the economist’s argument for the existence of an annuity puzzle. Buried inside that post is something rather important, which didn’t receive proper consideration since it was secondary to the annuity issue. I’d like to return to that.

A general assumption in safe withdrawal rate research is that people plan to spend a constant inflation-adjusted amount for as long as they live. That is intuitive and it is connected to the idea of consumption smoothing. People like to spend the same amount over time and don’t want to experience reductions to their standard of living.

However, this spending plan is actually not optimal for any reasonable set of preferences about the tradeoff between spending now and later, even if we assume that future market returns are known in advance.

Before explaining why, I do want to make one point clear: there is an unrelated issue that retirees may gradually wish to reduce spending as they age for other reasons. They just slow down with time and don’t get out as much. I reviewed evidence about that in a recent column at Advisor Perspectives. But please ignore that for now. It is a completely separate matter from what I am about to discuss. (Or maybe it isn’t, perhaps people are just behaving rationally after all with a plan to reduce spending)

The issue today is: since your survival probabilities decline with time, it is rational to spend more earlier on while you are more likely to be alive, and to spend less later on when the probability of still being alive is lower. You should intentionally plan to decrease spending as you age to account for the lower probability of living to each subsequent age.

Financial economists have known this for a long time, but I don’t think the message about it has gotten out very well because the result is usually obscured in a mathematical equation rather than being written out with words. We only see it if we try to graph those old equations.

So it is optimal to reduce spending as you age, but by how much? The answer to that depends on what financial economists call **risk aversion**, but which I would like to rename as **spending flexibility** for the retirement period. How flexible are you about letting your spending decrease? Are you willing to spend more now with an understanding you may have to cut back later, or would you be willing to spend less now to help ensure you can spend just as much later? Generally people want to smooth their consumption, but again the hangup is that this may not always make sense when the probability of survival declines over time. A larger number for spending flexibility means the retiree is less flexible and wants greater consumption smoothing, as retirees care less about upside and really wish to maintain as high of spending as possible even in the low probability event that they happen to live a very long time.

I will assume retirement date wealth of $100. This amount doesn’t impact the results. I assume a male retiree at 65 and use the Social Security Administration 2007 Period Life Tables to obtain survival rates past this age. At retirement, retirees choose their annual spending amounts for ages 65-100. Financial markets are simplified to one asset which always and forever provides the same fixed return. Since retirees know the future investment returns, making these plans is easy to do. They don’t know how long they will live, but they can decide on how much they will spend each year should they still be alive.

There are now two competing tradeoffs: you want to spend the same amount every year for as long as you live to get the most lifetime value from your spending, but you also want to frontload your spending to early retirement when you have the highest chance for survival.

The following figure shows the optimal spending path for different degrees of spending flexibility when asset returns are 0%.

Someone with flexibility of 1 is quite willing to let their spending decrease over time to reflect the low probability of survival as they age. Spending starts higher but declines to very low levels by one’s 90s. With flexibility of 2, more effort is made toward keeping a smooth level of spending. But again, it is still optimal to frontload spending. You can also see for coefficients of 5 and 10 how we obtain greater smoothing even in the face of the decreasing survival probabilities. How much lower would you let your spending fall in your 90s to allow more spending in your 60s? It’s an important and highly personal question. But if you want something even flatter than the spending flexibility=10 case, it means you are quite risk averse about spending reductions. The constant inflation-adjusted spending assumption creates very extreme inflexibilities and risk aversion on the part of the retiree, and it may not be what retirees really want! Do you want it?

As the market return increases, you know that your remaining portfolio will grow at a faster rate, allowing you to spend more earlier in retirement. At the same time, you have some incentive to delay spending a bit so that you leave more wealth in your portfolio to grow at the higher rate and support even more spending later. Here we can see the spending pattern when asset returns are 4%:

Naturally as well, the less flexible you are about letting your spending fall, the more valuable a fixed income annuity becomes. As I discussed in the previous blog post, some with flexibility=10 case would require 90% more wealth to be just as happy with not annuitizing as if they had just annuitized in the first place (under the basic assumptions I used). For those with more flexibility, the value of annuities is less than this.

**A key point here is: The assumptions of constant inflation-adjusted spending used in safe withdrawal rate studies, though intuitively appealing, is not optimal even in the case that there is no uncertainty about future market returns.**

It will be great to move more and more toward combining the theoretical insights and rigorous methods used by finance academics with the real world practicalities and understandings of people and financial planners developing retirement solutions. I think this is a good example of where there is some ample ground for the cross-fertilization of ideas.

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Very interesting, if not altogether unexpected. Can you tell how these spending curves are calculated (or direct me to the relevant papers with equations)? Thanks.

Hi, it is hard to write the equations without access to an equation editor. The specific source which prompted me to try this out are the equations starting on page 77 of Mark Warshawsky’s new book, Retirement Income: Risks and Strategies. One of these days I will feature that book. It’s a good one!

It is a standard eveconomics problem: choose the consumption path to maximize expected utility using a constant relative risk aversion utility function, and subject to the constraint that you can’t spend more than your initial wealth and subsequent portfolio returns.

Thanks, I’ll check it out. I did some research; seems like this all started with Yaari in the 1960s. It is not a trivial problem, with the need for Euler-Lagrange equations to solve.

Wade –

I’ve read things suggesting that Herbert Simon and Daniel Kahneman might like to revise that calculation assignment.

Simon might like to advise the professor “Tell your students to go out and get evidence that ‘maximize expected utility’ and ‘CRRA’ represent real people’s values, BEFORE the students do the calculations.”

Simon might secretly think the students will not be able to find evidence supporting those theories.

Kahneman might say he has some evidence that people’s priorities are based on a “reference point,” and ask the professor to tell the students to analyze the alternatives using “prospect theory.”

He might hypothesize that for this analysis, the reference point might be “sufficient” annual retirement income, and the prevailing priority might be “Don’t risk going below it.”

Can you describe how you might approach this decision area from a Kahneman prospect theory perspective?

Dick Purcell

PS — I like your graphing of alternatives better than ANY selection theory – it INFORMS the person so SHE can make the choice for HER life.

Wade –

I have flaming disagreement with the “financial economists” you cite, who “have known this for a long time.”

To me, that’s a big red flag. It’s the same ivory tower crowd that has for two decades kept planners, advisors, and investors in the MPT sinkhole of choosing portfolios based on conjuring “utility functions” purporting to represent Granny’s tradeoff between return-rate arithmetic mean and return-rate standard deviation – instead of doing the decent, responsible thing of showing her how the portfolios compare in result probabilities for her purpose, her future dollar needs and goals.

Now they threaten to do it to us again. For the next two decades?

For a tiny minority of the richest, for whom living expenses are a tiny fraction of the spending rates on the graphs, that planned decline can make sense. But for MOST people it is nutty. Do we want to lead Granny on a path where if she lives long, she has to move out of her apartment where her remaining friends live and take up residence in that roomy cardboard box under the Sixth Street bridge?

Those tenured, TIAA-CREF-secured ivory tower smuggies who “have known this for a long time” are lost in the imaginary math of their “expected utilities.” The first, default consideration should be avoid risk of horror, not “expected utility.” They have no right to be dropping such MAL-advice down on us peasants down on the ground.

Dick Purcell

PS – I think the spending flexibility numbers are backwards. My advice to Granny is NO flexibility, flat horizontal line on the graphs. I think the numbering should make this spending flexibility = 0. SPIA, SPIA, SPIA – inflation-adjusted.

Dick,

You seem angry.

Actually, Anon, I’m pleased as punch that Wade has converted the math from the “financial economists” into his graphs, so Granny can see what horrors await if she follows said “financial economists” advice and continues to live.

Maybe some of those “financial economists” will learn from Wade and become educators instead of obfuscators.

Dick Purcell

Dick,

Thanks for the reality check. Certainly, no real person is that flexibility=1 case (which is just log(income)… maybe that is a bad baseline)

but it is hard to argue against the general idea that people may be sacrificing a whole lot for the present to be able to spend more than they may need should they live a very long time.

Of course, the math here started as a way to justify using annuities. So now we have to figure out what people may want to do if they refuse to annuitize. We are now in the realm of second best solutions.

And we can’t avoid this problem. We could leave survival probabilities out of our evalation tools for retirement income strategies, but the problem shows up in other ways. How long of horizon do we plan for when not using survival probabilities? 30 years? 40 years? 50 years? Your answer to that in some sense is correlated with your view on this spending flexibility issue.

This being said, I also emailed about this blog post to a few leading planners and I am getting the impression that this may not be a good avenue for real world research. Even if someone could agree on a plan to reduce spending over time, when the time actually comes to reduce spending they may balk. And if they don’t reduce spending, it means they spent too much at the start and are now in jeopardy.

I understand your point. But it seems to me that it is impossible to work around the need for annuities of some kind — better to confront it head on. To put all this in simplest form: Without annuitization, if retirees are going to have enough money to support themselves at age 90 or 95 or perhaps 100, the many who die at age 85 are going to leave a lot of money on the table. Assuming no bequest motive, the only solution is some kind of annuitization, either standard or perhaps as longevity insurance.

I do think partial annuitization needs to be strongly considered as a part of retirement plans. Having an income floor, along with Social Security, would also change the shapes of these curves.

One reason that I would hesitate to plan for reduced spending as I get older is that I would expect that healthcare related costs, including the possible need for assisted living, would become a larger and larger proportion of my spending. And those are going up faster than inflation. So while I may reduce spending on things I would WANT to spend on, spending as a whole could actually increase.

Yes, health care costs are the big unknown. And I don’t think there is any consensus yet on how to best plan for them. Thanks.

Hi Wade, I think your perspective on this is VERY thought provoking (and the comments are very interesting as well). I really appreciate you renaming risk aversion to spending flexibility. That simple translation will help me explain this concept to clients in much plainer English than “risk aversion.”

I actually think there is some good merit to front-loading spending earlier in retirement (assuming some decent level of lifetime floor income, such as Social Security and annuitized income). After all, who doesn’t want to spend now rather than save for later (witness our dismal retirement saving behavior as a nation)? So why not ramp up “fun” spending, to a degree, in the early years of retirement, recognizing you’ll need to scale back in the later years (assuming you live that long)? Census Bureau data seems to indicate that we do indeed spend less as we grow older.

Thanks for pushing me to think outside the box!

Mike

Mike,

Thanks for the input. I’m still thinking about how to best incorporate this issue into research about retirement income strategies.

What you are saying does make a lot of sense.

Wade

Am I correct in thinking that the retiree’s choice of spending amounts for ages 65-100, once made at age 65, can’t be changed by the retiree in later years based on their remaining wealth if they are still alive?

I think it would be more realistic to work out what optimizing retirees would spend at each age, given that they can change their planned spending if they are still alive each year, and that they know in advance that they can do this.

Perhaps one way to work this out would be to assume that the retiree, if they have survived that long, faces a 100% chance of dying on their 120th birthday. They therefore will plan to spend all their remaining wealth during the year after their 119th birthday. Therefore one can work out what proportion of their remaining wealth they would spend at age 118 for various levels of spending flexibility, then use this to work out spending for age 117, and so on back to age 65.

Given that mortality rates are very high after age 100 or so, this should give a very good approximation.

Hi,

Yes, the planning should be more dynamic to account for market returns.

But in this simple example, it is possible for the retiree to do the planning at the start because of my unrealistic assumption that they already know all the future investment returns they will get. In this simplified case, the person can do what you are suggesting at the start.

But this will still define the sort of path one will take with appropriate adjustments for market returns.

A more realistic model might be declining spending with a large step up at the end, to model the costs of assisted living/long term care.

In theory, one should be able to insure away the bump at the end, but currently available long term care policies are term polcies so that the premiums rise with age. Furthermore, most of the policies have little or no deductable so that the claims rate is relatively high.

Thanks for the input. It’s a good idea. One could also model the random appearance of huge expenses showing up throughout retirement and see how that impacts decisions earlier on. There has got to be something that could help understand better about what to do for health expenses.

Hi Wade, I appreciate your site and love the discussion in the comments.

I have thought about this spend down problem for years and have struggled with the best approach, knowing that a 67 year old retiree will spend significantly more than a healthy 88 year old. In fact, I encourage clients to assume a greater level of spending in the front years as they are able to travel and do the things they’ve desired to do in their golden years.

The real question though is on average, what is that percentage of pre-retirement expenditures that average retirees actually spend? Is it 120% at 67 (year 1), 85% at 75, 50% at 85, and 40% at 95 (excluding inflation and LTC expenses)?

When we get those numbers it will be a powerful tool to couple with your “risk tolerance of flexible spending” that will be awesome, and I’m sure you are working on this.

To echo some of the comments on this board….

Personally, I casually embraced the LTC issue and spoke about it in investment reviews in the past, but never really was an emphatic believer, but recently had a relative face these issues at age 87. It doesn’t matter how much wealth a person has, writing $6,000 a month checks for a nursing home or AL facility makes you cry out for LTC coverage and rant and rave about the idea that the wealthy do not need LTC since they have significant assets. As LTC carriers exit and/or as LTC policies continue to become more expensive planners need to believe that perhaps solution that involves a semi-protective strategy of partial coverage may be best since many clients and advisors look at the world in black or white (no coverage or total coverage). Even if a client has $130 a day in coverage, that is still $4000 a month in asset protection.

Jason

Thanks Jason, especially for the thoughts about LTC.

About the replacement rate at the start of retirement, I think the average is in the 70-80% range. But the important point is that this is just an average across the population looking at spending for different age groups, and people are probably better off thinking about what will be more appropriate for their own personal situations rather than to just assume that this range will be best for them.

Standing at the edge looking out at the rest of life without earned income, the real world impression is one of great uncertainty. You don’t know rates of return, interest rates, inflation, or life expectancy over a possible 20-30 yr period, yet alone the effect of political/regulatory change on your savings. Huge polka-dotted swans are swimming in the back yard. This is why it may be that many if not most have decreasing relative risk aversion, not CRRA, and are loathe to spend any more than necessary as they retire, unless they are (very) well-funded. As time goes on, the uncertainty from the period gone by dissipates, the period of uncertainty that lies in front is reduced by as much, and the DRRA type may feel more comfortable spending more, not less, even if, being older, there is less energy or interest to spend it. Coupled with end-game healthcare cost, the curve may well ramp up dramatically in the last few periods, if only from deferred legacy gifts and dispositions, the inverse of the spending flexibility mentioned here.

Thanks for the comment. About it, I understand your point, but I wonder if the “spend more” you describe means substantially increasing your withdrawal rate as a percentage lower of remaining assets, rather than actually planning to spend a greater amount. I need to think about this some more.

[…] age, it is somewhat natural to plan for a reduced spending pattern over time. You would have to be extremely inflexible with your spending or extremely averse to outliving your wealth to prefer a strategy of constant spending over […]

[…] people may naturally spend less as they slow down at later ages. Second, it is rational to plan to intentionally reduce spending since the probability of survival decreases with age. Both of these links explain how this allows […]