Saturday, April 28, 2012

Fixed Time Horizons vs. Survival Probabilities for Retirement Planning

The planning horizon for the 4% rule is 30 years, but how long will your retirement last?

One of the key difficulties of planning a retirement income strategy is that none of us know for sure how long we will end up living. There are two general approaches to deal with this uncertainty, planning for specific retirement durations and making plans which specifically incorporate mortality data into the calculations. 

In “Choosing a Retirement Income Strategy Systematically,” I described various measures for comparing and quantifying the performance of retirement income strategies. Some of those measures used mortality data and some didn’t.
Today I’d like to describe more about the implications behind each of these sets of longevity assumptions.

Planning for a Fixed Retirement Duration

The idea behind planning for a specific retirement duration is to choose a sufficiently long time horizon that one is unlikely to outlive, and then plan based on that. Bill Bengen thought that 30 years was a reasonable planning horizon for 65 year olds. Those who are either younger or older than 65 may need to plan for more or less than 30 years. And even 65 year olds may wish to plan for different retirement durations depending on how conservative they wish to be with their choice. Someone planning to live to 100 or 105 would need to plan for a 35 or 40 year horizon. 

This is important because longer time horizons will guide optimal retirement income solutions toward:

  • using a lower withdrawal rate from one’s savings
  • using a more aggressive stock allocation with one’s savings
  • but also relying more on guaranteed income retirement products such as single-premium immediate annuities and variable annuities with guarantee riders
Writing in Harold Evensky and Deena Katz’s Retirement Income Redesigned, Bob Curtis made a convincing case for fixed horizons. He argued that longevity is not a “probability problem” but a “possibility problem,” adding, “What possible sense does it make to tell your client that she can spend more money now because you’re assuming in some of the Monte Carlo iterations that she’ll die early? How does a person die ‘some of the time?’” 

Good question. But at the same time, does it really make sense to lower one’s spending now, because you are specifically planning to spend just as much when you are 105 as when you are 65, despite the less than 1% chance of living to 105? 

Because the risk (and this risk varies from person to person depending on how much value they would get from additional spending) of planning for an overly long retirement is that you cut spending and miss out on enjoying your hard-earned wealth. It is conservative to plan for a longer horizon, because it means you will need to spend less and may end up leaving a larger than planned bequest. This risk is missing from traditional safe withdrawal rate studies which focus only on minimizing failure. One the other hand, the risk with planning for a shorter horizon is that you may overspend and end up outliving your wealth.

Planning with mortality data

The second general approach to dealing with the question of longevity is to incorporate survival probabilities directly into the analysis. Implications of doing this include:

  • a shorter effective retirement duration than the standard 30 years
  • support for higher withdrawal rates
  • greater use of bonds for systematic withdrawals
  • less need to annuitize part of one’s assets

The argument for using survival probabilities is that for a typical person retiring at age 65, conservatively assuming a 30-year remaining lifespan will needlessly cause one to use too low a withdrawal rate. In this view, the probability of running out of wealth should be defined as the probability of running out of financial wealth before death, rather than within an arbitrarily long period of time. With 2007 Social Security Administration Period Life Tables, and when considering a traditional 30-year retirement duration assumption, for 65-year olds the probability of surviving another 30 years to age 95 is 6 percent for males, 12 percent for females, and 18 percent for at least one member of a couple.

Another implication from using mortality data to investigate retirement income strategies is that for the measures I discussed here, such as average lifetime income, spending shortfalls below an income floor, and the value of lifetime spending (utility maximization), optimal behavior will favor strategies that have larger spending earlier on and potentially less spending later on, simply because the probability of surviving to those later ages is less. Optimal behavior means planning to spend less over time for reasons unrelated to the idea that retirees may simply want to spend less over time anyway (this latter point I explored in a recent Advisor Perspectives column). 

This is a case where the rational optimizing behavior from the economic model may not match what people think to do in reality. Leaving aside other issues about how spending may change by age for other reasons (including important potential health and care expenses), people may more naturally think in terms of spending the same at 90, as at 80, as at 70, etc. But at least I do think it makes some sense to accept the idea that if you do end up making it to a really advanced age, you will be willing to live a frugal lifestyle and keep the memories of all the more you enjoyed with the additional spending earlier in retirement. 

What Is This Decision Really About?

I think a good case can be made for considering the outcomes with both approaches. This gives more perspective and balance. It would be nice if both approaches provide consistent results, but I did explain some discrepancies, such as how guaranteed income retirement products will look more attractive as more weight is placed on spending deep into retirement, even though the probability of living to those advanced ages is small. By using both approaches, better decisions can be made by then thinking more deeply about how much weight you want to put on the distant future.

The choice between fixed horizons and mortality is really about determining how averse you are to outliving your wealth, and how much lower you are willing to reduce spending early in retirement in order to protect against adverse outcomes later on. Your appropriate planning age is an extremely personal decision. Since longevity is uncertain though, I think this does suggest making sure you at least have a floor in place of guaranteed income sources to meet your basic living needs for no matter how long you may live.

Related reading: Bob Powell’s MarketWatch column, "Planning for retirement? Plan to live to 100"


  1. This is an excellent discussion of an important issue for retirement planning. I admit that in my research work I have tended to use survival probabilities because it added sophistication. However, I agree with the Curtis point that for deciding on a "safe" withdrawal rate it makes sense to use a conservative fixed horizon. For a question like, what can I expect to leave to the kids, it's probably worth doing the exercise with survival probabilities (or just using the expected lifetime). Also, using survival probabilities can be useful for general research--pointing up issues like how poorly bonds perform as retirement investments when variable mortality is considered.

    Finally, one slightly geeky consideration. How do you figure out how conservative to be in choosing a fixed horizon? If one were indifferent between positive and negative bequests, it would be appropriate to use life expectancy. If negative bequests were 10 times as bad as positive bequests in a utility sense (10:1 loss aversion), then one could roughly balance the outcomes by choosing a planning age with a 1/11 chance of outliving. I'm not sure I'd really get that technical myself, but I offer the thought.

    1. Joe,

      Thanks for sharing. About bequests, I never focused too much on them myself. But now I do need to incorporate them, as I am looking at variable withdrawal strategies which may withdraw different amounts and so comparing with bequests at the same time is vital to help ensure fairness in evaluating among strategies.

      I was going to keep writing that this is why I don't follow what you are saying, but actually now I do see your point better as I'm writing. I was going to say that the focus is on how averse you are to running out of wealth, but that is the same as what you are saying, I see.

      Perhaps you are describing a good way to think of it. How badly you view negative balances to positive balances could help define what time horizon you should plan for. Interesting!

    2. I can tell you how my wife and I handle this issue when planning for our retirement using ESPlanner. For each of us we keep the default maximum lifetime age at 100 in ESPlanner.

      I am eight years older than my wife. When I reach 83 in our plan the household standard of living index is decreased from 100 to 99. We continue to decrease our HH living standard by 1 as each year passes. Once my wife reaches 83 we decrease the living standard by 2 as each year passes. Once I reach my maximum age of 100 we freeze the living standard index at the level.

      These decreases in the living standard index are done primarily because the probability of us both surviving to advanced ages is relatively low, and not because we think we will be spending less if we are both alive at advanced ages. If we get to the point where we are both over 83 and alive and kicking we would freeze the living index at that level and look at ways to get income out of our house.

    3. Thanks for the input. It is useful to hear about someone planning to spend less later on specifically because of the low probability of survival.

  2. "But at least I do think it makes some sense to accept the idea that if you do end up making it to a really advanced age, you will be willing to live a frugal lifestyle and keep the memories of all the more you enjoyed with the additional spending earlier in retirement."

    Wade, it seems to me the biggest variable not mentioned here is unreimbursed health care costs. Even at age 63.5 (with an average life expectancy of 18.3 years, I've just determined), I'm finding my personal costs for deductibles, co-pays, prescriptions, tests, and the like shooting up significantly over the past few years and who knows where or when it'll stop. The 95-year-old may be able to live a more frugal lifestyle otherwise, but what if he/she needs long-term care and doesn't have insurance, or has a disease requiring expensive unreimbursed treatment?

    1. Thanks Larry, and yes, that is a big wild card. I don't know how much extra savings should be planned to cushion for that as health care costs continue to rise faster than inflation. As I haven't looked much into that, I do have a sort of implicit assumption that people have long-term care insurance, but there still may be a variety of growing and uncovered expenses.

      As an aside, living in Japan may be causing me to not have full appreciation about the costs of health care. Though most things are more expensive here, health care is much cheaper. And I mean total costs including what the insurer pays. A short visit to the doctor which might have a total cost of $200 in the US (my last experience) is about $10 here. The consumer pays 30% of that... 210 yen or about $2.50

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