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"

Choosing a Retirement Income Strategy

This post picks up from a line of thought started in “Variable Withdrawals in Retirement.” I’m going to present a simplified scenario for two different withdrawal rates and explain about some quantitative ways to answer the question: How do you decide which spending path is more desirable?

The classic 4% withdrawal rate rule is about constant inflation-adjusted withdrawal amounts. The benefit of this approach is that it provides a smooth and predictable income stream for as long as wealth remains. But wealth can run out. 

Another rule is to spend a constant percentage of the remaining portfolio each year. This allows for spending to increase when wealth grows. As well, though spending amounts may drop to uncomfortably low levels, this spending rule prevents wealth from ever running out. The main disadvantages of using this rule are that the spending path is unpredictable and spending fluctuates widely over time.

The simplified scenario I will discuss consists of one set of paths for the real income and real remaining wealth provided by these two strategies. This is one simulation out of 10,000 or so that might typically be part of a Monte Carlo simulation study on retirement income. I will consider the case for a 65-year old female. In this simplified case, she can see the evolving path from these two outcomes when she is ready to retire. She wants to know which is better. 

She retires at 65. A market boom in the first year of retirement allows her spending to rise from the initial level of 5. Her wealth grew from a retirement date value of 100 to nearly 140 in the first year. After year 8, her wealth begins to decline. Though the constant inflation-adjusted amount stays the same at 5, the constant percentage spending amount fluctuates quite a bit. In the 34^th year of retirement (her 98^th year), she uses the last of her wealth with the constant amount strategy. Should she make it to 99, nothing is left. With the constant percentage strategy, she still has income through at least 105 (40 years after retiring) that is somewhere around 30% of the initial retirement value of 5. 

The big uncertainty she faces is that she doesn’t know how long she will live. She has to choose her income strategy in advance without knowing this. Also, though the constant inflation-adjusted withdrawals can result in no income at some point in the future, we can suppose that while this is a very undesirable outcome, there is a safety net in place such that she does not necessarily need to absolutely prevent this outcome. How can she decide in a systematic way about which of these strategies to use?

Failure Rates

Traditional safe withdrawal rate studies focus on failure rates, often over a fixed retirement duration. For the constant amount strategy, failure is represented by wealth depletion. In this case, if the retirement duration is 30 years, her failure rate is 0%, but with a 40 year horizon her failure rate is 100%.  Trying to apply this same concept to the constant percentage strategy doesn’t really work though, since the strategy never runs out of wealth. It fails in the sense that spending is below the desired real amount of 5, but it succeeds in the sense that it always provides some spending power and some remaining wealth. Basically, we need to throw the failure rate concept out the window when considering retirement income strategies with variable spending amounts.

Average Lifetime Spending and Average Bequest Value

Retirees may like a strategy that provides the highest average lifetime income and the highest amount of remaining wealth to leave as an inheritance. To calculate these, we need to incorporate mortality data.

Average lifetime income is the average of income in each year of retirement multiplied by the probability of surviving to that age.

Average bequest is the wealth remaining in each year of retirement multiplied by the probability of that being the final year of the 65 year old’s life.

These survival and death age distribution probabilities, derived from the Social Security Administration Periodic Life Table from 2007, are shown in Columns G (survival probabilities) and Column H (death probabilities)  in the spreadsheet at the end of this post.

For the constant amounts strategy, average income is the sum of Column C times Column G, divided by the sum of Column G. It is 4.97. Though wealth runs out in year 34 of retirement, the probability of the 65 year old female surviving to her 99^th birthday is 3.9%. Earlier income receives a greater weight because it has a higher probability of being achieved. Likewise, for the constant percentage strategy, the average lifetime income is 5.23 (sum of Column C times G, divided by sum of Column G). The extra spending early in retirement accounts for a lot.

As for expected bequests, for constant amounts, this is the sum of Column D times H, the wealth remaining in each year times the probability that it ends up being the final bequest (i.e. the probability of death). It is 73.97. As for constant percentages, it is the sum of Column F times H. That is 69.75.

The constant amounts strategy has a slightly lower average income, but a slightly higher bequest.

Spending Shortfall Below a Desired Floor Level

Average bequest may be helpful since it gives some indication about the surplus provided by the strategy, but average lifetime income may not be completely satisfactory.

A risk averse retiree may instead choose to focus on how often and by how much spending power may fall under a minimally acceptable flooring level. This floor may vary from person to person, and it represents the spending level that you really hope to avoid broaching because it may mean a serious reduction in your quality of life, such as a need to move to a cheaper home or give up some important spending.

To demonstrate this, I will use an income floor of 3. It is arbitrary, but our hypothetical retiree really hopes she can avoid experiencing spending shortfalls below the level of 3. Surely, she would like to be able to spend more than 3, and 3 is just her basic level of necessities. With this measure, we focus on downside and forget about the upside. Over the 40 year period, the total amount of spending shortfall below the floor of 3 with constant amounts is -18. There are 6 years with income of 0, which represents a shortfall of 3, and 6 x 3 = 18. The corresponding sum for the constant percentage strategy is -20.83.  If we add up the shortfalls weighted by the probability of surviving to the age of the shortfalls, we get a deviation with constant amounts of -.016, and the deviation for constant percentages is -.1051.  Constant percentages had more shortfalls earlier in retirement (the first shortfall happened in the 24^th year), and there are higher probabilities for experiencing these shortfalls.

While this measure tells us about the downside, and in a sense it provides a modified form of failure rates that can be applied to variable withdrawal strategies, it does ignore any upside potential.

The Value of Spending (a.k.a. utility maximization)

A final measure I will look at provides an attempt to translate spending amounts into something that may more closely represent the value of that spending to the retiree.

A couple of issues will be at work here. First, more spending is better than less, but the additional value provided by more and more spending diminishes as spending increases. The additional value of increasing spending from 1 to 2 is very high, because this is helping you to fulfill same basic needs that vastly improve your quality of life. But the same 1 unit increase in spending from 9 to 10 may not provide much more value. That high spending might mean living in a home with 1800 sq. ft. instead of 1600, or it might mean 50 bottles of champagne per year instead of 30. The additional life-improving value provided by spending will surely be less as spending grows.

Another important aspect is that I will include the floor described in the previous section. Again, I will consider a floor of 3 as a reference point. Spending may fall below 3, but the value plummets for spending below 3. A spending drop from 4 to 3 is not nearly as bad as a drop from 3 to 2.

To discuss the value of spending, I will adopt the same basic function used by Joe Tomlinson in his February 2012 Journal of Financial Planning article, except I will reconfigure it to a new context. He calculated one value based on the lifetime outcome of how much wealth or total shortfall remained at death. I will translate each year of spending into a utility value and then add these up after multiplying them by the probability of surviving to that age.

In other words, this measure is similar to average lifetime spending, except that I don’t use spending from each year directly. Instead, I translate each year’s spending into a corresponding value based on the relationships seen in the following figure for two different loss aversion ratios (which measure the impact of how bad it is to fall under the floor of 3).

A few things to note about this: First, it will be hard to identify the precise shape of the function for real retirees. The shape depends on several parameters including one which explains the steepness of the curve, and also one which defines the appropriate floor level, and the loss aversion ratio that defines how bad it is to fall below the floor. More research is needed on this aspect. But we can still gain some insights by looking at outcomes. Also, note that this is only about spending power, and bequests are not incorporated into the calculations at all. But an important aspect here is that the measure does incorporate both downside risk and upside potential. Unfortunately, there is no connection between the value of spending in successive time periods. Real people may grow accustomized to a particular spending level, so that their frame of reference changes as spending changes. More research can eventually incorporate this aspect, as well as the possibility that the minimum acceptable floor could change over time. Finally, please keep in mind that the numbers defining the utility value are abstract and don’t have any direct meaning. What matters is the relative value of different spending levels, and not their absolute value. We don’t have to worry about utility being negative for levels below the income floor, it’s all relative.

This being said, we can calculate the “expected utility” of each spending path using this function which translates spending into a corresponding value, and then weighs these values by the probability of surviving to that age. With loss aversion of 2:1, the constant amount strategy provides expected lifetime utility of 0.387, while the corresponding value for the constant percentage strategy is 0.361.  Again, these numbers by themselves have no meaning. What matters is that 0.387>0.361 and the constant amount strategy provides higher expected utility in this case. With loss aversion of 10:1, a value function that more strongly punishes spending deviations below 3, the constant amount strategy provides utility of 0.364, which is more than the constant percentage’s strategy of 0.161.

As a final point about utility maximization, Michael Kitces recently wrote:

The reality is that utility functions are not new to the analysis of economic and financial problems, but these research papers are some of the first instances that we have seen in trying to apply utility functions in the context of financial planning, and potentially represent a significant step forward in determining effective solutions for clients. 

Putting it all together

For these two spending paths, we’ve considered 8 ways to quantify which strategy provides a more satisfying outcome. Failure rates were inconclusive, and the constant percentage strategy provided a higher average lifetime income. For the other six measures, the constant amount strategy performed better.

But understand that this is not the whole story. This was only one simulation. It doesn’t provide a final answer. We need to consider the outcomes for many more simulations, such as 10,000. Then we can look at the distributions of these measures and think more systematically about which strategy gives the best chance for the most satisfactory outcomes. 

We can also include more asset allocation and withdrawal rate choices, and more retirement income strategies such as partial annuitization with SPIAs or GLWBs, strategies which use buckets for different time horizons, the impacts of delaying annuitization, the use of bond ladders, the decision about when to begin Social Security, and so on.

Please stay tuned and keep reading, because all of this will be considered here in the coming weeks and months.