# Retirement Income - Will It Last a Lifetime?

A person on the threshold of retirement or recently retired is confronted by a new challenge: the challenge to make his or her retirement income last a lifetime. Meeting this challenge requires decisions to be made in the face of uncertainty—uncertainty about longevity, uncertainty about the future investment performance of the retirement portfolio and uncertainty about future infl ation. Making decisions in the face of these uncertainties will require planning in terms of probabilities, and more specifically, planning to maximize the probability that retirement income will last a lifetime.

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This challenge is more significant for the current generation of retirees than for earlier generations because of greater longevity. Greater longevity makes the retiree more vulnerable to two separate effects that can combine, absent appropriate planning, to increase the likelihood of the exhaustion of the portfolio, of “running out of money,” during the retirement years. One effect is inflation—the longer the retiree lives, the more his or her nominal income will have to increase to maintain the same level of consumption. The other effect is the volatility of the securities markets—the longer the retiree lives, the more likely he or she is to incur periods when the securities in the retirement portfolio are declining in value while the portfolio is drawn upon to pay living expenses.

This article will discuss three important concepts for any retiree who is trying to make retirement income last a lifetime:

- Although “life expectancy” is the age a person is “most likely” to reach, there is nonetheless a substantial likelihood of living beyond that age. Running out of money at the end of one’s life expectancy, but before the end of one’s life, is not a pleasant prospect.
- Inflation and the volatility of the securities markets require retirees drawing on their retirement portfolios to think very differently about investments during retirement than they did before retirement.
- A retirement portfolio that includes annuities as well as securities provides a significantly enhanced probability that the inflation-adjusted retirement income, hence its purchasing power, will last a lifetime.

## Increasing Longevity

How much is the current generation’s expectation of longevity, and how has it changed since the previous generation? The conventional way to think about longevity is in terms of “life expectancy”; a better way is to think in terms of the person’s probability of reaching a stated age.

## Single-Life Probabilities

Under the unisex tables currently mandated by the IRS for certain pension purposes, a person who is age 65 has nearly a 30-percent probability of reaching age 90, and a greater than 11-percent probability of reaching age 95. By contrast, under the IRS tables in effect a generation ago, a 65-year-old had less than a 20 percent probability of reaching age 90 and about a seven-percent chance of reaching age 95. Thus, the probabilities of a 65-year-old reaching the ages of 90 and 95 are now about half again as great as they were a generation ago.

## Joint-and-Survivor Probabilities

Another important aspect of increasing longevity is the probability that one or the other or both members of a couple reach the age of 90 or 95. (This can be referred to as “joint-and-survivor” longevity.) Under the current IRS tables, there is about a 50-percent probability that at least one member of a couple who are now both age 65 will reach age 90. And there is a greater than 20- percent probability that at least one member of the couple will reach age 95. A generation ago, the comparable figures were 35 percent and 15 percent. Thus, the joint-and-survivor probabilities have also increased substantially over the last generation, although not as much as the single-life probabilities.

These periods of longevity, for 25 years (from age 65 to 90) and for 30 years (from age 65 to 95), will relate to the economic analyses discussed later in this article, dealing with the sustainability of distributions from retirement portfolios for periods of 25 years and 30 years.

## Whose Retirement Prospects Are Affected by This Increased Longevity?

The retirees most likely to be affected by this increased longevity are those whose primary sources of retirement income are investment portfolios, often held in accounts in defined contribution retirement plans or IRAs. These retirees are faced with the challenge to make the retirement income from these accounts last a lifetime. But which retirees, from among all those whose primary sources of retirement income are investment portfolios, are most likely to be affected by this increased longevity?

Obviously, if the retiree’s annual income from the portfolio is small compared with the value of the portfolio, the risk of portfolio exhaustion during the retiree’s lifetime is minimal, even in the case of increased longevity. On the other hand, if the retiree’s annual income from the portfolio is large compared with the value of the portfolio, the risk of exhaustion of the portfolio during the retiree’s lifetime is quite high, even without increased longevity. Therefore, the question of who is affected by the increased longevity depends upon the meaning of “small” income and “large” income in the context of sustainable distributions from portfolios. Alternatively stated, the retirees most likely to be affected by this increased longevity are those who are drawing from their portfolios at rates near the portfolios’ maximum sustainable distribution rates.

Economists and financial planners have done research to determine the maximum sustainable distribution rates from investment portfolios over specific periods of time. They have analyzed historical data for the entire period following World War II and have also done Monte Carlo simulations to determine probable future results. These are discussed in ”The Economists’ Studies,” below. The important item to note here is their conclusion: the retirees most likely to be affected by the increased longevity are those whose annual incomes from their retirement portfolios are, in the early years of retirement, in the range of four to five percent of their portfolio values, and thereafter are adjusted for inflation. For example, if a retiree begins retirement with a portfolio worth $1 million, and his or her annual retirement income from this portfolio begins in the range of $40,000 to $50,000 (and future income is adjusted for infl ation), he or she is likely to be affected by the increasing longevity. Thus, in this context, “small” means less than four percent and “large” means more than five percent.

## Economic Impacts of Inflation and Volatility—Illustrations

This section provides examples that illustrate why it is important that a retirement income program take into account inflation and the volatility of the retirement portfolio.

## Inflation

Common experience leads most people who have reached retirement age to understand the effects of inflation. Before retirement, their income has generally risen, at least to some extent, to offset the impact of infl ation. In retirement their income must do the same thing.

Even a modest inflation rate of three percent per year will diminish purchasing power by 52 percent over a period of 25 years, and by 60 percent over a period of 30 years. Thus, if inflation remains at the rate of three percent, to maintain the same purchasing power, a $50,000-per-year retirement income received by a retiree at age 65 will have to grow to $104,000 by the time the retiree reaches age 90, and to $121,000 by age 95. A fixed income in retirement, therefore, means a continuing decline in purchasing power. Infl ation is quite insidious over a 25-year period, and even more so over a 30-year period. Planning for retirement cannot be realistic or effective if it does not take infl ation into account.

## Volatility

As noted above, common experience leads most people who have reached retirement age to understand the effects of infl ation. However, people who have not yet spent some time in retirement, experiencing the periods of declining portfolio values coupled with the need for income from the portfolio, may not yet have developed the understanding of the effect of volatility that comes with that experience.

Consider a simple example:

Suppose there are two portfolios, each one starting out with $1 million. Suppose that one portfolio earns five percent per year regularly (i.e., is nonvolatile) and the other one earns an average of five percent per year but is volatile. Thus, in two successive years, the nonvolatile portfolio will go from $1 million up to $1.05 million and then up to $1.1025 million. The volatile portfolio might lose 15 percent in the fi rst year and then gain 29.71 percent in the second year. In that case, it would go from $1 million down to $850,000 and then up to $1.1025 million. For those two years, the volatile portfolio has average earnings of five percent, just like the nonvolatile portfolio. The volatility has no effect.

Now consider these two portfolios each paying out annual retirement income of $50,000 (which is five percent of $1 million) at the end of the year. The nonvolatile portfolio would just pay out its annual earnings and never change its $1 million value. The volatile portfolio would, in the first year lose 15 percent and pay out $50,000. Thus at the end of the first year, its value would be down to $800,000. This amount would then grow at the rate of 29.71 percent in the second year, reaching $1.0377 million. But it then pays out the second year’s retirement benefit of $50,000, leaving it with $987,680. In other words, the volatile portfolio ends up with less money than the nonvolatile portfolio, even though its average earnings rate is the same as the nonvolatile portfolio, and it paid out the same retirement benefit. The volatility caused this loss because a benefi t payment occurred when the portfolio was in a “down” part of its earnings cycle. Over time, such a pattern can lead to portfolio exhaustion.

Why have a volatile portfolio? Because an aggressive portfolio, which is inherently a volatile portfolio, generally has a higher average earnings rate than a nonvolatile portfolio. As will be seen below, despite their volatility, the more aggressive portfolios, with their higher average earnings rates, provide a higher long-term probability that retirement income will last a lifetime.

## The Economists' Studies

An excellent article on retirement income planning, recently published by a group of research economists, examines these issues in great detail.2 The article describes a series of studies that these economists performed, some directly using historical data on securities markets performance and on infl ation, and others using Monte Carlo simulations based on the historical data. The objective of the studies was “to explore the issue of portfolio liquidation using a combination of methods and tools, from simple analysis of past experience to Monte Carlo simulations of many thousands of hypothetical scenarios.” In addition, the authors explored “several possible ways to make the liquidation process more stable and certain—in other words, to increase the likelihood that an initial portfolio liquidation rate can be sustained all the way to the end of a retiree’s life.”

## Historical Scenarios

The historical results for the 30-year periods beginning in the 1960s and ending in the 1990s show that portfolios consisting primarily of stocks but including some bonds had maximum sustainable distribution rates of about five percent. This means that if the retiree had a portfolio worth $1 million at the beginning of his or her 30-year retirement period, the retiree could have taken a distribution of about $50,000 for the first year, adjusted the distribution for inflation every year thereafter, and would have been able to receive the inflation-adjusted distributions for all 30 years. Only then would the portfolio be completely exhausted. On the other hand, if the retiree had drawn more than five percent from the portfolio in the first year, and then adjusted subsequent distributions for inflation, the portfolio would have been completely exhausted before the end of the 30-year period. The historical results for earlier postwar periods showed substantially higher maximum sustainable istribution rates, even as high as 11 percent (for the period with 1949 as its first year and 1979 as its final year). No postwar period has shown results where the maximum sustainable distributions began with a rate below 3.5 percent of the portfolio.

These results are interesting historically, but for at least two reasons are not very useful for planning by people now approaching or beginning retirement. First, they are quite old: any 30-year period for which we have complete data began at least 30 years ago. And second, the historical scenario only constitutes one sequence of investment returns and infl ation behavior out of an infinite number of possible sequences. A better way to consider the future, with its variety of possible outcomes, is to use Monte Carlo simulation based on the historical data.

Monte Carlo SimulationsIn simplest terms, a Monte Carlo simulation works as follows: A computer program randomly selects the values for the uncertain elements of a scenario that can occur, such as the volatility pattern of investment returns and the inflation rate pattern. It then determines the outcome of that scenario, such as: the portfolio runs out of money in the 18th year. The program continues to randomly select scenarios, one after another, and determines the outcome of each one. A typical Monte Carlo simulation runs many thousands of scenarios (technically referred to as “trials”) nd then draws conclusions from the outcomes of these trials. The program is designed so that the probability that any particular value of an element of a scenario will be selected corresponds to the probability of its occurrence in reality, based on historical data. (For example, the probability that a 15-percent infl ation rate will be selected for any year is much lower than the probability that a five-percent infl ation rate will be selected.)

The results of the economists’ studies that are examined here are whether or not the portfolios ran out of money by the end of the chosen time periods. Thus, in a set of 10,000 trials using a particular kind of portfolio, if 700 trials result in portfolio exhaustion before the end of 25 years, then the probability of portfolio exhaustion for that kind of portfolio before the end of 25 years is said to be seven percent.

## The Portfolios

The simulation studies consider four kinds of portfolios, described as follows:

- Conservative—20 percent stocks, 50 percent bonds, 30 percent cash
- Balanced—40 percent stocks, 40 percent bonds, 20 percent cash
- Growth—60 percent stocks, 30 percent bonds, 10 percent cash
- Aggressive—85 percent stocks, 15 percent bonds

The economists then repeated the simulation studies with each portfolio modified to include an additional ingredient, the often-neglected component of retirement planning—the fixed annuity. The portfolios in the simulations with annuities were created by replacing a portion (either 25 percent or 50 percent) of the securities, pro rata, with fixed annuities.

The studies of these portfolios begin with a retirement distribution from the portfolio (as a percentage of the portfolio’s value) for the fi rst year of retirement, and then increase the distribution for infl ation each year thereafter, and test whether these distributions can be sustained by the portfolio for hypothetical lifetimes of the retiree. Ten thousand trials are performed for each of the four portfolios described above, without annuities, with 25 percent annuities and with 50 percent annuities. In each trial, a rate of investment return for the portfolio and an infl ation rate are randomly selected for each year. (As noted above, the probability of selection of any value of these variables corresponds to the probability of its occurrence in reality, based on historical data.)

The first year’s retirement distribution from the portfolio in each trial is 4.5 percent of the value of the portfolio, and for each year thereafter, the distribution is adjusted for inflation. The inflation adjustment is Monte Carlo simulated but is correlated with the securities market performance, which is also Monte Carlo simulated.

The starting figure of 4.5 percent if the portfolio is chosen because this is the largest distribution amount that has any reasonable probability of being sustainable (with inflation adjustments) over time periods of 25 years or more. If the initial year’s retirement distribution is larger than 4.5 percent of the portfolio, the probability of running out of money in fewer than 25 years is quite significant. The results of the study are summarized in the next section and are set out more fully in the economists’ article cited above. We will focus on the results for hypothetical lifetimes in retirement of 20 years, 25 years and 30 years.

## The Results of the Studies

The results are set out in Tables 1, 2 and 3, which give, for each portfolio type, the probability that the portfolio will be exhausted before the end of the specified lifetime in retirement. The operational definition of “portfolio exhaustion,” or “running out of money,” is that the portfolio can no longer pay the full amount of the inflation-adjusted annual distribution. (Thus, if in later years the securities have been consumed and the annuities pay an amount that is less than the full inflation-adjusted annual retirement distribution, the portfolio is said to be exhausted.)

### Table 1: Probabilities of Portfolio Exhaustion, with and Without Annuities in the Portfolio

Lifetime in Retirement: 20 Years

#### With No Annuities

Conservative: 0.9%

Balanced: 0.9%

Growth: 1.2%

Aggressive: 1.7%

#### With 25% Annuities

Conservative: 0.1%

Balanced: 0.1%

Growth: 0.4%

Aggressive: 0.5%

#### With 50% Annuities

Conservative: 0.0%

Balanced: 0.0%

Growth: 0.0%

Aggressive: 0.1%

### Table 2: Probabilities of Portfolio Exhaustion, with and Without Annuities in the portfolio

Lifetime in Retirement: 25 Years

#### With No Annuities

Conservative: 24.8%

Balanced: 8.1%

Growth: 5.8%

Aggressive: 4.8%

#### With 25% Annuities

Conservative: 8.8%

Balanced: 3.4%

Growth: 2.6%

Aggressive: 2.2%

#### With 50% Annuities

Conservative: 1.3%

Balanced: 0.6%

Growth: 0.6%

Aggressive: 0.9%

### Table 3: Probabilities of Portfolio Exhaustion, with and Without Annuities in the portfolio

Lifetime in Retirement: 30 Years

#### With No Annuities

Conservative: 67.4%

Balanced: 23.7%

Growth: 12.6%

Aggressive: 8.4%

#### With 25% Annuities

Conservative: 46.7%

Balanced: 14.9%

Growth: 7.8%

Aggressive: 5.4%

#### With 50% Annuities

Conservative: 18.7%

Balanced: 5.5%

Growth: 3.3%

Aggressive: 2.5%

From Table 1, it is clear that a 20-year time horizon does not give rise to much risk of portfolio exhaustion, no matter which type of portfolio is used, and no matter whether or not annuities are included in the portfolio.

For longer time horizons, the results are dramatically different among the types of portfolios and are dramatically different when annuities are included in the portfolio. And, as noted earlier, the longer time horizons are increasingly important for the current generation of retirees.

From Table 2, it is seen that the conservative portfolio without annuities has nearly a 25-percent probability of portfolio exhaustion before the end of the 25-year retirement period. In other words, in the Monte Carlo simulations, a rather significant percentage of the portfolios that had not run out of money during the fi rst 20 years did so during the subsequent five years. However, the inclusion of annuities in the portfolios substantially reduced the percentage of portfolios that ran out of money during those five years.

Equally noteworthy in Table 2 is the fact that the more aggressive the portfolio, the lower the probability of exhaustion. Thus, the conventional wisdom that a retiree should have a conservative portfolio is contrary to the results of these studies.

The 30-year table (Table 3) shows that the conservative portfolio has a greater than two-thirds probability of exhaustion before the end of the 30-year retirement period. Even when annuities are included in the portfolio, the probability of its exhaustion is nearly 19 percent.

By contrast, the aggressive portfolio, even without any annuities, has less than a 10-percent probability of running out of money during the 30-year retirement period. And with annuities that probability drops down to near five percent or below.

A rather simplistic qualitative explanation of how the annuities help the portfolio avoid exhaustion is the following: Fixed annuities provide a steady flow of cash income to the portfolio4; therefore, to make the annual retirement distributions, the portfolio with annuities needs to sell fewer securities than the portfolio without annuities. Selling fewer securities, particularly when the values of the securities are in a “down” part of their cycle, tends to make the portfolio last longer.

## Conclusions

Because one cannot predict how long he or she will live after retiring, and cannot predict the future performance of the securities markets or the future behavior of infl ation, retirement income planning must take into account the probabilities of various future scenarios. More specifi cally, decisions must seek to minimize (or at least reduce) the probability of portfolio exhaustion during retirement.

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Contrary to the common wisdom, an aggressive portfolio provides a lower probability of becoming exhausted than a conservative portfolio for retirement periods of 25 years or longer.

The substitution of fixed annuities for a portion of the securities in a retirement portfolio significantly diminishes the probability of the portfolio’s becoming exhausted during retirement, for retirement periods of 25 years or longer.

An annuity generally leaves nothing for the retiree’s beneficiaries after the retiree’s death; however, if the portfolio without annuities is exhausted before the retiree’s death, there is nothing left for the benefi ciaries, anyway. Using a portfolio with securities and annuities will not only decrease the probability of the portfolio’s exhaustion, but correspondingly will increase the probability that the securities will remain for the benefi ciaries. The mixed securities and annuities portfolio leaves a substantial part of the portfolio exposed to the securities markets, to take advantage of possible increases in those markets, and also remains as a potential legacy following the death of the retiree.

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