Using Stochastic Modeling to Analyze Retiree Income Strategies

Using Stochastic Modeling to Analyze Retiree Income Strategies

By Mark Shemtob

In an effort to enhance their income in retirement, retirees are required to make some important decisions when creating their personal financial plans. In formulating their plans, some retirees may have many decisions, yet others just a few. Here are some examples of decisions that retirees may need to consider:

  1. When should I start collecting Social Security?
  2. Should I purchase an insured lifetime income product; if so, which type(s) and with how much of my retirement savings?
  3. If I am entitled to an employer pension should I elect an annuity payment (and if so, in what form), or should I select the lump sum option if permitted?
  4. If I have retirement funds in different sources (pretax, Roth, and after-tax), in what order should I withdraw them to minimize taxes?
  5. How should I invest my retirement savings among different investment classes such as stocks and bonds?
  6. If I have home equity value, should I use it to create income through a reverse mortgage?
  7. If I have debt, should I pay it off with some savings?
  8. Should I purchase long-term care insurance or plan to finance from retirement savings, should the need arise?
  9. Should I relocate to another state for tax purposes?
  10. Should I maintain or buy life insurance for estate tax or legacy goals?

The list above is not exhaustive. Many individuals will not have as many decisions to consider. Nevertheless, regardless of the number of decisions, appreciating the interdependencies of each decision is critical. For example, if one chooses to purchase a fixed-income insured life annuity, does that impact the decision about investment allocation? As a retiree faces more decisions, it follows that more potential strategies will be available. Even a few decisions can lead to thousands of unique strategies.

An Illustrative Example

Let us look at a simple example to get a better understanding of how stochastic modeling can be used to help a retiree decide on a strategy. A hypothetical 62-year-old would-be retiree wishes to consider the following three decisions in developing a retirement income strategy:

  • When to start collecting Social Security (ages 62 to 70);
  • Whether to purchase a fixed-income life annuity with a portion of her retirement funds; she will consider only four potential levels (0%, 25%, 50%, 75%); and
  • The investment allocation to be used with the remaining retirement savings modeling a passive equity fund and a passive fixed-income fund with 11 potential allocations (0% to 100% of each investment class in 10% intervals) Even this basic example has 396 alternative strategies (9 × 4 × 11).

Our hypothetical retiree’s primary goal is to secure an inflation-adjusted pretax income starting at $X per month that will last her lifetime. The income will be generated from Social Security, a fixed-income life annuity, and an investment portfolio with periodic withdrawals. Stochastic modeling can provide an analytical approach by comparing alternative strategies using economic and longevity assumptions. Using stochastic modeling, the 396 alternative strategies can be tested to determine which strategy provides the greatest probability of success in securing the desired income—success being defined as having sufficient income to last an uncertain lifetime. The success probabilities are determined based on generating thousands of scenarios for each strategy using Monte Carlo simulations. Each scenario will be based on alternative rates of return (based on mean and variance for each investment class), inflation expectations, as well as life expectancies (based on a life expectancy table considering current age, gender, health, and income level). Once the strategy is determined, she could consider the following, if not satisfied with the strategy produced:

  • Test for a different income level, especially if the success probability is very high or very low;
  • Test the impact on the success probability if one or more of the optimum strategy components are modified; and
  • Once an income amount and strategy are finalized, she can investigate the amounts that would likely be available as liquid investments or an inheritance each year in the future.

Alternatively, our retiree might wish to have modeling performed based on a success percentage (e.g., 90%) as opposed to a monthly income. The result of this modeling approach would be to determine the maximum inflation-adjusted income that can be generated with the desired success level. The details of this strategy would also be illustrated. Once the optimum strategy is determined, she could consider the following if not satisfied with the strategy produced:

  • Test for a different success percentage, especially if the income level is very high or low;
  • Test the impact on the monthly income if one or more of the optimum strategy components are modified; and
  • Once an income amount and strategy are finalized, she can investigate the amounts that would likely be available as liquid investment or an inheritance each year in the future.

One might think that our hypothetical retiree would need to provide an overwhelming amount of information for this analysis. This is not the case. All she would need to supply is the following, in addition to either a monthly income or success percentage:

  • Date of birth;
  • Gender;
  • Smoking history and general health information;
  • Social Security information; and
  • Retirement savings.

However, in the case of more complicated applications where more decisions need to be considered, more input information will be required.

Technical Considerations

Modeling will be dependent on a variety of parameters built into the program that will require periodic updating. Stochastic methods provide modeling under a range of assumptions using Monte Carlo simulations. Some of the parameters to be incorporated include:

  • Standard mortality tables by gender;
  • Mortality table adjustments to account for personal health and income levels;
  • Capital market expectations for expected returns and variances of alternative investment classes;
  • Expected inflation rates; and
  • Others, depending on complications of the model (annuity purchase rates, tax rates, LTC premium rates, etc.).

The use of unreasonable rates of returns for investment classes would have the impact of favoring certain strategies over others. For example, it would cause the value of delaying Social Security to be understated if unreasonably high rates of return are assumed. Higher-than-reasonable rates of return would also have the impact of discouraging consideration of insured lifetime income product purchases. The opposite results would occur if unreasonably low rates of returns were assumed. Another important assumption is the rate of future inflation. This directly impacts the benefits that can be paid from Social Security and will have indirect effects on other decisions.

The use of unrealistic mortality assumptions would also affect the appropriateness of the results that are generated. Longer-than-reasonable expected lifetimes would tend to emphasize the value of insured annuity products and delaying Social Security. Shorter-than-reasonable expected lifetimes would have the opposite impact. Of course, longevity is impossible to predict, but information regarding gender, smoking habits, general health, and income level would help to make the decision-making process more appropriate. Information provided by the retiree would be used to modify the standard mortality table to better reflect the expected mortality of the retiree.

Impact of the overall household income should be considered, including that of a spouse or partner. Modeling on the basis of a single individual when there are shared resources and expenses may not be the most efficient approach.

Current Market Offerings

Stochastic modeling has been used for over a decade in the modeling of retirement financing scenarios. Many of these tools are proprietary and available for use by advisers when recommending the products or investments offered by the various financial institutions. These can be biased and may not consider strategy components that the financial institution would not offer or benefit from.

Other modeling tools have been created for independent financial advisers and generally provide for more flexibility in strategy options. However, biases of the adviser may impact the strategies tested. For example, some fee-based advisers may not consider the use of fixed-income annuity or deferred-income fixed annuity products for their clients.

Some financial organizations that offer investments directly to retirees may offer modeling tools. Historically, they have been more focused on the retirement accumulation period as opposed to the more complex decumulation stage.

Retiree Behavior

What is unclear is how retirees will use the power of these tools effectively. For example, how will a retiree be able to appreciate the value of a 90% probability of success as opposed to a 70% level? What level of additional retiree income warrants what percentage drop in success level? In addition, the lifetime income level determination may not be the sole consideration for some retirees. It may be very important to also quantify the legacy implication of different strategies—leaving a sizable inheritance may be a high priority for some retirees, for example. Balancing these two interests could be an issue.

Some individuals will be capable of using the information made available by these new applications to make well-informed decisions to initiate strategies without the assistance of an adviser. Others may not be positioned to do so. Much will depend on the sophistication of the retirement plan specifics and the individual’s understanding of retiree financial risks. Regardless of whether an individual works with or without an adviser, it is critical that the retiree has an understating of the key retiree financial risks, which include:

  • Longevity risk;
  • Investment risk;
  • Inflation risk; and
  • Uninsured medical and long-term care cost risk.


Interactive tools that use complex, sophisticated statistical applications such as stochastic modeling hold great promise. Consumer-created web applications may be especially valuable for individuals with modest retirement account balances who cannot attract the expertise of an unbiased adviser with retirement planning decumulation expertise. However, as an individual’s personal situation becomes more complex, requiring many different decisions, the potential application value may be compromised unless a qualified adviser is retained.

This article is solely the opinion of its author. It does not express the official policy.

MARK SHEMTOB, MAAA, FSA, is a member of the American Academy of Actuaries, a fellow of the Society of Actuaries, a member of the American Society of Pension Professionals and Actuaries, and an Enrolled Actuary under ERISA. He is an active member of the Academy, serving on the Social Security Committee, the Lifetime Income Task Force, the Pension Committee, and the Pension Forward Thinking Task Force. Shemtob has taught as an adjunct professor at Rutgers University in the finance department on financial retirement issues. He is the owner of Abar Retirement Plan Services LLC.

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