There has been much hype about Monte Carlo software and how it can help clients plan for retirement. But some of that enthusiasm has been tempered by frustration over the correct way to use the software. Moreover, there are limitations to the existing Monte Carlo methodologies and uncertainty among many advisors over how to interpret Monte Carlo findings. For instance, consider the following proposition:

Q. Monte Carlo results show that one of your client’s assets have a 50% probability of lasting for 25 years, and that another’s assets have a 65% probability of lasting for the same period. Which client is better positioned to fund his retirement?

A. Without considering the clients’ respective ages, you can’t assess their relative chances of success. In this particular case, if the first client is a 72-year-old widower and the second is a husband aged 55 and a wife aged 51, then the former has a much better retirement prognosis than the latter.

Client age and life expectancy have always been key elements in the structuring of an effective retirement plan. However, few Monte Carlo methodologies available today do an adequate job of integrating client life expectancies into their analyses.

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We will demonstrate how the next generation of Monte Carlo methodologies can quantify the role of client life expectancy in evaluating analysis results. This is accomplished through use of a success coefficient that defines the probability that the client will live out his projected post-retirement lifespan without depleting his assets. This coefficient characterizes in one parameter the results of a sophisticated Monte Carlo analysis that spans and addresses every year in the retirement scenario. This parameter answers the question that every client ultimately asks: “How likely am I to live my life without running out of money?”

The greater the retiree’s remaining life expectancy, the longer the retirement assets must support her. Thus, the asset lifetime for a young retiree must be longer than that for an older counterpart.

In a Monte Carlo context, however, asset lifetime isn’t a single-point value. Rather, a Monte Carlo analysis models fluctuations in return (and, in some cases, inflation) to calculate a range of asset lifetimes. These results can generate a success probability curve showing the probability that assets will last to any specified point during retirement.

Similarly, while a retiree does have a definite expected remaining lifetime, there is a range of probabilities that she will die before or after that specific date. Actuarial data can be used to develop a life expectancy curve which is analogous to the success probability curve in that it shows the probability that a retiree will live to any specified point during her retirement. For a couple, the same approach can be used to develop a joint life expectancy curve that shows the probability that at least one member of that couple will be alive at any point during retirement. This latter consideration is important, since these joint life expectancies are higher, often significantly so, than individual life expectancies for either member of the couple.

The probability distributions defined by the asset success probability and client life expectancy curves can be analyzed to calculate the joint impact of both curves upon overall retirement prospects. That impact can then be integrated over the life of the retirement to derive the overall probability that the retirees will not outlive their assets. This probability is defined as the success coefficient. Success coefficients can then be used to directly compare and rank, on an apples-to-apples basis, the overall effectiveness of different sets of assumptions and alternate retirement scenarios.

**A Case Study**

A short case study involving the two clients addressed in the opening question will be used to illustrate this approach. Client 1 (see below) is a 72-year-old widower. Client 2 is a couple consisting of a 55-year-old husband and a 51-year-old wife. Pertinent parameters for these two analyses are as follows:

Client 1 Client 2

Initial Asset Package Value$1,000,000$1,650,000

First Year’s Withdrawal$60,000$95,000

Annualized Return7.5%9.0%

Standard Deviation for Return0.0950.165

Annualized Inflation4.0%4.0%

Standard Deviation for Inflation0.032 0.032