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.

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

In Figures 1 and 2 (following page), the vertical axis represents probabilities and the horizontal axis represents years since start of retirement. The blue curves are the success probability curves defined earlier, and show the probabilities that assets will last for any specified duration based on the input parameters listed above. Both analyses inflate withdrawals after the first year in accordance with the specified annualized inflation rates. The analyses vary inflation as well as return to yield populations for these parameters whose annualized values and standard deviations are as specified above.

The shaded yellow area in each figure represents the retiree's life expectancy curve based on gender and age at start of retirement. These show the probabilities that the client(s) will live to any specified point in the retirement. Since Client 2 includes both a husband and a wife, the shaded yellow portion of Figure 2 represents the joint life expectancy of the couple. Their individual life expectancies are displayed as the red curves, with the top curve representing the wife and the bottom curve representing the husband.

The success probability and life expectancy curves allow you to compare the relative probabilities that the client's assets will last as long as, or longer than, the client's life for any point in retirement.

We utilized the Decipher software package to develop the results presented here. This software, developed by Financial Numerics, automates the evaluations required to implement this approach, and was selected because it is the only methodology we found that adequately integrates client life expectancy into Monte Carlo analysis.

Think of the life expectancy curve as representing the normal life expectancy of the retirement, assuming that adequate funds are always available to support the retiree. At the point at which the success probability curve begins to dip below 100%, the probabilities of "unsuccessful" outcomes begin to interact with the normal retirement life expectancy probabilities. These interactions can be evaluated to yield an "impacted" life expectancy curve, which shows the reduced retirement life expectancies resulting from the prematurely shortened retirement cycles growing out of the Monte Carlo analysis. This curve is shown as the green curve in each figure.

The difference between the normal and impacted life expectancy curves visually represents the impact that the Monte Carlo results have on the normal course of the retirement. Visual impressions, however, are hard to compare--the difference must be quantified to allow objective comparisons between different cases. Decipher uses the probability data from both curves to perform a normalized integration of the impact across the 50-year span of the analysis. This result is used to calculate the success coefficient defined earlier. That coefficient, shown in the upper right corner of each figure, gives the probability that the client(s) will not outlive their assets.

In looking at the two figures, it is apparent that both the success probability and the life expectancy curves drop off much more rapidly in Figure 1 than in Figure 2. In terms of the prospects for the client not outliving his assets, however, the difference between these two curves is much more important than the absolute value of either.

The success probability curve for Figure 1 falls off rapidly after about the 15-year point in the retirement, and shows only a 20% probability that assets will last beyond about 35 years. However, the retiree's life expectancy falls off even more rapidly, and shows essentially no probability that the retiree will live beyond 35 years.

There is a substantial margin between these two curves except for the region beyond about the 25-year point. However, there is only a 25% probability that the retiree will live to that point in retirement, so that the weighted contribution to the overall success coefficient by that region is relatively small. In the regions of the curves where the retiree has a high probability of surviving, higher weightings coupled with greater margins between the two curves lead to a healthy overall success coefficient of 94.4%.

Figure 2 shows higher asset success probabilities than Figure 1, especially during the latter stages of the retirement. This is due primarily to its higher returns and lower withdrawal rate relative to the initial asset package value. However, the longer life expectancies represented in Figure 2 more than consume the advantage represented by those higher success probabilities.

The joint life expectancy curve in Figure 2 is substantially greater than the individual life expectancy curve for either the husband or wife alone. This increased joint life expectancy depletes much of the margin between the success probability and individual life expectancy curves. In addition, the greatest margins occur during the lower-weighted latter years of the retirement. This contrasts with Figure 1, where the greatest margins occur during the higher-weighted years near the beginning of the retirement. These factors all contribute to a substantially reduced success coefficient of 81.5 % for Figure 2, translating into an 18.5% probability that at least one of the retirees will outlive the retirement assets.

Interpreting the above Monte Carlo results based on asset lifetime probabilities alone would lead to the conclusion that the higher asset success probabilities in Figure 2 represent a superior retirement prognosis relative to Figure 1. Injecting the age and life expectancy elements into the evaluation leads to a more pertinent and quite different interpretation. In fact, Figure 2 has nearly 3.5 times the probability of Figure 1 that the retiree(s) will outlive their assets over the normal course of their retirement.

Adding the success coefficient element quantifies this interpretation and allows the advisor to objectively compare cases. This becomes more important when comparing different scenarios for the same client, since differences in the relationships between the success probability and life expectancy curves are likely to be more subtle.

Clients expect the advisor to squeeze every possible advantage out of each retirement scenario. However, the more optimistic the outcome, the closer the advisor moves toward a liability in the event that retirement assets do not last as long as the client expects. The added analytical dimension provided by Monte Carlo techniques helps the advisor resolve these conflicting objectives by demonstrating that a retirement cannot be characterized by a single specific outcome. Rather, every retirement has a range of possible outcomes, largely influenced by the client's own decisions.

Quantifying the probabilities for these outcomes broadens the common ground for discussing and evaluating these results with the client. However, as is the case with non-Monte-Carlo approaches, age must be retained as a key planning parameter. The analyses presented here demonstrate how performing Monte Carlo analyses in the absence of age and life expectancy considerations can often lead to conclusions that are inaccurate and, in many cases, misleading.

This approach impresses on the client (and documents, via the success probability curve) the fact that small yet definite probabilities do exist that assets can be depleted early in retirement. In addition, the success coefficient forces the client to recognize that, except for extremely conservative scenarios, there will always be some probability that retirement will be impacted by a shortage of assets. This case-by-case quantification of results makes it practical for the client to take a strong hand in defining the timing and magnitude of these probabilities. The client does this by balancing concerns over unfavorable probabilities against lifestyle decisions regarding retirement timing, assumed levels of risk and return, withdrawal rates, and other parameters.

The precision with which we perform these calculations far exceeds the accuracy of such long-range projections. That precision does have a value, however, in that it allows quantifiable differentiation between scenarios. This allows--and forces--the client to recognize, through parameters such as the success coefficient described above, the direction and magnitude of the effects of the choices they make as part of their input to the planning process.

This approach provides clear documentation of the planning process and results in a manner easily understood by the client. This allows informed client participation, and assures that the clients understand the implications and results of their decisions. This is also the key to an equitable sharing of liability between client and advisor.