## Executive Summary

Monte Carlo analysis has become a fairly widespread tool for financial planners to use to understand the implications of market volatility and return uncertainty on the ability of clients to achieve their goals.

Yet the uncertainty in retirement isn’t just about the returns that will be earned on investments that are necessary to support spending, but also how long that spending must last. Notwithstanding the uncertainty of mortality, though, most financial planners select a fixed – albeit conservative – time horizon for the portfolio, such as 30 years for a 65-year-old couple. But can this strategy make the plan too conservative? After all, a 90% probability of success – which corresponds to a 10% chance of failure – is actually only a 1.8% probability of failure when it assumes the couple will live until age 95 (given the low likelihood of a client actually surviving that long), and in turn means the client may be saving more, spending less, or retiring later than is really necessary!

Which raises the question – are we being too conservative with our mortality/longevity assumptions?

The inspiration for today’s blog post is the recent article “Spending Flexibility and Safe Withdrawal Rates” by Michael Finke, Wade Pfau, and Duncan Williams in the latest issue of the Journal of Financial Planning. The focus of the article was about how optimal safe withdrawal rate decisions might shift once accounting for risk tolerance, but along the way, they made an interesting point about the intersection of our longevity assumptions, and Monte Carlo probabilities of success.

For instance, the article points out that planners are often conservative in their desire for a portfolio to last a long time, such as a 90% probability of success for a 30-year retirement for a 65-year-old couple (planning for longevity until age 95). Yet according to the mortality tables, there is only an 18% probability of one member of a 65-year-old couple still being alive in 30 years. Which means in reality, a 90% probability of the portfolio lasting for 30 years – which in turn means only a 10% chance of failure – is itself only relevant 18% of the time. And a 10% chance of failure in a scenario that only occurs 18% of the time means the couple actually has only a miniscule 1.8% probability of experiencing both adverse results simultaneously (poor returns and extended longevity)! The 90% probability of success is actually a 98.2% probability of success.

Which means the probabilities of success – or alternatively, the risks of failure – are actually much more conservative than our typical projections imply, because we may not only be looking at a conservative probability of success in the first place, but *also *a conservative mortality assumption as well.

The chart below, from the Journal article, shows the survival probabilities for a male, female, or joint survivorship (the second to die) at age 65, based on the Social Security Administration period life table for 2007.

As the chart reveals, even joint survival rates decline precipitously for clients from their mid 80s to their mid 90s. What is a roughly 70% probability of at least one survivor at age 85 is less than a 20% probability of any survivors by age 95. Which means that adding a few more years onto a projection can quickly turn it from aggressive to conservative.

Accordingly, the table below shows the “true” combined probability of success for a time horizon of either 20, 25, 30, or 35 years for a 65-year old couple (to ages 85/90/95/100, respectively), assuming either an 80%, 90%, 95%, or 98% probability of success in Monte Carlo (MC).

85 (20 yrs) | 90 (25 yrs) | 95 (30 yrs) | 100 (35 yrs) | |

80% in MC | 85.7% | 91.0% | 96.5% | 99.3% |

90% in MC | 92.8% | 95.5% | 98.2% | 99.6% |

95% in MC | 96.4% | 97.8% | 99.1% | 99.8% |

98% in MC | 98.6% | 99.1% | 99.6% | 99.9% |

The results are quite striking. For instance, they reveal that if the planner assumes a 30-year time horizon for a 65-year-old couple (to age 95), even “just” an 80% probability of success in a Monte Carlo projection actually translates to a more-than-96% overall probability of success, as it is the combination of “only” a 20% chance of failure for a longevity that itself “only” occurs 18% of the time. It also highlights that with a 30 year time horizon, there’s remarkably little difference overall between an 80% probability of success and a 95% probability of success… because the difference between a 20% chance of failure and a 5% chance is failure isn’t very high when it’s built on what is only an 18% survival assumption in the first place.

Alternatively, the chart highlights that if a 35-year time horizon is selected, there’s virtually no difference between an 80% or 95% probability of success, as *all *the scenarios are incredibly remote given the “extreme” longevity assumption that has only a 3.7% chance of occurring in the first place. And in the other direction, even using “just” a 25-year time horizon (to age 90) with an 80% probability of success is actually a combined 91% probability of success.

Overall, what this suggests is that because planners have a tendency to select an arbitrarily long and conservative longevity assumption – such as 30 years for a 65-year-old couple, or “until age 90/92/95” from any particular retirement age – our true probabilities of success are much higher than is initially implied from the Monte Carlo projection alone. In fact, if the longevity consumption is conservative enough, even a relatively “aggressive” probability of success in Monte Carlo is still incredibly conservative plan overall.

On the other hand, this also reveals that to get a clear retirement picture, it’s more important than even to know not just the probability that the plan lasts to a certain extended mortality age, but also how quickly it can fail in an adverse scenario, as discussed previously on this blog. For instance, a plan that has a 90% probability of lasting for 30 years but a 2% chance of failing in 20 years is *far *riskier than a plan that has an 85% probability of success for 30 years if its 2% failure rate still lasts 27 years. Because the reality is that living 30 years (or even 27 years) is itself a relatively low probability event, while living 20 years is actually quite likely. Accordingly, a plan that has *any *risk of failure in the first 20 years is *far *more risky than a plan that only fails in 27-30 years, *even if* it’s slightly more likely to fail in 27-30 years*; *while the latter might have a 5% higher failure rate overall, its worst case scenario is a whopping 50% less likely to be an issue in the first place because of mortality!

**So what do you think? Are planners being unreasonably conservative in their longevity/mortality assumptions? Should we choose much lower Monte Carlo probabilities of success if the plan is otherwise viable under extended longevity assumptions? Is the better alternative to also randomly model mortality in Monte Carlo, in addition to returns, as the Journal article did for their analysis? Would you change your assumptions about what constitutes success and failure, or what is a conservative or aggressive plan, in light of the results of combining return and mortality assumptions?**

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