### 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?**

David Jacobs says

FYI, Wealthcare/Financeware includes mortality probabilities in their Monte Carlo simulations.

And don’t forget you must pay attention to what failure looks like as well :-).

David

tom brakke says

This is an important question. I’d like to see calculations in combination with analyses that use very conservative return assumptions.

The price of being wrong regarding longevity estimates is very high, so conservatism should be in order.

That’s true in spades for expected returns, but the investment industry persists in using long-run historical returns as the baseline for most analyses.

Instead, there should be a “haircut” applied, before asset allocation models are run or Monte Carlo simulations are done.

For a more detailed look at this (including the fact that the same error occurs at the institutional investor level as for individual investors), here’s a posting about the idea: http://researchpuzzle.com/blog/2012/01/03/the-haircut/

Richard Rosso says

MC is based on assumed distribution curve of random outcomes. Most use Gaussian distribution so the “randomness” generated by most MC models will significantly vary from reality of markets. Most MC planners don’t do a good job with secular market trends. So I don’t believe planners are being overly conservative as long as they build flexibility into the retirement withdrawal plan.

Michael Kitces says

Richard,

Actually, the Gaussian distribution is remarkably accurate when modeling Monte Carlo analysis for financial planning projections with ANNUAL returns. It’s daily volatility that fails the test; but financial plans aren’t projected on the basis of daily volatility.

More information in my prior blog post at: http://www.kitces.com/blog/archives/255-Are-Black-Swans-Just-A-Short-Term-Distraction.html

Respectfully,

– Michael

Tough questions to answer. To me, this depends greatly on the rest of the assumptions used in the model. Per some of the previous MC discussions here, if the planner models conservative return assumptions, conservative spending assumptions (either by over-inflating or ignoring the reality that people spend less as they age), conservative longevity assumptions, and bases their advice on conservative Monte Carlo results (ie. 95% instead of 85%), then yes, I think a planner could do a great disservice to clients.

From a personal standpoint, I think it would be emotionally devastating to work with someone “successfully” through 20 years of retirement, growing their assets and net worth to levels they never imagined, only to have them look across the table and tell me they wish they would have taken that big family trip with all their kids and grandkids while their health was still good enough to do it.

We have a duty to help people manage their resources throughout their lifetimes, but we can’t underestimate the risk and impact of advising them against a life well lived.

I totally hear what you’re saying, Joe. But I think it would be equally devestating – both emotionally and professionally – if that same client wants to know how he/she is going to pay for anything on just Social Security at age 85, since the portfolio ran out of assets.

The idea of planning to well beyond census-level data life expectancy always struck me as being on the right side of Pascal’s Wager.

As an aside, I think the SSA table covers the average population, when in fact most folks who work with financial planners generally skew higher in terms of assets and access to health care, which should prolong life expectancy.

Ben,

It’s worth noting that the mortality curve gets pretty steep in the final years.

Even if the ‘average’ financial planning client is materially healthier due to access to medical care, I’m skeptical if it adds more than a year of life expectancy to someone already in their 80s (which would actually be huge given the rapidly escalating mortality rate in old age). And a 1-year extension will not materially change the plan.

– Michael

Michael,

As with most things, I suppose it all depends on the individual. But I believe I recall some CDC data that said that people who live in a Continuing Care Retirement Community (as a good number of our older clients do) see a 1.5 – 2 year extension of life expectancy.

If I’m running a plan for a 65-year old single non-smoking woman, using the Annuity 2000 Mortality Table in MGPro indicates a life expectancy of 23 years (to age 88). There’s a 40% chance she makes until age 90. But if one of her goals is to move into a CCRC, then wouldn’t it make sense to adjust her life expectancy accordingly?

Ben,

My point is that if you change the projection from “you might live to age 88, plus or minus 10 years” to “you might live to age 90, plus or minus 10 years” or even “you might live to age 91, plus or minus 10 years” – the “plus or minus 10 years part” (the UNCERTAINTY of mortality) still has so much more impact than the target/average age, that I’m skeptical the PLAN will actually be that different.

The difference in safe withdrawal rate between a 23, 25, and 26 year time horizon is minimal.

Sorry for the delayed response, Ben…was traveling the last 24 hours.

You are unquestionably right in your statement about running out of money and I agree with erring on the side of longevity overall.

My point is that there is a much bigger gray area here than people realize, and the advice we give them has a really, really profound impact on the way they live. We can’t take that responsibility even the slightest bit lightly.

I am certain most planners recognize that there is some gray, but given the sensitivity of certain variables and assumptions we are inputting into our modeling programs, we must be far more responsible about it than sticking with the same (inflation / return / standard deviation / longevity / withdrawal rate) assumptions mentality that is so pervasive in our industry.

Every model we create must have its own personality to account for the various ways our clients live their lives. Some people have much lumpier spending patterns. For them, our “plans” must be much more dynamic.

Buffett states often that he would rather be approximately right than precisely wrong. He has applied that mentality to his investment portfolio for a half century with some pretty decent success. Why don’t we consider adopting more of that mentality in our planning?

We all get a bit of a false sense of security from making our projections and models more precise. After all, they are “more thorough” that way, right? 🙂

I am not advocating that we adopt a more cavalier mentality toward this stuff by any means. But I’m not sure we really spend enough time thinking…truly thinking about our clients and how their lives might play out. I also worry that we (intentionally or unintentionally) put too much stock into these projections without recognizing how laughable it is going to look (in either direction) 10, 20 and 30 years down the road.

We don’t have to get it exactly right…but we have to be in the ballpark. As long as we are in the ballpark, we can guide our clients through course corrections along the way. However, when we deviate too far in either direction, disasters happen.

Are Planners being too conservative? Most definitely… The problem is using linear projections of longevity in an exponentially changing world.

As the article referred to below says, for those able to survive 20 years in reasonable health, radical life extension will be possible.

http://goo.gl/x4M0v

Cheers, Michael

It’s dangerous for financial planners to refer simply to population life expectancy (and when was the data you cited collected Michael?) when estimating an appropriate term for retirement adequacy calculations. I am not sure the research has been done yet, but my guess would be that the average financial planning client is likely to live longer than the population average – by dint of being better educated, healthier, and perhaps also genetically predisposed to longevity.

Another problem is that statistics can have little value when applied to specific instances. (Just because there is a 50/50 chance of tossing a head, doesn’t mean that if I’ve just tossed tail my next toss will be head.) Financial planners need to select a projection term for a particular client that reflects their client’s lifestyle, health, medical history and family background (and they need to know about these things). Planners must also be ready to increase that term as appropriate as their clients age, moving into older (and likely longer living) cohorts.

Finally, the problem is asymmetrical. Running out of money 5 years early is likely to have more significant consequences for a client (and potentially for their adviser) than the alternative problem of having 5 years’ cash still in the bank when the need runs out. A bias toward conservatism is entirely appropriate when estimating the appropriate term for retirement adequacy.

Simon,

I don’t disagree with the asymmetrical nature of the consequences of longevity, but bear in mind that there is also an asymmetry to longevity itself. The mortality curve is not symmetrical around life expectancy – it has a HUGE negative skew. There are people who predecease life expectancy by years, decades, or even half a century, but it takes VERY extreme outliers to make it 20 years past life expectancy.

In other words, the older you are, the LESS variability there is in life expectancy. The standard deviation of longevity for those who live beyond life expectancy declines every year.

When you’re young, almost anyone can easily live another 5 years. Once you reach your late 80s or early 90s, more than 50% of people don’t make it another 5 years.

– Michael

Do these MC assumptions include advisory fees or taxes into the model?

Brian,

The illustrations here are simply about the intersection of Monte Carlo probabilities and longevity survival probabilities.

The Monte Carlo probability itself is based on whatever assumptions you used to arrive at that Monte Carlo probability. If your MC probability was 80% included fees and taxes, then it’s 80% included fees and taxes. If it was 80% not including fees and taxes, then it’s 80% not including fees and taxes.

The point here is simply that if it’s 80% in Monte Carlo – with WHATEVER assumptions – and you’re running the projection out to age 100, the 80% is really 99.3% because there’s an extremely high likelihood the client will have passed away before age 100 anyway.

– Michael