### Executive Summary

Over the past decade, Monte Carlo analysis has been slowly replacing its retirement planning predecessor - the straight-line projection - which was overly reliant on a single distant outcome, with no acknowledgement of the potential impact of volatility on the final results and the success of the plan. By contrast, the virtue of Monte Carlo analysis is that it shows a range of possible outcomes, and quantifies results not with a single and inevitably inaccurate estimate of final wealth decades from now, but instead a probability of success/failure that captures how many of a wide range of outcomes are projected to be successful or not.

However, as Monte Carlo analysis has become increasingly popular, the focus has unfortunately shifted once again towards a single projected outcome - the probability of success/failure - without fully acknowledging the range of outcomes and their nuances, such as the fact that a plan with a higher probability of failure may actually be the more appealing option if it's accompanied by a less severe magnitude of failure. Perhaps most significant, though, is simply that the labels "success" and "failure" do little to connote the true reality - that "success" actually means an excess left over, and that failure merely means that some kind of mid-course adjustment may need to occur.

Yet the reality is that while these differences are arguably mere semantics and nuance, how results are framed matters, and can significant impact real world client behaviors, given the difficulty our brains have in trying to interpret Monte Carlo's probabilistic results. Which means if the truth is that "failures" merely require mid-course adjustments and that "successes" actually leave over excesses, perhaps it's time to relabel Monte Carlo results accordingly as "probability of adjustment" and "probability of excess" to ensure clients are making the proper decisions!

## Probability Of Failure... Or Adjustment?

When crafting a retirement plan using Monte Carlo analysis, the general goal is typically to craft a plan with a probability of success that's comfortably high and a corresponding probability of failure that is "acceptably" low. After all, failure means running out of money, which is a pretty horrific outcome for most retirees; with perhaps visions of living under a bridge or eating pet food to survive, a recent survey from Allianz found that fear of running out of money ranked even higher than fear of death (61% versus 39%, respectively)!

Yet the reality is that for most retirees, spending doesn't simply continue unabated until one day, the retiree wakes up to find that the investment accounts bare and the checks are bouncing. Instead, at some point as wealth is depleting, it becomes clear that the path is unsustainable, and that some adjustments need to be made. Of course, the later the intervention, the more severe the adjustments may have to be.

Nonetheless, the point remains that since most people don't fail their retirements in the manner that a Monte Carlo "probability of failure" suggests, where everything continues as normal right up until the day it can't. Instead, most people can indulge in some flexibility and make adjustments by choice before a total catastrophe occurs, which actually goes a long way to stave off the potential of a more severe "involuntary" adjustment in the future.

For instance, traditional safe withdrawal rate research finds that a 5% withdrawal rate equates to a roughly 10% probability of "failure" that the retiree will run out of money before the end of the time horizon. However, research by Guyton in 2006 found that if the retiree is able to reduce withdrawals in the short term, and make it up later, that a 5.2% withdrawal rate is sustainable. In other words, as long as the client has some adjustment decision rules to navigate with along the way, a 10% probability of failure is actually just a 10% probability of making mid-course *adjustments *and a near-0% probability of total failure; furthermore, Guyton actually found that if the client is flexible enough to make those adjustments in difficult times and recover them later, total lifetime spending remains almost exactly the same, without any material failure risk, despite the higher starting point!

Which means perhaps it's time to call a probability of failure what it really is: a probability of (mid-course) adjustment, which is actually far less frightening... and also easier to manage!

## Probability Of Success... Or Excess?

Not only does a probability of failure really just represent a probability of mid-course adjustments, but in a similar manner the probability of success is also arguably mislabeled... a more apt description might be the probability of excess, instead. (Hat tip to David Loeper of WealthCare, who was the first I heard to coin this term.)

After all, as I've written in the past, while a 4% safe withdrawal rate is designed to ensure "success" - defined as not running out of money even in the worst market scenario in US history - the reality is that the 4% rule also leaves a 96% probability of leaving over 100% of starting principal, and a 50% probability of more than *quadrupling *the client's wealth by the end of retirement! In other words, while we might focus on getting that probability of success up to 100% (or as close as possible), doing so also dramatically increases the probability of *excess* and the potential that a very significant amount of unused money is left over!

Viewed another way, this means that having a high probability of success also means having a high probability of extra money to hedge unexpected longevity, and/or a high probability of leaving a legacy. And due to compounding, the higher the probability of having an excess, the more sizable the excess is likely to be! While this may be desirable for some clients who do in fact have legacy goals or longevity concerns, for others having a high probability of such outcomes with huge amounts of money left over is actually *not *a desirable outcome, as they'd rather spend the money along the way instead!

## Framing Matters

So what's the point of all of this? The reality is that how retirement risks, opportunities, and trade-offs are framed to clients impacts the decisions that are ultimately made. If a client is considering a 5% withdrawal rate that has "only" a 90% probability of success and a whopping 10% risk of failure, it sounds scary; by contrast, framing it as a 10% risk of making modest mid-course adjustments and a 90% chance of leaving a potentially significant legacy sounds far different. Especially given that behavioral research suggests that our brains don't even know how to really evaluate things like a 10% "probability of failure" in the first place - instead, we tend to envision the severity of the risky outcome, and then react accordingly. Which means framing adverse outcomes as a probability of "failure" that makes it seem more severe than what it usually really is - a probability of mid-course "adjustment" - can actually stoke client fears and make them act in a more extreme manner than is necessary!

Notably, this doesn't mean we should get rid of Monte Carlo analysis altogether. It's certainly still *far *better than the straight-line projection alternatives, which do even less to take account of risk, uncertainty, and planning nuances. Nor does this mean we shouldn't continue to work on ways to evolve a more sophisticated "next generation" Monte Carlo analysis tool that does a better job showing not just the outcomes of the analysis, but also the sensitivity to the inputs so clients really understand the potential impact of working longer or retiring early, changing their spending, or being impacted by unexpected market or inflation risk.

In addition, the reality is that we could do far better expressing not just the probabilities of retirement planning successes and failures, but also their magnitudes; after all, the reality is that the plan with the lowest probability of failure still might not be the most desirable approach if it results in failures that really are far more severe (or alternatively, that would require more extreme mid-course adjustments to get back on track). On the other hand, if that were framed in terms of a probability (and magnitude) of adjustment, the decision might be even clearer - would you prefer a plan with a 10% probability of needing 5% adjustments, or a 5% probability of needing 20% adjustments? When put in the context of adjustments, rather than striking fears of abject failure, the decision-making process can actually become clearer, and most people might happily pick the plan with the higher probability of adjustment if the adjustments are likely to be more modest.

Which, ultimately, is the point - good framing can help facilitate good decisions. So the next time you're discussing the results of a retirement projection with your clients, trying explaining it as the probability of mid-course adjustment (not failure) and the probability of excess (not success), and see if/whether/how you and your clients view the results a little bit differently!

Steve Smith says

Beautiful. And of course the initial plan should have already reviewed what some of those mid-course corrections might entail.

Russ Thornton says

Thanks for the Wealthcare mention! Your topic is perfect timing, we’re releasing a new whitepaper tomorrow on safe withdrawal rates and why presenting MCS results in terms of “success” or “failure” is misleading. Check it out…

http://www.wealthcarecapital.com/ruminations/WP_SafeWithdrawalRates.pdf

John Nowak says

Great post, best I’ve seen on framing results for a client. Anyone know of best practices on Monte Carlo assumptions for correlations, standard deviation, etc? Seems most use long term metrics. This makes sense for 30 year retirement, but the first 5-10 are most important for retiree and can differ from long term.

Tim says

Bravo! As one who has migrated to Monte Carlo analyses (and obsessively tried every one I can find on line), I appreciate this clear-headed framing. I run the Monte Carlo several times with variable inputs to test the sensitivity you mention. My plan is to re-run the analyses periodically during retirement, to alert for the opportunity of a course correction as early as possible. Maybe the periodic analyses will tell me I can comfortable increase my spending – or at least increase my buffer account against a 2008 – 2011 scenario. I would caution my fellow amateurs to look closely and test underlying assumptions in the on line calculators. Only by reviewing projections carefully and testing them against common sense have I found those assumptions are sometimes too optimistic, sometimes too pessimistic. Special care is needed in accounting for the typical, gradual reduction in spending experienced by many retirees. Thanks for the great insights.

tim says

Monte carlo has other flaws as well. For example, What if in scenario 1 shows a client with 90% success rate. 5 years later, the client sticks to the plan perfectly but the market had a 40% decline. Now the monte carlo shows a 60% chance of success. Which scenario is correct? Both scenarios are supposed to take into account market fluctuation so why wouldn’t scenario 2 also reflect a 90% success rate. unfortunately, the market doesn’t take into account market valuations or any fundamental factor. if it did, the likelihood of success wouldn’t change. Thoughts Michael?

Michael Kitces says

Tim,

That’s not a flaw of Monte Carlo. That’s exactly how it’s SUPPOSED to work. The client who had a 90% success rate and a 10% failure rate is now progressing down the potential-failure path, which makes the odds of failure higher.

Think of it this way. What are the odds I flip a coin twice and have it come up heads twice in a row? It’s 25%.

Now I flip the coin once. It comes up heads. From THAT moment forward, what are the odds I get two coin flips in a row that are heads? NOW the odds are 50/50, because I already got the first heads, and I only have one (50/50) coin flip left.

The fact that AFTER getting the first heads the odds of having heads twice rises from 25% to 50% doesn’t mean the probabilities were wrong the first time. It’s simply a reflection of how the probabilities shift after you go down that path.

So just as the odds of two-heads rises from 25% to 50% after you flip heads the first time, in your example the probability of failure rises from 10% to 40% after you get a market decline and the probabilities update accordingly based on what already happened…

– Michael