Visualizing A Missing Piece of Monte Carlo Simulation in 3D

Running out of money at 75 and living to 95 is much more catastrophic than depleting savings at 84 and dying at 85, but both cases are treated the same in determining failure rate. - Joe Tomlinson

One of the many and manifest shortcomings of doing MonteCarlo simulation -- along with: a) the opacity of the meaning of a fail rate, b) the insufficient acknowledgement of likely behavioral changes in the face of an early fail warning, and c) the usual lack of a proper "triangulating context" ... among other things -- is the failure to quantify or visualize the magnitude of the "fail:" what age, how long, how much, etc.  This is often commented upon but I have never seen it visualized.  It may be out there, I just haven't seen it.  So with my new playthings (beginner-level R and scatterplot3D) I thought I'd throw a visualization out there just to see what it looks like.

I ran a generic MC [1] sim to set the stage. The assumptions are below but it is a kind of standard assemblage: $1M endowment, 4% spending, 1%fees, 60/40 allocation, age 60 start, 10000 runs, etc.  The notable odd assumptions might include: longevity is random within a Gompertz distribution, there is a suppression of returns in the first 10 years more or less like we might expect today, and there is an age cap at 105 to reflect the fact that few of us really live to 120...yet.

The result was an approximate 34.6% fail rate (taxes, fees, constant inflation-adjusted spending, and longevity risk will do that to a retiree) or 3,464 of the 10,000 runs ran out of money before the end of life in the model.  That is appalling enough just as it is.  But I suppose there are reasons to be skeptical (see Blanchett on this in a recent WSJ article).  Even if it were to be a 5% rate, though, it would be more or less meaningless in isolation without looking at other context.  But let's ignore all that because my purpose here is not to tease out meaning, isolation or not, it is merely to take this one fake sim at face value and see if we can quantify and/or visualize the magnitude of the fails.  This effort will not necessarily redeem any of the faults of simulating stuff, it just provides another way of thinking about bringing some context to the table.

This is what it might look like:

x = age at shortfall
y = duration of fail after shortfall (death age - fail age)
z = magnitude of fail (absolute value of terminal wealth[2],
      note that all these data points are negative or zero)

Conclusions? I won't throw too many out there because in my opinion the visual is the conclusion (not to mention several really deep flaws[2] in the assumptions). But I will say that while I can probably manage a 34% fail rate estimate with enough advance warning, I sure don't want to (or plan to) end up being the guy in the upper left corner of the cube, analytical flaws or not.

------------------------------------------

[1] Custom simulator I built a couple years ago to factor in some of the things I don't see in the free simulators one can find out there.

[2] There are some serious problems here. By negative terminal wealth I mean that the simulator just keeps running its spending past zero whenever it gets there. It's too dumb to stop and do anything else. It is also too dumb to stop applying returns to negative wealth so the terminal outcomes can get really, really silly, like the -20M above. I might fix that in another version of the simulator though there is no real reason or incentive to do so. For the purposes of visualization, though, the negative values give me something to look at. In any case I have to remind myself that this is all fake and all I'm trying to do is tease out visual ways to address a flaw in MC sims. Most people do not spend themselves into the ground at 70 and then keep spending super-high forever. Usually there is some behavior change before one hits the wall (that's another flaw in MC simulation: most people realize that we do not have 10,000 re-dos in real life, we only have one bite at the apple and most of us don't want to screw it up). Also, we have a safety net in the US so the negative values in the sim are mostly without meaning. For the purposes of this illustration, if you hate the negative wealth thing, maybe focus more on the Y axis (duration of fail) as a main dimension of "magnitude" and then let the z axis represent something else such as: what is going on in the world in terms of things like inflation and market returns. The purpose here was to expose the fact that simulator fail rates can be an empty concept without some sense of "when, how long, and how much" which I think the 3D visualization I'm thinking about here still accomplishes in some small way. If I were to do this again, which I probably won't, perhaps the "magnitude" might be defined as something different like the cumulative value of lifestyle foregone over and above social security (or other baseline income) during the years between a shortfall event and one's eventual demise. That would be pretty hard to measure, though. But if it were measurable, the scatter mass might actually look not too dissimilar to the chart above, but with maybe less of a geometric shape-thing going up the z axis. So for the time being I'll let "negative wealth" stand in (here in this post anyway) as a temporary proxy for magnitude and acknowledge the deep intellectual flaws in doing so. I was just pitching the idea of a visualization so it probably doesn't matter either way.

Terminal values are not time-discounted.

endquote:  

...the reality is that while “failure” from the Monte Carlo perspective means the client ran out of money before the end of the time horizon, in truth most clients will not simply continue to spend on an unsustainable path right to the bitter end. Instead, if the plan is clearly heading for ruin, clients begin to make adjustments. Some failures may be more severe than others, and consequently some plans may require more severe adjustments than others. M. Kitces

Other Reading. This is not comprehensive, just some stuff I've run into over the last x months/years. 

• Is The Retirement Plan With The Lowest "Risk of Failure" Really The Best Choice?(Kitces)
• The Key Problem with Monte Carlo Software - Advisor Perspectives (Tomlinson)
• It’s Time to Retire Ruin (Probabilities). (Milevsky) 
• How to Understand the ‘Probability of Success’ Metric for Retirement (Blanchett)