It's good stuff but it also got me to thinking. In particular, I got to thinking because in first two or three pages he made the same point four times. For only one occurrence I might have passed by and not noticed. Four times I noticed. Like this:
"A simulation model that does not address these two key factors [random longevity and mean reversion] —and the author is not aware of single model that addresses both factors — ...
All retirement simulations known to the author require the user to specify a fixed number of years in retirement in order for the simulation to run. [emphasis added]
Unlike any other retirement simulation model the author is aware of, RSS treats the number of years in retirement as a random variable and models stock returns as mean reverting.
Surprisingly, although a massive amount of work has been done modeling random stock returns, the author is not aware of a single retirement simulation study where the number of years of retirement is treated as a random factor." [emphasis added]
Here were some thoughts on those for plus some other points after reading:
- Ok, I realize that with three readers I am not very visible or necessarily credible but one of the first things I put into my vanilla simulator was random lifetime. And that was three years ago. It was pretty obvious and pretty simple to do. I'm quite sure it was done before me by other credible analysts.
- And in fact if one happens to review the literature of retirement finance, it is fairly sprinkled with quite a few analyses using random lifetime. Granted, some of the work out there is analytic (via differential equations and such) rather than simulation, or consumption utility rather than fail rates, but all of it usually tends to address the same general topic of which safe withdrawal is one part. Maybe this is apples to oranges, but off the top of my head without looking I can think of these: Yaari as far back as 1965 in a seminal paper; a ton of work by Milevsky and his collaborators; a 2007 paper I just read by Robinson and Tahani; work in Germany by Albrecht and Maurer; references to the topic in lit reviews by Patrick Collins; and not least the (random) lifetime probability calculus of Komogorov which dates to, what, the 1930s? My point is that it is out there, maybe not exactly in mainstream commercial monte carlo simulation but it's all over the place. All you have to do is look.
- While I modeled random draws on lifetime in a bunch of my work in both traditional simulation and more consumption-utility models it also sometimes has drawbacks. First of all it is probably more of a research tool. For retail advisory (or me for myself) the concept of living 10,000 lives each ending randomly might be a concept too far. The intuition for mortals might be a little opaque. Sometimes it really is more useful to pick a fixed horizon as a what-if. The trick there, though, is to make sure you move the horizon out at least once to test a "superannuation what-if." The intuition here for retail consumers is more obvious I think. Second, just in modeling terms, doing a random draw on life duration in the models I have run personally sometimes does not produce stable results without very high numbers of iterations. I had a sim doing an expected value of lifetime consumption utility that did not stabilize below 250,000 iterations when I did it with random draws. I just read a paper where the guy ran 400,000 iterations for, I assume, the same reason. There are ways around this while getting to the same place by using infinite horizons and conditional survival weightings but that's another topic.
- The use of random draws, in order to make any advisory conclusions, still has to pick numbers based on some central tendency of the output. Since longevity distributions are not normally shaped, the conclusions can be a little skewed if care is not taken. In addition, by still "picking numbers" the issue of superannuation is a bit glossed over. Using a random life draw may generate 90% success rates at spend rate x for return y but that is still not a reassuring assessment for the people who will, in fact survive to 100. This is perhaps where moving a fixed horizon dynamically to test that particular risk could provide some better illumination.
- He used the SSA table which is a planning choice. It is not particularly conservative give the generalness of the cohort. For a more conservative approach one might use a different table like the SOA IAM where things like selection bias create a population that lives longer or thinks they will. Alternatively, if we really want to play with random lifetime, we can do it analytically via Gompertz math. This is all over the literature too. Mostly I'm thinking Milevsky but there are plenty of others. With that tool one can either fit a curve to SSA or SOA or any other table (say non-US) or alternatively, when in research mode, shape it to something extreme to test future hypotheticals or some counter-factual worth seeing in action.
- With respect to his use of market history: That's fine. It is common practice and I know why it is done. But I also think it is almost certain that the data-set from the past will only be a subset of the future. This is the purpose of simulation: blow it out a little. The same kind of thing could be said for hewing too closely to the idea of mean-reversion modeling as more "accurate." Perhaps we under-conservatise when we do this because we have only imagined the future by sticking too closely to what we know of the past...including our experience with mean reversion. I realize I'm over-playing this and that the alternative is likely proper and will help me spend more now. This is great but when the money's gone it's gone and a clever modeler won't be there to write me a check when all hell breaks loose later.
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