Probability that Living Standard Lies Within Specified Range of Projected Trajectory

I don't understand what this Monte Carlo report is trying to tell me. It has columns that go all the way to 200%. Not sure how there can be a 200% probability of anything.


dan royer's picture

Those reports are not percentile distributions but I believe showing the trajectory range where 100% is the specified mean and 200% is twice that mean and 50% is half of that mean. Then the single or double-digit numbers in those rows represent the percentile. So the numbers across the row should all add up to 100%. So if there's a 1 in the 200% + column that would mean that in that year represented by that row the distribution of 100 cases (or however many are running) just 1 had the trajectory at 200% or higher than the mean. That's the way I understand it anyway, but if you have doubts, I can double check with Kotlikoff.

They add up to 100. In the vast bulk of the years almost all the entries are above the 75% column. As I understand it then there a very high probability the living standard will be 75% or more of the specified mean. Is that correct?

Yes, that is correct. Dan's explanation is right on.


Related question, but what is the 75-100% of mean forecast living standard calculated in reference to? E.g. if the report showed that 100% of Monte Carlo simulations required discretionary expenditures in a certain year to be 75-100% of the specified mean real return, but instead one spent at 125% of the SMRR, what would happen?

dan royer's picture

If I understand your question . . . well, nothing would happen other than you simply spent more than the model anticipated for that year. The MC analysis is just a statistical projection of probabilities given the variance of your asset classes. So in practice we reset the balances every year based on a new projection provided by the fresh model.

Even a small probability doesn't mean it won't happen, and when it does, it doesn't mean the projection was "wrong."

To ask the question in another way-- if the report forecasts a "permissible" or "allowable" band of discretionary spending for a certain year, permissible or allowable in comparison to what metric, and how is that metric calculated? For example, the program could hypothetically calculate permissible in terms that discretionary spending + taxes + housing for a certain year should not exceed income and investment gains for that simulation scenario.

dan royer's picture

OK, it's looking at per-adult living standard (which is equivalent to household discretionary spending assuming two can live as cheaply as 1.6). So it's looking at the deviation from the mean living standard (which is listed there in the same report). But it doesn't refer to "permissible" of course. For one user anything less than 90th percentile is not permissible, for another it could be some other percentage. It also depends on how variant the numbers are. It could be that with a conservative allocation that there is very little difference between the 5th and 95th percentile. For another aggressive allocation the distribution could be extremely wide. It's subjective what permissible would be.

OK, got it. It's just an arithmetical calculation of how much should be left for discretionary spending, vs. the specified mean return, in that year for that return scenario, rather than something more complicated, like a probability of running out of assets before end of plan, etc. I guess I was overthinking it.

dan royer's picture

That's right. The conventional MC looks at running out of money because it does not use the programming to consumption smooth and get you to the end with zero assets left on the very last day of life. It does not adjust spending for you like ESPlanner does. Instead, YOU stipulate spending and it tries to build a model from there and then reports on how successful that model is statistically. ESPlanner is building a successful model based on the inputs but then shows the distribution of upside and downside possibilities in any given year. But yes, you have it right.

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