That's way different from M-C and random sequences. Maybe a financial model could answer questions like - what happens if we have 10 years of high inflation next? But to me, that's way different than saying that running some random sequences give us any indication of how much we might expect the future to be worse than the past.
There's a wide variety of MC models. Some are like Fred123's bootstrap which is essentially just rearranging the existing the data and there are others which have both a deterministic and random component (e.g. some of the models by Pfau).
But here is how I would approach that (and now that I think of it, this is my informal 'fudge factor', now we could apply some math to that to make it seem more 'real'- but in reality, our terms will just be 'fudge-factors' anyhow). So let's take the entire range of results from a historical run, and then pick some StdDev that we like (a fudge-factor), and see how much we might vary from past results. I think that makes more sense than randomizing the data sequences. Thoughts?
From a practical perspective, I think using historical and adding a safety factor is actually a pretty good way to go. It prevents one from being too clever and outsmarting oneself (lots of bright people put too much faith in their models and got burned).
Regarding random sequences, if you are talking about Fred123's specific method (bootstrap), I think there are some good and bad things about it. On the good side:
- bootstrap can yield confidence bounds and give a distribution of results instead of a point estimate as with FIRECALC
- bootstrap avoids the issue of certain years being overweighted (appearing in more runs than others)
- bootstrap avoids the issue of overlapping 30 year periods which introduces statistical dependencies (very bad and hard to deal with)
- if you believe there is no serial correlation then the resampling is more or less fine
On the bad side
- bootstrap resamples the existing data, so there's no chance of any single year being worse than history. Obviously there is some (hopefully small) chance that we could have a worse year than in the past.
- because bootstrap is not based on a model, we can't run what if scenarios or tailor the analysis to account for things like high valuations
- if you believe there is serial correlation or reversion to the mean, the bootstrap assumption is not very appealing as it is WRONG
For this last point, even if you believe the assumption (no serial correlation) is wrong, I think you can still get useful information out of it. As the bootstrap assumes no reversion to the mean, we know that drawdowns are likely going to be longer and deeper than FIRECALC. So this gives us a pessimistic estimate which is also helpful in planning.
The more complex MC models, such as those used by Pfau are nice in that they allow what if scenarios but I'm somewhat skeptical of the work. From the papers I've seen, they use quite a few equations/parameters and don't detail how they are computed or spend any time in the paper validating them. Also, given how few people work in this area, probably nobody has replicated their simulation. It would be very easy for them to have bugs or other errors.
I guess my philosophy is to start with the historical record (ala FIRECALC) and then use the MC simulations to get an idea of how FIRECALC might be biased (what direction and by how much -- this can also feed into how you determine the safety factor). MC methods are also helpful to understand the behavior of various drawdown algorithms (e.g. Kitces/Pfau tested their rising glidepath method with MC and it would have been very difficult for them to draw any conclusions from just Firecalc) and in this case, model imperfections are not as problematic due to the paired comparison.