When you look at Dory36's outputs, you see that there are very few independent answers. If every start year were independent (as intercst was trying to claim), then the failures (which are displayed in red) would have been distributed randomly. They are not. They are clustered together.
That is the context. Estimating the safety of different withdrawal percentages is a different issue.
Thanks for the clarification, John. I knew I was missing something. Now that I understand the context, it seems to me that this paucity of independent data is a serious problem that will beset if not ruin any approach to analyzing safe withdrawal rates. Even waiting two hundred years to develop a few more independent data points would not help because the economy will change so much in that period. As it is, I'm uncomfortable making plans for the next thirty years based in part on what happened in the rather different US economy of 1871. I'll be happy to be shown some other result.
Don't I recall someone's Monte Carlo approach to address this problem of too few independent sequences by taking a series of thirty random annual returns from the data, and iterating to estimate SWR for a thirty year plan? If I remember correctly, that led to rather low estimates of SWR. That approach, randomizing the order of observed annual returns, would seem to have the handicap that it ignores serial correlation in the original historical data. A possible remedy would be to impose the historically observed amount of serial correlation during each iteration by modifying the randomly selected annual return by some increase or decrease. Is that a legitimate approach?
An aside on my experiment at Dory's site mentioned in my last post, using nominal numbers like a million dollar stash and a thirty year planning horizon: (I think I used 4% inflation too, but I'm not sure.) With the nominal 4% withdrawal rate, Captain Bill said that the median or average final stash in that plan was worth $4,274,913. Correcting that for 4% inflation produces a purchasing power at the end of the plan of $1,256,216. So then, according to this data and my understanding of it, most of the thirty year plans would achieve my goal of not eroding the purchasing power of the initial retirement stash. I would have liked to see Dory's report make explicit that the final four million dollar figure had not already been corrected for inflation, as well as a count of the number of sequences in which purchasing power of the final stash was less than the original amount, or maybe a histogram of what those final values of purchasing power were.
Thanks for your patience. I seem to lose the thread of the conversation sometimes.