tag:blogger.com,1999:blog-6167053228142922997.post5940749532760879082..comments2023-10-30T11:57:40.433-04:00Comments on Wade Pfau's Retirement Researcher Blog: Monte Carlo Simulations vs. Historical SimulationsAnonymoushttp://www.blogger.com/profile/04168922717655562721noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-6167053228142922997.post-33834610595962354182014-08-29T07:50:13.805-04:002014-08-29T07:50:13.805-04:00Sorry, but block bootstrapping is perfectly legit ...Sorry, but block bootstrapping is perfectly legit statistics. Who doesn't like central periods to be overrepresented can just use circular block bootstrapping instead, or correct the weightings. <br />What is not statistics are "outliers", you can't pick only the data that looks nicer and pretend that to be representative. There are no outliers, only bad models; fit a t distribution and so called "outliers" (for a gaussian) will be taken care of nicely.<br />Last but not least, historical simulation is just Monte Carlo on the empirical distribution, it's a false dicotomy. You can have all sorts of "hybrids" inbetween by using semiparametric models. Is there a LOT of data? Then go HS. Too little data? Sure, HS is bad, but so is MC too: fitting a normal/whatever not only imposes a false model, but has large estimation error anyway and gives a false sense of security and good coverage.Quartznoreply@blogger.comtag:blogger.com,1999:blog-6167053228142922997.post-18961761773673141372012-05-10T15:08:39.065-04:002012-05-10T15:08:39.065-04:00It depends on how you implement it and what you co...It depends on how you implement it and what you compare it against. On the margins, monthly draws with replacement from a fatter tailed historical distribution will typically yield more extreme outcomes compared to monthly draws from the normal. As the sampled period size increases you can hit a cross over point, but if you sample with replacement you typically produce results that are at least as extreme... assuming parameterization based on the same historical distribution you are sampling from. <br /> <br />Extreme outcomes are a double edged sword. For every double-great-depression generated there is an uber-bull market on the other side of the . <br />distribution... and there are some deep rooted philosophical problems arising from the frequency approach to probability implicit in the simulationRobert Klosanoreply@blogger.comtag:blogger.com,1999:blog-6167053228142922997.post-41223623366915073302012-05-08T08:58:05.270-04:002012-05-08T08:58:05.270-04:00Dick,
Let me just answer for myself. In the conte...Dick,<br /><br />Let me just answer for myself. In the context of my safe savings rates article, I would say that the answer is yes. Historically, pre-retirement bear markets are followed by post-retirement bull markets and vice versa. Low sustainable withdrawal rates usually follow prolonged bull markets (so you have more wealth at retirement anyway).<br /><br />But with the i.i.d. assumptions of Monte Carlo, you can't rely on this. No matter how bad things were pre-retirement, you would still be left using the safe withdrawal rate since the post-retirement period is independent. This means getting very low income.Anonymoushttps://www.blogger.com/profile/04168922717655562721noreply@blogger.comtag:blogger.com,1999:blog-6167053228142922997.post-46383383387762297032012-05-08T08:31:27.674-04:002012-05-08T08:31:27.674-04:00Wade --
1. I agree: I also prefer Monte for asses...Wade --<br /><br />1. I agree: I also prefer Monte for assessing future probabilities, but we can learn from historical-sequence simulations too. EG, seeing mean reversion in history.<br /><br />2. Question: Are the benefits from PE-based strategies that you and Michael Kitces have reported entirely dependent on mean reversion?<br /><br />Dick PurcellDick Purcellhttp://www.dickpurcell.comnoreply@blogger.comtag:blogger.com,1999:blog-6167053228142922997.post-87799164361515797682012-05-08T02:53:19.553-04:002012-05-08T02:53:19.553-04:00Thanks Fred. I see you vote for Monte Carlo.
At t...Thanks Fred. I see you vote for Monte Carlo.<br /><br />At the same time, some people swear by historical simulations. I am still shamed to have not read Jim Otar's books yet, but I looked at them enough to know that he hates Monte Carlo and thinks that historical simulations are better. However, I thought the reason he gave didn't make sense. He said to picture gazelles wandering around randomnly on the savannah until a lion shows up and then everyone runs off in the same direction... Monte Carlo misses that. But I disagree. Well, while Monte Carlo doesn't specifically model the appearance of the lion, some of the simulation outcomes will naturally look just the same as if that lion had appeared.<br /><br />Getting back on the subject, I think I do tend now to preferring Monte Carlo. But I can understand why some people like historical simulations better. It is nice to compare the results from each.Anonymoushttps://www.blogger.com/profile/04168922717655562721noreply@blogger.comtag:blogger.com,1999:blog-6167053228142922997.post-58197166222044542582012-05-08T02:47:10.667-04:002012-05-08T02:47:10.667-04:00Robert,
Thanks for the input. And thanks for men...Robert,<br /><br />Thanks for the input. And thanks for mentioning about bootstrapping by putting together strings of sequences (such as 3 or 5 periods or more) instead of one at a time. I have played around with that too and I was thinking to mention it, but figured it was esoteric enough to leave out. Did you find that this lessened some of the more extreme outcomes?Anonymoushttps://www.blogger.com/profile/04168922717655562721noreply@blogger.comtag:blogger.com,1999:blog-6167053228142922997.post-20307881953922731722012-05-07T12:56:22.447-04:002012-05-07T12:56:22.447-04:00Why is anyone utilizing historical simulations??? ...Why is anyone utilizing historical simulations??? "Rolling periods" analysis is not statistics no matter how often Jack Bogle or the professors at Trinity do it. Your mildly stated reservations are too mild Wade. If I recall correctly the DJIA was up about 53% in 1954, how many times is that outlier of a year for stocks being counted? "Overlapping moving averages are not each independent data points or degrees of freedom." Paul Samuelson, Journal of Portfolio Management, Fall 1994. <br />I think you are being soft on these folks.Frednoreply@blogger.comtag:blogger.com,1999:blog-6167053228142922997.post-23326915545545334882012-05-07T09:41:31.659-04:002012-05-07T09:41:31.659-04:00Wade,
OSFI (Canada's financial services regu...Wade, <br /><br />OSFI (Canada's financial services regulator) has published their view on the use of mean reversion by insurers in capital models. They conclude that their use is not warranted. I think this generally supports Dick'<br />s point. It is worth a read.<br /><br />I have been using a hybrid approach for retirement income planning . Instead of drawing from the historical distrubution 1 period at a time (which destroys structure) or using rolling periods (with all the issues you cite and then some), we select a starting point at random from the historical time series and then pull a block of returns of random length (say 1 to n years of monthly returns as an example) and build up the time series through repeated iteration. The blocks could also be defined explicitly and the recombined. It preserves fat tails, some of the correlation structure and (at least partial) market cycles while allowing the generation of multiple different scenarios. It also avoids many of the issues associated with paramater estimation. But in the end there is no escape from model risk.Robert Klosanoreply@blogger.comtag:blogger.com,1999:blog-6167053228142922997.post-10444047439539722112012-05-07T00:42:49.831-04:002012-05-07T00:42:49.831-04:00Thanks Dick, this is a good point. Monte Carlo wo...Thanks Dick, this is a good point. Monte Carlo would provide more conservative results by not relying on mean reversion after big downturns. It would also provide more overall optimistic results on the upside as well, but we should be focusing more efforts on the downside anyway.Anonymoushttps://www.blogger.com/profile/04168922717655562721noreply@blogger.comtag:blogger.com,1999:blog-6167053228142922997.post-24130466415190618902012-05-06T20:33:26.268-04:002012-05-06T20:33:26.268-04:00Wade –
That point you make about Monte Carlo anal...Wade –<br /><br />That point you make about Monte Carlo analyses standardly excluding mean reversion is commonly viewed as a weakness. But it may – just may –make Monte Carlo better (or “less worse”) in our attempts to assess probabilities for longer-term stock market investments.<br /><br />Back on April 13 you posted about potential of lower future return rates. (http://bit.ly/JI9zYy)<br /><br />There and elsewhere, you’ve pointed out enough about our future-assumption uncertainties to wobble our confidence in all this future-probabilities stuff. But if in the stock market as a whole, reversion will continue in the future nearly the same as it has in the past, Monte Carlo’s not including it is a pretty good “uncertainty cushion.”<br /><br />In Bogleheads months ago, I think it was Verde who reported that historically, reversion has been strong enough that for 30-year periods, the dispersion of results has been only about half what Monte would show using single-year SD and random walk. Turn that around, that means that for a 30-year investment result, Monte Carlo’s exclusion of reversion doubles the uncertainty spread of the distribution.<br /><br />For the 30-year retirement plans you assess, the cushion is not that cushy because some of the money (hopefully not all of it) is taken out before 30 years. Still, it’s cushy . . .<br /><br />Dick PurcellDick Purcellhttp://www.dickpurcell.comnoreply@blogger.com