tag:blogger.com,1999:blog-5621914599310831423.post1232588131635641533..comments2019-06-17T06:25:25.680-07:00Comments on The Retirement Café: The “Future” of Retirement PlanningDirk Cottonhttp://www.blogger.com/profile/05616143752082768155noreply@blogger.comBlogger21125tag:blogger.com,1999:blog-5621914599310831423.post-77428140966289879932018-04-15T06:42:43.406-07:002018-04-15T06:42:43.406-07:00Ed, with all due respect, what you suggest is a ne...Ed, with all due respect, what you suggest is a near-perfect explanation of how Monte Carlo simulation <i>doesn’t</i> work.<br /><br />The reason MC, developed for the Manhattan Project, exists is to generate lots of scenarios that are likely and far fewer that are unlikely, usually based on a normal distribution. The extreme scenarios you suggest are incredibly unlikely to show up in a simulation. The probability of a MC model generating the outcome you imagine as common to simulation (30 consecutive years of losses and 30 consecutive years of gains) is infinitesimal.<br /><br />The problem with using actual historical returns is there aren’t enough of them to generate a reasonable confidence interval; otherwise, we would. If they were to be selected randomly, as you suggest, that would remove the momentum you say you want to include. (Autocorrelation can also be simulated.)<br /><br />More importantly, you ignore sequence risk. The ten best and worst scenarios of any simulation are unlikely to have the 10 best and worst market returns. They are more likely to have the 10 best and worst <i>sequences</i> of those returns from among the simulated scenarios.<br /><br />If Monte Carlo simulation is so flawed, as you suggest, why do you think that virtually all academic research on this topic is based on it? And, why would a Nobel laureate in Economics (William Sharpe) develop Monte Carlo retirement simulation software and distribute it freely?<br /><br />Monte Carlo simulation of retirement scenarios is imperfect, as I will describe in my next post, but it is the best alternative available for developing a starting point for a retirement plan.<br /><br />Thanks for sharing your thoughts!Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-80793417156114057972018-04-14T19:21:09.948-07:002018-04-14T19:21:09.948-07:00Hi Dirk,
Intersting research.
In this case, I ag...Hi Dirk,<br /><br />Intersting research.<br /><br />In this case, I agree with Anonymous, however. Monte Carlo simulations are not 10,000 possible outcomes. The bottom and top 5-10% are clearly not possible.<br /><br />For example, the lowest line would be 30 2008s in a row. That is certainly less likely than 30 8% years in a row.<br /><br />The point is that stock market returns are not random - especially at the extremes. Large gains and large losses typically follow each other.<br /><br />For example, 100% of the calandar losses greater than 20% in the S&P500 in the last 150 years were followed by a gain of more than 20% (except for 1929-32).<br /><br />After a major decline, a major recovery almost always happens. Monte Carlo does not describe actual stock markets. It just uses statistics to create thousands of possible and impossible scenarios based on mean and standard deviation.<br /><br />Whenever you use Monte Carlo, I would suggest to ignore the bottom and top 5-10%. They are impossible.<br /><br />Using a random selection of actual stock market histories is far more accurate and informative.<br /><br /><br />EdEd Rempelhttp://www.edrempel.comnoreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-34031065433434734322018-04-09T07:47:00.235-07:002018-04-09T07:47:00.235-07:00Good question.
More scenarios is better but with ...Good question.<br /><br />More scenarios is better but with diminishing returns. In Chapter 4 of William Sharpe’s paper on RISMAT (easy to Google), he provides a statistical argument that 100,000 scenarios will provide a good analysis, so I don’t bother with more.<br /><br />I can run 100,000 scenarios in a few seconds but rarely see a significantly different answer than with 10,000, given all the uncertainty of predicting the future.<br /><br />Is 500 scenarios “enough”? It depends on how you define “enough.” It’s certainly a lot better than the one scenario you get with the spreadsheet approach.<br /><br />10,000 scenarios would provide more information than 500 but will it be different enough to cause you to change strategies? Hard to say.<br /><br />There are many, many free simulators on the web, though, so I’d try to find one that runs more scenarios.<br /><br />Thanks for the question.Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-22195014009638111662018-04-09T06:46:55.615-07:002018-04-09T06:46:55.615-07:00Dirk, you mention running 10,000 scenarios in your...Dirk, you mention running 10,000 scenarios in your simulations. How many runs are required to make a valid conclusion? Some retirement models out there use fewer runs. Would say, 500 runs, be OK?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-77011446091467828332018-04-07T09:56:40.836-07:002018-04-07T09:56:40.836-07:00"if 3.5% was the constant annual return, comp..."<i>if 3.5% was the constant annual return, compounded over time, that led to your 50th percentile result, it sounds to me as though it is indeed the compound annual growth rate (CAGR), aka geometric mean, of that outcome</i>."<br /><br />It is not. It is merely one among countless CGRs that could result in that median terminal portfolio value.<br /><br />Your argument seems to assume that the median terminal portfolio value results from the (singular) median compound growth rate. While that is correct with a simple compounding portfolio and will appear correct from a spreadsheet model that ignores volatility, that relationship does not hold when spending from a volatile portfolio.<br /><br />When spending from a volatile portfolio, the terminal portfolio value is more a function of the sequence of returns than of the returns themselves, so there is no one-to-one relationship between a single CGR and a TPV. There will be countless CGRs that can produce that same TPV, given the right sequence of those returns.<br /><br />This is visualized in the third chart above that shows 15 paths (scenarios) that lead to the median terminal portfolio. In reality, there are countless more paths. Because each scenario consists of randomly-generated returns, the CGRs for each of those paths is different, yet they all end at the median TPV. You cannot work backward from the median terminal portfolio value to determine the median compound growth rate for the simulations, which, as I previously explained, is 5.29%, not 3.25%.<br /><br />Don't let that arithmetic/geometric-mean concern cause you too much pain — it's coincidental in this example and irrelevant.<br /><br />Cheers...<br /><br />Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-42155542271625501412018-04-06T17:55:53.747-07:002018-04-06T17:55:53.747-07:00Dirk –
Thanks for the quick and thoughtful reply....Dirk –<br /><br />Thanks for the quick and thoughtful reply. To follow up just a bit: the 3.5% realized return number I mentioned was my interpretation of your statement that you had to drive the spreadsheet return down to 3.5% to come up with the median simulation result. Perhaps I misunderstood, but if 3.5% was the constant annual return, compounded over time, that led to your 50th percentile result, it sounds to me as though it is indeed the compound annual growth rate (CAGR), aka geometric mean, of that outcome. In other words, 20 years of returns, averaging 5.25% and with a 12% standard deviation, averaged over 10,000 simulations, seem to center on a CAGR of 3.5% -- even as you have confirmed that “the mean annual growth rate” of your scenarios is almost exactly 5.25%. This discrepancy is analogous to the observed return on stocks from 1926 to the present: 7% real CAGR, or geometric average annual return, but 9% real annual return as an arithmetic average. <br /><br />Much as it pains me to say this (since I also think the geometric mean is the superior measure of return!) I submit that the correct value to input as the mean of your Monte Carlo distribution is, in fact, the arithmetic mean of the portfolio return distribution you’re trying to model. Take a look at this 12/27/2017 article by Michael Kitces. (Not sure if the link will translate, but hopefully you can find it by date and author.) <br /><br />Apologies for taking up more space on this rather abstruse point. Keep up the great work!<br />Retired Keithhttps://www.blogger.com/profile/11256195177752216462noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-47941125948994002062018-04-05T14:30:42.934-07:002018-04-05T14:30:42.934-07:00Retired Keith, thanks for the question. The short ...Retired Keith, thanks for the question. The short answer to your long question is yes, the model used the expected return I really intended.<br /><br />I'm not sure how you calculated 3.5%. The model parameter was 5.25% annual compound growth with 12% annual standard deviation. The mean annual growth rate after 10,000 scenarios was 1.05293, or about 5.29%, as expected. If I ran it many times, it would converge to 5.25%.<br /><br />You may be confusing arithmetic and geometric returns of historical returns with <i>expected</i> returns. The Malkiel numbers you quote are inflated; I use real returns and I don't expect future returns to be as high as past.<br /><br />Each scenario (blue line) has its own geometric mean that can't be calculated until <i>after</i> the simulation. Each year's results for each scenario are the product of the previous year's ending portfolio balance (minus annual spending) and a growth rate, not an arithmetic average. I'm not sure it's possible to make the error you suggest.<br /><br />Even had I mistakenly used an arithmetic mean of historical returns instead of a geometric mean as my expected return (I didn't), the same return would have been used and applied as a growth rate in both models and wouldn't explain the difference.<br /><br />The red line won't always have the same relationship to the blue lines that this graph shows, so wondering why it is so much higher in this particular example won't be helpful. It's acceleration will depend on the withdrawal rate assumption. Regardless, it won't be representative, which is the point.<br /><br />The reason the red line is so different is due to — as I might have mentioned in the post, he said with tongue in cheek — longevity risk and sequence of returns risk. When I set the MC model's standard deviation of market returns to 0% and life expectancy to 30 years (as the spreadsheet models assume) all of those blue lines converge into the red one. <br /><br />Long questions are fine, by the way. I often have to figure out what short questions are really about. And keep checking my math. We all make mistakes.<br /><br />Thanks for writing!<br /><br />Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-51131824665273521112018-04-04T19:49:05.811-07:002018-04-04T19:49:05.811-07:00I recently discovered your blog, and am having a g...I recently discovered your blog, and am having a great time working my way through your posts. I particularly like your engaging and enlightening “Unraveling Retirement” posts, which have really helped me clarify my thinking on retirement planning and spending. <br /> <br />I completely agree with this post’s message that it’s vital to take account of uncertainty in retirement planning. Still, I was struck by the fact that the (no-variance) spreadsheet model end result is higher than the great majority of your Monte Carlo results. This seemed (to me, at least) pretty counterintuitive. After pondering it a bit, I believe the explanation lies in the distinction between the geometric and arithmetic means for your assumed rate of return. <br /><br />Let me illustrate. Using an assumed 5% investment return (rounded from 5.25% to simplify the math), two years’ worth of returns using the no-variance spreadsheet would cumulatively result in an increase of just over 10%. That is, $100 on day 1 would become $110 (and change) after two years of returns – in line with what we would expect for 5% return. If, on the other hand, we use returns that are one standard deviation away from the average – the first year up at 117%, the second year down at 93% -- we end up with slightly less than a 9% increase after 2 years, i.e., a little under $109 --close to the no-variance return, but a bit lower. If we look at two years of more extreme returns, this time two standard deviations away from the average (129%, then 81%), we’re quite a bit lower -- $104.50 at the end of two years. In all three cases, the “average” annual return is 5%, but the realized return varies – in the last case, it has dropped to a little over 2%! The results are similar if you carry this comparison out to, say, four years. Interestingly, the order of the returns (high, then low, or the reverse) doesn’t matter. <br /> <br />What this example illustrates is the difference between the arithmetic mean (add up the annual returns and divide by the number of years) and the geometric mean (the constant annual return that would result in the final amount). In your post, the 5.25% spreadsheet return is both the arithmetic and the geometric mean. In your Monte Carlo simulation, on the other hand, I believe the 5.25% is the arithmetic mean around which your scenarios cluster -- which, if I’m reading your results correctly, results in something like a 3.5% realized annual mean return. With a withdrawal rate of 4.5% and a (geometric) return of 3.5%, it’s not surprising that, on average, the portfolio ends up lower than it started!<br /><br />Burton Malkiel (2007), using Ibbotson data, noted something similar: large company stocks returned 10.4% (7.4% real) between 1926 and 2005 when calculated as a geometric mean, but the same return was 12.3% (9.3% real) when calculated as an arithmetic mean. So – is your Monte Carlo simulation model using the mean return you really intend (e.g., 9% arithmetic average return on stocks, if you’re using history as a guide)?<br /> <br />Sorry for the blog-length (book-length?!) comment. Keep up the great work!<br />Retired Keithhttps://www.blogger.com/profile/11256195177752216462noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-58915553421225659062018-04-04T07:32:41.982-07:002018-04-04T07:32:41.982-07:00Jim, the answers to your questions are visualized ...Jim, the answers to your questions are visualized in the second graph of this post. The information that your approach provides is shown by the red line and you can see that the blue lines provide a great deal more information.<br /><br />The shortcoming of your approach is that its (singular) prediction is based on a single factor (expected annual market return), which isn't even the most important consideration. <br /><br />This is somewhat like trying to guess someone's weight given just their height. This strategy is probably better than a poke in the eye but you would make a far better guess if you also knew the subject's age, gender and nationality.<br /><br />A good model will consider several other factors. The most important is length of retirement and the second most important when you plan to spend from a volatile portfolio is market return variance (the sequence of market returns in this case is more important than the returns, themselves). Your model considers neither of these.<br /><br />If you lower your expected return, you bend the red line downward but you still have only one red line that appears to never fail. You still know nothing about the probability of achieving the "red line" outcome or how likely you are to prematurely deplete your portfolio given planned spending. In effect, you are saying that you know your prediction is optimistic so you will lower the return by some guess in hopes of making it less optimistic. You will spend less to be a little safer because you know your model doesn't make good predictions.<br /><br />Since you plan to "adjust the sails" yearly, you have a variable-spending strategy. That's good — it makes it harder to deplete your portfolio than fixed spending would. It doesn't, however, guarantee that the safe amount that you calculate to spend each year will meet your expenses. You probably won't go broke but you may well lose your standard of living to a poor sequence of market returns.<br /><br />But I suspect your real question is "what could go wrong if I use the spreadsheet approach?" There are two big concerns. The first is that your intrinsically optimistic view of the future will repeatedly suggest a higher <i>current</i> spending amount and possibly leave you with less available spending later in retirement.<br /><br />The second concern is that your approach provides no insight to guide planning for bad outcomes. (It never <i>has</i> a bad outcome.)<br /><br />Essentially, the spreadsheet approach ignores the most important risks of retirement.<br /><br />I hope that further explanation helps but let me add that my goal is to inform you, objectively, of the pros and cons of each strategy. Once you understand them, then I firmly believe you should choose the strategy that makes you happy.<br /><br />Thanks for writing!<br /><br /><br /><br /><br />Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-36320993875981221552018-04-03T18:25:59.326-07:002018-04-03T18:25:59.326-07:00I enjoy reading your posts as it is clear you take...I enjoy reading your posts as it is clear you take the time to think things through. Yet here is my question as I am one of those spreadsheet guys. Assuming one starts with a decent sized portfolio, lowers expected returns, and adjusts 'the sails' yearly, what is wrong with using a correctly set up spreadsheet?Jimnoreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-72685177408541120422018-04-03T14:54:19.163-07:002018-04-03T14:54:19.163-07:00Now, THAT is an interesting story. :-)Now, THAT is an interesting story. :-)Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-5849504222490976482018-04-03T11:15:40.992-07:002018-04-03T11:15:40.992-07:00Too complicated for me. can we just KISS?
Heard a ...Too complicated for me. can we just KISS?<br />Heard a former school teacher put all in dividend paying stocks and never sale any of them. it took her over 20 years to cross 1 million mark at age 69. Now she is 97 years old and receiving over $900K income from those stocks every year. with that one would guess the value is over 30 millions.jjhttps://www.blogger.com/profile/14819327603346206049noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-27606878705468745062018-03-31T17:14:41.034-07:002018-03-31T17:14:41.034-07:00Excellent presentation of Monte Carlo and enlighte...Excellent presentation of Monte Carlo and enlightening people to this vs straight line approach. Thanks. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-57889189761204765862018-03-31T12:47:02.079-07:002018-03-31T12:47:02.079-07:00OK! So, there are at least three of us. The simula...OK! So, there are at least three of us. The simulator is a work-in-progress but one day. . .<br /><br />My philosophy is that if retirees understand the benefits and risks of retirement strategies and retirement tools then they should choose the one that makes them happy. That might not be the one that makes <i>me</i> happy, but my situation is probably different than yours and ultimately you're the one who has to live with the decision, not me. None is perfect. And since the outcomes are stochastic, no one can be certain which bet is best. The goal should be to make a <i>good</i> bet.<br /><br />I'll probably misquote Michael Finke here, doing it from memory, but I like what he said and I'll catch the spirit. "<i>It's our job to make retirees happy and sometimes what makes them happy is less risk in their investment portfolio."</i><br /><br />I'll talk about the weaknesses of simulation next time and then move on to how to best use these tools.<br /><br />Thanks for the comment!Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-82199730082411890362018-03-31T11:01:07.961-07:002018-03-31T11:01:07.961-07:00Thanks, Matthew and Dirk, for bringing up and answ...Thanks, Matthew and Dirk, for bringing up and answering the "where's the code?" issue. Dirk, it may be true that few of your readers know about R. For those of us who do, though, it's wonderful to have you doing the coding and us doing the benefiting. I (and at least one other person; Matthew) look forward to your posting that code on Github. <br /><br />And, to reinforce you once again, thanks for this article. You address the strengths and weaknesses of modeling in a fair manner. Presenting both sides of something is uncommon in most recent discourse--on just about any topic. Francis Gilberthttps://www.blogger.com/profile/18147039767761041234noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-68751075036795787972018-03-31T10:11:47.942-07:002018-03-31T10:11:47.942-07:00Thanks, Larry. I agree with your assessment. I thi...Thanks, Larry. I agree with your assessment. I think the issue you raise is making the assumption that one runs this simulation at the beginning of retirement and assumes those probable future states are constant throughout retirement — I don't.<br /><br />I believe they need to be re-run every year with revised facts and assumptions, which would obviously create a new set of likely future scenarios every year. "Possible future states" is a valid interpretation of the data if the underlying assumption is "valid until information changes", which is always mine.<br /><br />I find a sailing trip representative. When you set sail for a destination you have a plan and a heading and an ETA. Whether you're off course by 5 miles or a hundred at the end of each day, you have to create a revised plan based on a new set of likely future outcomes. It would be irrational to use yesterday's heading without replanning.<br /><br />I suppose I could be more explicit and say, "these are likely future scenarios based on what we know and think today but their likelihood will be different once either or both of those things changes significantly."<br /><br />I agree with your last paragraph and, frankly, don't see a rational alternative. I'm not sure why anyone does. I hope my readers understand by now that any retirement planning method (including simulation) needs to be reviewed and possibly revised as new information comes available and as our life expectancy inexorably declines with age.<br /><br />Thanks for joining in!<br /><br />Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-83888016423530444892018-03-31T09:46:44.280-07:002018-03-31T09:46:44.280-07:00A very interesting post Dirk, and thanks for the s...A very interesting post Dirk, and thanks for the shout-out.<br /><br />This is an interpretation of simulation runs over set time periods. The problem with the data generation is that the cash flows are time sensitive based on age. As one gets older, the time frame for the simulation period gets shorter. Shorter time periods generate different cash flow capability (you can spend more with less time remaining oversimplifying the concept). Different cash flows for those shorter periods (older ages) result in different portfolio balances at each and every subsequent age as a result. The graphs would look different for both income and portfolio balances as a result.<br /><br />"Basically the derivation and remainder values of today’s calculations/simulations are interpreted as possible future states. The research on yesterday’s post shows “possible future states” (remainder values) is not a valid interpretation of the data because the subsequent year’s solutions would be different; because the time frame for those solutions are different due to aging and period life table statistics, not fixed as viewed today as a result of calculation methodology." ... quote from my post summarizing research on the rolling calculation solution to this simulations interpretation issue https://blog.betterfinancialeducation.com/sustainable-retirement/part-ii/ <br /><br /><br />Your point about modeling is spot on. They are useful for decision making and planning. My example was hurricane plots that keep changing as time goes on and the possible paths get updated with new data inputs and reviews over time. Thus, interpretation of today's retirement model would also be modified each year the model is rerun with updated age and portfolio characteristic results along with life table adjustments.<br /><br />Retirement planning is not a "one and done" model. It is a "rinse and repeat" model.<br /><br />Great post Dirk!Larry Frankhttps://www.blogger.com/profile/17516328219004197356noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-35766763314481141072018-03-31T08:15:56.279-07:002018-03-31T08:15:56.279-07:00Thanks, Matthew. I use R for just about everything...Thanks, Matthew. I use R for just about everything, nowadays, including those graphs. I have posted some of my Retirement Cafe code at github (under "Dirk Cotton") but I doubt many of my readers have even heard of R so I try to provide spreadsheets, instead, from time to time.<br /><br />The simulation script is large and complex but as soon as I have adequate confidence in it, I will post it at github. I'm currently doing some research with a UNC economics professor and I'll post that R script after the paper is published, as well.<br /><br />Thanks for writing and for your kind words.Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-77277837623846866682018-03-31T08:08:09.632-07:002018-03-31T08:08:09.632-07:00Great questions!
Yes, that's how Monte Carlo ...Great questions!<br /><br />Yes, that's how Monte Carlo simulations work and, yes, this implies the return each year is independent of the prior year <i>but only if</i> you choose not to build autocorrelation into your model. I'm not convinced it's worth the trouble, so I don't bother but that is a subjective choice on my part and not a limitation of Monte Carlo simulation.<br /><br />I guess the more important question is whether you believe you can predict next year's market return from this year's. I don't, so IID seems a reasonable guess.<br /><br />A key point of this post is not that the stock market "works like that" but that the stock market doesn't "work like anything." It's uncertain.<br /><br />The other key point is that when you can't predict how the market will perform, it's helpful to generate a large number of scenarios of how it might perform and make sure your strategy works across most of them.<br /><br />Would it be more meaningful to use rolling histories of actual stock market performance? More meaningful in what way? Would it help you predict your individual retirement outcome? Nothing will — it's uncertain. If you believe that the stock market will perform in the future as it has throughout its limited history, then it would be more meaningful. I'm not very sure of that.<br /><br />Would it generate more potential future outcomes to consider? Clearly not, since we only have 200 years or so of actual market data, or about seven unique 30-year periods to study.<br /><br />Some studies try to get around that sample size limitation by using rolling periods, as you suggest, but there are only about 170 or so of those (better than seven) and rolling periods aren't used evenly. The returns from the earliest and latest years aren't used as often as those in the middle. (Assuming 200 years of returns data, the first and last year's returns would only be used once, for example.)<br /><br />Regardless, if you use the relatively small amount of historical market data available, you end up with a small sample size and a large confidence interval.<br /><br />Would it also be useful to take into account that we are currently at a very, very high valuation level? I would say "prudent" instead of "helpful."<br /><br />Current market valuations are historically high but if most investors agreed that they are unreasonably high, then the market wouldn't still be climbing. (I think they are.) "Very, very high" then becomes your subjective evaluation assuming that future market returns will follow history.<br /><br />When we say "valuations are high", we are typically implying that we believe returns tend to mean-revert, so they are more likely to be lower in the future than in the past. This is also a subjective assessment but I tend to agree. It turns out to be fairly simple to adjust Monte Carlo simulations when you suspect valuations are high and that markets mean-revert — just lower the expected future market returns.<br /><br />When Wade Pfau says that the sustainable withdrawal rate may be closer to 3% than 4% due to historically high market valuations and historically low bond yields, he means that those conditions make it more likely that future market returns will be lower than in the past, assuming mean-reversion, resulting in a lower sustainable withdrawal rate in the future. You test that by simulating lower future market expectations than historical market returns would suggest. If you're using an online simulator you can typically enter your own estimate of future returns. Just lower it.<br /><br />Ultimately, however, market returns are uncertain, so we can't know with any certainty that's how things will play out in our lifetimes. Monte Carlo simulation just provides a much larger set of possible future outcomes to consider and that's its goal — not predicting the future from the past.<br /><br />Thanks for writing.Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-15158940305091537882018-03-31T06:47:21.169-07:002018-03-31T06:47:21.169-07:00Very good article. Did you use R to create the gra...Very good article. Did you use R to create the graphs? Have you ever considered posting the code on GitHub for others to use? (Similar to what Nick does over at www.ofdollarsanddata.com)<br /><br />Thanks!Matthew Bradyhttps://www.blogger.com/profile/12215375986173202718noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-14353366279516068442018-03-30T20:20:23.746-07:002018-03-30T20:20:23.746-07:00if i understand the monte carlo models correctly, ...if i understand the monte carlo models correctly, they randomly select a return for each year out of a distribution of annual returns. this implies the return each year is independent of the prior year. but i don't think the stock market works like that. wouldn't it be more meaningful to use rolling histories of actual stock market performance? and wouldn't it also be useful to take into account that we are currently at a very, very high valuation level?Anonymousnoreply@blogger.com