tag:blogger.com,1999:blog-5621914599310831423.post2526630197940337911..comments2020-02-19T05:59:48.291-08:00Comments on The Retirement Café: Death and RuinDirk Cottonhttp://www.blogger.com/profile/05616143752082768155noreply@blogger.comBlogger15125tag:blogger.com,1999:blog-5621914599310831423.post-27247372211080548012016-01-31T10:21:00.280-08:002016-01-31T10:21:00.280-08:00I don't believe it is important to know the pr...I <i>don't</i> believe it is important to know the probability of ruin at a given age for an individual retiree. I do believe it is important to know how that probability changes with age.<br /><br />You're still focused on predicting results for an individual retiree, and that isn't the point of the research. (And it isn't achievable.)<br /><br />Thanks for writing.Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-72175187719479599022016-01-31T10:15:59.821-08:002016-01-31T10:15:59.821-08:00You certainly may. I always try to do that, but I ...You certainly may. I always try to do that, but I don't always remember. Sometimes, as in my upcoming post, I write a summary of key points of the past few posts.<br /><br />I'll try to be more vigilant.<br /><br />Thanks for the suggestion!Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-16353058067271139842016-01-31T10:11:27.508-08:002016-01-31T10:11:27.508-08:00Love your blog. Might I suggest a summary paragrap...Love your blog. Might I suggest a summary paragraph at the end of each blog where you summarize the key take-aways. It would help me and I'd bet others. Thanks.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-36782239574093411602016-01-30T06:44:44.991-08:002016-01-30T06:44:44.991-08:00This could be useful for pricing longevity insuran...This could be useful for pricing longevity insurance.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-47648142102831617732016-01-27T16:05:08.122-08:002016-01-27T16:05:08.122-08:00Interesting discussion.
The calculation I'm p...Interesting discussion.<br /><br />The calculation I'm proposing (and actually do, in my own calculator) is similar to what you suggest, as I mentioned in my first post. Randomly sample m sequences of returns from a portfolio distribution for N years (say 50), so there will be m experiments of length N years. For each experiment, determine if the portfolio is exhausted at t < N. If it isn't exhausted, then assign 0 to the result. If it is exhausted, then assign 1*p(S(t)) where p(S(t)) is the probability of living to age t given an initial starting age. Sum up all of the results and divide my m and that gives you the probabiliy that the retiree will be ruined before dying.<br /><br />Why is it important to know the probability of ruin at a given age? It's pretty obvious that someone who lives to be 115 has a much higher chance of running out of money than someone who lives to be 70, but why would knowing that probability be helpful? I suppose you could argue that it would not be good if the chance of failing at a relatively young age is high for given withdrawal rate and a retiree faces the prospect of living solely on SS; on the other hand, that same information is reflected in a higher failure rate in the age independent calculation. And, finally, what about error bars? They are going to be pretty big for later ages and that might limit how much you can actually say about survival probability at, say, 90. So, ultimately, I don't think this type of analysis is particularly helpful.<br />Fred Rogershttps://www.blogger.com/profile/04072447059614160606noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-19487842123274360352016-01-27T10:42:42.578-08:002016-01-27T10:42:42.578-08:00The probability that a retiree is still alive at a...The probability that a retiree is still alive at a given age <i>and</i> has exhausted her savings is simply the product of the probability that she is still alive at that age and the cumulative probability of portfolio failure to that age. The shortcoming of that "absolute probability" calculation, which isn't the calculation you are suggesting, is that it doesn't show the timing of ruin. An 82-year old woman with a depleted portfolio might have depleted it anytime between the ages of 65 and 82. K-M graphs show that timing and enable us to say, "If you live to age X, your probability of failure will increase this much."<br /><br />Absolute probabilities have other uses, as I will show in a future post about competing risks analysis.<br /><br />My bigger concern is your statement that "Graphs of portfolio failure rates vs age are only useful if you are fortunate (or perhaps unfortunate!) enough to know how long you are going to live."<br /><br />The usefulness of a K-M analysis is the understanding it provides of how the risk of ruin changes with age and spending rates. This type of research will never be useful to predict the future of a single retiree. Model's explain the underlying financial processes. They're not very good at predicting the future. (Nothing is.)Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-30967154099671836872016-01-26T17:16:53.672-08:002016-01-26T17:16:53.672-08:00No, I'm calculating the probability that the r...No, I'm calculating the probability that the retiree is alive and that she has exhausted her savings. Perhaps it's a different question than the one you are attempting to answer with the KM estimator, but isn't it really what a retiree wants to know? Graphs of portfolio failure rates vs age are only useful if you are fortunate (or perhaps unfortunate!) enough to know how long you are going to live. <br />Fred Rogershttps://www.blogger.com/profile/04072447059614160606noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-39115642980407557682016-01-26T10:12:42.158-08:002016-01-26T10:12:42.158-08:00Fred, I'm really not sure what the probability...Fred, I'm really not sure what the probability you suggest calculating would actually mean. Part of what you are suggesting (weighting) calculates the probability that a retiree would be both alive AND have savings remaining. KM calculates the <i>cumulative</i> probability of portfolio survival <i>conditional upon reaching a specific age.</i> <br /><br />Conjunction is the probability that both A and B will occur. Conditional probability is the probability that A will occur <i>given the assumption that B has already occurred.</i><br /><br /><a href="https://en.wikipedia.org/wiki/Conditional_probability" rel="nofollow">Conditional probability</a> and <a href="https://en.wikipedia.org/wiki/Logical_conjunction" rel="nofollow">conjunction</a> are two very different measures. I'm not sure what your proposed statistic would measure, but KM tells us the percent of portfolios that will be expected to have survived when a retiree reaches each age throughout retirement, in other words, the cumulative probability of portfolio survival given that the retiree has survived to age X.<br /><br />Lastly, and importantly, KM removes portfolios from the probability's denominator when they are no longer at risk of outliving their savings and the calculation you suggest does not.<br /><br />If you're still curious, I suggest walking through the steps to calculate KM probabilities <a href="http://vassarstats.net/survival.html" rel="nofollow">here.</a><br /><br /><br />Thanks for the question!Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-324982596720429522016-01-25T16:36:26.907-08:002016-01-25T16:36:26.907-08:00Interesting post, but I'm curious: what's ...Interesting post, but I'm curious: what's the advantage of using KM vs just weighting the simulation results by the probability of surviving to the age at which the portfolio is exhausted (calculated from the actuarial tables you are using)? For instance, say the first simulation result sampled from your log-normal distribution fails after 20 years, and the probability of surviving to 85 is 0.5. The second simulated result fails after 5 years, and the probability of surviving to 70 years is 0.8. Then the calculated probability of exhausting the portfolio before dying after two simulations would be (0.5+0.8)/2. Fred Rogershttps://www.blogger.com/profile/04072447059614160606noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-3988275718888869132016-01-23T11:41:44.809-08:002016-01-23T11:41:44.809-08:00That's the key, Brad – you may have a lifetime...That's the key, Brad – you may have a lifetime probability of ruin of 5% but early in retirement it's 0%. It changes over time.<br /><br />My other son tells me that Cary has a "scary brain", but let it be known that I out-shoot him more often than not. Well, for now, anyway.<br /><br />Cheers!Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-76005394325655541092016-01-23T11:34:40.542-08:002016-01-23T11:34:40.542-08:00Actually, I did mention "simulated" in t...Actually, I did mention "simulated" in the post.<br /><br />We didn't use a portfolio allocation directly. We simulated a log-normal distribution with a real mean return of 5% annually and a standard deviation of 11%, which roughly equates to a 50% equity portfolio since 1928, assuming 3% inflation. What it might be going forward is speculation.<br /><br />The purpose was to model the risk. Changing these parameters wouldn't have a large impact on those findings. You should observe the general characteristics of the curves and not apply the absolute findings to your own situation. You should also use your own expected returns for whatever allocation you select.<br /><br />Lastly, I'm not a fan of backtesting. Backtesting suggests that you believe future returns will look like past returns and I see little support for that assumption. (Past returns are just one of countless scenarios that might have happened.) We don't have enough actual data on market returns to be confident that we understand the underlying processes, which is why we run simulations.<br /><br />Simulation can make the same assumptions, which is why we shouldn't believe that simulations are predictive. They're great for studying underlying mechanisms, but not at predicting your future.<br /><br />I'll let you know when and where the paper is published. I'm expecting summer.<br /><br />Thanks!Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-58045076972848423122016-01-23T11:06:10.807-08:002016-01-23T11:06:10.807-08:00Very interesting. Thanks!
What is the composition...Very interesting. Thanks!<br /><br />What is the composition of the portfolio? <br /><br />Also you generated random lifetimes, but I didn't see any mention of where the portfolio performance came from. Was it backtested or simulated?<br /><br />I look forward to seeing the paper when it is available.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-8809180501615466472016-01-22T12:28:07.543-08:002016-01-22T12:28:07.543-08:00Well said.Well said.Dirk Cottonhttps://www.blogger.com/profile/05616143752082768155noreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-46094489736861815822016-01-22T11:27:03.506-08:002016-01-22T11:27:03.506-08:00The "Death and Ruin" series of blog post...The "Death and Ruin" series of blog posts is very interesting. I think one of the things that it does is quietly highlights the critical importance of Social Security benefits over the past half-century. the concept of "portfolio ruin" is largely a problem for the middle-class and wealthy since about half of the population has little in the way of a portfolio and is effectively entirely dependent on Social Security and any pensions.<br /><br />Similarly, bankruptcy does not necessarily mean a large change in the standard of living for many, especially the poor since they don't have assets to lose unless their SS benefits can be garnisheed.<br /><br />The progressive nature of Social Security benefits calculations means that the working poor can largely replace their previous income with SS if they worked for much of their life and paid FICA taxes. Similarly, SS can largely replace their income for the lower middle-class. Any pensions (still common in the public sector) are also important.<br /><br />Another key area that makes portfolio ruin more of an issue for the more well-off is that there does appear to be a statistical linkage between income and life expectancy. So people with smaller portfolios to begin with are more likely to "withdraw" from the study earlier. https://www.minnpost.com/second-opinion/2013/03/income-gap-plays-out-us-life-expectancy<br /><br />So bankruptcy for the elderly is more likely to occur to people with assets who get hit with something like a massive medical bill. Ultimately, those people are likely to retain rights to their SS benefits, pensions, their house (assuming that wasn't a major cause of bankruptcy), and at least some of their retirement assets (especially 401ks and annuities) so that even the bankruptcy is likely to be a hit to standard of living, not a fundamental ability to put dinner on the table.<br /><br />The population with a large enough portfolio to make it to an age where they can have portfolio ruin are also usually going to have decent SS benefits and possibly pensions/annuities as well. So they may still have enough income to match the median household income even if their portfolio is fully depleted. Their pensions/annuities may have lost substantial ground to inflation but the SS benefits shouldn't have.<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5621914599310831423.post-19600092371922876852016-01-22T10:54:09.341-08:002016-01-22T10:54:09.341-08:00Dirk, ah the benefits of having a smart son that a...Dirk, ah the benefits of having a smart son that allows for different disciplines to collaborate. We are all the beneficiaries. I really like the curve display of portfolio survival. More meaningful (with age dimension added) to me than just typical 95%. Can't wait to see the competing risk analysis. BradAnonymousnoreply@blogger.com