This was not an "everyman" or every-person type analysis, though. This was a custom simulation tuned to some particulars I happened to be looking at. Assumptions of note included:
-Age 58 start with stochastic longevity within a Gompertz distribution (87.5/9.5).
-Constant spend with probability based step-downs at age 68 and 85
-Spend rate of initial step is unusually low (<=3%)
-Inflation random, bootstrapped off history
-Stock/Bond returns random, boostrapped off history[2]
-Stock/Bond Return Correlation
-Allocation: 60/40 stocks/bonds, 70/30 tbills/tbond
-.6% fees and simulated tax drag
-Longevity capped at 105
-Tactical suppression of near term (10 years) returns
The fail rate, for what it's worth, was 4.1%.[3]
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[1] Some data was stripped out like longevity paths < 5 years, most negative terminal wealth states raised to a non-whole power, etc. That latter strips out most of the "fail before death" scenarios but not all. I don't know what that would mean for a serious analysis but then again this is not serious: I just wanted to see what it looked like.
[2] I took out or capped some of the higher returns of the early 20th century. Also, the first 10 years of simulation runs have returns suppressed a bit to try to match some prevailing expectations about returns ahead of us for a few years.
[3] See some of Dirk Cotton's posts at theretirementcafe.com where he points out that sequence risk can look trivial when put up against bankruptcy and positive feedback loops. Here is a taste:
Losing your savings due to market volatility [i.e., sequence risk or "normal" probabilistic risk] is only one risk of retirement and it isn’t the worst outcome... About half of us won’t live long enough to be exposed to sequence of returns risk [which] will rarely be a big contributor to bankruptcy and it takes decades [for sequence risk] to erode savings. Bankruptcy will strike like a bolt out of the blue as a result of spending shocks and may cost much more than just your savings. (All four of the families I wrote about in Positive Feedback Loops lost their homes, too.) The crisis will be difficult to stop once it starts…. When a planner tells you that you have a 5% probability of depleting your savings, she typically means a 5% probability of going broke as a result of market volatility. Alas, there are other ways to go broke. If spending systems are chaotic, which I suspect but can't prove mathematically, there are conditions under which their outcomes are unpredictable and probabilities don't help.
hi
ReplyDeletenice post - thx for sharing.
a few questions:
1) stock/bond correlation - what did you assume - assumptions don't seem to be listed
2) allocations - what do you mean 60/40 and 70/30?
3) it seems you are assuming only two asset classes even though most folks have portfolios with more asset classes. from a modeling pov do you think simulating at just the stock/bond level as opposed to something more granular is appropriate? obviously there are tradeoffs in any modeling exercise, and, to properly quantify what you "lose" by moving to a "simplified" two asset class model vs a more complex asset allocation, you'd probably have to build the more complex asset allocation model to test against the simple model, in which case then you'd probably just use the more complex model anyhow!
pls let me know what you think. thx!
1. Rather than a totally random stock return and a random bond return and rather than just bootstrapping off historical data independently I had the model randomly pull stock and bond returns from the same year so that the model wouldn't have wildly weird or unrealistic divergences in stock and bond returns. I don't know how good that is for a model like this and it certainly shrinks the simulation universe quite a bit but it felt like it was closer to reality for my own planning. I also feel like as a non-academic and non-practitioner I can get away with tweeking assumptions like that here and there. data was from Aswath Damodaran at the Stern School based on Fed data (St. Louis) http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html
ReplyDelete2. 60 40 is the stock bond allocation. Within the 40, bonds are allocated 70/30 to tbills/tbond. Bonds returns are total returns by the way.
3. Yes, correct, this is completely a simplifying assumption to make modeling life easier. It was a relatively complex thing for me to build as a non-programmer and when I first built it, it was more or less a self-challenge to myself just to see if I could do it at all so I wasn't thinking too far beyond "get something up and running...2 assets is good enough." The idea of making it more complex from an asset allocation perspective is a good one but I doubt I have the energy to pull it off and I'm not sure how much of a lift I would get for the effort. For a type of comparison that may or may not be relevant: in another effort where I model mean-variance for 5 assets, a relatively non trivial modeling exercise for me, the addition of additional asset classes has interesting effects on the efficient frontier over shorter time horizons (a few years, say) but over long time horizons, the 2-asset frontier for SPY/AGG, or stocks and bonds, seems like it wants to be the same frontier as the 5-asset frontier more often than not. In the end I feel like 2 assets is close enough...for me anyway...for now. Also, note one of the footnotes. Most retirement projections and calculations forget that the real effects of spending shocks and bankruptcy would overwhelm more probabilistic methods and models. The important differences between 2 assets and n assets would probably fade pretty quickly if I modeled in spending shocks (which I did, it's just not turned on here). Not sure if any of that convinces; not sure if I am convinced.
Regards and thanks for my 2nd comment on the blog.
Here are some additional thoughts now that I have woken up (since my 5am original response). First, if I could actually edit my reply, for "2 assets is" I might substitute "the choice of 2 assets is" so I don't sound like a complete moron. Then on the third item above I had some more thoughts as I was driving kids to school.
DeleteSince I am using historical data at an annual level as a source of return data it is relatively hard for me to get asset class returns for much other than stocks and bonds far enough back to get a reasonably large distribution for random access by the model. Maybe the data exists but I haven't tried to look very hard. Also, since portfolio returns are a weighted average (and I don't worry about portfolio standard deviation here) the other asset class returns would have to be consistently outside the boundaries of stocks and bonds over enough years and have a sufficiently high portfolio weighting to have a significant impact. I have not studied that question but I'm guessing that stock returns are going to dominate the equation especially since the stock data has a US 20th century bias.
The other way to do it, and I think some of the common free simulators do this, is to fabricate a distribution of returns (again because portf returns are a wtd avg) from scratch based on the mean return and variance of return one might expect for a multi-asset-class portfolio. I suppose ideally the distribution would have to have different types of skew and kurtosis for different compositions of asset classes but that is maybe above my pay grade for now. I guess it is a question of what one is trying to model and how one wants to set return expectations for the future and what one will do, in the end, with the simulation results. Models are always imperfect and reality will always throw curveballs so I am cautious about leaning too much on what sims say.
As a side note, when I have run my simulator, based on the same assumptions, against some popular free internet simulators as well as some deterministic formulas by various academics and practitioners, where I assume more effort was put in on those than I did on mine, my model seems to compare pretty closely. That gives me comfort that I am close enough for now. That, then, allows me to push my model in other areas that the others don't like: spending shocks, stochastic longevity, tactical suppression of returns over the next 10 years, a spending step-down function that matches my personal plan/expectations, etc. In other words the pros and cons of getting the return modeling more right than not are less important to me than testing other things with the model as a whole.