New SWR estimation methodology: little help?

[brewer12345]

In the November-December issue of the Financial Analysts Journal, Moishe Milevsky & Chris Robinson published an article that might be of interest to us: "A Sustainable Spending Rate Without Simulation". They lay out a mathematical means to estimate safe withdrawal rates that uses both the expected return and standard deviation of the portfolio as well as the actuarial estimate of a retirees life expectancy. This is done without simulation, historical data, etc. The withdrawal rates they come up with are surprisingly low compared to what we have seen in the Trinity study and other studies (50YO retiree would be 93.6% safe with a 3% inflation-adjusted withdrawal). Clearly this does not jibe with the historical record or many of the other studies. I'd love to understand why they come up with these low withdrawal rates, but frankly, the math is beyond me. Can anyone else comment?

 

[Nords]

Can anyone else comment?

Brewer, could you do us all a huge favor?

Please post this over at M*'s Vanguard Diehards board. ***** has been so SWR-starved over there that he'll grab the hook and run with it, getting him kicked off his umpteenth major discussion board and making it safe again for the rest of the posters.

If you're not interested then let me know if I can do it for you (with appropriate credit, of course). This is just the sort of question that drives those DHs into a frenzy.

Gosh, it might also start a discussion on good SWRs here. This is the article, right? Will it ever go free or at least for a free registration? I'd love to look over the math and see what kind of controversy this provokes...

 

[MasterBlaster]

I'll pass on whether their model is any good or not.

However, All models make some assumptions. The output of the model is then only as valid as the assumptions made. See the spherical Chicken joke... http://www.geocities.com/SouthBeach/Lagoon/5923/story.htm

I'd like to know who funded this study. That often tells you much about what the study concludes.

 

[brewer12345]

Nords, you can feel free to wave the red flag in front of hosuc, but I don't want any credit, Yes, that;s the right article.

MB, Milevsky is an academic and retirement income is his principal area of specialization. I don't think that he gets funded by anybody.

I suspect that the difference between the model and the historical record is the models assumptions about returns. Any less math-challenged opinions would be appreciated.

 

[yakers]

Brewer, could you do us all a huge favor?

Please post this over at M*'s Vanguard Diehards board.  ***** has been so SWR-starved over there that he'll grab the hook and run with it, getting him kicked off his umpteenth major discussion board and making it safe again for the rest of the posters. 

If you're not interested then let me know if I can do it for you (with appropriate credit, of course).  This is just the sort of question that drives those DHs into a frenzy.

Oh, oh....better go warn the Diehards....active dieharder here but not often poster to their site. The local DH meetings I have attended and hosted managed to never get in a SWR war. Very polite discussion, not enough *passion* iI expect.

 

[unclemick]

I don't need no stinking math - the SWR is the same as it was in 1948 when I got off the Kindergarten bus - dividends and interest plus a little lagniappe once in a while in a good market year when I get old.

Worked for Ms Wright (aka the Norwegian widow) - works for me.

Now a model that that takes into effect various forms of currency devaluation over different decades - that's what I'd like to see. Gold coins in the safe deposit box notwithstanding.

Heh heh heh heh heh

Boy oh boy - here we go again - one more time.

 

[mb]

I've noticed a similar discrepancy between FIREcalc and the TRP Monte Carlo simulator. For example.

With the following input FIREcalc gives a 100% confidence level:
- $1m porfolio
- $40k/year withdrawal (e.g. 4%)
- 30 years
- no changes in withdrawal rates, etc.
- 80% stocks/20% 5-year treasuries
- 0.18 expenses
- PPI inflation

But TRP gives ~ 90% (slightly less actually) confidence level for the following similar() input:
- $1m portfolio
- $3.333k/month withdrawal (i.e. 4%)
- married
- 60 year retirement date
- 30 year withdrawal period
- 80/20 stocks/bonds

Apart from the obvious (historical data versus whatever assumptions TRP is making for distribution functions, etc.) I haven't looked into possible sources for the differences. (I doubt that TRP would release the info necessary to really understand it.)

I looked at the abstract that Brewer mentioned but wasn't able to get the full article.

MB

 

[intercst]

I've noticed a similar discrepancy between FIREcalc and the TRP Monte Carlo simulator.  For example.

With the following input FIREcalc gives a 100% confidence level:
- $1m porfolio
- $40k/year withdrawal (e.g. 4%)
- 30 years
- no changes in withdrawal rates, etc.
- 80% stocks/20% 5-year treasuries
- 0.18 expenses
- PPI inflation

But TRP gives ~ 90% (slightly less actually) confidence level for the following similar() input:
- $1m portfolio
- $3.333k/month withdrawal (i.e. 4%)
- married
- 60 year retirement date
- 30 year withdrawal period
- 80/20 stocks/bonds

Apart from the obvious (historical data versus whatever assumptions TRP is making for distribution functions, etc.) I haven't looked into possible sources for the differences.  (I doubt that TRP would release the info necessary to really understand it.)

I looked at the abstract that Brewer mentioned but wasn't able to get the full article.

MB

The last time I looked at the TRP calculator they had a mutual fund expense ratio of about 1.00% hard wired into the program. That could explain a lot of the difference. Here's the assumptions they use.

http://www3.troweprice.com/ric/RIC/

For each asset class, we deducted from their simulated performance the following expense ratios based on the mean averages for each comparable Lipper no-load mutual fund category:

Corporate Debt A rated .72% (Investment-Grade Bond)
Growth 1.09% (Large-Cap Stock)
High Yield .82% (High-Yield Bond)
International Equity 1.21% (International Stock)
International Fixed Income .96% (International Bond)
Small-Cap 1.17% (Small-Cap Stock)
Short-Term Investment Grade .61% (Short-Term Bond)


intercst

 

[WhodaThunkit]

The supplemental material to the abstract has a link to an appendix that gives some insight into the math (but not a complete picture).  Evidently they assume log-normal distributions, to give a longer "tail" than a normal (Gaussian) distribution would, and therefore a higher likelihood of "abnormal" events.

A principal concern in a paper like this one is that the model be analytically tractable.  Any such model assumes that the underlying random variables are stationary (statistics hold constant wrt to shifts in time).  Which may, or may not, be the case in real life.

This suggests using feedback of some sort in making portfolio withdrawals, like Henry Hebeler's "retirement autopilot," ESR Bob's 4%/95% method, or Stein and DeMuth's four-years-and-reset method.  With feedback, you won't be caught flatfooted if the market is not a stationary process, in which case none of the analytic, monte carlo, or historical models works.

 

[mb]

Intercst, your comments regarding expense ratio seems to explain much if not all of the differences between the FIREcalc and TRP MC results that I posted.

(1) I plugged expenses of 1.0 into FIREcalc without changing the other inputs and got a 96% confidence level --- closer to the MC results.

(2) Perhaps more revealing.  I took some of the year-by-year FIREcalc results (a different simulation) for a 50 year, 60/40 stock/bond ratio and looked at the the worst case year (in terms of when the portfolio was depleted not the minimum value at the end of the 50 years).  I calculated the differences in total expenses for a 0.2 and a 1.0 expense ratio.  For the higher expense ratio you would have paid an additional $334k in expenses up to the year that the portfolio was depleted.  But at the end of the 50 year period the portfolio value was only -92k.  The worst case in terms of minimum portfolio value at the end of 50 years was -236k.  So for this case the difference in expenses was the same order of magnitude as the portfolio short fall at the end of 50 years.

Obviously as we have all heard before, expenses matter.

MB 

 

[sgeeeee]

I think this is the work Milevsky did for the Society of Actuaries. They make his simulator available as a download for free:

Society of Actuaries
Retirement Probability Analyzer Software

http://www.soa.org/ccm/content/area...ion/retirement-probability-analyzer-software/

They also provide a fairly detailed paper concerning the mathematics of the simulator as well as a powerpoint description of the program (same url).

I looked at the paper and decided it looked like work to go through the math in detail. But it appears that it does a probabilistic calculation based on an assumed gaussian distribution of returns for the various asset classes in your portfolio. This is the same assumption many Monte Carlo simulators make, so the simulator should provide similar results and exhibit similar limitations. The goal of the actuaries is to get you to use some of your money to buy annuities. The simulator helps you determine that some money spent on annuities is good for you. But if you don't like the results, you can modify your allocation mix and revise the expected mean and standard deviation of the returns for each asset class till you get what you want.

Regarding Monte Carlo vs historical simulation -- Monte Carlo simulators have to assume something about the distribution of returns for each asset class. If you modify the assumed returns distributions for a Monte Carlo simulator, you can get it to match almost any result you want. Many of the simulators (but not all) use Gaussian curves and try to fit the curves to the observed historical distributions. Others use actual historical data by year and select them at random. But no matter what they assume for distributions, they cannot account for all of the correlations in the data. Values are chosen at random without regard to previously chosen values and how they might be correlated. This means that Monte Carlo simulators should (and do) produce results that are slightly more pessimistic than historical data.

 

[WhodaThunkit]

According to this link

http://www.cfapubs.org/collections/pdf/MilevskyRobinsonSupplemental.PDF

which comes from the abstract provided by Nords, the distributions are assumed to be LOG normal, not normal . . .

 

[brewer12345]

According to this link

http://www.cfapubs.org/collections/pdf/MilevskyRobinsonSupplemental.PDF

which comes from the abstract provided by Nords, the distributions are assumed to be LOG normal, not normal . . .

Ok, s for the math-challenged among us, what does that mean in the context of estimating SWRs?

 

[WhodaThunkit]

Ok, s for the math-challenged among us, what does that mean in the context of estimating SWRs?

One thing that it means is that outlying events such as unusually high or unusually low returns, for example, are more likely to happen than would be expected using a gaussian (normal) distribution.  The "tails" or extremes of the log-normal distribution are "longer" than those of the gaussian distribution.

 

[sgeeeee]

. . . which comes from the abstract provided by Nords, the distributions are assumed to be LOG normal, not normal . . .

Sorry.  You are correct.  But it really doesn't matter to my discussion.  You put in a mean and standard deviation to describe each asset allocation.  You try to fit the distribution curve to historical data.  (Try it.  you may be surprised how poor the match is regardless of the distribution you use.)   And it is still not possible to account for correlations between the data or from year to year.  The distribution curve you fit data to has no effect on the correlation problem.

Although there is literature that discusses whether the use of normal or log normal distributions is best for modeling returns data, this issue is probably of second order importance relative to monte carlo retirement simulation or to this particular technique based on PDEs.  There are some significant advantages . . . and some significant limitations to using monte carlo simulations over historical simulations.  Even if a "perfect" method to model return distributions were identified, the primary advanatages and limitations remain unchaged.   

 

[WhodaThunkit]

You try to fit the distribution curve to historical data.  (Try it.  you may be surprised how poor the match is regardless of the distribution you use.)   And it is still not possible to account for correlations between the data or from year to year.  The distribution curve you fit data to has no effect on the correlation problem.

I think that you are exactly right. These are big problems for the modelers. On the same point: Mandelbrot (the fractal man) has a new book out called something like "The (mis)behavior of markets." Of course, he wants to use a fractal model, which he thinks fits better than any of the "finite moment" models. I haven't read the book yet, and probably wouldn't be able to tell whether he is correct or not even if I did

 

[cute fuzzy bunny]

I guess if you could come up with a tool that would let you put in the characteristics of your investments and the economic environment at any particular time in history, and that tool could then accurately predict what we now know happened for a period of time after that, which correspondingly also figures out your actual life span...that'd be worthwhile.

Aside from that obvious unlikelihood, calculators are an interesting exercise to sooth the savage early retiree prospect, but not very useful because they can neither accurately predict a lifespan or a set of future returns in short term periods.

May I suggest a far simpler "prarie dog" approach to the "problem"? Free from gaussian correlations and logarithmic ferris wheel analysis? Using simple long term average rates of return/inflation/expense?

Whats the long term rate of return for your port structure? Isnt it something like 11% for most broad equities over the last 30 years and about 6 or 7% for broad bonds? 8 or 9% for the usual 60/40 balanced index? Isnt average inflation over that period something like 3 or 4%? Isnt the average early retiree going sometime in their late 40's/early 50's, with a 20-30 year lifespan? Isnt it fairly well accepted that for broad indexes, the rate of returns over 20-30 year periods are fairly predictable?

So barring the odd pandemic, nuclear disaster or other doom and gloom prospect, cant you simply pick your portfolio poison, subtract average inflation, and take some portion of that remainder (looks like ~3% if you're all in bonds or up to 7% if you're all in equities) and feel fairly "safe"?


Makes the old 4% look pretty conservative, unless you're all in bonds. Even at that, if your portfolios large enough and your lifespan isnt too excessive, you'll probably make it.

 

[HFWR]

Uh, oh...

Time for another acronym: DCM (defenders of the conventional methology)

Hosuc just blew a head gasket!!

:

 

[cute fuzzy bunny]

Eh, its just one of those "how many angels can you fit on the head of a pin" deals.

At the end of the day, nobody knows, its all mythic, and theres no way to know. On top of that, it almost doesnt matter.

 

[sgeeeee]

In the November-December issue of the Financial Analysts Journal, Moishe Milevsky & Chris Robinson published an article that might be of interest to us: "A Sustainable Spending Rate Without Simulation".  They lay out a mathematical means to estimate safe withdrawal rates that uses both the expected return and standard deviation of the portfolio as well as the actuarial estimate of a retirees life expectancy.  This is done without simulation, historical data, etc.  The withdrawal rates they come up with are surprisingly low compared to what we have seen in the Trinity study and other studies (50YO retiree would be 93.6% safe with a 3% inflation-adjusted withdrawal).  Clearly this does not jibe with the historical record or many of the other studies.  I'd love to understand why they come up with these low withdrawal rates, but frankly, the math is beyond me.  Can anyone else comment?

Hi Brewer,

We got caught up talking about distribution assumptions and monte carlo vs historical and it occurs to me that we probably didn't answer your real question.  

What I think Milevsky wanted to examine was the effectiveness of using annuities as part of a retirement portfolio.  The problem with using either historical or monte carlo simulators is that they do not include longevity probability.  In order to include that effect, you would have to run dozens of simulations with different retirement periods, then combine the results with longevity tables.  This process would have to be done for every assect allocation (including annuity amount) of interest.  

The solution he came up with is interesting (in a nerdy math geek kinda way).  By writing analytic expressions for all of the return and longevity data, he is able to write a set of partial differential equations that describe investment and life performance in a probabilistic manner.  This allows him to run optimization runs and examine the effectiveness of using annuities.  But he has to make a lot of approximations along the way.  For example, if I remember his article correctly, he assumes a no fee annuity (try and find that).  I also don't recall him including any social security benefits or pensions (which should be considered as an annuity portion of a portfolio).  I don't know how much time he spent trying to fit his distribution curves to real data.  I don't recall him discussing that.  I would say his results are qualitatively interesting.  

If you use his simulator with appropriate return distribution curves, the results should be very similar to basic monte carlo simulation results, but because the simulator includes longevity tables, it will also examine length of retirement variations.  

 

[brewer12345]

Hi Brewer,

We got caught up talking about distribution assumptions and monte carlo vs historical and it occurs to me that we probably didn't answer your real question.  

What I think Milevsky wanted to examine was the effectiveness of using annuities as part of a retirement portfolio.  The problem with using either historical or monte carlo simulators is that they do not include longevity probability.  In order to include that effect, you would have to run dozens of simulations with different retirement periods, then combine the results with longevity tables.  This process would have to be done for every assect allocation (including annuity amount) of interest.  

The solution he came up with is interesting (in a nerdy math geek kinda way).  By writing analytic expressions for all of the return and longevity data, he is able to write a set of partial differential equations that describe investment and life performance in a probabilistic manner.  This allows him to run optimization runs and examine the effectiveness of using annuities.  But he has to make a lot of approximations along the way.  For example, if I remember his article correctly, he assumes a no fee annuity (try and find that).  I also don't recall him including any social security benefits or pensions (which should be considered as an annuity portion of a portfolio).  I don't know how much time he spent trying to fit his distribution curves to real data.  I don't recall him discussing that.  I would say his results are qualitatively interesting.  

If you use his simulator with appropriate return distribution curves, the results should be very similar to basic monte carlo simulation results, but because the simulator includes longevity tables, it will also examine length of retirement variations.  

SG, I think you are looking at the wrong article. The one I referenced specifically mentioned in the title that it was an effort to work out the problem WITHOUT simulation. The article I read had nothing to do with annuities (actually the possible solution Milevsky mentioned was to put on zero cost collars on equity positions).

 

[sgeeeee]

SG, I think you are looking at the wrong article.  The one I referenced specifically mentioned in the title that it was an effort to work out the problem WITHOUT simulation.  The article I read had nothing to do with annuities (actually the possible solution Milevsky mentioned was to put on zero cost collars on equity positions).

I don't think so, Brewer. I believe this is the same methodology he developed for the Society of Actuaries but applied to a more academic problem. There may be modifications or augmentations to the technique, but the description sounds the same. He says it is without simulation because he arrives at a solution without having to simulate a whole bunch of retirement scenarios year by year then evaluate the statistics of hundreds or thousands of scenarios. Instead, he simply solves one set of PDEs that give him resulting statistics. I think he is justified in drawing a distinction between his approach and traditional monte carlo or historical simulators by saying he does it without simulation. But he still has to solve the PDEs and that's what I referred to as "simulation". I should use the word "calculation" and avoid the inconsistency with his title.

 

[deserat]

Oh man, PDEs, HOTs and DEs - reminds me too much of my summer-have-to-do-this-to-graduate-on-time class my sophomore year in engineering college. I yawned a lot and copied a lot of greek symbols.

Personally I like the 4% rule with ESRBob's 95% withdrawal backup in times of distress.

PDEs - Partial differential equations
HOTs - higher order terms
DE - differential equations

If I understand fractals, it allows a nonlinear approach to looking at things - biological formations seem to follow the fractal approach more so that linear approximations. Oh, I do remember that PDEs and DEs could only be answered for linear equations.....

Long time ago - way too long ago......

Bridget aka Deserat

 

[mb]

SG, I agree that there could be significant model error in a Monte Carlo simulation if the distribution functions for different asset classes are not realistically correlated.  I haven't seen to many cases where R2 with say the SP500 is zero.  However, I don't think that it would be that hard to do it.

MB 

 

[sgeeeee]

SG, I agree that there could be significant model error in a Monte Carlo simulation if the distribution functions for different asset classes are not realistically correlated.  I haven't seen to many cases where R2 with say the SP500 is zero.  However, I don't think that it would be that hard to do it.

MB 

I think it wouldn't be that hard to include some of the correlations (eventhough most monte carlo simulators don't do it). But it would be impossible to include them all since they are so complex that we can't quantify them -- or even identify them. It would be pretty straight forward to approximate correlations between equity returns, bond returns, and inflation for example. But annual returns and inflation are also correlated (in some fashion) to performance experienced in previous years. Several irrational exuberance years in a row are likely to be followed by less stellar performance. Recessions tend to be followed by booms. etc. These kinds of correlations are nearly impossible to capture and approximate.