New SWR estimation methodology: little help?

[brewer12345]

Quote:

Originally Posted by ((^+^)) SG 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]

Quote:

Originally Posted by brewer12345 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]

Quote:

Originally Posted by 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*

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.

[bongo2]

I had some time on a couple of plane trips last week, so I managed to carefully go through this article and recreate some of his numbers.* Like any paper, you have to take the formulas presented for what their worth, and not treat them as the final answer, but I am going to use his “short-cut” formula in my personal planning, and I would think that it would be very useful to everyone else as well.

The biggest reason that Milevesky comes up with SWR numbers lower than something like FIREcalc is that he uses different assumptions.* The FIREcalc data uses years with equity returns that average almost 9% over inflation, with about a 19% standard deviation.* If we use 75% equities and 25% TIPS at 2.5%, then we have an expected 7.4% and standard deviation 14.3%.* Someone with a 30 year median life expectancy has about a 10% ruin probability using a 4.6% withdrawal rate with those assumptions.* The number can get a lot lower if you make an assumption about future returns that don’t match the period used by FIREcalc.* The result you state (94% safe at 3% WR) uses 5% / 12% for mean / standard deviation.

Of Milevesky's two simplifying assumptions (lognormal asset returns, and constant force of mortality), the force of mortality assumption is the most troubling to me.* For an ER you might be working with a median lifespan of 45 years (say a 35 year old living to 80).* This would give a constant force of mortality of 1.5%.* However, your initial mortality will be something like 1/10th that.* So Malkiel is dramatically overestimating the probability of death early in the plan.* For example the constant force of mortality might give you a 85% probability of a 35 year old making it 10 years, while standard mortality would give you about a 98% chance.* Dying young can “bail you out” of bad investment results.* A constant force of mortality does show an unreasonably large probability of living to 150 or more, but that won’t upset your plan as often, since after you’ve made it 50-100 years you have most likely built up a large investment surplus.* For this reason Malikiel’s formula tends to underestimate the probability of ruin, and will only overstate it when the withdrawal rate is very low (and you need a lot of years to blow out the plan).

So, it’s not perfect, but it is very interesting to think about, and the errors in his method really pale in comparison to the uncertainty around what the correct inputs are!

[HFWR]

Reminds me of an Operations Research class I once had in kollidge. Real brain twister, learning how to solve matrices and such. But the irony, to me at least, was that they pulled most, if not all, of the input for the equations - utility functions, mostly - out of their a$$es...

Made a B though, and was happy to run like hell and never look back!! :P

[sgeeeee]

Thanks, bongo. In retirement I've become too lazy to read this kinda stuff unless I am really interested.

[mb]

I'm confused? (Not necessarily an abnormal situation )

The original topic was a Mikevsky and Robinson paper.* Where did (Burton?) Malkiel's paper come in?* I didn't see it mentioned until your post, Bongo?* Did I miss something?* Are they the same?

MB

[rmark]

I've tried to read Mandelbrots book. Basically argues that there are more market crashes than normal distributions imply, typically making planning based on that distribution too optimistic.

I think Henry Hebeler is one of the few retirement planning writers with a good grasp of how investor and portfolio behavior interact.

I suspect the typical 60/40 stock and bond, past high return at index fund costs, 25 year retirement, 3% inflation = 4% (more or less) falls apart if retirees really hold 40/60 (seen it here!), we use past higher costs with past high returns, and use the IRS life expectancy data (example. married couple at 62 = 29 yr life expectancy).

[bongo2]

"Where did (Burton?) Malkiel's paper come in?"

Whoops! He wrote the previous article in the magazine! I've edited my post.