One last look at my joint probability approximation tool for estimating lifetime risk of ruin

This, hopefully, is the last look at the tool I created to approximate "lifetime ruin risk," which is same thing that the Kolmogorov equation evaluates (but with some opacity in what it is doing) as do most well designed Monte Carlo simulators (also sometimes with a little bit of opacity in the design assumptions, biases, and underlying process). My tool does the same thing as the K-equation and simulators but it does it a little differently by evaluating the joint probability of two things: the probability of being alive in any future year and the probability that an age-independent net wealth process will go insolvent within the years that life represents.  Both of those can easily be derived empirically or by simple algorithms and then joined.

A third look at a joint probability approximation for ruin risk

This is a quick extension of the first two posts

1. The aha moment
2. a second look: Running it with different spend rates

Acknowledging that someone has probably already done this before, this third look is merely running the joint probability (net-wealth duration, being alive) process with different levels of return volatility. Check back to the other links for the main description, background info and assumptions.

A second look at a joint probability approximation for ruin risk

In my last post I wrote that it had finally dawned on me that ruin risk can be approximated (within the narrow bounds that I've actually tested it, anyway...and this may not be new to others by the way, just to me) by a joint probability of: a) the chance still being alive in x years, and b) the chance of a failure of the net-wealth process in x years. Just to make sure it was not a fluke I thought I'd take a second look. To un-fluke, the second look attempts to put the approximation in a context (against the kolmogorov equation and two monte carlo simulators one of which is internally structured at least three different ways) over a narrow range of at least one variable that I might care about (3 to 6 % spend rate beyond which boundaries I am not yet interested)[1]. When I run all of them with the various assumptions in note 1 we get this:

Ahhhhh...Now I get it! Ruin risk is a joint probability of separate distributions

In my last post "a riff on Hoffstein's "Lie of Averages" it was all there right in front of my face and I didn't even see it (ok it was maybe an hour later that I saw it).  All the components of the Kolmogorov equation (and many Monte Carlo simulators) were there (age, force of mortality or longevity expectations, spend rate, wealth units, real return, and volatility) and I had even simulated wealth depletion paths using Kolmogorovs coefficient  mw - 1  to create a distribution of "portfolio lives" in that last post.   All I had to do now was realize that I had the two probability distributions[1] I needed to finish the job (job = decode or hack ruin risk without using complex simulators or PDEs): one for the probability of still being alive at some future age and one for the probability that net wealth (or wealth units here) will burn out at any given remove from the present for the returns and spending assumed.  That's all it was and all I had to do was put it together by joining the probabilities which is no more than asking "what is the probability I will run out of money given that I am still alive i.e., ruin risk appears to be:  P(future wealth crash) * P(still alive) [2].

First let's start with a little calibration.  For three ginned-up scenarios (that's all I'm doing this afternoon) the question is: what does the excel-VBA version of the K-equation that I got from Dr Milevsky say for fail/ruin rates.  Then we'll see if I can get close with my amateur hack. This is the set-up, with the numbers in the big box being the scenario ruin rates calculated with the Kolmogorov math:

The first step was to use the SOA annuitant mortality table data (for my age), pull a probability distribution out of it, and then create a CDF.  Taking 1-CDF I'll have the probability of being alive at any age after 59 (I think...pretty sure anyway). So right there we have a rough proxy for the K-equation "force of mortality" at my age though it is not exact since that force is a moving target as one ages.  

A riff on Hoffstein's "Lie of Averages"

The other day, Corey Hoffstein did a great piece over at thinknewfound on the concept of the lie of averages. And I'm not just saying that because it did a big favor to me by highlighting and complimenting one of my better posts (but, well, ahem...ahem, you know, um, well....[dialogue drifts off...we hear whistling and someone kicking the dirt while drooping their head over their feet]).  So I thought I'd do a little riff on the lie of averages concept, too.  In this case I'll be looking at how calculating means can be deceiving in retirement planning if more extreme realities were to come into play for two particular variables (portfolio and personal longevity) for some given individual.  I don't know if this is exactly his point but it's probably a good tangent either way.

For this we will look at two things: 1) the concept of portfolio longevity and its possible distribution, profiled in one of my recent posts, and 2) the distribution of personal longevity expectations for a 59 year old male (me) using SOA annuity table data.  Using the same illustrative but very conservative, maybe unrealistic assumptions for returns (2% real, 10% vol) and a rudimentary spreadsheet sim for wealth depletion (along with a 4% spend) we might expect a mean portfolio longevity of something around 38 years or let's call it to age 97. We might also expect a mean personal longevity, using the more conservative SOA table (vs the SS life table), of around age 86 or 87.  Looks pretty good. This should work, right?  If we were to plot the PDFs of personal and portfolio longevity with the mean expectations of each highlighted in the same color it'd look something like this:

Weekend Links - 9/28/17

QUOTE OF THE DAY

In other words, to disagree well you must first understand well. You have to read deeply, listen carefully, watch closely. You need to grant your adversary moral respect; give him the intellectual benefit of doubt; have sympathy for his motives and participate empathically with his line of reasoning. And you need to allow for the possibility that you might yet be persuaded of what he has to say. Bret Stephens 

GRAPHIC OF THE DAY

RETIREMENT FINANCE AND PLANNING

Coping with Sequence Risk: How Variable Withdrawal and Annuitization Improve Retirement Outcomes, Joe Tomloinson

Both the level and the sequence of investment returns will have a big impact on retirement outcomes. Poor returns during the early years of retirement are bad news. However, the particular withdrawal strategy used affects sequence risk, and an approach where withdrawals are variable and respond to portfolio performance can improve retirement outcomes. I’ll examine the evidence and then use my own modeling to show how a strategy that combines variable withdrawals with partial annuitization using a single-premium immediate annuity (SPIA) maximizes the cash available for consumption. 

A Multi-Objective Decision Framework for Lifecycle Investment, Timmermans et al.

In this paper we propose a multi-objective decision framework for lifecycle investment choice. Instead of optimizing individual strategies with respect to a single-valued objective, we suggest evaluation of classes of strategies in terms of the quality of the tradeoffs that they provide. The proposed framework takes inspiration from psychological theories which, on the one hand, assert that humans analyze risky choice situations in terms of several competing factors, and, on the other hand, recognize that attribute overload is detrimental to decision making. In particular, we use SP/A (security-potential/aspiration) theory as developed by Lopes and co-authors. The proposed approach is illustrated in a simple lifecycle model. As decision factors, we consider (a) the contribution paid, (b) the ambition level (targeted level of retirement income), and (c) the guarantee level (a level of retirement income that will be achieved with high probability). In terms of the tradeoffs generated between these indices, we compare a class of traditional lifecycle strategies, defined in terms of a glide path, with a class of so called collar strategies.  

Annuitized Income and Optimal Asset Allocation, Blanchett and Finke.

An investor who either buys an income annuity at retirement, or who has a higher level of guaranteed income through a pension or Social Security, should hold a different asset allocation than an investor who holds little guaranteed income. We use current annuity and bond prices to estimate optimal equity allocation for retirees with varying levels of guaranteed income who have higher and lower preference for income stability and bequests. We find that increasing annuitized income has a strong impact on optimal equity allocation. The average retiree will see their optimal equity allocation increase by roughly one percentage point for each percentage point increase in annuitized total wealth. Our results provide insight into prudent asset allocation recommendations for clients who haver higher levels of annuitized income. [emphasis added] 

Framing Longevity Income, Guillemette et al. Texas Tech

This paper analyzes the effect of framing on the stated demand for longevity income products. We test whether longevity income framed as “insurance” is more attractive than longevity income framed as an “annuity,” since pure life longevity income is consumption protection. In a sample of 1,425 respondents, we find that when longevity “insurance” is shown before a longevity “annuity” that respondents are less likely to state a demand for a longevity “annuity.” In addition, we identify characteristics of respondents who are more likely to succumb to longevity annuity framing effects. Implications for financial planners and annuity providers are discussed. 

Taking another look at visualizing sequence risk

I will now contradict my last post where I said there are diminishing returns to complexity. Here it's the opposite where a little more complexity might help. I'll figure it out someday...

I was playing around with a new formula [ mW - 1 ] today for several reasons: 1) it is the net-wealth-process coefficient of the second term of the Kolmogorov PDE profiled earlier on the blog; I thought I should get to know it better, 2) using it in a simple version makes it relatively easy to do a spreadsheet sim of a wealth depletion process without getting into a lot of programming, and 3) it gave me an easy way to see some stuff on sequence of returns risk I had been meaning to check out.  m here is a real return/growth rate most likely net of fees and taxes, W is a "wealth units" thing (a 4% spend rate on $1 means 1/.04 = 25 wealth units), and the "1" -- I finally got through my thick skull -- is 1 wealth unit spent (really, it took me a month to figure that out?).  I'm assuming I can use this the way I will below so I will.  The way I'll use it is in this form: 

equation 1

which I guess means spending is at the end of a period. If anyone objects, email me.  I'm curious if I am going too far off road with this.  

On diminishing returns of financial modeling complexity

A reader of mine has been consistent over time in asking me what I think about the concept of strategy evaluation and the question of whether ever-increasing sophistication and complexity in financial modeling (like simulation) has diminishing (or maybe even negative) returns in [for me: retirement] financial planning.  I have an opinion of course (which I'll share) but I don't think I can answer that directly or convincingly because I do not have deep or serious domain knowledge in modeling or a background in operations research or economics. Patrick Collins does a better job than I could do in "How risky is Your Retirement Income Risk model" (SSRN 2015) which is worth the read if you are into retirement finance modeling topics. I had forgotten that I had read this once but that was in an earlier stage of RH when I had not yet done a bunch of financial modeling.  I won't over-summarize or digest it here but I will at least mention it in passing as I move on to the "opinion" part. Reading him reminded me I had been asked the question.

One of the main points of the Collins piece is that overly simple models can understate risk and lull retirees into a false sense of security and that more sophisticated models can do a better job of evaluating risk in anticipation of strategy formulation and decision making (this is often said with a straight face by someone with a really expensive model or service to sell you).   But, as he points out, that begs the question (not really satisfyingly answered) of how far do you go.  Returns too normal? make them less so with other distributions (say: Beta, Extreme, Gamma, Laplace, Logistic, Lognormal, Pert, Rayleigh, Wakeby, and Weibull) or methods (two-state regimes, autoregression vectors, etc) . Inflation too static? Randomize it. Same for longevity and make sure it's a match to SOA data not the SS life table. Fees? Add them of course. Then maybe tier them.  Taxes? Add, and then try your mighty best to get more accurate per individualized client. Spending? add rules, shocks, trends, jumps, regimes, etc.  You get the idea.

But is it worth it? and how far do you go?  Before I get to that (opinion), Collins points out two other things I hadn't thought about: 1) Bonini's paradox (that was new to me: more complete models get less understandable; the more accurate, the more it is as difficult to understand as the real-world process being modeled), and 2) How, exactly, do you rank heterogeneous outcomes amongst many sophisticated models? Good points.

Weekend Links - 9/21/17

QUOTE OF THE WEEK

…“more” is not always the best way to “Great”.  Fritz 

GRAPHIC OF THE WEEK

Variable Withdrawals via Stochastic Dynamic Programming 

2050 here would be age 65 retirement 

Gordon Irlam AAcalc.com   

Rather than a rule of thumb it is also possible to compute an optimal variable withdrawal strategy if it is assumed annual returns are from a known distribution that is independent over time by using the Stochastic Dynamic Programming (SDP) algorithm ... To compute the variable withdrawal strategy using SDP it is only necessary to treat the withdrawal amount as a dimension to be optimized over analogous to an asset allocation dimension. That is working backwards by age, for each portfolio size, we consider every asset allocation and withdrawal amount and pick the best one.

RETIREMENT FINANCE AND PLANNING

Planning for a Non-Retirement, CFAinstitute

Much of financial planning focuses on retirement. But what if your client isn’t planning to retire? 

Multivariate Density Modeling for Retirement Finance, Rook, Stevens Institute

The purpose of this research is to develop a multivariate PDF for asset returns that is suitable for quantitative retirement plans. The model fits any set of returns, however the curse of dimensionality will limit the number of securities. We propose a multivariate mixture having fixed mixture marginals using normal components. The model is motivated by the claim that a lognormal PDF is virtually indistinguishable from a mixture of normals. Whereas the lognormal PDF is intractable with regard to weighted sums, the normal mixture is not. The lognormal PDF is only justifiable when short-term returns are iid and the PDF is CLT-compatible for the given sample size. A typical retiree could endure several market crashes and we should not expect the historical sample to represent all possible extremes. We can stress test a retirement plan by subjecting it to a return PDF that has been fit on the historical sample seeded with black swan events. The normal or lognormal PDF are unhelpful in this regard as neither can accommodate such outliers.  [commentary in note [1] ]

  

Can I project a geometric frontier that reflects spending?

I'm not sure I can really do this post justice nor am I sure this even makes analytical sense in a coherent way relative to the theory and models of others but I'll give it a shot if only just for fun. This is where autodidacts, of which I consider myself one in this area of retirement finance, often fail.  They (read: me) have a scatter of spots where they know "something" but none of it is all that deep and most of it is not particularly integrated or synoptic where it is even correct.  The area where I want to fall on my face today is one where I have posted before and where an integrated and wide understanding of finance math and theory would help quite a bit: "geometric return frontiers."  But now I want to also add something else to the mix: a portfolio choice component related to spending on top of the geometric return frontier. Can I really do that? Let's assume that I can and so ignore that question as well as things like the literature and models of others or utility theory and see what happens.... Most of this is just play anyway.

One of the big complaints I mutter to myself when I read finance theory and portfolio choice is that it seems like it focuses more on institutional or theoretical abstract retail investors that have very long or infinite time horizons that can be treated as "one period" and where the investors often have no spending requirements or constraints[1].  This looks nothing like a retiree-investor who has:

A quick check-in on my home rolled systematic alt risk (HRSAR) strategy

I haven't checked in a few months so I thought I'd take a look at my HRSAR strategy.  Ignoring the details of pesky considerations like: inflation, the exact methods of and rationale for the methods for projecting the components (ret, sd) of a monthly time series to a longer (let's say annual) horizon, what exactly the risk free rate should be over my time frame, the pros and cons of my comparatives, my exact methodology, tax inefficiencies of the strategy in question, my inability to match my Sharpes to outside sources, and the unhelpful brevity of a 36 month lookback, this is what I see when considering AGG, SPY, a tangency portfolio of AGG&SPY and my own HRSAR...

what	~Sharpe	~cost
AGG	0.69	n/a
SPY	0.92	n/a
P~tangent	1.21	n/a
HRSAR	1.53	~7bp*

* 36 month look-back only and before allocating my time and some 

software costs, maybe a max of 10-15 bp all in, ex-labor?

This may look like a minor brag -- which no doubt it kinda is (until we consider that it is more or less tax inefficient, has not really been tested by a downturn, the underlying returns aren't that huge, and you can't eat a Sharpe ratio) -- my point is and always has been that ordinary mortals can home-roll pre-tax efficient portfolios made up of systematic rules-based alt-risk strategies for a lot less than 2 and 20 and all that with no lockups, opacity, gates or side-pockets.  In a retirement world where volatility and fees can matter this matters.

Retirement finance theory vs. the "other stuff"

I post a lot about retirement finance for a variety of reasons but there is a lot of other "stuff" when it comes to retirement finance and I thought, for myself at least, I'd try to contextualize it a bit. At the risk of being reductive, here (maybe a little like Maslow) is my hierarchy of retirement. For now anyway:

1. Purpose
2. "last-mile" Tactics
3. Retirement Battle Plans
4. Strategic Plans
5. Retirement Finance Theory

My view of the current ret-fin world tells me that 2 & 3 are the bread and butter that are served to the retail retirement crowds, as it very probably should be.  But it is 1, 4, and 5 where I think there are some serious shortfalls and inefficiencies in the material available to the retail (me) crowd.

#3 (Battle plans) is, to my mind, the mainstay of advisory work and retail retirement planning.  This is stuff like planning around spending considerations and lifestyle, Monte Carlo simulation, portfolio design and asset allocation choices, insurance and annuities, etc. etc. These are "The Plans" in capital letters.  #2 (Tactics) is what I'll call "last mile" stuff and includes things like Soc Sec claiming strategies, Roth ladders and conversions, determining what sequence of withdrawal from what account, day to day implementation of spending rules, exact timing of retirement,  estate planning considerations, etc.  I will probably never touch #s 2 and 3 here at rivershedge because: a) others do it way better than I could (see earlyretirementnow.com, theretirementcafe.com, canIretireyet.com, howmuchcanIspendinretirement.com for some of the best on this stuff -- or your advisor) and b) I do not yet really feel in the thick of it, though I really am if I were to be more self-aware about my situation.

What about 1, 4 and 5, though? Here are some thoughts:

Weekend links - 9/15/17

QUOTE OF THE WEEK

The worst 10 year period of any backtest is the next 10 years. Michael Batnik 

GRAPHIC OF THE WEEK

My image of how hurricanes and retirement planning are similar.  The real path never matches what you plan for...

RETIREMENT FINANCE AND PLANNING

The Butterfly Effect in Retirement Planning, NewFound

By boosting returns through a combination of broader asset class and strategy diversification, considering lower fee options for passive exposures, and nailing down how retirement spending will evolve over time, we can arrive at retirement success projections that are both more reflective of a retiree’s actual situation and more in line with historical experience. 

There is No Perfect Retirement Spending Strategy, Mike Piper

I think there are many parallels between selecting a spending strategy and selecting an asset allocation. That is, in each case you have an endless list of options, and there’s a ton of research on the topic. But no matter how sophisticated the research, nothing can actually tell you the future.

The behavior of geometric returns over time with volatility and spending present

Question: What do geometric returns look like when exposed to time, spending and volatility?

I went back to this topic, one that I covered before a few times, for a couple reasons the most important of which was that I had some code errors (resolved) and some design trade-offs (not really perfectly resolved) in presenting the analysis via my R-script that I was concerned about. I'm a little more comfortable now but not 100%. It's a good thing I can't get fired. I did this analysis in the past, and here, using the formula picked up at ERN:

where right of the arrow is the "perfect withdrawal rate" version of the formula presented here in the past month or so and left of the arrow is the "FV of $1" version based on compound returns and spending (C1 is the compound total return before spending, w is consumption, Ct is the backward products that are summed, w[sumCt] is an opportunity cost concept, and s is a scaling factor not used here, pt is pensionized income which I typically ignore for simplification).

On the affinities between hurricanes and retirement

Me waiting for Irma on Sunday 9/10/17

During my recent encounter with Hurricane Irma, an experience that ranged somewhere between hair raising and terrifying, I had the opportunity to ruminate on some of the similarities between hurricane forecasting and retirement planning and not just because hurricane forecasts are really Monte Carlo simulations -- just with more complex modelling and bigger computers. I thought I'd pass along some of those reflections.

Acknowledging the acknowledgement

I grew up in mid 20th century Minnesota (culturally very Scandinavian and German -- in case you've never listened to Garrison Keillor who mostly got it right -- this was the stew in which I cooked my Anglo-Saxon-Norman dna). That means I am more prone than not to reserve, self-deprecation and the avoidance of self-promotion or the elevation of self-interest above all else, the latter of which sometimes appears to be the motto of, if not the state of FL, at least the tri-county area of southern FL. That lead-in is, of course, a set-up for self-promotion. 

After 324 posts, 5 followers, and a year and a half of time, I finally got a little validation which looked like this:

That should be random but I guess it's really not.  Those two guys I have actually been following pretty closely for a couple years. Both seem to get the modern financial landscape in ways that a traditionalist might not yet fully embrace.  The Hoffstein (NewFound Research) validation in particular I appreciated because he describes one of his approaches in ways that resonate eerily with the main alt strategy I have pursued since ~2011.  I can't speak for him but what I try to do for myself is marry an essential and assertive commitment to traditional financial theory (no tea leaves for me) with a thoroughly modern view of classical and alternative risk premia and their behaviors.  That means in my case I use a base of collateral yield with a fairly aggressive interpretation of credit risk on which I stack whatever evidence based risk premia fit my capabilities to capture through systematic rules-based adaptive methodologies (think fixed income momentum, volatility risk premium, functionally informed equity risk, etc.)  This has produced almost four years of extremely efficient risk-adjusted returns any way it is measured. I have to presume he seeks to do something similar. Someday I will ask.  ReSolve (Butler @GestaltU), for its part, if you look closely, appears like it is playing the same game. In addition, both, if I recall correctly, comprehend that we do not live in a single-period universe with no consumption.  That's a bigger story but has profound implications for decumulation strategies and retirement which is important because not everyone is an institution with an infinite "single-period" horizon and no spending.

So, validation and acknowledgement appreciated.

Reader update

To all (3? 5?) readers (including my sister, I know you are lurking out there) here is an update since it looks like I left a misimpression that became more evident when a reader pointed it out. Here's a variation of my reply to him which stands as my status:

One tree down but otherwise unscathed. Very lucky.  Not sure I want to go thru it again.  I can see where the impression I was quitting cold might have been inferred but mostly I was thinking I was facing months of rebuilding and weeks or more without power. During Wilma, power was out for close to a month for some of my neighbors. TV was saying that Irma might be worse and "the strongest storm in history." It would have been a rough time with kids and school etc. And that would have meant less or no time for coding and hardcore analysis but not necessarily dead-ending the blog.  Since the worst didn't happen I'll more than likely still be throwing stuff out there as I run into it like I did before. As it is, though, there is still a fair amount of damage and work down here. My kids' school is down for the count thru next Monday.  My girlfriend's house is still without power and boarded and needs work moving stuff back to where it belongs. I drove around yesterday and it is a crazy mess out there. Immense tree and power line damage. Beach area streets are one big dune and cordoned off...

So, that's the scoop. And don't forget, I'm still only on the first (pretty rough) draft of that Kolmogorov post.  I still need to finish that up.  Except that I still need to find someone that knows differential equations that is also willing to walk me through some of it.

Regards,


RH

Rivershedge Lives!

Some tree damage.  Lost power for about 5 hours. A bunch of branches in the yard.  Some widespread destruction around me, though.  Not so bad except that it was generally pretty terrifying the whole way through.  Three days ago I thought I was going to be living in a tent, rebuilding a life and a house brick by brick. Now? What's my takeaway?  It's either: a) I dodged a major bullet and got very very lucky and I should, as soon as I can or at least when my kids are a little older (does 5 minutes count as older?), consider finding a way to move out of this nutty state to someplace I actually want to live, or b) blow off the next cat5 hurricane that comes my way as no big deal, I mean, hey, I survived "the strongest storm in the history of the Atlantic."  Readers of the blog would not be surprised to find me leaning a particular direction.

Rain

ok, I haven't gone totally silent... here's a nice rendition I picked up at Mike's weather page -- a precipitable water map.  I'm guessing I'll see a little of this precipitable water on Sunday.

Update: RiversHedge going silent, at least temporarily, as of this post

Gotta complete my hurricane prep.  Tomorrow, I'll be hunkered down in a relatively dangerous zone that has a minor advantage re storm surge, but we'll see.  After that, there is a good chance of no power and a long hard cleanup in the near future and for weeks to come. On the back end of all of this it seems doubtful that I will continue this blog in the same way for several reasons:

1. My readership is too tiny to attract advertisers and while that was never my goal, I thought maybe I could have some minor stream of income at some point.  Of course I did not market particularly well (at all) but that is something for another day.  The payback is all personal and while that is gratifying and all...

2. My goal has been achieved in fact.  The goal was to use the blog as a way to force myself to learn retirement finance; document it in a formal, retrievable way; and then put it out to the universe in case one other human found what I just learned useful in any way.  And, you know, I have learned a s**t-load about retirement finance.  I'm not totally sure what would be next besides being a practitioner or an academic, neither of which is going to happen, or at least not this year.  Ask me if I still have house on Monday.

3. I'm guessing I am going to have an awful lot of time I need to spend on other things in the next 2-6 months or more.  Blogging is fun and useful but other things, as is often the case, are more important in the end.

After the hurricane I'll probably come back in some form but maybe something different than frantic coding and spreadsheets and maybe some more reviews, commentary, etc.  But the same idea from me: don't sell, don't lecture, don't tutor, just learn something new and report. For now: family (and pets) first, hurricane second, blog later.

Regards,

RiversHedge

here we go again...

Simulation vs PDEs and other analytic methods

I'd be curious what a mathematician thinks but I've seen things like the PDE I used in my Kolmogorov posts referred to as an analytic solution sometimes contrasted against simulation which is described an alternative "brute force" approach.  I'm not so sure anymore.  In watching the software do the finite differences approximation for the PDE I see it do this: it creates a little fake world in a matrix with 200 increments of time in one dimension and 5000 increments of wealth units in another.  Then it does 5000 calculations by passing one direction through the wealth dimension and 5000 calculations going another direction and then repeats that another 199 times over the time dimension.  Maybe that's not "simulation" but it's an awful lot of work in a fake world to come up with a guesstimate that will become rapidly unreliable shortly...sounds an awful lot like simulation to me, just by another name.

The same, I think, could be said for PWR (sometimes called the maximum withdrawal rate) where it's a dead analytic equation that assumes it has a known sequence of returns.  Cool enough, but it doesn't really come to life until you breath volatility into it through simulation.

They (analytic and simulation) are all destined to be failed crystal balls, though, because they are trying to make an end run on the future which is, in the end, unknowable.

PWR v Kolmogorov v MC simulator

This is a follow up to a past post where I put up a Monte Carlo simulator against a partial differential equation to see how they stacked up in "fail rate probability" over a spend rate range I probably care about (2% to 5%) with an age that makes sense to me (60) and with a return profile that stands in as a proxy for a 60/40 real return after taxes and fees (4% r, 10% std dev).  Now here I am adding the PWR ("perfect withdrawal rate," see previous several posts) into the fray. The PWR here uses the same return profile as above but I've added to PWR the same stochastic longevity distribution assumption as the Kolmogorov PDE (87.25 mode, 9.5 dispersion; in other words I let the periods over which the PWR was calculated in 10000 iterations vary with the shape of a longevity distribution). A difference here is that I am reluctant to use the phrase "fail rate probability" for PWR.  Rather, I am saying that in the distribution of PWRs that comes out of calculating it 10000 times, on the CDF that results, x% of PWRs were higher than the one at the spend rate in question so instead of a 5% fail rate, I'd be saying 5% of PWRs were lower than the one in question. The reader can interpret the meaning. I'm just charting it:

Conclusion: no hard conclusions, just checking out what it looks like. I'm not surprised that all three are relatively close since they are all more or less playing the same game underneath the covers, There are minor differences but: a) they are small enough that it probably is not worth interpreting, b) small changes in assumptions would probably drive a major divergence, and c) it would probably be worth my while to see what happens past .05 spend rate.

Prelim. study of PWRs and stochastic longevity

This is preliminary because I have not gone back to double-check to make sure I didn't make some dumb coding errors which I have often enough done in the past. I thought I would open up a post on this anyway though just to start down the path.

PWR is "perfect withdrawal rate" or the constant rate that -- knowing in retrospect what the return series was or were, -- would result in (in this case) a zero fv at the end or as quoted in a previous post ""the maximum withdrawal rate possible over a fixed period of time if one had perfect foresight of investment returns."  My other links/posts are in footnote [1]. A visualization of the math is here.

In one of the papers on PWRs that I used in my past posts, the authors mention that someone somewhere should in the future explore stochastic longevity and PWR rather than using a fixed number of periods (like 30). So I did. In doing 10,000 iterations (simulation) where I randomized a return of .05 with a standard deviation of .15, in place of using 30 periods for returns within the 10k iterations, I randomized the periods using Gompertz math for longevity using a mode of 90 and a dispersion of 9[2]. I assumed a 60 year old where I needed an age.  For a comparison base-case I ran the same assumptions for a fixed 30 period term, which for a 60 year old would be to 90.

Here are some of the base case stats:

Weekend Links - 9/1/2017

QUOTE OF THE DAY

It is not in our human nature to imagine that we are wrong.  —Kathryn Schulz 

RETIREMENT FINANCE AND PLANNING

Front-Loading Your Spending Budget by Treating TravelExpenses as a Non-Recurring Expense, Ken Steiner.

After our last post, we received several questions on what we meant (and what would be involved) when we suggested that retirees might wish to consider treating certain expenses as non-recurring to “front-load” their spending budgets.  This post will present an example that might be helpful in explaining this particular “budget-shaping” approach.  

Getting a Mortgage When You Have Assets But No Income, Darrow Kirkpatrick

So I’ve learned that if you’re a retiree with little to no documented income, but plenty of assets, you can certainly get a mortgage to buy a house. And you can probably find a competitive interest rate. But you’ll need to shop around. Some mortgage brokers won’t be familiar with these asset-based kinds of loans. And others won’t necessarily have competitive products to offer. [been thru the same hoops…] 

The Ultimate Guide to Safe Withdrawal Rates – Part 18: Flexibility and the Mechanics of CAPE-Based Rules. ERN

when it comes to Sequence of Return Risk, there is a zero-sum game between the saver and the retiree…  dynamic withdrawals don’t really avoid sequence risk. True, you mitigate the impact of sequence risk on the final portfolio value, but it’s at the cost of lower withdrawals along the way. There is no free lunch and there’s no way to completely avoid sequence risk!  …we can’t just set the initial SWR and then never touch it again. We should keep updating the subsequent withdrawal rates to reflect changing economic and financial conditions 

Three Degrees of Bad, Dirk Cotton

A floor guarantees income; it does not guarantee that income will exceed expenses…The term "ruin" better applies to bankruptcy than to portfolio depletion, which may or may not lead to bankruptcy…there is a valid argument that depleting an investment portfolio before the end of retirement and relying on fixed annuities and Social Security benefits thereafter can be the most efficient way to fund retirement in some scenarios.

Personal finance links: life planning, Abnormal Returns

[I was going to read and link some of his better links but they were all pretty good] 

Mesmerized by Kolmogorov - draft 1, me

…encapsulating the entire retirement problem in a single, distilled drop of self-documenting genius…

[ if my links are a little short this week it is  because I spent a little too much time working on this Kolmogorov thing, just ask my girlfriend.  It is, however, something I've been meaning to take up for about 5 years.  I might take it a little further still because I don't quite have a full grasp of this yet. On the other hand this may be about as far as I go.  I set out a few years back to see if I could "see" retirement finance in some essential way.  Many of the efforts on this blog, this link included, have gotten me pretty close to where I want to go. Past that I'm not sure what is left besides the details of living day to day in an "early" retirement.  That and beating the eff. frontier a little bit...]