Collected Formulas

I seem to pick up retirement formulas like the colds I get from my kid's middle school: often and sometimes with similar effect. Rather than posting each one separately or re-titling a past post from "5 formulas" to "6 formulas" and so on I put them all on their own page here (tab at top of site) called "Collected Formulas."  I'm up to 11 now (actually 12 if you count carefully). In a world where one must adapt and where one might also be suspicious of or resentful of proprietary black boxes, fee based or otherwise, transparent formulas can sometimes be quite useful and sometimes reassuring.

My First Whack At Simulating A Floor-and-Upside

This is necessarily very imperfect because: a) my simulator is not nearly sophisticated enough or well enough tuned to do what I am trying to do, and b) my first "whack" used some idiosyncratic "software-testing lab" assumptions more than anything remotely generalizable.  Mostly I just wanted to see what would happen.

The basic idea was this, for someone with the asset capacity to be able to execute a floor-and-upside strategy: 1) conceptually commit some portion of  assets to an income floor, 2) for simulation purposes zero out that portion of assets and convert it into an (at risk) income stream that grows at some rate[3], 3) allocate any "excess" assets 100% to an upside risk portfolio as a long term upside option (this is a kind of Kelly criterion bet because the hold-time-frame is long and the equity wager has an edge that often says go all-in in cases like this), and then 4) run a sim and see what happens.  Step 5 might be to add back any residual value of the income producing assets at the end to the terminal wealth created by the upside-option but that'd just be icing on the cake with legacy planning implications.  

Weekend Links - Fri 2/24/17

QUOTE OF THE DAY

The heterogeneity of personal financial plans and the interplay between economic considerations and individual aspirations make the problem of personal finance one of the most challenging in economics.    -- Medova, Murphy, Owen, and Rehman.

CHART OF THE DAY

RETIREMENT FINANCE AND PLANNING

The Impact Of Decreasing Retirement Spending On SafeWithdrawal Rates. Kitces.com  And what researchers have found is that both the composition of spending and the level of spending vary throughout retirement – with both tending to change in some predictable ways. As it turns out, on average, most retirees actually experience decreasing rates of real spending throughout retirement… Overall, the results reveal that reduced spending scenarios result in a safe withdrawal rate increase of at least 0.32%, and as much as 0.75%... there is still such thing as being “too” conservative and potentially constraining a retiree’s lifestyle unnecessarily.   [comment: the sharp-eyed will note I wrote on this a year ago.  Also regarding being "too conservative:" just remember, as someone once wrote: the disutility of running out of money is infinite.  ]

Retirement Spending and Biological Age, Huaxiong, Milevsky, Salisbury, York University.  We solve a retirement lifecycle model in which the consumer's age does not move in lockstep with calendar time. Instead, biological age increases at a stochastic non-linear rate in chronological age, which one can think of as working with a clock that occasionally moves backwards in time. Our paper is inspired by the growing body of medical literature that has identified biomarkers of aging which -- practically speaking -- offer better estimates of expected remaining lifetime and future mortality rates. It isn't farfetched to argue that in the not-too-distant future of wearable technology, personal age will be more closely associated with biological time vs. calendar age or time. Thus, after introducing our stochastic mortality model we derive optimal consumption rates in a classic Yaari (1965) framework adjusted to our proper clock and time. In addition to the normative implications of having access to biological age, our positive objective is to partially explain the cross-sectional heterogeneity in retirement spending rates at any given chronological age. In sum, we argue that biological age is not a sufficient statistic for making economic decisions and you need information about both your ages to behave rationally. 

Minimum and Maximum Retirement Spending Boundaries?

I was reading an article recently on maximum spending rates (Maximum Withdrawal Rates: An Empirical and Global Perspective, Estrada, 2017) and thought I'd take some of his math out for a test drive just for fun.  You can read the paper on your own but the main question he asks himself, as a comprehensive way to assess retirement strategies, is "Given a desired bequest [say zero, he says later], what are the maximum inflation-adjusted withdrawals an individual could make during his retirement?" He points to related literature from Suarez (2015),  Clare (2016), Blanchett (2012), and Miller (2016).  His own answer (to cut to the chase) by a simple derivation you can check out in the link, is that when the bequest at time T (the end) is 0 the max withdrawal rate (MWR) is:

A checkpoint on my current "geo-location" in retirement finance

The other day I responded to an email from an academic/professor that I had received on a question I had sent to him where I had asked about portfolio optimization.  In writing my response to his response, which included a paragraph on why I was doing what I was doing, I realized it was a concise summary of my ret-fin journey to date.  Since I have been down this road for about three or four years now I think it's reasonable to pause, step to the side, take a breath, and see where I am. This is consistent with the purpose of the blog which is to publicly record my journey by which means I intend to consolidate my own understanding of what I am doing and maybe (or maybe not) help at least one person out there that might or might not be on the same parallel path.   

One more extension to my asset allocation optimization journey

I thought I'd try another amateur hack at optimizing an asset allocation, this time using the Kelly Formula for bet sizing.  I'm pretty sure I don't have the math chops to get this completely right, hence the "amateur hack" comment.  I'm giving this a shot because I just finished "A man for all Markets" by Ed Thorp  and I'm in the middle of "Fortune's Formula" by William Poundstone that, among other things, profiles the Kelly math for optimizing bet-sizing for a given size of capital if you know odds and payouts.  What I'll do is a little bit of a bastardization of the math because I don't really understand what I've read on this in the book and other papers very well even though I have used rules of thumb in systematic trading that are vaguely similar.   So let's do this[1].  We'll make some really simple assumptions using some discrete numbers and analysis, some of which might be mis-matched to each other (or innumerate), like:

Weekend Links - 2/17/17

QUOTE OF THE DAY

I think the maximum extent to which we can quantify risk premia is with a 0 or a 1. Either the premium exists based on a sufficient set of broad criteria, or it doesn’t. Trying to quantify the absolute or relative value of premia is a fool’s errand, which makes strategic asset allocation based on even the most robust mean-variance optimization equally foolish. - Adam Butler 

CHART OF THE DAY

RETIREMENT FINANCE AND PLANNING

To Enhance Lifetime Retirement Security, Use ReverseMortgages or Immediate Annuities? Warshawsky, JFP.  Results show that for three timeframes with different interest rate levels, the life annuity produced higher income for individuals of almost all ages and both genders in retirement, while for couples, the reverse mortgage produced generally higher incomes, although the income from the annuity improves relatively when the age spread among the couple widens and as they are older.  

Spending from a Portfolio in Retirement, Mike Piper.  there are three broad questions you have to answer: 1. Which account(s) to spend from each year (i.e., Roth, tax-deferred, taxable), 2. Which assets to spend from (i.e., stocks first, bonds first, or both at the same time), and 3. How much to spend per year.  

Taleb, the Barbell Portfolio and Safety-First Financial Planning, Michael Edesess.  An important question is, does such a strategy pay too much for too absolute a level of protection (and therefore sacrifice too much upside)? Analogies abound. How much is it worth paying to make your travel by automobile absolutely safe? Should you drive a Sherman tank? Is it worth it?... This is a very difficult question to answer conclusively. There is no clear method of cost-benefit analysis that can answer it.  Along with the safety benefit of the safety-net approach, one important benefit is that it should drastically reduce the investor’s vulnerability to panic…Whatever is the right way to look at how to control risk in a portfolio (and there can never be only one “right” way, because people’s concepts of risk are kaleidoscopic), it is a breath of fresh air to read a paper that doesn’t automatically assume that risk is the standard deviation of a portfolio’s returns distribution. We need, in order to give meaningful practical advice on investing in real-world circumstances, to break free of the straitjacket of modern portfolio theory. 

How hard can a Sharpe Ratio be?

I finally got around to calculating a (3-year) sharpe ratio for my systematic alt-risk program.  It's a pretty simple thing to do but I haven't bothered because the discussion sometimes gets clouded depending on whom one listens to.  The nuances are in stuff like annualizing monthly data, deannualizing annual data, agreement on risk free rates, which square roots to use, whether to annualize the ratio or not, etc. etc. Go onto sites like quant.stackexchange.com or quora and one gets an onslaught of opinion from otherwise pretty smart people that have opinions that range from naive and wrong to formal and often correct.  Me? I punted and used a Morningstar definition with some dumbed down assumptions to make it easier for me.    

Three responses to my money machine question

I have received three responses to my money machine question so far. Thank you. 

1. The first one asked whether the cost of "electricity" would go down too since I had sold a fractional share of a machine.  Good question and perceptive.  I maybe wrote my "metaphor" wrong.  The electricity is a proxy for my spending which wouldn't change with the selling of shares. 

2. Here is part of response two: "...Making an equivalence leap of faith for these two companies--as an investor I can own X shares of Company D, receive annual dividends, and my X shares will not grow in value. Or I can own Y shares of Company G, whose shares are growing in value, and sell enough shares each year so that my total investment in Company G remains level. The annual proceeds from selling shares will equal the dividends from Company D. If these amounts (dividends and share sale proceeds) were not equal, relative market prices of the shares of the these companies would adjust to make them equal."

Yep. That's my question.  Econ theory says equal and I agree, but I failed, in the money machine example, to clearly distinguish between the instruments and the strategy that uses the instruments.  The instruments are the machines or, more accurately, the dividend payer/retainer pair and I agree with the theory of equivalence up to a point and accept arb theory as a possible influence too. It is in the area of life-cycle strategies and execution over time where I am confused.  And by "strategy" I mean funding a spending program with instrument 1 (retainer) or instrument 2 (payer), neither of which strategy should have an impact in market arbitrage/pricing, I think. I agree that in year 1: a) collecting a div and using it to fund expenses and b) liquidating shares to fund expenses looks equivalent (all else equal).  But in year 2 it gets more interesting assuming I have not mis-modeled or misunderstood which is entirely possible. Let's look at it in more detail....

My money machine problem [updated 2/12]

This post is a question for anyone that can help me answer it.  I no longer have access to professors, colleagues, staff, teaching assistants etc. so I'm not sure how to get at this and while I've been asking around I still can't figure it out myself yet.  The money machine metaphor is a cover for dividend  investing in retirement but since the word dividend can trigger some people I'm hiding that word for now.

The Machine.

Let's say I buy two money machines for $100 each.  The machine itself is basically free but there is $100 inside each.  Each year the money machine prints a dollar. One machine prints it and stores it inside while the other machine prints it out and I put it in my pocket.  At the end of N years I get to open each machine and keep whatever I still have a claim to plus whatever I have in my pocket at which point the machine is broken and worthless. 

Weekend Links - Feb 10 2017

QUOTE OF THE DAY

Last year Morgan Housel observed that hedge funds outnumber Taco Bells (1.6:1). irrelevantinvestor 


CHART OF THE DAY

this should be handed out to all middle-schoolers 

RETIREMENT FINANCE AND PLANNING

Retirement Floors and Implications for Evensky'sCash-Reserve Strategy, Pfau at Advisor Perspectives. 

The Safety-first, Goals-based Approach to Financial Planning, Pfau at Advisor Perspectives.  

An extension to my asset allocation optimization journey

Previous post is here.

In the last post on allocation optimization I was trying to home in on a reasonable asset allocation that might be "best" given my age, endowment, risk sensibility and, importantly, the objectives against which I would judge any optimality or near optimality, objectives that are quite a bit different for a retiree than they would be for a young person or an institution where risk-return (mean variance) is the gold standard and long time frames are the norm.  Using a combination of a simulator, with all the implied flaws of simulators that comes with it, and the hopefully strong economic insight provided by using backward induction (BI) and dynamic programming to suggest optimal allocations, I figured out that something around a 40% risk allocation using some combination of a static or dynamic allocation (using 40% as a base in the dynamic case) probably made a lot of sense for the reasons I described before.

Now I want to see if I can push it a little further.  In writing up an addendum to the prior post it dawned on me that when I happened to simplify the BI map of suggested allocations -- I was looking at spending shocks in the addendum at that point -- into a simple binary of 100% stocks when the map said 100 and 70% stocks when the map said 70 (year of plan and portfolio size are the keys to the map) I happened to end up with a strategy that dominated anything else I was looking at (for that shock-scenario only).

An optimal asset allocation journey for me

I used to believe that there was some secretly optimal asset allocation out there in the universe that I didn't have and that I needed to get.  The certainty, though, that there is "one optimal portfolio" and that it can be determined ex-ante or that it can be held for very long even if it were to be determinable has slipped over the years. Mostly it's because I think the instant that one can come up with expected returns and covariance terms (when thinking in MVO terms, that is) is also the instant that one starts to be wrong so a forward-looking optimization always seems a little doomed to fail.  Maybe there is better MVO these days but I haven't kept up.  Certainly a simple MV-optimal portfolio can be seen in retrospect.  For example here is a mean variance map for 2 asset (spy and agg) and 5 asset (spy, agg, efa, iyr, gld) portfolios looking backward over the last three years or so which may be laughably short:

Ben Carlson on How the Bogle Model Beat the Yale Model

In this great little article (How the Bogle Model Beats the Yale Model) Ben Carlson does a great take down on the endowment model in terms of how little they move the needle given all their efforts and resources.  That's a good lesson.  Here is the gist of it:

"I have to say that the numbers this year surprised me. I would expect the simple index fund portfolio to beat the average returns (that’s just math), but the fact that the Bogle Model portfolio was in the top quartile and even top decile of endowment returns is insane when you consider the depths these universities will go try to beat the market and how sophisticated they are in the eyes of other professional investors. These funds are invested in venture capital, private equity, infrastructure, private real estate, timber, the best hedge funds money can buy; they have access to the best stock and bond fund managers; they use leverage; they invest in complicated derivatives; they use the biggest and most connected consultants, and the vast majority of these funds still fail to beat a low-cost Vanguard index fund portfolio."

So the numbers are close but the implication is that the endowment model is like riding a bike in first gear: a whole lot of motion and effort for not a lot of forward progress. It looks like this:

A Reasonableness Check on My Backward Induction Optimization

In my recent post (On Hacking Out a (Really) Rough Asset Allocation Optimizer by Using Backward Induction and Dynamic Stochastic Programming) I showed some results from my attempt at trying to come up with optimal asset allocations by using game theory and backward induction. My "game" was to come to some insight on what allocations, at any given retirement year and portfolio level, might be optimal by working backwards from the end of a planning horizon -- an approach that appears to be a rigorous and mathematically/economically correct way to do it.  In my prior post I concluded that I had done "something" and I guessed that it looked "ok" or was at least correct for my "can I even do it?" objective. This was good enough because this was all more of a lark than a serious effort.  I mainly just wanted to see if I could do it but why do something if it's meaningless or wrong.

Today, on the other hand, I was wondering if it was even remotely reasonable as an outcome.  So to cut to the chase I asked Gordon Irlam, the guy whose article sent me down this path and a guy that takes this stuff many, many orders of magnitude past what I can and want to do, whether I was even in the ball park. His reply is below.

Weekend Links - Feb 3 2017

QUOTE OF THE DAY

To paraphrase Thomas Edison, good risk management is 1 percent quantification and 99 percent beating the cocksure over the head with a stick. - Michael Zwecher

MAP OF THE DAY

RETIREMENT FINANCE AND PLANNING

The Middle Game, Dirk Cotton. Life expectancies are dramatically lower during the Middle Game than in the Opening Game and this fact alone makes the Middle a significantly different game…Hopefully, the retiree has implemented a variable-spending strategy rather than having tried to spend a fixed percentage of initial savings each year. This will act to mitigate the risk of portfolio depletion over time. In my simulations, few retirees deplete their savings before well into the Middle Game…As in chess, the primary objective of the Opening Game in retirement finance is to set up a winnable Middle Game. The best strategy for a retired household's Middle Game will depend largely on how well they were positioned coming out of the Opening Game and they won't know that until they get there. That position will be the result of decisions made in the Opening Game, like Social Security claiming and spending decisions, and luck, like health, mortality, and market returns.  

So Long Longevity Randomizer, Nice Working With Ya...

Longevity risk is one of THE big planning risks along with investing risk, spending risk, inflation, spend shock risk, and some others.  It is so important that when I built a simulator I made longevity randomizing an important part of it.  In fact I did it twice, once with a distribution using the SS 2013 Life Table and a second time with code for an option to use a Gompertz distribution so that I could play around with the shape of the PDF.  This kind of thing is great for research and fun to play around with[1] but it is a little abstract and I realized that my own planning is not abstract it's very real.  It's not just that I don't plan to die at 97 and 82 and 88 or that I don't plan to die at 97 or 82 or 88 it's that I expect to do it just once.  And that one age, for planning purposes, I want to be a conservative number and I want to know as much as I can about what will happen to "the plan" if I get to that age.... or beyond.

Why retirement/decumulation portfolios are different than accumulation

"Unless we keep the strict interpretation of preferences defined only on the mean and variance of the portfolio, we move to floor and upside portfolios.  The risk-return framework still applies, but risk means degradation of lifestyle not simply volatility."          - Michael Zwecher 

I'm only about 50 pages into  Retirement Portfolios: Theory, Construction and Management by Michael Zwecher, 2010 but by page 15 I had already received a little gift of some solid conceptual differentiation between accumulation and retirement portfolios.  I thought it was a helpful way to visualize what is going on in both quantitative and contextual terms.  There is no real value-add here by me except maybe putting it into two side-by-side columns. I'm just reporting or sharing.  Sharing helps me codify my own understanding which is my real purpose here.  This below is a repackaging paraphrasing by me of what he writes on pp. 15-19.

Here is a simple example that he contrived:

1. Take two simple portfolios