Hindsight 1: Monte Carlo simulation

If I were to ever depart these blogging shores (as in leaving blogging, not dying), which is always a possibility, I would want to document, for myself, some things that I know now that I am either glad I know or wish I had known a little earlier.  I'm not sure how long of a list that is but if it gets long then it would probably be as tedious to read as I'm guessing it would be for me to sit down at one sitting and write.  For that reason I'm thinking of an open ended series of short posts I'll call "hindsight." The audience is me and the effort is intended to help me consolidate what I think I know about some stuff I've learned over the last couple of years. I'll seed the ground with the first one on Monte Carlo simulation.

Weekend Links - Thanksgiving edition 11/22/17

QUOTE OF THE DAY

“The single greatest challenge you face as an investor is handling the truth about yourself.” – Jason Zweig [delete "as an investor" and we are closer to the truth]

RETIREMENT FINANCE AND PLANNING

Robert Merton on the Promise of Reverse Mortgages and the Peril of Target-Date Funds, advisorperspectives.com

For every retirement product, Merton said, the measurement of success should be income. …“Why would think that it would be remotely possible that a single statistic – age – would be good enough to get you to a decent retirement?” Merton asked.  … “One of the biggest global issues is how to fund retirement,” Merton said. “It is faced by every country – large and small.”  … The implication of longevity means that we go from a 40-year working career and a 10-year retirement to a 40-year career and a 20-year retirement. The implication, approximately speaking, is that we must save 33% of our working earnings for retirement instead of 20%. Without reverse mortgages, the alternative, Merton said, is to reduce consumption or work longer.  … If we can find ways to get more out of the assets we accumulate, Merton said, then we can enjoy greater longevity without sacrificing standard of living…The house should be viewed as an annuity while you live in it and a financial asset that ultimately gets sold.

The Crisis in Retirement Planning, Robert C. Merton, HBR [2014]

The trouble is that investment value and asset volatility are simply the wrong measures if your goal is to obtain a particular future income. Communicating with savers in those terms, therefore, is unhelpful—even misleading. To see why, imagine that you are a 45-year-old individual looking to ensure a specific level of retirement income to kick in at age 65. Let’s assume for simplicity’s sake that we know for certain you will live to age 85. The safe, risk-free asset today that guarantees your objective is an inflation-protected annuity that makes no payouts for 20 years and then pays the same amount (adjusted for inflation) each year for 20 years. If you had enough money in your retirement account and wanted to lock in that income, the obvious decision is to buy the annuity … Ironically, therefore, laws intended to protect consumers would have the unintended consequence of prohibiting savers from holding the risk-free income asset … The seeds of an investment crisis have been sown. The only way to avoid a catastrophe is for plan participants, professionals, and regulators to shift the mind-set and metrics from asset value to income. … So what should retirement planners be investing in? The particulars are, of course, somewhat technical, but in general, they should continue to follow portfolio theory: The investment manager invests in a mixture of risky assets (mainly equity) and risk-free assets, with the balance of risky and risk-free shifting over time so as to optimize the likelihood of achieving the investment goal. The difference is that risk should be defined from an income perspective, and the risk-free assets should be deferred inflation-indexed annuities.

Bitcoin madness

In April 2014 I bought a single bitcoin.  This was not an exercise in investing or technology but just an investment in attention and education.  I knew extremely little about blockchain but I figured it would be important in the future.  Past experience told me that having skin in the game helps me focus my attention so I bought 1 coin.  For $430.  It is now worth about $8000.  By my calc that is something like 125% compound growth.

Now what? I have no idea.  I am in no mood to sell and in no mood to buy.  The original purpose stands.  I have used my position to go out of my way to read papers, articles and even standard internet dreck to update what I know and what I know is still "not much."  My position could go to zero or infinity tonight and I guess I don't care (ok, infinity would get my attention).  I will continue to keep my finger on the pulse of what is going on, though, and we'll see what happens.  My guess is that there will be volatility and uncertainty about everything (taxation, hacking, forks, fraud, illegality, etc) pretty much forever.  The big question for this blog is to ask to what extent this "thing" has anything to say to the forces of retirement finance.  For now I'd say nothing but it's possible that the future of retirement jurisdiction shopping for places that are friendly to late age retirement capital could theoretically include a blockchain component.  Who knows.  Today it's Florida.  Tomorrow...no idea....

Some thoughts on investing vs retirement wealth processes

Weekend Links - 11/16/17

QUOTE OF THE WEEK

In high school, I was a nerd and a loner.  Harry Markowitz in 2016 interview.


GRAPHIC OF THE WEEK

RETIREMENT FINANCE AND PLANNING

Deciding Whether to Take a Pension Lump Sum: The 2 Opposing Methods, Darrow Kirkpatrick.

Despite the fact that a lump sum is a losing mathematical proposition, people will still consider taking the lump sum for any number of reasons based on their personal situation. Those reasons may range from pure want to true need. In some rare cases where inflation plays a role, the math may even make sense. Other pensioners may simply not realize a lump sum comes at a discount (for the pension fund)  

Self-Annuitization, Ruin Risk in Retirement and Asset Allocation: The Annuity Benchmark, Albrecht and Maurer, Univ. of Manheim [2001]

The present paper considers a retiree of a certain age with an initial endowment of investable wealth facing the following alternative investment opportunities. One possibility is to buy a single premium immediate annuity-contract. This insurance contract pays a life-long constant pension payment of a certain amount, depending e.g. on the age of the retiree, the operating cost of the insurance company and the return the company is able to realize from its investments. The alternative possibility is to invest the single premium into a portfolio of mutual funds and to periodically withdraw a fixed amount, in the present paper chosen to be equivalent to the consumption stream generated by the annuity . The particular advantage of this self annuitization strategy compared to the life annuity is its greater liquidity. However, the risk of the second opportunity is to outlive the income stream generated by this investment. The risk in this sense is specified by considering the probability of running out of money before the uncertain date of death. The determination of this personal ruin probability with respect to German mortality and capital market conditions is the objective of the following paper. 

Annuity Valuation, Long-term Care, and Bequest Motives, John Ameriks, Andrew Caplin, Steven Laufer, and Stijn Van Nieuwerburgh Pension Research Council Working Paper [2007]

Financial security in retirement has traditionally meant having a steady flow of annuity income as long as one lives, a definition enshrined in the Social Security system. Our earlier research has stressed a more holistic approach, which focuses on the match between resources and spending needs. This formulation enables us to estimate annuity values given long term care concerns and bequest motives, where these estimated values are consistent with low observed demand for standard annuities. This chapter uses this model to value non-standard annuities with various security-enhancing features that we believe may be of value to retirees. 

Rational Decumulation, Babbel & Merrill

In particular, high levels of annuitization are shown to be rational under a wide range of risk aversion levels, even when stock market returns and annuity price loadings are assumed to be much greater than is generally the case. Ours is also the first study to model individual behavior under the possibility of default by the insurer issuing annuities. We find that even a little default risk can have a very large impact on annuity purchase decisions.  

Waiting for my DIA vs shifting longevity expectations

In this post I am wondering about the idea of waiting after my current  age (59) to hedge out longevity risk (after, say, age 85) with a deferred income annuity, a tool I know from academic papers and my own simulation that would enable me to increase consumption now for a level of risk that could be similar to that which might be held before a DIA purchase. Then I want to throw that "waiting idea" against the idea of longevity expectations increasing in the future due to something like med-tech innovations, something that has already been going on for a while now.  That would make the purchase of a DIA in the future relatively more expensive to the extent that insurers have not already figured this out...which they have. The Society of Actuaries already does something like this by providing a projection factor against its annuitant mortality tables.  Since I haven't figured out how to do that projection factor yet I'll try to look at this a different way.

Notes in a 2001 German paper about ruin estimation math

Albrecht and Maurer

I just (11/14/17) ran into the following in a 2001 German paper (Self-annuitization, ruin risk in retirement and asset allocation : the annuity benchmark by Albrecht and Maurer, Univ. of Mannheim; end of Appendix B).  It is precisely the same as what I often use here and accurately describes what I built earlier this year in my FRET algorithm...except that I am not using German actuarial tables from 1994.

Excerpt from the paper:

On the immense conviviality and generosity of the retirement finance research crowd that I've run into

Over the last several years I have gone to the effort of throwing some pretty stupid (and a few other) questions towards some of our leading luminaries in what I'll call retirement finance though really we are talking about a broader field.  I have been absolutely surprised by how generous (and fast...and real and helpful) the responses have been.  I thought there was going to be a big wall between the dumb amateur hack like me trying to wend my way through retirement finance and some leading lights in the industry.  Not a chance.  Almost all of the people I have reached out to have responded to questions I have thrown out there and have done so with vigor and wit and intelligence and grace.  Here, in short, and in no particular order, are some of the names that have been quite helpful and deserve a round of thanks and appreciation.  I know I am probably missing a few...

Moshe Milevsky, PhD
Gordon Irlam, aacalc.com (big  help on my backward induction engine)
Joe Tomlinson
Darrow Kirkpatrick, CanIretireyet.com
Dirk Cotton, theRetirementCafe.com
Tadas Viskanta, abnormalreturns.com
Wade Pfau, retirementresearcher
Evan Ingliss, Pension section of SOA
David C, PwC (my one of two readers, I think)
Tim Taylor, conversableeconomist.com
David Blanchett
Michael Finke
Michael Kitces
Corey Hoffstein. ThinkNewFound
Larry Frank
James Picerno, capitalspectator.com
Javier Estrada
John Walton
Bo Boland
Barton Waring
Luke Delorme
Ken Steiner
Attilio Meucci ARPM

Ben Carlson
Andrew Clare, City U of London
Dante Suarez
and others....who am I forgetting???

Here, on the other hand, and for the record, is who has not been helpful -- in case anyone was wondering about the dark side...there is always a dark side, right?

I live in south Florida.  Not a single person to whom I have reached out to in the area of finance anywhere in South Florida (FAU, Broward College, Nova Southeastern, UM, etc etc) has responded to a single question or email I have ever sent to anyone...ever.  Hmmm.  But I guess based on my experiences in the grocery stores here and on the road, I am not  totally surprised.  I once even had a short 10 minute "date" with a relatively well known finance professional down here and THAT is a story worth telling some day.  I've always told myself that the state motto or the logo on the FL flag should be "self interest above all else." (Hence my plans for a future move back to CO or MN). But hey let's end positive...

Regards to my helpful interlocutors...totally appreciated.

A quick, dirty, amateur look at DIAs

A reader asked me recently why, if I had (sorta) proven to myself that by hedging out age 85+ lifestyle with a deferred income annuity (DIA) I could probably increase current spending by up to 15%, I didn't pull the trigger and do so immediately.  No idea, really. I am guessing it is some combo of behavioral reasons and ignorance of the product/concept.  I thought I'd start working on the latter first.  This is my new project: understanding the pros and cons of pooled risk as well as what the annuity paradox means to my own personal planning.

Weekend Links - 11/9/2017

QUOTE OF THE WEEK

...for many entrepreneurs, they spent a lifetime reaching just beyond their grasp, always reaching for the next goal, he said. “It’s a really lucky person who can say I have enough. I am comfortable with what I have.” NYT on wealth anxiety 

IMAGE OF THE MOMENT

may daughter's cat sitting next to me helping with the weekend links...

RETIREMENT FINANCE AND PLANNING

Does Failed Retirement Income Planning Really Result In Bankrupt Financial Ruin? Derek Tharp at Kitces.com

This declining rate of bankruptcy in among retirement-aged individuals is notable, because the greatest risk for retirees is outliving their money. Yet with bankruptcy rates decreasing among older adults, the data suggests that bankruptcy in retirement may not be (at least primarily) the result of depleting a portfolio due to longevity or inadequate savings going into retirement! A 2010 study from Deborah Thorne at the University of Ohio on the interconnected reasons that elder Americans file for bankruptcy found that credit card debt and illness/injury (which can trigger substantial medical expenses, which may subsequently turn into unpayable medical debts) were the two leading causes of bankruptcy among the elderly (based on self-reports from those who had filed for bankruptcy). As Dirk Cotton has pointed out, sequence of return risk does not appear to be a significant contributor to bankruptcy among the elderly, as only 6.7% of filers reported “retirement” as the source of their bankruptcy, and again bankruptcy rates are highest in the early years of retirement—when failures due to sequence of return risk (based on reasonable withdrawal rates) are mostly non-existent.  

The Shockingly Simple/Complicated/Random Math Behind Saving For Early Retirement

EarlyRetirementNow.com

How sensitive is the savings horizon to different rates of returns? What happens if we use historical returns instead of one specific expected return assumption? How important is the asset allocation (stock vs. bond weights) on the path to early retirement? How much does the equity valuation regime (e.g. the initial CAPE ratio when starting to save) matter? 

Annuities and Trusts, John L. Olsen, Michael E. Kitces, Thinkadvisor

In the following discussion, we will examine some of the problems advisors may encounter when annuities are owned by, or made payable to, a trust, and the rules (i.e., the tax rules and the contractual provisions and administrative policies of annuity issuers) that are not well understood. 

Playing around with an EOYS free boundary sustainability metric

EOYS stands for what I want to call getting to the "edge of your seat" and is more or less what Patrick Collins suggests one do when one's retirement consumption portfolio starts to approach the boundary between feasible and infeasible a little too closely or maybe a little too fast[1].  Most of the following is just me parroting or trying to internalize what he is saying and then expressing it in some software and in a metric designed to gauge risk or sustainability in a way that might be more useful than probability of lifetime ruin. Or at least maybe this can be something that augments the sense of sustainability over time. I recommend the paper over this post; this is just me teaching me the concept.  Also much of this may be of no interest to those that are substantially over or under funded.

To visually paraphrase part of his paper, I have illustrated the basic idea like this:

To quote directly:

"Although penetrating the boundary is not an event that generates an explicit signal—there may be many thousands of dollars remaining in the portfolio at the time the boundary is breached—it nevertheless is an event that the investor should not take lightly. In terms of portfolio management, it is perhaps the single most critical piece of information that the investor should know. The existence of the feasibility condition puts a premium on intelligent monitoring. It is crucial to know how likely it is that even a one standard deviation move to the downside of the forecasted mean return could prove to be an economically non-survivable event. The investor needs to know whether they are in trouble, not whether their equity position has outperformed the S&P 500...This is a solvency question; or, in terms of the free boundary problem, it is the amount of wealth that separates the region of feasibility from the region of infeasibility. It is not a future oriented prediction; it is a question of the adequacy of current resources. Determining shortfall risk and quantifying solvency by locating the free boundary are both important components of risk assessment, and both provide important feedback regarding asset management dangers and opportunities."

Prototype of an "annuity price as a proxy for a free boundary" concept

Inspired by a recent reading of a Patrick Collins paper[1] on the concept in the title above (he's got some good stuff out there, by the way. Another paper of his on total return trusts[2] is one of the better descriptions of the "retirement problem" I've read out there) I decided to prototype a "free boundary" visualizer similar to something he had in his paper.  The idea here is that rather than wait around for ruin and bankruptcy, which is no fun at all, one might rather consider (if one has the capacity to do so) locking in a pooled risk lifestyle (by way of a single premium immediate annuity, say) if one is approaching the boundary where a portfolio might fall below the cost to "lock-in" a preferred lifestyle and also if one is uncertain, if the portfolio were to fall below the lock-in price and no lock-in were to take place, whether the portfolio would ever recover enough to maintain a tolerable lifestyle.  Since that boundary will move around with age and prevailing interest rates among other things this would be more of an exercise in ongoing portfolio monitoring rather than a specific concrete answer to a specific question but probably something worth knowing along the way.

Walking back my comment on fail magnitude...

In a recent post I played down the concept of fail magnitude. This was said in the context of times when one (me) is strictly looking at lifetime and portfolio longevity probabilities rather than when looking at the difference between a fixed planning date (say "30 years" or maybe "to age 95" or something) and when a simulator says you might go to zero or below some threshold. Without the hard stop of a specific age or a planning duration it seemed like a slippery concept.  I'm now thinking I was misguided.

In reassessing my opinion I decided to surrender and say it probably is important and I just needed to figure out how to measure it in the context/tool I was using.  If I figured this out in my traditional MC simulator, I can figure it out for my ruin estimation tool, too.

In the end it is as simple, I suppose, as just picking a threshold of interest. In the ruin tool I'm working on now, that is more or less arbitrary so I just created a boundary that I can change as needed later. In this case I decided to measure the distance in years between when the cumulative probability of portfolio failure is greater than, say, 5% and the point where the likelihood of still being alive is less than 5%. Arbitrary but it at least tells you something.

In the following chart I used some generalized placeholder assumptions (4% spend, age 60, 4% net real returns, 10% vol, modal life expectation of 90, etc). I set the threshold for magnitude at .05 for each distribution and let it run.  It looks like this. The arrow is drawn not graphed:

The lifetime probability of ruin comes out here to be 12.9% and with the threshold set as described there is a 17 year distance between the selected boundaries.  By itself that is probably not very meaningful. In comparing two strategies it might be more useful. But either way this adds a little more information, I think.  My guess is that the "area" under the green and blue would be more interesting in terms of a magnitude metric but also pretty hard to interpret.  "Years" has a more human meaning so I'll stick with that. I don't do a ton of strategy evaluation anyway so it probably doesn't matter much for now.  I also probably need to figure out a meaningful threshold level.

The other thing I want to add at some point is some type of "free boundary" measurement concept where one gauges, in any future year, the distance between some percentile in the portfolio distribution for that projected year and the cost to annuitize a baseline acceptable lifestyle at that age. The option to step out of a self-annuitization process as things go south but while one still has the capacity to lock in a pooled risk lifestyle probably has a ton of value (assuming one started with capacity, I guess). But that is another post on another day. 

On renaming my ruin estimation tool, my guess at its notation and some other considerations

The Re-naming

Have I mentioned that I do not have much formal training in statistics or calculus? I will sandbag in that area again, not as a lead-in to a humble-brag, but because my innocence in such things can lead to misleading errors or embarrassment. The latter I can handle but the former makes me uncomfortable and I think I engaged in the former by calling my recently built ruin estimation tool a "joint probability approximation" of lifetime ruin risk.  I don't think that is quite right because I am combining a pdf with a weighting factor (1 - cdf) rather than strictly another pdf. I don't know if that is a "joint" thing or not and will leave it to others that know the math better.

I had a rough idea of what I was doing when I posted the formal definitions before (when I linked to Milevsky's paper on ruin calculus[1]).  In that paper, on a recent re-read, he was pretty clear on what I was trying to do:  "One can heuristically think of the integral as ‘adding up’ the probability of [portfolio] ruin at t, weighted by the probability the individual will survive to this time." ...or the way Milevsky characterized it in the paper: "the quantity...is precisely the probability of lifetime ruin." When I spoke to him in person, I didn't ask about the joint probability thing but he did confirm that my approach was consistent with the above and was a direct expression of the P[T≥L] ruin concept which also satisfies the PDE. So, not a "joint probability approximation" I gather. It's something else. Time for a new name.

Given the opportunity to rename the tool, I first came up with the folksy sounding FRED (flexible ruin estimation device).  But that didn't hit me quite right so I shifted the last letter to a T. That gave me FRET for "flexible ruin estimation tool." That had the virtue of being both an accurate description of the software and also being an accurate description of what I do when I spend too much time thinking about lifetime ruin risk.  So FRET it is.

Alternative Option to Portfolio Rebalancing via short options strategies, AQR

This is another one of those "I haven't read it yet but looks interesting" papers.  Since I am pretty consistently short options I'll have to take a look at this when I get through the other 20 papers I have printed off for reading later....


An Alternative Option to Portfolio Rebalancing, Israelov and Tummala, AQR

We explore the use of an option selling overlay to improve portfolio rebalancing. Within a multi-asset class portfolio, portfolio weights deviate from targets as asset values fluctuate. Investors typically use a rebalancing process to bring portfolio weights back to their desired strategic allocations. However, between rebalances, investors are exposed to unintentional timing bets as weights deviate from targets. These timing bets introduce basis risk to their policy portfolio. A short option overlay can assist with hedging this unintentional exposure. We solve for the overlay construction that provides the desired rebalancing trade upon option expiration and backtest an illustrative overlay. Our analysis shows significant reduction in the portfolio’s uncompensated timing exposure. Furthermore, by selling options, the overlay earns the volatility risk premium and thereby adds alpha to the portfolio. Lastly, we show that an option overlay for rebalancing is implementable even when considering transaction costs and real-world constraints.

Weekend Links (early edition) 11/1/2017

MILESTONES THIS WEEK

These may be small beans to you but are high-water marks for me:

1. lifetime clicks went over 15,000.  First of all I know that's not all that big.  Second of all, 13,000 of those clicks were probably me, maybe 500 were my sister and the rest were Russian hacker-bots with a few left over at the end for David, Corey, and Tadas and a couple others. 

2. A single post finally cracked the 1000 click mark.  I thought it was going to be my retirement as hurricane planning post (2nd place with 862) but it was my tongue-in-cheekish 2017 Best-of awards (1002 and climbing).  I figure I could get an ad revenue stream of a few cents per month for volume like that.


QUOTE OF THE WEEK

There was another guy in the anteroom [where Harry Markowtiz was waiting for dissertation choice advice from his advisor]. He was a broker. We started talking about why we were there, and he said, “Why don’t you apply mathematical and statistical techniques to the stock market?” Some biographer later wrote, “That’s the best advice a broker has ever given.”  Harry Markowitz in 2016 interview. 

WEEKLY  GRAPHIC

Kelly allocation bet with regime suppression?

I think I tried something like this before but I am still not sure if I have this right or if this is a corrupt way of applying the principle but since I am neither academic nor practitioner I can proudly wear my amateur hack hat (I should make some real RiversHedge amateur hack hats for give-aways) just to play around and see what happens.  Now that I have a few more readers, maybe someone can step up and guest-post some better math for us if they think I am too far off track.

Here is the basic setup for the baseline (if I am taking us in the right direction).  I have some annual S&P data from Stern which I mainly use because its in an excel sheet on my PC where I can remember to find it, which is why it is still only current to 2015.  This is convenience data not rigor-data.  I split it into two: winner returns and loser returns.  That allows me to get a win rate and lose rate 73%:27% and an average win .208 and loss -.137.  Now I normalize the odds to 1.52:1 and calculate the edge as 1.52*w% - l% or .834. Edge/over odds is 54.8% so, if I am doing it right, I'd allocate ~55% of my wad to equities in a series of bets (here's where that sequential-independent thing might give me pause...)

Now I want to go darker or at least more conservative.  To do that I: 1) clip the 5 top returns from the win pile to take out some of the odd ducks from the early 20th century as a conservatising assumption , 2) I subtract an arbitrary .02 from both piles because all those genius pundits tell me I should expect lower returns for a long while, 3) I move any wins that are now losers to the lose pile, and 4) I recalculate.  w/l = .67/.33, avg win is .175, avg loss is -.1405, normalized odds are calculated as 1.25 rounded, edge as 1.25*w% - l% = .516.  So edge over odds in this darker regime suppression scenario would be .413 or a ~41% allocation "bet" on the risk asset. 

Even if that is not legit, it is not totally out of the bounds of reasonable experience I think.  That's also roughly about the shift I made in mid 2007 which saved me a bundle going into March 2009 even though I had no idea what a Kelly criterion was back then.   Maybe I should think about trying that shift again.