Aug 31, 2017

Kolmogorov vs RH40 spending rule

I think I might've done this before but since I spent the last week going overboard looking at the Kolmogorov equation I thought I'd go retro and look at RH40 again and put it up against a "solve for withdrawal rate given a fixed risk" version of the K equation.

In one corner: RH40 = withdrawal rate at age n = [age / (40 - age/3)]  (black)

In the other corner: Kolmogorov partial differential equation. Age varies per chart, wealth = $1, mode = 90, dispersion around mode = 9,  = .04, s = .10, spend rate is solved for fail probability = .05.[1]  (red)



Some minor difference but otherwise this lines up pretty well.  The biggest divergence is at ages where it may not really matter.  For a dumb rule of thumb RH40 works ok. This mainly shows that: 1) using age to drive expectations about longevity probability (whether explicitly in equations or simulation or by proxy in a rule of thumb) as well as to adjust spending can be a pretty powerful part of the analysis and is also why the 4% rule always tripped on its own simplicity, 2) the RH40 formula is very conservative, which was the point when I created it in the first place, and 3) if you can't do a finite-differences-approximation solution to a differential equation in your head, having a simple rule of thumb doesn't hurt...if you need it, which is the other reason I created it.  

-----------------------
[1] return and standard deviation are basically from a 60/40 allocation mutual fund with mean arithmetic return of around .08 but then ding-ed for inflation, fees etc.  The mode and dispersion are conservative and more or less comport with the Society of Actuaries table for annuitants for a certain age...though not exactly.




Aug 28, 2017

Visualizing Sequence of Returns Risk

This is from a few past posts I did on withdrawal rate analysis. Any references or credits can be found there.  I hope I got this right but if I didn't (my skills at notation are pretty limited) the basic idea is the same.  This shows visually how sequence of returns risk can affect the success of a withdrawal rate.  I did this for myself to be able to see it and I thought I'd pass it along.




Note - this is true for "one path" of particular spending of course but sometimes it shows better if one sims it out about 10,000 times in which case you get a distribution of withdrawals.  The "sequence challenged" withdrawal rates would be on the left side of each distribution:


Since one never knows which path one will get in real life, one generally has to plan for that left side.

Aug 25, 2017

Weekend Links - 8/25/17

QUOTE OF THE DAY

[strategy decay] doesn’t happen in a field like physics. Gravity doesn’t get arbitraged away due to popularity. Morgan Housel 


GRAPHIC OF THE DAY



RETIREMENT FINANCE AND PLANNING

All together, by slashing fund expense ratios from 1.0% to .10% and the advisory fee from 1% to .40%, the retiree could receive $32,000 additional annual retirement income — or roughly $2,600 more each month between the ages of 70 and 95. Clearly, the impact of portfolio costs is huge.  

Risk really matters when you no longer have human capital and are planning to live off your investment earnings for the remainder of your days…Sequence of return risk can be painful if you’re on the wrong end of it but it becomes a double whammy if you end up being a forced seller of stocks when they’re down. This can be avoided through portfolio design, diversification and intelligent deployment of cash flows.  

If you over-estimate your future spending liabilities, you run the risk of underspending today.  If you under-estimate your future spending liabilities, you run the risk of overspending today.  Clearly, the more “conservative” strategy is to over-estimate your future spending liabilities and spend less today.  On the other hand, if you are too conservative, you may be denying yourself the lifestyle you really want to enjoy today and may be unintentionally increasing the amount you ultimately leave to your heirs.  This is perhaps one of the most difficult trade-offs that you (possibly with the help of your financial advisor) will have to face in your financial planning. [He estimates a 22% reduction at 65. I estimate a ~17% reduction at 68.  In addition I get even more aggressive after 85-86 where I assume I am statistically dead and then factor in a very-minimal "income"/expense for a longer superannuation regime between 85 and ?] 


Aug 23, 2017

Putting an adaptive PWR up against changing longevity estimates

Here is another "on a roll" type post.  While I still had it fresh in my mind I thought I'd run PWR analysis ("perfect withdrawal rate" links here, here, here, here and here)[1] through an "adaptive" cycle of changing longevity and then compare it to my old self-made rule of thumb [RH40 = age adjusted spend rate estimate = age/(40-age/3)]. I showed in past posts (not linked here) that RH40 is a good proxy for a conservative constant risk (5% fail rate) spend estimate and that it even won some CRRA utility games (for high risk aversion) in some of the spend games I did a while back (not linked here either). It stands in here because: a) it tracked well with both programmatic simulation and analytic simulation when they were set to pretty conservative assumptions, b) it is easy to remember and apply, and c) generally it keeps fail rate risk on a forward estimated basis around a constant 5%, which I like.  The basic idea here then is:

1. Use the PWR approach to calculate a spend rate at each age (starting at 60) given an evolving longevity estimate (plan duration) that is based on the SSA life table at the 95th percentile expectation for that age (i.e., really conservative). That expectation moves around each year and extends out the older you get (all else equal). The PWR at the 5th percentile is used as a proxy for 95% success rate which it more or less is if I have all of this right.  This, by the way, is a reminder on the formula for PWR in the Clare article:

Which, if you look closely and think carefully about Ct, is the same as in the ERN link ...

Investing and Fear - a behavioral study

I thought this was interesting.  Here is a study out of Austria on individual risk preferences, trading behavior, and asset prices.
Does Investor Risk Perception DriveAsset Prices in Markets? Experimental Evidence
Jürgen Huber (juergen.huber@uibk.ac.at), Stefan Palan (stefan.palan@uni-graz.at) and Stefan Zeisberger (s.zeisberger@fm.ru.nl)  No 2017-05, Working Paper Series, Social and Economic Sciences from Faculty of Social and Economic Sciences, Karl-Franzens-University Graz 

Here are some key points:
  • "We are the first to explore how individual risk perception influences prices and trading behavior in a market setting by exposing subjects to a number of differently shaped return distributions which they then trade on.  

  • Our findings confirm previous studies on risk perception at the individual level, especially by Anzoni and Zeisberger (2017). In particular, we observe that investors perceive risk mostly as the probability of incurring a loss. More importantly, we further observe that individually elicited risk perception predicts prices in asset markets  

  • Risk perception directly drives trading behavior and, by consequence, prices. Hence, variance of returns is not the main driver for risk perception or for market prices, while the probability of losing is.  

  • The probability of incurring a loss explains roughly 96% of the variation in perceived risk, which in turn explains roughly 94% of the variation in average prices.  

  • As we observe an average trading price of 119 for asset NoLOSS, subjects actually incur losses with this asset in about 80% of all cases (as 80% of the possible realizations are below 19% return). However, we find most subjects to be either ignorant of this fact or ready to accept the (moderate) losses associated with the asset.  

  • While standard finance theory predicts identical prices for most of our assets we find average prices to vary by up to 20 percent, with assets perceived as being less risky trading at significantly higher prices. "  


Comment: 

The implication is, I suppose, that selling low risk assets to the risk averse (e.g., selling option premium or some structured products) could be expected to have excess returns.  


Some PWR acknowledgements and comments

I posted recently on trend following and withdrawal rates.  I was responding mostly to an article by Clare et al. "Can Sustainable Withdrawal Rates Be Enhanced by Trend Following?" where I used some math from that article as well as from earlyretirementnow.com.  I think this is an interesting and under-mined area of the current ret-fin world and I wanted to acknowledge them again as well as point to several other sources for this type of analysis. So far, what I've read, run into, or seen referenced when it comes to PWR (perfect withdrawal rates) in its various forms are as follows though there may be quite a few others:
Some comments:

Aug 21, 2017

Eclipse 2017


Max eclipse in Fort Lauderdale ~ 2:57 pm
TV85 with solar filter & 40mm eyepiece
camera = iPhone 6 (not ideal but it works)

Trend Following Can Enhance Withdrawal Rates - Part 4

This is hopefully the last of my series on trend following and withdrawal rates covered in part 1, part2, and part 3. Not only the last, I am also going chartless here!  Note also that I am not really going to be explicitly talking about trend following at all (see part 3). But since I was on a roll with "perfect withdrawal rate" analysis, I thought I'd round things out with a nod to all those things that can suck the life out of a withdrawal program -- especially, in this post's case, an explicit "regime" of low returns superimposed on top of otherwise normal randomness.  None of this will be very science-y or systematic; I just wanted to see what happens for one set of assumptions with simple variations of that theme.

The Basic Plan

The idea: start with a (linear) return distribution that is vaguely similar to a 60/40 portfolio, then ding it with a proxy for fees and taxes, then ding it again for superannuation risk by adding some extra duration, then, finally layer on an explicit "extra" suppression of returns for x years, and finally bring in vol a little bit (could be from trend following, could be something else) to see how much of the withdrawal program can be redeemed after beating it over the head[1].  During all of that, calculate "perfect withdrawal rates" (PWR - the withdrawal rate that would have worked with hindsight to spend a dollar of wealth to zero in a world of random returns) along the way. Then look at the 5th percentile (i.e., the place where 95% of the path-dependent withdrawal rates were better) of the PWR distributions to see: a) how much the "dings" hurts in total at that percentile, b) how much each step contributes to the total, and c) how much vol reduction can help at the end.

Aug 20, 2017

Trend Following Can Enhance Withdrawal Rates - Part 3

We can probably ditch the "trend following" part of the title.  I just wanted some continuity in titles based on the prior two posts

Trend Following Can Enhance Withdrawal Rates [part1], and


Those posts describe the original article about trend following and withdrawal rates as well as the math that the original authors and others use.  Since we determined that trend following is not necessarily the game that is really afoot but rather portfolio efficiency and since early retirees play a different game than traditional retirees, we are going to look at retirement duration effects on PWRs here. That means that this post can be better titled: "Duration effects on PWRs" where PWR means: "the maximum withdrawal rate possible over a fixed period of time if one had perfect foresight of investment returns." And by duration effects I mean what happens to the distribution of PWRs if we change the duration of periods from 20 to 50 in 3 (10 year) increments (and what happens if, as an extra test, we nudge volatility of returns down by 1 point in each of those scenarios). I had used an arbitrary 30 periods in the last post.

Aug 19, 2017

Retirement finance in Viking terms

I just ran into this in a random Netflix show.  I will not be mentioning this word to my children, especially after all the college bills have been paid.

Ättestupa 
From wikipedia the mythical practice of senicide during Nordic prehistoric times: elderly people are said to have thrown themselves, or were thrown, to their deaths. According to legend, this was done when the old people were unable to support themselves or assist in a household. Even though there are many places in the Nordic countries that are said to have been used as ättestupa, today it is not thought that the practice actually existed.  

Aug 18, 2017

Trend Following Can Enhance Withdrawal Rates - Part 2

I finally had the chance to read Can Sustainable Withdrawal Rates Be Enhanced by Trend Following? Clare et. al 2017 (though a little quickly; I'll go back).  I was surprised by how familiar it looked. Well, it was familiar because I had run into the math before.  Earlyretirementnow.com (PhD econ) did a cover of it here and I had covered him on the same topic here and here and maybe a couple other places. I have not applied any rigor to make sure it's exactly the same but it's the same in principle even if I'm off.

The Clare paper does the same thing that ERN math does: solve for a withdrawal rate using the following formula (this means that in a simulated and stochastic return environment a withdrawal rate -- "PWR" in this case, over a given period, solved for a fixed end wealth (say zero in my case) -- will be a distribution).

Since the denominator, as Clare et al point out, is a sum of a series of backwards products [1] that looks like this

Aug 17, 2017

Weekend Links - 8/17/2017 - The economics of envy and unhappiness



“if people are envious by caring about relative wealth, then free trade may make all parties richer, but may cause envious people to be less happy. If economics misunderstands human nature, then free trade may simultaneously increase wealth and unhappiness.” Burnham, Dunlap, and Stephens (2015)



IMAGE OF THE DAY



RETIREMENT FINANCE AND PLANNING

High Equity Valuations and Retirement, blog.thinknewfound.com
High valuations suggest that retirement withdrawal rates that were once safe may now deliver success rates that are no better - or even worse - than a coin flip.  This outlook is by no means a call for despair, but rather highlights the increasing need for taking control of one’s destiny by controlling both investment and non-investment factors that can improve the odds of successfully meeting one’s retirement goals.  [I haven't thought of Newfound as a retirement or lifecycle finance gurus before but this is pretty insightful] 

Using Robert Shillers data, I have plotted all possible retirement periods from 1871 in the following graphs. Comments are located within the images. Black color inside a square means "portfolio failure" (value is less than zero). All returns are real, meaning including inflation and with reinvested dividends. Diagonal lines show 30-year, 45-year and 60-year periods.  Compared to the Swedish stock market, the US markets appear much more stable, especially around the world wars. On the other hand, the 70s seem to have been harder for the US than for Sweden.  [cool charts]

We examine the consequences of alternative popular investment strategies for the decumulation of funds invested for retirement through a defined contribution pension scheme. We examine in detail the viability of specific ‘safe’ withdrawal rates including the ‘4%-rule’ of Bengen (1994). We find two powerful conclusions; first that smoothing the returns on individual assets by simple trend following techniques is a potent tool to enhance withdrawal rates. Secondly, we show that while diversification across asset classes does lead to higher withdrawal rates than simple equity/bond portfolios, ’smoothing’ returns in itself is far more powerful a tool for raising withdrawal rates. in fact, smoothing the popular equity/bond portfolios (such as the 60/40 portfolio) is in itself an excellent and simple solution to constructing a retirement portfolio. Alternatively, trend following enables portfolios to contain more risky assets, and the greater upside they offer, for the same level of overall risk compared to standard portfolios.  

Trend Following Can Enhance Withdrawal Rates

I thought this was worth highlighting outside of my usual links-post. This paper (Can Sustainable Withdrawal Rates Be Enhanced by Trend Following? Clare et. al 2017) suggests that trend following can enhance withdrawal rates asymmetrically - less negative effect with no great loss of positive outcomes. In the paper's summary (PWR is "perfect withdrawal rate" or the maximum withdrawal rate possible over a fixed period of time if one had perfect foresight of investment returns) they conclude thus:
The application of a trend following filter to the assets within each portfolio substantially improves the performance by reducing volatility and maximum drawdown without any loss of return. A result of this is much less variable PWRs, particularly through eliminating many of the lowest PWRs, but without too much reduction in the chance of unusually high outcomes. Trend following enables portfolios to contain more risky assets, and the greater upside they offer, for the same level of overall risk and significantly less maximum drawdown and sequence risk compared to standard portfolios.
I have not read the whole thing yet but as a fan of momentum and trend following I can intuit without the paper that in the presence of sequence risk, techniques to try to convert some of the worst draw-downs into something less severe can have a positive impact on withdrawal rates over the long haul.  I have seen in my own strategies -- the ones that use, among other things, trend following -- that fairly significant gains in efficiency can be had that deliver equity like returns with bond like vol (up and left, I say). For a retiree with a multi-period plan with consumption present, that is a holy grail.   Here is how they visualize it. 



Aug 15, 2017

Asset allocation and risk aversion in the absence of human capital

In a recent paper on ssrn.com (Human Capital, Social Security, and AssetAllocation) , Gordon Irlam does another superiorplus job of illuminating optimal life-cycle analysis.  I recommend the read and I will probably send it along to a child of mine in a Stanford econ program (have I bragged about that yet? I live vicariously now...) for whom it is more relevant since my own formal human capital is greatly diminished these days.  

In the article he inserts one of those pungent analytical comments I have grown to love in the ret-fin literature: "For a fixed lifespan, a constant relative risk aversion utility of consumption function, asset classes exhibiting geometric Brownian motion, and a risk free asset class, both Samuelson (1969) and Merton (1969) famously showed the optimal asset allocation is a static allocation independent of age and wealth. Their work destroyed the long held folk wisdom that one's asset allocation should decline as you age."

He goes on to provide the math: "In the absence of human capital the solution to Merton's portfolio problem may be used to determine the optimal asset allocation. The optimal solution is independent of age and portfolio size. The proportion of equities that should be held is given by: π = (μ - r) / (σ2 . γ) where μ and σ are the equity geometric Brownian motion drift [that's a random compounding/trending process i.e. a stock market random walk] and volatility, r is the risk free rate of return, and gamma the coefficient of relative risk aversion. If ra and σa are the mean annual equity rate of return and volatility: μ = ln(1 + ra )  [and]  σ = sqrt(ln(1 + σ2 / ((1 + ra ) 2 )) For my scenario, after taking into account management expenses, μ = 6.2% and σ = 16.2%. This then gives 34% and 67% equity for coefficients of relative risk aversion 6 and 3 respectively. By way of approach verification, in the absence of any human capital related income, my numerical approach also gave values of 34% and 67%."


Aug 11, 2017

Weekend Links - 8/11/2017


When you view the illiquidity of assets, like PE and VC, as a commitment device then they make a lot more sense. -- Tadas Viskanta 



RETIREMENT FINANCE AND PLANNING

Stress-test Your Financial Independence,  tenfactorialrocks.com
On one hand is a thrill of finally reaching financial independence or early retirement (FIRE).  A long cherished goal for many aspirants.   The 4% rule is a widely used standard to mark this accomplishment or if you wish to read up and become very conservative, you could use 3.27%, but who’s quibbling? On the other hand is a real worry you may outlive your portfolio.  The media fuels this fear constantly. It’s hard to remain unaffected. 

The main reason why I think more Americans aren’t doing financially better is due to a lack of education. Why aren’t personal finance fundamentals indoctrinated in kids by the 12th grade, I don’t know…To be between 56 – 61 and only have $163,577 in your retirement account means you are going to be living a spartan life once work stops. If you spend just $33,000 a year in retirement, your money will run out after five years. Hope must come from Social Security benefits to help them make it through the golden years. 

The researchers find a straight-line relationship between the percentage of people in a country who are working at age 60 to 64 and their performance on memory tests. The longer people in a country keep working, the better, as a group, they do on the tests when they are in their early 60s.  

[normally, I am not all that interested in insurance companies but it's worth keeping an eye on how one's potential counterparty views risk.  Interest rate and longevity risk shouldn't surprise, I guess.  Given that we have lived through a decade where the advantage has (except for the bull market) not been strictly in the retiree's favor, I'm hoping that will shift…soon) ]


Aug 9, 2017

Kelly Criterion vs. a short options strategy

I wrote something in the past on the Kelly criterion (KC) which is an algorithm for optimizing the geometric return (or, rather, optimizing the bet sizes) in a sequence of independent gambling wagers
where the wager-er has an real edge and known odds. Note that I am not an expert on this and that the countervailing theory that economists seem to like is utility based. I just wanted to try it out on a short options strategy, where my risk return is upside down, to see what happens. [1]

KC has some affinities with investing propositions and particularly systematic rules based systems and especially for sizing the risk of trading positions. It doesn't translate perfectly but it's usable.  The basic distilled math is: size of bet = edge / odds or more specifically f = (bp-q)/b where f is the fraction to bet, b is net odds received, p is the probability of winning and q is the probability of losing or 1-p.

Since there are a bunch of reasons that investing is not the same as gambling (usually) the full Kelly criterion can be a little dicey while still mathematically interesting.  Here is an off-the-top-of-the-head list of what one might worry about:


Aug 2, 2017

Links - 8/2/2017

Early edition...gotta do some college tours...


QUOTE OF THE DAY

Crash risk has been high throughout the post Financial Crisis period, yet there has not be a crash. mrzepczynski 

…when will the damn break? Or maybe we should be asking will the damn break? These dizzying returns will stop at some point… but when that is — is the million dollar question. Which camp are you in? rcmalternatives.com 



RETIREMENT FINANCE AND PLANNING

It is just kind of silly to assume that your expenses are going to remain constant in Real Dollars from year to year.  At some point during your retirement, you or your spouse is going to decide that your house needs a new roof, the kitchen needs to be remodeled, you need one or more new cars, etc.  As the old saying goes, “Expenses Happen.”  And these larger expenses are unlikely to fit into your recurring annual expense budget.  This is why
we suggest that you establish reserves for unexpected expenses and other non-recurring expenses (in addition to your reserves for Long-Term Care and bequest motives, and general Rainy Day Funds to dip into if your investments perform poorly).  To the extent that these expenses are covered by reserves for this purpose, there may be no effect on your annual recurring spending budget (although you may have to build the reserves up again for the next unexpected expense, and this could reduce your annual recurring spending budget). [I have not yet found a reason to disagree with one of Mr Steiner's posts. I have written before that spending is, contra retirement finance papers written by people that have not retired, not smooth it is a random variable which has consequences.]    

Regular readers here might be disappointed that I still don’t have a consistent personal “system” in place for withdrawing retirement income. I’m an engineer, after all. I prefer to solve my problems once and for all, by automating a solution. It would be very appealing to simply have a retirement “paycheck” show up every month, on autopilot, no human intervention or decisions required. And that’s my long-term goal. But the reality is that I’m not there yet.

As a byproduct, using our own estimates, we are able to confirm the intuition shared by many in the financial planning community. Namely, given the empirical evidence on the cost structure of annuities, the adverse selection implicit in annuity mortality tables together with the long- run propensity for equities to outperform fixed income investments, otherwise known as time-diversification, it makes very little sense for consumers under the age of 80 to annuitize any additional marketable wealth. In essence, the rate of return from a life annuity can easily be "beaten" using alternative investment assets. The exception to this rule is the event in which (mean reverting) interest rates are extraordinarily high or when consumers have private (asymmetric) health information that would lead them to believe that they are much healthier than average, both of which rarely occur.  

Aug 1, 2017

Taking Tomlinson's annuity logic out for a test drive for a 59 year old

In this article (What Advisors Need to Know About Annuity Mortality Credits) at advisorperspectives.com, Joe Tomlinson lays out his explanation of Mortality Credits and how to use them in decision making around annuities.  He also makes a case that the environment for annuities isn't as dire as past research makes it sound. I don't know anything about that. The last thing I read was about annuities, SDP, and optimal annuitization age by G. Irlam where he says that if one is making an all or nothing wager on annuities then sometime before 80 makes sense and probably earlier if legging in. That and there are combinations of age and wealth that will make it more optimal to annuitize than other combinations.  I'm guessing that whether Joe is right or not in this article, and I'm sure he is, age 59 is just a little bit too early any way you cut it unless one were to be hyper-risk-averse.

Here I just wanted to make sure I understood Joe's math and methods for my future use.  I tested it out on me. Here are what I took to be the steps:

1. Look at the SOA mortality table. I couldn't make sense of the longevity extension adjustments they (SOA) do but the basic table I get. I can transform that table for a given age and it's probably close enough without the adjustment for this post's purpose. For a 59 year old the mean expected value is age 85.9. The median is around 86 and a half and the 95th percentile is over 99.  We are using the mean later for pricing a bond with similar duration.  Note that the SOA data assumes a healthier pool because of selection bias among other things. I suspect there is a little bit of an extra conservatising gouge in there too since the main users are more often than not insurance companies...but maybe that's too close to conspiracy theory territory for today.

2.  Price an annuity.  I used AAcalc.com to estimate a payout for a 59 year old Floridian and a money's worth ratio of .95. Using a corp bond assumption I come up with $5734 for a payout on $100k.  I validated that using immediateannuities.com and had at least one quote for a simple life annuity of 5712. Close; let's use aacalc 5734.  I don't have access to CANNEX data.

3. Weight the annuity price by survival probabilities.  Take the percent remaining alive estimate in the 59+ age vector and multiply by the annuity payout.   Combine that with the 100k purchase and perform an excel IRR calc. I do this and come up with 3.07%. Recall that the industry term Payout would be ~5.73% which can be considered, depending on how you look at it, meaningless.

4. For some year calculate the 1 year survival probability. For a 59-60 step in this scenario that is 99.58%.

5. Determine the mortality adjusted return (MAR) for that same year.  Take the IRR and divide by step 4 so: (1+.0307)/.9958 - 1 = 3.50%

6. Figure the mortality credit at age.  Mortality adj return minus the IRR: .0350-.0307 = .0044 mortality credit (rounding effects).

7.  Price a bond for similar duration.  The diff between mean mortality and 59 is close to 27 years so let's look at the 30 year treasury which was yielding ~.0287 today.  Add a little fudge for a spread (Joe uses 1%+). So lets call a yield estimate at ~.0387 or more.

8. Compare the bond and the MAR.  bond = .0387  MAR = .0350 so the difference is -.37%

9. Decide about the annuity. If the result, which includes a little fuzz, is zero or negative, that is supposed to mean no-go for the annuity decision.  The result? No go. Maybe next year...or age 75.