Perfect withdrawal rates, trend following, and stochastic longevity

In the post right before this one I linked a paper from the cfa inst. by Andrew Clare and his collaborators on sequence risk and trend following.  I have to admit I haven't read it yet but I have printed it off so I can read it later on a plane flight because I think it'll be interesting.  But before I read it -- since I know he uses the perfect withdrawal rate method (PWR: what withdrawal rate given a particular sequence of returns would work out perfectly to result in a FV of zero, I think is the right way to put it. I'll check on that later) -- I wanted to run a little test with my own PWR tool and my own strategy's trend-informed return distribution to make sure I understand what is going on before I actually start reading.  I figure it'll help me get what he is saying more efficiently.  In addition I want to add an embellishment that I have not seen him or anyone else use: I make the periods over which PWR is calculated stochastic in a way that matches actuarial longevity similar to what is in the SOA annuitant table for me at age 59.  This is not a rigorous analysis by the way, just a quick-hit to see what happens.

Reducing Sequence Risk Using Trend Following and the CAPE Ratio, Clare et al. 2017 CFApubs.org

Reducing Sequence Risk Using Trend Following and the CAPE Ratio, Clare et al.

[abstract] The risk of experiencing bad investment outcomes at the wrong time, or sequence risk, is a poorly understood but crucial aspect of the risk investors face—particularly those in the decumulation phase of their savings journey, typically over the period of retirement financed by a defined contribution pension scheme. Using US equity return data for 1872–2014, we show how this risk can be significantly reduced by applying trend-following investment strategies. We also show that knowing a valuation ratio, such as the cyclically adjusted price-to-earnings (CAPE) ratio, at the beginning of a decumulation period is useful for enhancing sustainable investment income.

http://www.cfapubs.org/doi/abs/10.2469/faj.v73.n4.5

Portfolio longevity, defective distributions and some small thoughts on fail magnitude

It's possible that I am skating on thin ice here but I wouldn't even be on this part of the lake if Prof Milevsky hadn't encouraged me a bit.  In particular, when we were talking about portfolio longevity he schooled me on defective distributions and the effects of things like returns and vol on that type of distribution.  I mean I'm in my 60th year and he pressed and quizzed me like a sophomore in the second row of an intro finance class and it was just the two of us in a hotel coffee shop.  "What is the name of this distribution?" [mumble] "try again" [mumble] "try again" [pause] "the answer is that it is portfolio longevity in years...now what happens to the shape if we increase vol?" [uh, it shifts left?] "ok but what happens to the defective right side where we count the number of occurrences of infinite longevity?" [uh, it goes down?] "yes, now again, let's look at...." I didn't think I was going to sweat but it was like being 19 again in the crosshairs of the seminar prof. Whew.

Some thoughts on investment horizons

The fact that stocks usually go up makes permabulls look like idiots once in a while and permabears look like geniuses once in a while. -- Michael Batnick

Michael Batnick is one of the better bloggers writing out there today.  I think the Rithotlz org must force their crew to write and write well.  It must be some kind of organizational totalitarian positive force thing.  In this post "Playing the Odds" Michael's main point, to which he is taking the other side, a view of which -- the other side that is -- I am sympathetic, is that if you (you who are selling investment or advisory services) say the sky is falling often enough, when the sky falls just a little bit, not only are you vindicated but your marketing is now officially effective for the next 10 years. 

My thoughts were elsewhere, however. I was thinking about investment horizons.  Here is one of the post's charts with some emendations. To quote Michael on his intro to the chart "Sam Ro is fond of saying “stocks usually go up.” The *chart below supports the statement that historically over time, stocks usually did go up. This is why it makes good sense for financial pundits to play on the bullish side." :

What I was thinking about when I looked at this were two scenarios: A) investment horizon of greater or equal to 20 years with no spending constraint, and B) investment horizon of less than 20 years but more than 10 and there is a spending constraint[1].  It is a little ambiguous, given the chart and the setup, on what to think about these scenarios.  Scenario A is probably similar to a young person accumulating or an institutional investor.  Scenario B is more like a 60 year old that plans to annuitize some or all of a portfolio at around age 75.  Both scenarios can likely handle a decent amount of equity risk but Scenario B probably needs to think pretty hard about the plan or at least "plan B[2]" if bad things happen in the intervening years.   

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[1] Maybe also throw in something like our current market environment with iffy return expectations.

[2] no idea what plan B is, just pointing out some horizon risk.

Weekend Links - 10/26/17

QUOTE OF THE WEEK

In the middle of the 20th century, the US economy had the enormous advantage that its workforce was by far the most skilled in the world. That advantage has largely dissipated. Tim Taylor 

GRAPHIC OF THE WEEK

RETIREMENT FINANCE AND PLANNING

Replacing the Failure Rate: A Downside Risk Perspective, Javier Estrada

The variable proposed here, downside risk‐adjusted success (D‐RAS), addresses this shortcoming by taking a downside risk perspective, measuring risk with the semideviation, and therefore with volatility below a chosen benchmark. This modification leads to the selection of more plausible strategies than those selected by both the failure rate and RAS. 

The 3 Great Misconceptions About Retirement Saving, Darrow Kirkpatrick

What did we give up to retire early without having several million on hand? Two things, primarily: owning a large home, and international travel. Yes, home ownership is very important to many people, part of their vision of the “good life.” Just understand that owning a plush home is an emotional need, and often an expensive one at that. Likewise, international travel is a prominent image in retirement scenarios: white-clad seniors frolicking on exotic beaches. For me, at least, this too is an emotional or symbolic need. I’ll get a lifetime of enjoyment playing in our western mountains, mostly within a day’s drive of our home in Santa Fe. And, if you’re willing to search carefully, and visit when the crowds are gone, you can even find an exotic beach in the U.S.

In Search of the Optimal Retirement Planning Strategy, Ken Steiner

In his post, Mr. Kitces deftly summarizes the three Collins/Gadenne geometric metaphors and his understanding of the benefits and limitations of employing each type of retirement planning strategy.  In response to his question “What is the optimal shape of retirement planning?” Mr. Kitces concludes that the best approach for retirement planning may involve incorporating elements from all three shapes.  

What I use in my own process - draft 1

[Note: I say draft 1 because I know the second I press the publish button, things will change.  I say process because that's what retirement is.]

Back in July (2017) I started to write a post about the story of how I ended up in a semi-voluntary early retirement at age 50 which is part of the backstory on why I do this blog at all. That was fun for a while but after about 7000 words and 14 pages of unstructured nonsense even I started to lose interest.  I couldn't imagine anyone else slogging through it for more than a page.  While the story itself is pretty good if told right, and could maybe fall somewhere between tabloid grocery-store-style gossip on the one hand or maybe Dostoevskian-like pathos (I'm thinkin', though, that maybe bathos is a better word) on the other hand -- and keep in mind, this is a story that probably should be told at some point -- I still had two problems:  one, most of the protagonists of my story are still alive so maybe now is not the right time to open up on that front and two, I lost track of the main reason I was creating the post in the first place.   The main reason at that time was to delineate, since I am trying to write a retirement finance blog, the main tools I personally use to navigate this stage of retirement (before age 65) that I have been in for a while.  I was assuming that that might be useful to someone else, but in the end who knows?  We all have different situations, capabilities, and inclinations.   

But, let's give it a shot.  Here, then, in short form, or at least shorter form than I first tried, are the main things I bring to bear on my own situation, which at age 59 is starting to look a little more like a normal retirement rather than what felt like a too-early retirement at age 50 when I started back in 2008-2009: 

Some effects of longevity assumptions on ruin estimates

In shaking out my lifetime ruin approximator tool, the one that mimics the Kolmogorov differential equation for evaluating the lifetime probability of ruin (LPR), I had forgotten to look at the effect of longevity assumptions on ruin estimates.  I know from some past posts that, for a 60 year old, if I plug in mode (M) and dispersion (b) parameters of 85 and 10 it more or less closely fits the Soc Security life table for someone my age (keep in mind that that is a "hacker close fit" not an actuarial science close fit) and that the parameters 90 and 8.5 roughly fit a curve derived from the Society of Actuaries Annuitant mortality table for someone my age.  The former can maybe be characterized as an average expectation across all of us while the latter is an expectation for a generally wealthier and theoretically healthier cohort that self-selects themselves into annuities.  They tend to live longer, hence that becomes a "real world" conservative assumption, data-set or baseline.

I'll use those two assumption sets (SS and SOA)  as my boundaries for an "average" longevity assumption and "conservative" longevity assumption.  Or at least for when we are working with stochastic longevity.  In real life I often use a fixed age of 95 or more if I want to be both simple and hyper-conservative.

Weekend Links - 10/19/17

QUOTE OF THE WEEK

…for psychologists seeking to understand the apparent nexus of success and abuse, Weinstein’s apparent downfall is just the tip of an analytic iceberg.  -- Persaud & Bruggen   

GRAPHIC OF THE WEEK 

RETIREMENT FINANCE AND PLANNING

Why a Retiree Might Keep Going Back to that ATM, Dirk Cotton

Households with limited savings, on the other hand, may well find that their non-discretionary spending gradually overwhelms their portfolio spending. Even though the portfolio would be doomed by continued spending, they will still need to pay for groceries and housing and may have little recourse other than to keep spending and pray for a tremendous bull market. They may find themselves in a “spending trap” in which they must sustain their level of spending simply to meet non-discretionary spending demand with the knowledge that doing so will most likely soon bankrupt them…Sometimes a retiree may keep returning to that ATM for as long as possible because she has no better alternative. That's rational.  

Life-Cycle Finance in Theory and in Practice, Zvi Bodie [2002]

The paper suggests ways that advances in the theory of finance combined with innovations in financial contracting technology might be used to improve social welfare by designing and producing a new generation of user-friendly life-cycle products for consumers. It contrasts the old Markowitz single-period paradigm of efficient diversification with a new Mertonian paradigm that takes account of multi-period hedging, labor supply flexibility, and habit formation.  

Last ruin game (with CBOE iron condor index)

This is an abbreviated post. All assumptions are as in previous posts.  This time I am putting a normal return series (8% nominal with 10% sd) against the CBOE iron condor index (~7% nominal, 7.2% sd) which represents the concept of putting on a bull put spread and a bear call spread to get relatively high probability returns in low vol environments. I have no opinion on this strategy I am just using it as an alternative return profile to see what happens in a ruin probability experiment. 

Another game with non-normal returns (CTA index)

When I met with Professor Milevsly, one of his comments was that my code -- the code that replicates the Kolmogorov equation for the lifetime risk of ruin by a brute force application of the core probability principle -- has at least some advantages over the PDE because I can model non-normal returns. This, like the last post, is another turn in that game just to see how it goes.  His example at the table was a collared portfolio but one can just as easily demonstrate the principle with any distribution that leans away from Gauss. Here I am going to look at the CTA index and add it to a blended portfolio, a little like I did in 2010 in real life with some private placements.  According to the last paper I read on momentum I might be able to do this with a continuous distribution using chi squared math since that seems to have some affinities with trend following returns.  But that is some other day...

What would happen if I allocated 100% to my alt-risk strategy (in terms of ruin risk)

Here was an interesting little exercise with results I guess I wasn't expecting.  None of this is very real so I don't know if I can attach much meaning to it.  The question I asked myself was what would happen to my ruin estimate if I allocated 100% to what little I know about my private Alt strategy's too-short return profile.

First, without getting too far into the nitty gritty, my alt strategy is something like 30/50/20 credit risk, fixed income momentum, and volatility risk via short options -- though that internal structure changes and drifts a little more than I might want.  The goal was to get a moderate return and low vol profile that is at least as efficient or more so than a plausible multi-asset allocation when looking backwards at history. The purpose was to nudge my overall efficiency up and left a little bit. This I have mostly achieved since the beginning of 2012 shortly after I started this thing. I'd love a little higher return but it is what it is. The idea of allocating 100% to my Alt came to me just as a fake hypothetical in order to explore some things I've been working on related to ruin estimation processes.

For comparison I'll use the Vanguard 60/40 mutual fund since it might represent a reasonable baseline allocation like my own might be in practice.  This is a convenient fiction for posts like this so I'll go with it.

Paper on Momentum and Trend Following

Understanding the Momentum Risk Premium:An In-Depth Journey Through Trend-Following Strategies, Jusselin, et al. September 2017. 102 pages. SSRN


From the concluding remarks: "The momentum risk premium has been extensively documented by academics and professionals. There is no doubt that momentum strategies have posted impressive (real or simulated) past performance. There is no doubt that asset owners and asset managers widely use momentum strategies in their portfolios. There is also no doubt that the momentum risk factor explains part of the performance of assets. With the emergence of alternative risk premia, momentum is now under the scrutiny of sophisticated institutional investors, in particular pension funds and sovereign wealth funds. Therefore, Roncalli (2017) supports the view that carry and momentum are the most relevant alternative risk premia since they are present across different asset classes, and must be included in a strategic asset allocation. Nevertheless, the development of alternative risk premia has some big impacts on portfolio construction, because the relationships between these strategies are non-linear. In this case, the traditional diversification approach based on correlations must be supplemented by a payoff approach. However, most risk premia have a concave payoff. The momentum risk premium thus plays a central role as it exhibits a convex payoff, and we know that mixing concave and convex strategies is key for managing skewness risk in bad times. Sophisticated institutional investors need to profoundly understand these new risk premia in order to allocate them in an optimal way."

From the Abstract: "Momentum risk premium is one of the most important alternative risk premia. Since it is considered a market anomaly, it is not always well understood. Many publications on this topic are therefore based on backtesting and empirical results. However, some academic studies have developed a theoretical framework that allows us to understand the behavior of such strategies. In this paper, we extend the model of Bruder and Gaussel (2011) to the multivariate case. We can find the main properties found in academic literature, and obtain new theoretical findings on the momentum risk premium. In particular, we revisit the payoff of trend-following strategies, and analyze the impact of the asset universe on the risk/return profile. We also compare empirical stylized facts with the theoretical results obtained from our model. Finally, we study the hedging properties of trend-following strategies."

Random Quote: "In fact, we think that there is a misconception about CTAs. Many people think that CTAs are good strategies for hedging the skewness risk of the stock market. In reality, trend-following strategies help to hedge drawdowns due to volatility risk. For instance, CTAs did a very good job in 2008, because the Global Financial Crisis is more a high volatility event than a pure event of skewness risk. However, it is not obvious that CTAs may post similar performances when facing skewness events. For instance, the performance of CTAs was disappointing during the Eurozone crisis in 2011 and the Swiss CHF chaos in January 2015. "

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Most of the paper is over my head but it was still worth reading the few parts I could understand.

The 2017 RiversHedge 20 Best-of Awards

Here are the RiversHedge 2017 "20 Best-Of awards."  I suppose the language here is a little tongue-in-cheek but I am dead serious about my recommendations. These are the people that have influenced me and made a positive contribution to me, my family and, I'm guessing, an awful lot of other people out there, too.  This is a tough domain to work and write in so all of it is appreciated.  I know some folks are flogging blogs because there is an economic incentive in there somewhere but on the other hand some are just doing it because they have something to say that is helpful or maybe because they just have curious and communicative souls.  Bless them.  Maybe next year I'll offer T-shirts or something but this year it is just for fun.

2017 RiversHedge Best-of Awards

1. Best life-cycle blogger that leapfrogs ideas from "academia and the best practitioners" straight to retail investor-retirees. This, by the way, is a serious calling in my opinion and vastly underappreciated. I aspire to be one of those that helps bridge that kind of gap.  Dirk and I have corresponded and he is a very solid and friendly guy. I read everything he posts as soon as he posts it.

Dirk Cotton, TheRetirementCafe

 2. Best real retiree that has quant chops and serious purpose. Darrow and I have corresponded as well and I think he may also win the "blogger I most want to fly to Santa Fe and have a coffee with or maybe take a hike in the New Mexico hills with" award. He can analyse with the best of them but he also lives a life of purpose.  I aspire to be like him when I'm older. Oh, yeah, that's right...I am older.

Darrow Kirkpatrick, CanIRetireYet

3. Best ETF strategist that also gets the life-cycle part of life-cycle finance.   I have corresponded with Corey and he appears to be a very qualified and insightful hard-quant strategist.  His own blog posts aren't just solid, they appear to be accelerating.  I look forward to more.

Corey Hoffstien, ThinkNewFound 

Will un-retire (work) for health insurance...

... no really, seriously, if you have any ideas or want to work something out, let me know.  Here are the last 7 years with 2018 projected. A 22% compound rate!?!  I wish I could invest!  I can't see where this is going to end.

On Wong's "Random Walk Part 4"

This is a note I jotted down after reading

Random Walk Part 4 – Can We Beat a Radically Random Stock Market?
by Theodore Wong, 10/9/17, Advisor Perspectives

This series of 'papers' on markets and vol and risk is pretty good.  It takes a fresh empirically-oriented look at how risk and return work in practice and throws in a decent dose of probability thinking for good measure.  That's always a good thing, right? This last paper ties his thoughts together.  It was pretty interesting as far as it goes but I had a tiny bit of ambivalence about it at the end and I wasn't sure why so I decided to introspect and see what was holding me back.  Here is what I think I was thinking as I hesitated to embrace it fully. Most of this is pretty minor:

Weekend Links - 10/12/17

QUOTES OF THE WEEK

"I really wish my dad had spent more time at work instead of with me when I was a kid." <-- Said no one, ever. Vhalros onRedditt

But yeah, if you aren't a raging failure of a human being and actually enrich your children's lives, then [early retirement] is definitely the best thing you can do with your time. Csp256 on Redditt

[comment - I retired early to care for my kids so this is a wee bit of self-serving self-affirmation.] 

GRAPHIC OF THE WEEK 

The Shape of Ruin Risk
60 year old with moderate assumptions for net real returns
- RiversHedge

RETIREMENT FINANCE AND PLANNING

Two smarter ways to determine how much you can safely withdraw funds in retirement, The Globe and Mail

If you want to see a group of financial experts brawl, ask them how much it's safe to withdraw from your investment portfolio each year in retirement. One of the most common answers is to suggest some variation of the 4 per cent rule. Under this guideline, a retiree would take out 4 per cent of his or her original portfolio in the first year and continue to withdraw the same amount – but adjusted for inflation – each subsequent year. The 4 per cent rule offers the undeniable attraction of simplicity. But the more you examine it, the more unsatisfactory it becomes.  

Starting to look a little closer at my normal return assumptions

I've been using in my code a convenient fiction for returns by using the R normal distribution function.  How many times have I heard from other that returns aren't normal. Of course not. I know that but "they" are not trying to code while my kids want dinner. I use it because it is easy and I don't have to think too much.  I thought I'd take a closer look with respect to my recent ruin risk estimates.  This is not scientific or rigorous this is just another one of those "what does it look like" things.

A thousand years of the 4% rule: the naked, ugly glory of it all

The Estimates

Let's start with some ruin estimates just to set the stage. Here are 5 methods of estimating lifetime risk of ruin for a plausible set of assumptions[1] for a 60 year old with a balanced portfolio and a 4% constant spend:

Method	Age	Longevity	Returns	Vol	Spend	Ruin est
sim	60	95 fixed duration	Hist 50/50	hist	4%	0.270
sim	60	Soc Sec table	Hist 50/50	hist	4%	0.100
sim	60	SOA Annuitant	Hist 50/50	hist	4%	0.142
JPA	60	Gompertz 90/8.5	4% net real	10%	4%	0.127
Kolmog.	60	Gompertz 90/8.5	4% net real	10%	4%	0.132

Ok, so there is some moderately low level of risk here, nothing too scary except maybe that to-95 estimate and even that is probably manageable with some spending flexibility, some good portfolio design, and maybe a little tactical allocation thrown in if that can actually be pulled off.

The Quiz

Tuesday with Moshe

I had the privilege and honor this morning of being able to spend a half hour one-on-one in person with Moshe Milevsky.  That was great because his book (7 Equations) more or less triggered my ret-fin explorations over the last five years as well as this blog.  I had happened to email him a few weeks back to ask what he thought my joint probability approximation[1] was actually doing in the context of his paper Ruined Moments in Your Life: How Good Are the Approximations? [2003] and he very generously offered to explain it to me in person since he was giving a presentation about 10 miles away from where I live.  That was today.

My goal was to come away with at least three things: 1) figure out where my ruin approximation approach fits into the scheme of things in terms of the ruin approximations [approximations to the Kolmogorov partial differential equation (PDE) for ruin] listed in his paper, 2) get more insight into my probability density function (pdf) for portfolio longevity since I had some confidence issues due to the fact that it had some weird properties and I don't have a formal background in stats, and 3) I wanted a better verbal interpretation of the third term of the Kolmogorov equation.  That, and I also wanted to get a selfie with him for my twin sister who's spent 40 years in the financial services industry but I chickened out on that since at the end he was moving pretty quickly towards his next meeting.

What did I get from my chat?

The Shape of Ruin Risk

Using the setup, assumptions, and conclusions from the last post (A type of heat map of ruin risk arising from: age, allocation, spending, and return distributions) I thought I'd do one of those 3D visualization things to see what it looks like using one more dimension.  This graphic is based on the return, vol, allocation, and spend assumptions in the link but here it is limited to just age 60 (I only have ~8 months to go).

The chart can be characterized as the fail rate for different allocations to risk given the parameters in the link (one blue line for, say, a .03 spend rate) and then replicated for each spend rate from .03 to .07 in .01 chunks.  It was tricky to get a decent rotational perspective.  I thought about an animated gif but decided the effort to reward ratio was not in my favor. 

Fig. 1 - lifetime ruin risk for different allocations and spendrates

Thaler

Congrats to Richard Thaler for his  Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel for 2017.  To recognize this occasion let's recycle one of his retirement planning quotes:

For many people, being asked to solve their own retirement savings
problems is like being asked to build their own cars.
—Richard Thaler, University of Chicago

A type of heat map of ruin risk arising from: age, allocation, spending, and return distributions

Since I have been playing around with ruin risk math lately (I feel compelled to asterisk this with links to why ruin risk is often misused and misunderstood, but won't) I thought I'd try this post.  I did this for no other reason than I wanted to see what it looked like and because I can.  What I am trying to do here can be achieved by other means -- like simulation or my new joint probability tool or other analytic techniques -- of course but I chose to use the spreadsheet version of the kolmogorov equation I got from Prof. Milevsky because it is simple and fast to do the exercise.  Simulation would have taken me a couple days at least.  What I lose in customization of circumstances I gain in time spent with my kids.

The thing I am trying to do.

The thing I am trying to do here to see what it looks like to map out a color-coded ruin risk calc based on combinations of parameters for: age, returns, volatility, asset allocation, and spend rate.  I'm sure something like this has been done before but what the heck, I had a spare couple of hours.

My ruin approximation tool against 96 test conditions comparing it to the K equation

I found some minor coding errors in my tool (remember it estimates -- in order to mimic the Kolmogorov equation -- the lifetime risk of ruin using the joint probability of: a) a lifetime net-wealth "ruin" process and b) a mortality process using gompertz math ) so I thought I'd do a more comprehensive test of the resulting code changes to see if there were any approximation weaknesses.

I created 96 test conditions by varying:
- net returns between .03 and .05
- std dev beween .10 and .20
- start age between 60 and 80
- Mode/dispersion of mortality pdf between 85/10 and 90/8.5
- spend rates from .03-.06

The result, when I did a simple point difference between the baseline K-equation and the approximation tool (I hope that's the right way) for the 96 conditions, was a mean and median of difference hovering around zero (good) and a standard deviation of less than half a point (pretty good).  Min/max are both inside a 1 pt difference.  I'm not sure yet if there are pockets of difference in there that matter but the higher "volatility" conditions seem to have a little more variance from baseline.  Most of the variance, though, more likely comes from the fact that the lifetime process for a wealth fail is in fact a mini-sim with results that are a moving target so maybe the iterations can be nudged up a bit to fix that. 

All in all I think I can call this a wrap.  I not only successfully replicated a well known PDE with something way easier, I now have a way to explain the Kolmogorov PDE if I ever write up a draft 2 of what I wrote before on that.  In general I think I have a much better idea of the basic concepts and processes behind ruin estimation which was one of the original goals I started out with in the first place.

A CFA Institute post on volatility...

Here is a blog post from the CFA institute about whether volatility is risk. That is a good question and something we have touched on before.  It is a very short cover and has some constructive, additive points on the topic.  On the other hand it biases, in my opinion, against spenders a tiny bit though it does, thankfully and to his credit, not exclude them from the analysis.  It's just that he says that for them it's more or less not that big of a deal. I disagree.  It is entirely possible that spending and expected returns will in fact dwarf the effects of vol but neither is vol trivial for us. It seems dumb for me to "digest" a one page article but digest we will (it'll take one minute to read so click thru too). Here are some of the main points from the linked post:

1. Volatility is one of the biggest risks in investing according to conventional financial wisdom. A small minority of investors, mostly value investors — a group to which I belong — take a different view. We think it is the probability of permanent capital loss, not volatility, that constitutes the real risk.  Neither perspective is entirely correct.
2. Warren Buffett famously said that as a long-term investor he would “much rather earn a lumpy 15% over time than a smooth 12%.”
3. Long-Term Investors with Strong “Stomachs” -- volatility is not a risk
4. Short-Term Investors -- Volatility is a primary risk
5. Long-Term Investors with Weak “Stomachs” -- should treat volatility as a risk for behavioral reasons
6. Long-Term Investors Who Consistently Spend Small Portions -- Volatility matters to some degree, but it is not the main risk.

Weekend Links - 10/5/2017

QUOTE OF THE WEEK

"Everything simple is false. Everything which is complex is unusable."[1]  Paul Valéry 

GRAPHIC OF THE WEEK 

http://conversableeconomist.blogspot.com/2017/09/interview-with-lawrence-katz-inequality.html

RETIREMENT FINANCE AND PLANNING

What Age Do Most People Retire In America? Financialsamurai

The reason why most Americans are able to retire by 66 despite so little wealth is due to Social Security, a traditional pension, and retirement work plans. LIMRA reports that some 41% of retirees have annual income less than $25,000. Of retirees with income over $50,000 a year, about 80% draw from a pension or retirement plan… Unfortunately, virtually nobody under 40 is going to have a traditional pension any more.  

What’s Happening to U.S. Mortality Rates? Boston College

The cycles over the last 40 years have reflected developments in medical drugs and technology, access to health care, and risky behaviors such as smoking and those associated with obesity. The gains in mortality improvement have been skewed toward those with higher educational attainment and more income...The key debate is whether the future will mirror the past, with average rates of improvement of about 1 percent, or whether the pace of progress will slow. 

Kelly bet sizing for me with parameter uncertainty

Kelly criterion math is fun to play with because it has some neat properties and shows up in the literature as the way, ex-utility function conversations, to maximize geometric mean returns over time.  Even Markowitz in his 2016 book, vol 2 has some interesting (consistent with mean-var, even) things to say about it.  Given a demonstrable strategy edge it's totally the way to fame and fortune, right? I want to think so because after about a billion years of trying to trade I finally have a strategy with a small edge and I want to cash in and be a big shot (not really, but that'll be the set up in this post; I know for sure at least that I have been undersizing risk, though, and I want to try and fix that).  But wait, not so fast.  Forget that the strategy can be hair raising -- because in the intermediate years between the now and the later that it takes the strategy to work one's capital can get pretty low which brings behavioral issues to the table; also it may take more years than a lifetime to recover -- and  focus on the fact that edges (and odds) are not immutable facts of nature, they are transient ephemeral things that are either illusions or if not illusions at least not very stable.  If one's parameters are unstable what is to be done?  And if one has simultaneous "bets" along with parameter uncertainty, it's even worse, right? I suspect there is a whole body of literature out there that does all sorts of super-math on this kind of thing but that's not the plan today (contra my usual style I have not bothered to look but I should; I think Aaron Brown has written some things on this).  Today I'm just going to do one of those amateur hack things to see what might work for me as a retail investor for what I am trying to do.

Here is the theory behind my joint probability approximation (JPA) tool

I do not have a formal background in statistics and maybe less so in calculus. Since my new tool, what I am calling the joint probability approximation for lifetime ruin (JPA)[1], matches the output of the Kolmogorov equation pretty well, involves the combination of two PDFs for longevity and portfolio ruin, looks and smells like a practical application of  probability theory and integral calc, and at the end of the day works pretty darn well, I was guessing that it had some good theory behind it. It looks like this below (e.g., equation 20) is the theory which makes more sense now that I've coded it (but made no sense at all the first time I read it a couple months ago). This post, by the way, is for those few that might actually be interested in this kind of thing -- which might not exactly include the family and friends and otherwise supportive others that surround me here in FL[2]:

[This is from section 2 (The Probability of Lifetime Ruin. pages 2-5) of Ruined Moments in Your Life: How Good Are the Approximations?  by H. Huang, M. Milevsky and J. Wang York University1, Toronto, Canada 1 October 2003]

I had read this piece a few months back when I was trying to understand ruin and the Kolmogorov equation. I have to say that then and now most of this goes over my head.  On the other hand I will also say that now, having done it in practice in real life, it seems like it is actually quite a bit easier to do than the formal notation might imply.  I mean it took about an hour or two and one (one!) page of code to do what theorem/proof three above seems to imply.  And now that I've done that project, the calculus is a little easier to read and the aside about g_w(∞) makes perfect sense -- where before I would have no idea what he was talking about -- because that is precisely one of the things I did to make it work.

Now...if anyone wants to license my code, I'll warm up my ABA number for you.

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[1] I'm calling it joint because I am multiplying two probabilities and summing the product over a range so it seems like the right thing to say.  If there is a better way to describe this formally let me know; reread my first sentence.

[2] feel free to email me if you are interested. I'm just winging down here in la la land. I need a little help here and there and now and then with the large body of subject matter where I often find myself flying blind.

Swedroe on the Volatility Risk Premium

Here is a good cover on the Volatility Risk Premium and why I've been trying to play this game:

Swedroe: Volatility Risk Endures

On why the 4% rule was always a little bit of a head fake

It seems like an awful lot of people, myself included, have taken shots at the 4% rule (or should we call it what he later said was 4.5%?), many but not all of them for the right reasons.  Google "Bengen and 4% rule" for background on what it was and why it was so I don't have to write it up and so that here I can just take my new tool out for a spin and mention a few thoughts about why, in general it (4%) worked ok.  And also why it had unexamined risk. I believe much of this has been touched upon in the literature already.