This is a follow-on to part 1. That means I'll be a little too brief with descriptions and you'll have to go back and check the previous post for background. In short, we have been looking at the simple/basic effects of constant spend assumptions on residual wealth and forward-estimated fail risk that is dynamically recalculated each step (year) of the game. The difference here is that this post will look at: a) only 3% spend rate because it looked so sober and safe, and b) what happens to wealth and risk if we were to have a less-sanguine-than-5.7% return assumption. In this case we try 5% and 4.5% in addition to the original 5.7. That 5.7 number is an artifact of an old post where we picked it for a reason that made sense in that post. It has persisted through these analyses because I was too lazy to change it.

Retirement Finance; Alternative Risk; The Economy, Markets and Investing; Society and Capital

## Jul 30, 2017

### Some thoughts on constant spending in my spend-game context

I wasn't originally going to do a constant-spend (cs) chapter of my spend game. I think that cs is mostly an academic abstraction that is not how most people behave when push comes to shove. Either that or it is for those that fetishize constant smooth spending or don't want to look at or think about retirement math or (counter-intuitively, really, when you look at it) are extremely risk averse. But since the 4% rule of thumb is part of so many retirement conversations and because I work with advisors that avow personally knowing people who have been severely hurt by the 4% rule, it's worth another look. This post here is pretty thin and maybe even naive and certainly others have covered this better and deeper than I have, but I thought it was worth a look if for no other reason than to contextualize the previous games I was was working on. I will not do any utility math or certainty equivalents here because a lower constant spend rate, as far as I can tell, will

*always*have lower utility than higher constant spend. That is, I suppose, unless we open utility calcs to the idea that people have "utility" for other things like constant risk or growing net worth or something else like that.### Some thoughts on constant-risk spend paths

This isn't really a spending game like the last couple of posts. I just had some leftover material from what I was working on. I had collected the same info as before but now for three constant risk scenarios (where the dynamic spending "answer" is solved in each period for the appropriate simulated fail rate) for 10%, 20% and 30% probabilities of failure. I wanted to see what it looked like. Again this is not actually simulated (except for the fail estimates used to dynamically adjust spending) but just a deterministic simple process of starting with $1M, spending whatever the method says, growing the remainder at some fixed rate and then seeing what happens after converting spending and residual wealth to a present value to capture inflation/time value effects.[1] Simple and unrealistic but it helps me visualize.

## Jul 27, 2017

### A spending game with dynamic forward simulation and an annuity check

I was thinking about the last game in the last post. It probably seems a little silly to do a bunch of deterministic spending games that ignore the full ugly force of random returns, sequence risk, random inflation, etc. But I find the simplicity of the assumptions and the process, even though I could vary them a million different ways, helps me see the basic arc of what is going on underneath the surface. There will be time enough for more complex stuff later. I'm just trying to understand how this stuff works.

There are some new players here just to mix things up and so that we get a variety of approaches. In addition I have added a dynamic process. By dynamic I mean several things: 1) for a prescriptive rule like RH40 or even a dynamic rule like PMT, I am calculating at each step -- given the info available at the time (portfolio value, age, longevity using the SSA life table 95th percentile for each age[1], spend rate[2]) -- the probability of success in order to gauge a subjective sense of the risk taken along the path, 2) for the PMT function the spend rate depends on portfolio value and longevity (distribution period or DP = SSA 95th percentile for that age - current age) so it is dynamic by definition, and 3) for the dynamic simulated constant risk (MC sim and kolmogorov) approaches I will solve for a spend rate in each year -- given all ambient conditions in that year as in "#1" -- by a trial and error method in order to yield a 90% POS. Note that for "dynamic" I do not mean decision rules as they are normally understood the retirement finance lit nor do I mean "adaptive" in the way I define that term to myself. Me? I consider adaptive to be something like this: I get a bad medical diagnosis and I change my medical liability/reserve on my balance sheet from 0 to $1M and I change my longevity expectation from SSA 95th percentile to maybe 3 years and then I start from zero again with a new plan.

The Players:

There are some new players here just to mix things up and so that we get a variety of approaches. In addition I have added a dynamic process. By dynamic I mean several things: 1) for a prescriptive rule like RH40 or even a dynamic rule like PMT, I am calculating at each step -- given the info available at the time (portfolio value, age, longevity using the SSA life table 95th percentile for each age[1], spend rate[2]) -- the probability of success in order to gauge a subjective sense of the risk taken along the path, 2) for the PMT function the spend rate depends on portfolio value and longevity (distribution period or DP = SSA 95th percentile for that age - current age) so it is dynamic by definition, and 3) for the dynamic simulated constant risk (MC sim and kolmogorov) approaches I will solve for a spend rate in each year -- given all ambient conditions in that year as in "#1" -- by a trial and error method in order to yield a 90% POS. Note that for "dynamic" I do not mean decision rules as they are normally understood the retirement finance lit nor do I mean "adaptive" in the way I define that term to myself. Me? I consider adaptive to be something like this: I get a bad medical diagnosis and I change my medical liability/reserve on my balance sheet from 0 to $1M and I change my longevity expectation from SSA 95th percentile to maybe 3 years and then I start from zero again with a new plan.

The Players:

### Weekend Links - 7/27/2017

**QUOTE OF THE WEEK**

[patience is] a subversive act. On the other side of
impatience – if you can learn to wait out that jitteriness – lies power. OliverBurkeman

**RETIREMENT FINANCE AND PLANNING**

Research and Reality - A Literature Review on Drawing Down Retirement Financial Savings, 5 PhDs from the SOA.

[I thought this was a really good synoptic cover of the
universe of literature on retirement drawdown, self-managed strategies, and the
annuitization paradox. By 5 PhDs from the society of actuaries but very
readable. ]

we believe selection of an appropriate discount rate is
critical for many personal financial decisions.

Philosophy of Retirement Income Planning, Part 2, Pfau

The fundamental nature of risk for retirees is the threat
that poor market returns will permanently lower their standard of living.
Retirees must decide how much risk to their lifestyle they are willing to
accept. Spending more today based on assumed future earnings is risky business.
It may be reasonable behavior for the more risk tolerant among us, but most
people aren’t comfortable with it. The consequences must be considered in
advance.

Dependent risk analysis is a staple of many fields from
nuclear power plant design to insurance to aerospace engineering but it appears
to be rarely referenced in retirement literature. A Google search of
"dependent risk and retirement" turned up a single reference
including both terms and it's from the field of political science research[7]
referring to retiring from an election. Dr. Thorne's analysis of elder
bankruptcy data tells us that retirees should also be should be concerned about
it. …
This also raises the issue of how we can best deploy our retirement
assets to mitigate retirement risk. It appears that our goal should be to first
avoid the worst case, a chain reaction leading to ruin. A chain reaction will
likely have far worse outcomes than any individual risk.

## Jul 25, 2017

### A spending game with some new players

This is not a comprehensive or even necessarily accurate thing, it's just me playing around with some math and methods I've been working on lately.

As an introduction, the proximal reason for doing this post is the trigger I got from reading a 2012 paper by Larry Frank, John Mitchell, and David Blanchett (FMB) titled "Transition to Old Age (Superannuation) in a 3-D, Age Based, Dynamic, Serially Connected and Annually Recalculated Retirement Distribution Model." This is an unfortunately opaque paper and will appeal to few, if any, retirees and precious few practitioners. I say unfortunately because the basic concept is good: adapt plans each year in a sequential process for a lot of reasons but in particular because longevity expectations shift out a bit each year that you survive and if you happen to be one of those people that makes it to really late ages you really have to be careful. Here are some snippets from the paper:

As an introduction, the proximal reason for doing this post is the trigger I got from reading a 2012 paper by Larry Frank, John Mitchell, and David Blanchett (FMB) titled "Transition to Old Age (Superannuation) in a 3-D, Age Based, Dynamic, Serially Connected and Annually Recalculated Retirement Distribution Model." This is an unfortunately opaque paper and will appeal to few, if any, retirees and precious few practitioners. I say unfortunately because the basic concept is good: adapt plans each year in a sequential process for a lot of reasons but in particular because longevity expectations shift out a bit each year that you survive and if you happen to be one of those people that makes it to really late ages you really have to be careful. Here are some snippets from the paper:

## Jul 24, 2017

### Another close, disgruntled look at peer lending performance

A while back I posted an relatively positive note on peer2peer lending. That post got linked by a well known blogger and has received quite a few hits since then. My problem is that at that time I did not look very closely at the degradation of performance due to the pernicious effects of defaults on an aging portfolio even though that degradation was clearly there at the time. I knew at the outset that this kind of thing would happen so I was not completely naive but it has gotten quite a bit worse since my post so that I believe that my original reportage, while well intentioned, was inaccurate and it's getting more inaccurate by the day. Let's remedy that here. Here is the decay in three charts:

## Jul 22, 2017

### Animated 3D cost of safety [Updated]

Just for fun here is an animated version of the previous post showing a relationship between wealth (in $M), effective spend rates and fail rates for 4 fixed spends (25k, 35, 50 100 as red blue green gray). Mostly this was just to see if I could animate and gif it as well as to brush up on some R.

Update:

OK, I swear this is the last time. See prior posts for background. Just to be a little OCD and round this out as long as I was on this path, I added additional lifestyle lines in terms of a constant spend so now there is 25k, 35, 50, 75, 100, 125, and 150 (for a 59 year old among other assumptions. 75k is black and everything over 100 is grey). I've had my dose of simulations for the weekend so that wraps it up.

## Jul 21, 2017

### 3D cost of safety - an extended version

Here is another data visualization that was fun but won't (yet, I think) add value. This below takes the data from simulation[1] for 4 fixed, constant inflation adjusted (and presumably inelastic) spend rates (25k, 35k, 50k, and 100k) and then sees what the relationship is between those spend rates and effective spend rates at each wealth level and the related fail rate. This was just to see what it looked like. This is an extension of a prior post on "cost of safety." I was going to try to create a rotating gif but it was taking too much time. Maybe next week.

------------------------------------------

[1] Endowment 500k:4M by 100k, age 59, SS at 70, return suppression for 10 years, 50/50 allocation, etc.

For four different constant spend rates: relationship

between wealth level, effective spend rates, and

fail rates.

------------------------------------------

[1] Endowment 500k:4M by 100k, age 59, SS at 70, return suppression for 10 years, 50/50 allocation, etc.

## Jul 20, 2017

### Weekend Links - 7/20/17

**QUOTE OF THE WEEK**

Risk and time are opposite sides of the same coin, for if there were no tomorrow there would be no risk. Time transforms risk, and the nature of risk is shaped by the time horizon: the future is the playing field. PeterL. Bernstein

**RETIREMENT FINANCE AND PLANNING**

How ETFs might help retirees better manage distributions,
pionline.com

Although many legal boundaries stand in the way, instead of
receiving a cash lump sum, retirees could instead receive a balanced portfolio
of ETFs allocated based on a specific risk profile.

The holy grail of retirement income planning is finding
strategies that enhance retirement efficiency – strategies that simultaneously
allow you to spend more and leave behind a legacy you can be proud of, in a way
that other strategies may not. The definition of efficiency varies from person
to person as it depends on how long you will live. As mentioned in the first point, a number of
strategies can enhance efficiency over the long term (but not necessarily the
short term) with more spending and legacy.

Life-Cycle Earnings Curves and Safe Savings Rates, Tharp and
Kitces.

Results indicate that failing to account for more realistic
earnings curves throughout the life-cycle may overstate SSRs for lower-income
households while understating SSRs for higher-income households and understate
SSRs for younger households while overstating SSRs for older households.
Furthermore, historical SSRs of 10% or less are found for all but the highest
income households after accounting for more realistic earnings curves and
Social Security benefits.

### 3D cost of safety

There was no real reason to do this. Nor did I really gain any useful insights that I didn't already have. I just wanted to see what it looked like.

In a past post, riffing on some work done by aacalc.com, I tried to replicate his cost of safety curve where he shows that there are diminishing returns in terms of changes in fail rate for each unit of wealth saved. Then I did it in reverse where, for a given lifestyle (spend rate) changes in wealth (for the worse) will cause fail rates to become way more sensitive at lower wealth levels than high which means it can potentially be an important policy choice. Since the impact is muted for the already retired -- unless one has the ability to change wealth (continue working) or unless one has bad behavioral ticks (panic selling) -- maybe it's not that big of a deal.

Then it dawned on me that for some given inelastic lifestyle, as wealth falls, effective spend rates go up and so there should be a relationship between wealth, effective spend rates, and fail rates. 3D! And who doesn't like 3d? The relationship is probably not all that useful but driving around yesterday I was thinking: "hmm. I wonder what it looks like." This is what it looks like (35k spend rate and some idiosyncratic sim assumptions that match no one, not even me):

In a past post, riffing on some work done by aacalc.com, I tried to replicate his cost of safety curve where he shows that there are diminishing returns in terms of changes in fail rate for each unit of wealth saved. Then I did it in reverse where, for a given lifestyle (spend rate) changes in wealth (for the worse) will cause fail rates to become way more sensitive at lower wealth levels than high which means it can potentially be an important policy choice. Since the impact is muted for the already retired -- unless one has the ability to change wealth (continue working) or unless one has bad behavioral ticks (panic selling) -- maybe it's not that big of a deal.

Then it dawned on me that for some given inelastic lifestyle, as wealth falls, effective spend rates go up and so there should be a relationship between wealth, effective spend rates, and fail rates. 3D! And who doesn't like 3d? The relationship is probably not all that useful but driving around yesterday I was thinking: "hmm. I wonder what it looks like." This is what it looks like (35k spend rate and some idiosyncratic sim assumptions that match no one, not even me):

## Jul 19, 2017

### RH40 vs. analytically derived withdrawal using ERN math

One of my favorite retirement sites these days is earlyretirementnow.com. This is mostly because: a) he uses prodigious quant skills (PhD) to attack the problem, and b) he actively wants to retire so he has skin in the game and his self interest in the answers he is looking for is another way of saying I trust his analysis. That also means today that I wanted to run my RH40 age-based formula against some very elegant math that he uses in deriving his own solutions which, more often than not, he does analytically using the math in this note [1] and on his site. The basic simple version is this where Ct is cumulative market returns working backwards from T and w is the withdrawal rate:

or in his extended version it looks like this where the second term on the right side reflects future income and the third term is, as above (FV), there for legacy goals.

This is elegant but non-trivial stuff. It was hard for me to figure out. It is more or less the stringing together the results of a set of returns in complex ways over time so it becomes one of those multi-period geometric return things. Not for the faint of heart I think. But reasonable. The outcome is a withdrawal rate for a given set of assumptions and for a random set of returns[2] over some period of time. Since the RH40 rule of thumb comes up with a withdrawal rate as well I wanted to see how these two approaches stacked up just for fun. In a past post (I think this is the one) I did the same thing with RH40 vs other math like Blanchett's simple formula, excel pmt function and some others. The trick here in this post was to figure out 1) what return distribution do I use, 2) what other assumptions do I make, and 3) how do I execute the comparison?

or in his extended version it looks like this where the second term on the right side reflects future income and the third term is, as above (FV), there for legacy goals.

This is elegant but non-trivial stuff. It was hard for me to figure out. It is more or less the stringing together the results of a set of returns in complex ways over time so it becomes one of those multi-period geometric return things. Not for the faint of heart I think. But reasonable. The outcome is a withdrawal rate for a given set of assumptions and for a random set of returns[2] over some period of time. Since the RH40 rule of thumb comes up with a withdrawal rate as well I wanted to see how these two approaches stacked up just for fun. In a past post (I think this is the one) I did the same thing with RH40 vs other math like Blanchett's simple formula, excel pmt function and some others. The trick here in this post was to figure out 1) what return distribution do I use, 2) what other assumptions do I make, and 3) how do I execute the comparison?

## Jul 18, 2017

### A Retiree's Baby Steps in Algorithmic Trading

In a world of HFT, quant programming, hedge funds, immense pools of capital, and algorithmic trading all of which leads to bloody gladitorial combat down to the last nano-second, retail investors have a couple advantages still in their favor: 1) they have time or alternatively, to say the same thing a different and probably better way, they have patience. Time depends on how you look at it. As a soon-to-be or current retiree one's planning horizon may be less than infinite which is a more institutional point of view. And 2) they have the ability to trade small-scale marginally-liquid semi-sketchy stuff that most hedge funds of any scale can't touch. Among other things, the spreads are too wide, the capacity isn't there, the risk of moving the market is too present, and getting out when one needs to get out is famously hard. These factors are an edge to we the few who have patience and small scale.

On the other hand buying and selling these types of things that are relatively illiquid and that have wide spreads is an invitation to getting screwed by everyone else on the other side of the trade. And screwed I have been. But there are instruments that are accretive to my strategies that have all the attributes of things I shouldn't trade for that reason. My trading is infrequent enough that manual trading is probably no burden especially when that patience factor comes into play so most of the time it all works out just fine. But even so it's pretty easy to get screwed and not much fun. Enter, of all things, algorithmic trading. For the little guy. This is news, though, to no one but me. I am late to this game and there are billions of small scale algos already out there (see this article on the rise of the robots). For me it is simply now a process of using tools that, like ruby slippers, were already there. Step 1 is to use algorithmic order types available in the broker interface to work the bid-ask spread programmatically to get a better fill than the current ask at least some of the time. I made my first foray today. Step 2, a step that I have been working on in small pieces for a few months, is to create an algorithmic trading research environment with things like ubuntu and python and misc APIs. To the extent that I want to continue and/or scale what I do this seems necessary in today's world. The other option is to keep getting screwed some of the time or maybe alternatively do a real retirement, which is always on the table. I'll keep plugging away for now because it interests me to do so.

On the other hand buying and selling these types of things that are relatively illiquid and that have wide spreads is an invitation to getting screwed by everyone else on the other side of the trade. And screwed I have been. But there are instruments that are accretive to my strategies that have all the attributes of things I shouldn't trade for that reason. My trading is infrequent enough that manual trading is probably no burden especially when that patience factor comes into play so most of the time it all works out just fine. But even so it's pretty easy to get screwed and not much fun. Enter, of all things, algorithmic trading. For the little guy. This is news, though, to no one but me. I am late to this game and there are billions of small scale algos already out there (see this article on the rise of the robots). For me it is simply now a process of using tools that, like ruby slippers, were already there. Step 1 is to use algorithmic order types available in the broker interface to work the bid-ask spread programmatically to get a better fill than the current ask at least some of the time. I made my first foray today. Step 2, a step that I have been working on in small pieces for a few months, is to create an algorithmic trading research environment with things like ubuntu and python and misc APIs. To the extent that I want to continue and/or scale what I do this seems necessary in today's world. The other option is to keep getting screwed some of the time or maybe alternatively do a real retirement, which is always on the table. I'll keep plugging away for now because it interests me to do so.

## Jul 14, 2017

### Cost of safety...in reverse

In a prior post (B-Day Post and also the Cost of Retirement Safety) I was riffing on a page at aacalc.com that discusses the "cost of safety." In this case the author was explaining the economics of diminishing returns for increasing savings in order to reduce fail rate risk. Going from a 20 to 5% fail rate was more than 2x the incremental new retirement saving required than going from 35 to 20%. It dawned on me that this analysis can be done in reverse. In other words, depending on one's absolute spend rate one could estimate how sensitive the fail rate is to imminent changes in the endowment.

For example, in the prior post we had a 59 year old with a $35,000 spend rate among other things which meant, given the particular sim runs I did, going from a 13.3% fail rate at a $1M endowment to a 3.75% fail rate would require an additional 400,000 in savings which is quite a bit more than going from 22.9% to 13.3%. The other way to look at it though is to say that for that spend rate (lifestyle), if my savings were at $2M or $1.5M or $1M, how sensitive would my fail rate be to a 20% drop in my endowment all else being equal? The answer in points different is this:

2.0M 01.40 points more in fail rate risk for a 20% drop

1.5M 06.13 point increase

1.0M 22.03 point increase

So, non linear. Plus it points out a pretty stark policy decision one could make. By that I mean that if I have (and if I know I have) investment behavioral problems and if I have more or less inelastic spending ... and let's say I let someone along the way, an advisor or retirement guru perhaps, talk me into a more expansive lifestyle because they had some secret sauce for spending more, then I might be too deep into a plan (too far up the curve in other words) that is too sensitive to changes in my portfolio...for me, that is. See, that's the thing. I read all these savvy retirement finance papers on cool ways to maximize spending safely and what it means to me is not just that these people are taking you to the very frontier of what I consider as prudent, they are also taking you to the slippery slope of sometimes radically increased sensitivity to problems should problems occur. And those gurus and advisors will not be there to help you out with a check or cash when it happens, I can tell you that.

The policy decision part of this might be to do some analysis on risk aversion and on sensitivity analysis and,

For example, in the prior post we had a 59 year old with a $35,000 spend rate among other things which meant, given the particular sim runs I did, going from a 13.3% fail rate at a $1M endowment to a 3.75% fail rate would require an additional 400,000 in savings which is quite a bit more than going from 22.9% to 13.3%. The other way to look at it though is to say that for that spend rate (lifestyle), if my savings were at $2M or $1.5M or $1M, how sensitive would my fail rate be to a 20% drop in my endowment all else being equal? The answer in points different is this:

2.0M 01.40 points more in fail rate risk for a 20% drop

1.5M 06.13 point increase

1.0M 22.03 point increase

So, non linear. Plus it points out a pretty stark policy decision one could make. By that I mean that if I have (and if I know I have) investment behavioral problems and if I have more or less inelastic spending ... and let's say I let someone along the way, an advisor or retirement guru perhaps, talk me into a more expansive lifestyle because they had some secret sauce for spending more, then I might be too deep into a plan (too far up the curve in other words) that is too sensitive to changes in my portfolio...for me, that is. See, that's the thing. I read all these savvy retirement finance papers on cool ways to maximize spending safely and what it means to me is not just that these people are taking you to the very frontier of what I consider as prudent, they are also taking you to the slippery slope of sometimes radically increased sensitivity to problems should problems occur. And those gurus and advisors will not be there to help you out with a check or cash when it happens, I can tell you that.

The policy decision part of this might be to do some analysis on risk aversion and on sensitivity analysis and,

*if one still has the choice to save more*, maybe save to a point on the curve where one thinks one can handle the intensity of the changes in fail rate estimates that will come when a market correction arrives, one that goes too deep and/or lasts a little too long. This is probably similar analysis to floor-and-upside stuff but that might be another post.### B-Day Post and also the Cost of Retirement Safety

1. The B-day post part

Since I've passed through to the other side of another age (again, dammit) I thought I'd take a look at what that means in ret-fin terms. Let's see what has changed over the last year:

Age

Longevity expectations

Last year's returns have been realized

New return (and discount) assumptions have emerged

Last year's inflation has been realized

New inflation assumptions are in hand

Risk aversion has probably changed

Health, mental, and financial capabilities have probably changed

Another year's realized spending has gone out the door

Future spending expectations have changed

Insurability has shifted

Employability has shifted

One year closer to penalty free IRA distributions!

No doubt there are infinite other things that have changed

Frankly I do not know how people can do a set-and-forget static plan in retirement. Me I think about this stuff not in static terms and not really even in annual terms. I won't go as far as to admit the insanity of a continuous view of things but I

2. The Cost of Safety part

I was looking at aacalc.com again and I still marvel at how a youngish non-retired guy knows so much pretty darn advanced retirement finance math and knows it so well. Most of his stuff I can't touch (but do appreciate). One of his web pages talks about the cost of safety. This is the idea that the last dollar of savings has relatively less impact on the risk of failure than the first, or as his first paragraph puts it "When building a retirement portfolio for fixed withdrawals, the first dollars of the portfolio will have the biggest impact on your retirement success, and the last dollars the least. This is because the last dollars get spent only if the first dollars are inadequate due to either poor portfolio performance or a long life span. This much is obvious, what is less obvious is the speed, extent, and location of the transition from "first dollar" to "last dollar".

While I trust his math more than my own and he typically uses more complex and theoretically correct methods than do I, I wanted to see if could more or less replicate his chart and analysis and his claim that "This means it is difficult for those seeking absolute portfolio success according to the historical data; they must save twice as much as someone who is willing to accept a 4% chance of portfolio failure." The only way I could do this quickly was to use simulation and look at the fail rate for changing levels of endowment (500k to 4M in 100k increments [1]). You can look at the aacalc article for his stuff but my chart looked like Figure 1. This result is not too different from his though maybe the curve is a little different in delta-slope terms and choppier too in that I was doing relatively few sim runs to speed up the analysis. I used the same scale on x and y as the aacalc chart:

Since I've passed through to the other side of another age (again, dammit) I thought I'd take a look at what that means in ret-fin terms. Let's see what has changed over the last year:

Age

Longevity expectations

Last year's returns have been realized

New return (and discount) assumptions have emerged

Last year's inflation has been realized

New inflation assumptions are in hand

Risk aversion has probably changed

Health, mental, and financial capabilities have probably changed

Another year's realized spending has gone out the door

Future spending expectations have changed

Insurability has shifted

Employability has shifted

One year closer to penalty free IRA distributions!

No doubt there are infinite other things that have changed

Frankly I do not know how people can do a set-and-forget static plan in retirement. Me I think about this stuff not in static terms and not really even in annual terms. I won't go as far as to admit the insanity of a continuous view of things but I

*am*willing to think in continuously adaptive terms as "big enough" change arrives...as it will now and then.2. The Cost of Safety part

I was looking at aacalc.com again and I still marvel at how a youngish non-retired guy knows so much pretty darn advanced retirement finance math and knows it so well. Most of his stuff I can't touch (but do appreciate). One of his web pages talks about the cost of safety. This is the idea that the last dollar of savings has relatively less impact on the risk of failure than the first, or as his first paragraph puts it "When building a retirement portfolio for fixed withdrawals, the first dollars of the portfolio will have the biggest impact on your retirement success, and the last dollars the least. This is because the last dollars get spent only if the first dollars are inadequate due to either poor portfolio performance or a long life span. This much is obvious, what is less obvious is the speed, extent, and location of the transition from "first dollar" to "last dollar".

While I trust his math more than my own and he typically uses more complex and theoretically correct methods than do I, I wanted to see if could more or less replicate his chart and analysis and his claim that "This means it is difficult for those seeking absolute portfolio success according to the historical data; they must save twice as much as someone who is willing to accept a 4% chance of portfolio failure." The only way I could do this quickly was to use simulation and look at the fail rate for changing levels of endowment (500k to 4M in 100k increments [1]). You can look at the aacalc article for his stuff but my chart looked like Figure 1. This result is not too different from his though maybe the curve is a little different in delta-slope terms and choppier too in that I was doing relatively few sim runs to speed up the analysis. I used the same scale on x and y as the aacalc chart:

Figure 1. The Cost of Safety

According to my rudimentary sim runs, and taking $4M as "absolutely" safe given my input assumptions (though nothing is absolute) then the cost of being absolutely safe vs. a 4% chance of failure is roughly three times as much savings required. Using a .12% threshold for fail rate, which seems to be pointless but probably fine since that is effectively zero as well, the cost of being perfectly safe is about 2 times a 4% risk of failure. And, just to round it out, in this set of sim runs the cost of going from 20% to 5% failure was, without getting too rigorous on interpolation, a little over 2 x the cost of going from 35-20%. [2]

So, I gather now that I've done this: it really

*is*expensive to be more rather than less sure about one's retirement risk. I actually found this more useful than I expected, psychologically speaking. I guess aacalc's claim stands. But then again I am not surprised.
----------------------------------------------

[1] some standard assumptions in the sim: Endowment in increments, 35k constant spend, 50/50 allocation (static; his is dynamic), to fixed age 95, no SS, historical returns, return suppression of 1% for 10 years, no spend shocks or trends or variability, etc.

[2] This is not very scientifically fit but over the 1M to 2M range 1E+28W^-4.186 just about describes the relationship where W is the endowment.

[2] This is not very scientifically fit but over the 1M to 2M range 1E+28W^-4.186 just about describes the relationship where W is the endowment.

## Jul 13, 2017

### Weekend Links - 7/13/17

**QUOTE OF THE WEEK**

If attaining reliable lifetime income is the goal, let’s
start with this: The DB pension

architecture is the best system yet devised for spreading
the income from one’s

working life over one’s whole life. Laurence Siegel

**CHART OF THE WEEK**

This is an impressionistic riff on skewed risk by

earlyretirementnow.com Explains why I avoid lotteries,

extended warranties, and long options and also why

I short options instead.

**RETIREMENT FINANCE AND PLANNING**

The next asset section of the
RIO Map™ framework is the diversified portfolio. The diversified portfolio can
be used most effectively to meet lifestyle and legacy goals, which translate
into the liabilities related to discretionary expenses and legacy. Here we
review your investments as well as your views, attitudes, and knowledge about
investing.

Generating Retirement Income Before Age 59-½, Darrow
Kirkpatrick.

you could still have a big
problem, even if you have enough money saved in your retirement accounts….

I retired at 52 with a $3 million net worth — here are 10 things that surprised me about early retirement. Businessinsider.com

[ok, for
what it's worth he's only 9 months in so it reads like one those giddy articles
that new parents write about their new babies in parenting mags. I'd much rather have his perspective after
9 years. I'm almost 9 years in, btw]

## Jul 11, 2017

### Some Spending Games

No random variables today. I am playing a game here with some spending methods in "deterministic world." Note right off the bat that this is not rigorous or exhaustive. There are about an infinite number of ways to spend; I just happened to pick a few that I have been working with lately to see what they look like in terms of "lifestyle over time" by which I mean what do they look like in present value terms over time and relative to a constant spending assumption? In other words what trade-offs might I be making between lifestyle today and lifestyle tomorrow when using some different spending approaches.

## Jul 8, 2017

### Excel PMT function vs RH40 for different mortality table assumptions

Since more academics and practitioners appear to be absorbing the idea of dynamic, recalculated spend rates or fail rates, which I think they should, and since a number of papers use the math behind (or similar to) the Excel PMT function to illustrate the point (e.g., Waring and Seigel 2014, Frank and Brayman 2016) and since the question might always be "what longevity expectations should we use," I thought I'd take another run at seeing how my RH40 rule of thumb (see here, here, here, here , here and here) stacks up against PMT when taking real mortality tables into account.

I'll use two tables: 1) the Social Security 2013 Life table, and 2) the Society of Actuaries Individual Annuity Mortality table (a healthier, self-selecting, longer living cohort I gather). Depending on the need I either access the data directly or in some cases I borrow the work done at AAcalc.com where he uses the SOA 2012 IAM table with projection scale G2. I will also look at several different risk/expectation categories: mean, 80th percentile, and 95th percentile.

I'll use two tables: 1) the Social Security 2013 Life table, and 2) the Society of Actuaries Individual Annuity Mortality table (a healthier, self-selecting, longer living cohort I gather). Depending on the need I either access the data directly or in some cases I borrow the work done at AAcalc.com where he uses the SOA 2012 IAM table with projection scale G2. I will also look at several different risk/expectation categories: mean, 80th percentile, and 95th percentile.

## Jul 7, 2017

### SOA mortality table vs. Gompertz

Ok, I tried to imagine a reason why any of my four or five readers would be interested in how the Society of Actuaries Individual Annuity Mortality table could be modeled using a Gompertz equation for a 58 year old male. I could come up with no plausible scenario where the probability is greater than zero. Yet here we are.

I started looking the SOA table because Joe Tomlinson once tipped me off that the SS Life table (2013) that I used for stochastic longevity in my modeling was not very conservative (SOA assumes a healthier self-selecting cohort). Here is an overlay of the SOA IAM table's probability density for a 58 year old against a Gompertz approximation of the same. The key inputs, in case you ever need to know it, for the gompertz is a central tendency of 90 and a dispersion of 8.5. For what it's worth, the inputs for doing the same thing with the SS2013 Life table are 85.5 and 10 respectively. Not perfect but close enough for rough modeling if I need it; plus it's malleable.

I started looking the SOA table because Joe Tomlinson once tipped me off that the SS Life table (2013) that I used for stochastic longevity in my modeling was not very conservative (SOA assumes a healthier self-selecting cohort). Here is an overlay of the SOA IAM table's probability density for a 58 year old against a Gompertz approximation of the same. The key inputs, in case you ever need to know it, for the gompertz is a central tendency of 90 and a dispersion of 8.5. For what it's worth, the inputs for doing the same thing with the SS2013 Life table are 85.5 and 10 respectively. Not perfect but close enough for rough modeling if I need it; plus it's malleable.

## Jul 6, 2017

### Weekend Links - 7/6/17

**QUOTE OF THE WEEK**

As an investor you don’t have to be brilliant. Just not stupid. abnormalreturns.com

**VISUALIZATION OF THE WEEK**

**RETIREMENT FINANCE AND PLANNING**

Retirement is Risky Business – Here's a List, Dirk
Cotton. there are a large number of
financial risks that every plan should contemplate. Many of these won't come to
mind when we consider a list of major retirement goals for our mission
statement, but one major goal of the mission could be to mitigate as many
applicable common retirement risks as we can identify.

Does Monte Carlo Analysis Actually Overstate Fat Tail Risk In Retirement Projections? Derek Tharp at Kitces.com While
already included in most financial planning software solutions, Monte
Carlo analysis remains a somewhat controversial projection tool
for financial planners, due to the fact that it commonly relies on a normal
distribution to project the probability of future returns in a world where many
have suggested that returns are not actually normally distributed. Which raises
the question of whether or to what extent Monte Carlo
analysis projections might be understating the risk of a retirement plan? [my thoughts here ]

## Jul 5, 2017

### On "Growth Optimal Portfolios" by Corey Hoffstein and Newfound Research

Here is a great post to which I was tipped by an internet-blog friend:

Growth Optimal Portfolios, Corey Hoffstein. "… we explore geometric mean maximization, an
alternative to the traditional Sharpe ratio maximization that seeks to maximize
the long-term growth rate of a portfolio. Due to compounding effects,
volatility plays a critical role in the growth of wealth. Seemingly lower
return portfolios may actually lead to higher expected terminal wealth if
volatility is low enough. Maximizing for long-term growth rates may be incompatible with short-term
investor needs. More explicit accounting for horizon risk may be prudent."

This was of interest because I have put so much amateur-hack effort into understanding this subject area. Past posts include:

### Tharp on Whether Retirement Simulation Overstates Tail Risk

To my eye, one of the sharpest and most articulate of the new generation of retirement finance writers is Derek Tharp, now writing at Kitces.com. I will be watching his future contributions to the genre closely.

Derek has just written another top-notch and perceptive blog post, this one on simulation titled "Does Monte Carlo Analysis Actually Overstate Tail Risk In Retirement Projections?" This is a great post and demonstrates a solid command of the subject area. My interest here, though, is not to report on the article or summarize or even bullet-point what he is saying. You can read it yourself . I just wanted to highlight a couple things where I have a slight divergence of point-of-view. I suspect that one would actually have to read the article to understand where I am coming from but I'll leave that in your hands. With respect to simulators overstating risk via fat tailed distributions:

Derek has just written another top-notch and perceptive blog post, this one on simulation titled "Does Monte Carlo Analysis Actually Overstate Tail Risk In Retirement Projections?" This is a great post and demonstrates a solid command of the subject area. My interest here, though, is not to report on the article or summarize or even bullet-point what he is saying. You can read it yourself . I just wanted to highlight a couple things where I have a slight divergence of point-of-view. I suspect that one would actually have to read the article to understand where I am coming from but I'll leave that in your hands. With respect to simulators overstating risk via fat tailed distributions:

### Effective Withdrawal Rates - Part 2: Japanese overlay

This is an extension of a prior post (Effective Withdrawal Rates vs. the 1970s Plus Some Benchmarks) and it has all the same assumptions and disclaimers and it retains the same core question: how would a constant spend assumption have felt along the way. The difference here is that I added an overlay where I replaced the 60% allocation to the S&P starting in 1969 with a return series that represents the Nikkei between 1985 and 2016. The plan fails after about 26 years; it would have had me on the edge of my seat after about 15. Even a simulator would have to work hard to come up with a return series like that.

## Jul 4, 2017

### Constant risk, constant lifestyle and the '70s

58 year old, start 1969

Initial spend rate set to .028 to reflect conservative age-based spend rate at initial state age

60/40 allocation, n/a fees and tax

$1M

Proportional draw

Traces to age 80 only (tail end of optimal annuity "safe harbor?")

Ignores wealth states, sustainability, fail rates etc.

- Blue is spending ($1 compound) based on a continuously updated age-and-risk-aversion adjusted rule of thumb that represents constant risk. Starts from .028 at 58 to .06 at 80. Spend is calculated from beginning of year portfolio value.

- Red is the inflation of the initial lifestyle state (.028) in terms of the inflated value of a dollar over the period.

- Grey is the spread difference.

Interpretations are several; I'm still working on that. Final crossover is around age 72. I might try this with a higher initial spend rate. The main story is the tradeoffs between between lifestyle, inflation, and risk of course.

## Jul 3, 2017

### Planning Variations on Life Expectancy Projections

The main purpose of this is to visualize how inadequate the use of average expectations can sometimes be.

## Jul 2, 2017

### Effective Withdrawal Rates vs. the 1970s Plus Some Benchmarks

Anyone who has retired early (or wants to) or has an expectation for a long retirement, which is the same thing, needs to come to terms with the ugliness of the 1970s. And that is not a reference to disco. This is also assuming one has not simulated something worse than the 1970s which is entirely possible. I reference the 70s because according to some (like Wikipedia, a citation is needed here but not provided) the 70s were the worst event for retirees in the 20th and our slice of the 21st centuries -- and that's including the great depression and the events of 2007-9. The retiree-buzzkill was due to the effects of not so much market crashes but to the decade-long arc of bad returns and pernicious inflation -- this is sequence of returns risk on steroids supplied by inflation. Plus I have to say I lived through it and saw a retired parent on a dribble-income get smoked by what happened in those days.

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