The point of the post
The point should be that I thought for a second that I had mis-coded the software and that I might have to recant the last several posts. How embarrassing that would be.
The real point was to see if, based on the last post where a 50 or 60 percent allocation of initial wealth to lifetime income (SPIA) worked "best," whether a deferral of the allocation via DIAs would produce any incremental benefits, like it did when we deferred a 10% allocation where the answer was yes.
The short answer here was a very quick "no," so my goal pivoted to see: (a) if I had made coding or conceptual design errors, or (b) what went wrong or what explained the abrupt loss of lifetime consumption utility when it had worked so well in the allocate-10%-of-wealth-to-an-SPIA post. Originally I was going to see, since the 50 and 60% allocation to SPIAs were neck and neck in utility terms, whether deferring either would create any separation between the two. But basically, I just gave up after the first three scenarios because it was so obvious that this wasn't going anywhere.
Jun 27, 2019
Jun 26, 2019
Annuitizing Larger Portions of Initial Wealth in a Lifetime Consumption Utility Simulator
The Point of This Post
Almost everything I need to set this up was already done in Lifetime Consumption Utility "Frontier" and DIAs - With Different Deferral Periods on June 23. Start there first.
The purpose here is to take the exact same set-up as in the link and now find out how much initial wealth I can annuitize (using fake in-model nominal SPIAs as proxies for access to a "risk pool") in increasing increments. I want to see if or where the optimization benefits peter out when adding lifetime income...knowing that the "theory" says you are supposed to be able annuitize all wealth for optimality. We'll see.
Theory References
There are a bazillion references on this. I'll mention only two, however, and quote a salient fragment from each.
1. Yaari, M. (1965), Uncertain Lifetime, Life Insurance, and the Theory of the Consumer
The theory reference is important here because my post diverges from the famous conclusion in #1 and I need something like #2 or other reasons to to justify my results although it is probably fairly intuitive to understand the divergence at a superficial level. We might set it up like this. If my results differ from the conclusion in #1, we might say one of the following:
Almost everything I need to set this up was already done in Lifetime Consumption Utility "Frontier" and DIAs - With Different Deferral Periods on June 23. Start there first.
The purpose here is to take the exact same set-up as in the link and now find out how much initial wealth I can annuitize (using fake in-model nominal SPIAs as proxies for access to a "risk pool") in increasing increments. I want to see if or where the optimization benefits peter out when adding lifetime income...knowing that the "theory" says you are supposed to be able annuitize all wealth for optimality. We'll see.
Theory References
There are a bazillion references on this. I'll mention only two, however, and quote a salient fragment from each.
1. Yaari, M. (1965), Uncertain Lifetime, Life Insurance, and the Theory of the Consumer
"In Case C the consumer has no bequest motive but he is constrained to meet the requirement that his transferrable assets at time of death (i.e., those assets which become a part of his estate) should be non-negative with probability one. It turns out that this case is quite simple to analyse because the consumer's assets (or liabilities) will always be held in actuarial notes [i.e., more or less "annuities," but see Prof. Milevsky's comments below] rather than in regular notes."2. Yagi & Nushigaki (1993), The Inefficiency of Private Constant Annuities
The consumption stream without any constraints [by which I assume they mean “case C” where wealth is held in actuarial notes], which Yaari derived, is considered to be the first-best optimal consumption stream in an economy where insurance is available. The consumption stream with constraints diverges from the first-best consumption stream, and this divergence can be seen as a distortion created by the constraints. In other words, the constraints imposed by the insurer and the imperfect capital markets create a loss in efficiency.Divergence from Theory
The theory reference is important here because my post diverges from the famous conclusion in #1 and I need something like #2 or other reasons to to justify my results although it is probably fairly intuitive to understand the divergence at a superficial level. We might set it up like this. If my results differ from the conclusion in #1, we might say one of the following:
Jun 24, 2019
J.D. Roth on Retirement Purpose
This post by J.D. Roth is pretty good.
Beyond wealth: What happens AFTER you achieve financial independence?
I bookmarked this because I'll go back for a second and third look. The post shares a lot of affinities with how I have and how I will think about "financial independence." I do a lot of quant analysis here but that's more hobby than anything else. It's like a guy tinkering with a hog in the garage or a model railroad in the basement or astrophotography on weekends. The real issues in retirement often have more to do with meaning, purpose and identity than they do with optimal spend rates. The latter enables the former but the former gets you out of bed.
Beyond wealth: What happens AFTER you achieve financial independence?
I bookmarked this because I'll go back for a second and third look. The post shares a lot of affinities with how I have and how I will think about "financial independence." I do a lot of quant analysis here but that's more hobby than anything else. It's like a guy tinkering with a hog in the garage or a model railroad in the basement or astrophotography on weekends. The real issues in retirement often have more to do with meaning, purpose and identity than they do with optimal spend rates. The latter enables the former but the former gets you out of bed.
Jun 23, 2019
Lifetime Consumption Utility "Frontier" and DIAs - With Different Deferral Periods
The Point
The point of this post is to extend the last several posts by now looking at different deferral periods for an idealized, hypothesized, and entirely fake deferred income annuity (DIA) to see what that change in deferral does to the maximum lifetime consumption utility for different spend rates across different allocations to a (idealized, hypothesized....) consumption portfolio.
I mention the "idealized, hypothesized" thing because this model is doubtful in it's fidelity to anything real that will unfold in the world we live in. Also, note that my goal is not to give myself some perfect consumption rate here. Rather I want to look at the "shapes, movement, and ranges" of spend rates and allocations given the narrow constraints of the software I built. From that I might be able to intuit how things work a little better. Maybe others have done this kind of thing before me but I need to see it for myself.
The point of this post is to extend the last several posts by now looking at different deferral periods for an idealized, hypothesized, and entirely fake deferred income annuity (DIA) to see what that change in deferral does to the maximum lifetime consumption utility for different spend rates across different allocations to a (idealized, hypothesized....) consumption portfolio.
I mention the "idealized, hypothesized" thing because this model is doubtful in it's fidelity to anything real that will unfold in the world we live in. Also, note that my goal is not to give myself some perfect consumption rate here. Rather I want to look at the "shapes, movement, and ranges" of spend rates and allocations given the narrow constraints of the software I built. From that I might be able to intuit how things work a little better. Maybe others have done this kind of thing before me but I need to see it for myself.
Jun 21, 2019
Bodie and Cotton on Real Annuities
from ssrn.com
The only retirement contract that both insures against longevity risk and hedges against inflation is a life annuity that is linked to the consumer price index (CPI). It is denominated in the same units of account as Social Security benefits. We call it a “real annuity,” although it is also referred to as an inflation-indexed single-premium immediate annuity (SPIA). In computing a person’s replacement ratio of preretirement income, we can add Social Security benefits and the income produced by a real annuity to arrive at a meaningful number.
An annuity that is not linked to the CPI we call a “nominal annuity.” It is measured in units that are different from Social Security, so it would be a mistake to add the two in computing a replacement ratio. Despite those obvious facts, real annuities are largely ignored in practice and they comprise a tiny portion of the annuities market. The vast majority of income annuities sold are fixed in nominal dollars. From the perspective of rational economic decision-making, this is a puzzle. Let’s call it the “nominal annuity puzzle.” The purpose of this article is to explore the reasons behind this puzzle and to suggest ways to solve it. The lack of interest in real annuities can be explained by a lack of recognition that the purchase of a nominal annuity constitutes a speculative bet on future inflation rates and that the real annuity is the risk-free asset.
Hedging Against Inflation Risk with Real Annuities
7 Pages Posted: 12 Jun 2019
Date Written: May 31, 2019
Abstract
The only retirement contract that both insures against longevity risk and hedges against inflation is a life annuity that is linked to the consumer price index (CPI). It is denominated in the same units of account as Social Security benefits. We call it a “real annuity,” although it is also referred to as an inflation-indexed single-premium immediate annuity (SPIA). In computing a person’s replacement ratio of preretirement income, we can add Social Security benefits and the income produced by a real annuity to arrive at a meaningful number.
An annuity that is not linked to the CPI we call a “nominal annuity.” It is measured in units that are different from Social Security, so it would be a mistake to add the two in computing a replacement ratio. Despite those obvious facts, real annuities are largely ignored in practice and they comprise a tiny portion of the annuities market. The vast majority of income annuities sold are fixed in nominal dollars. From the perspective of rational economic decision-making, this is a puzzle. Let’s call it the “nominal annuity puzzle.” The purpose of this article is to explore the reasons behind this puzzle and to suggest ways to solve it. The lack of interest in real annuities can be explained by a lack of recognition that the purchase of a nominal annuity constitutes a speculative bet on future inflation rates and that the real annuity is the risk-free asset.
Jun 20, 2019
Adding a DIA to the last post that was looking at a consumption utility "frontier"
The Point
Lifetime consumption utility is, inter alia, a function of: allocation (return, vol), spending, longevity, risk aversion, and the presence of lifetime income. In the last post "Lifetime Consumption Utility "Frontier" with both Trend-following (fake) and Partial Annuitization (also fake)" I looked at the impact of partial annuitization (assuming a relatively fair annuity) by consuming 10 or 20% of initial wealth to buy a nominal cash flow by way of a modeled SPIA-like concept.
The point of this post is to compare the "10% of wealth" immediate SPIA with a "10% of wealth" purchase of a cash flow that starts at 85 i.e., a "deferred income annuity" or DIA or DIA-like thing, rather.
Lifetime consumption utility is, inter alia, a function of: allocation (return, vol), spending, longevity, risk aversion, and the presence of lifetime income. In the last post "Lifetime Consumption Utility "Frontier" with both Trend-following (fake) and Partial Annuitization (also fake)" I looked at the impact of partial annuitization (assuming a relatively fair annuity) by consuming 10 or 20% of initial wealth to buy a nominal cash flow by way of a modeled SPIA-like concept.
The point of this post is to compare the "10% of wealth" immediate SPIA with a "10% of wealth" purchase of a cash flow that starts at 85 i.e., a "deferred income annuity" or DIA or DIA-like thing, rather.
Jun 19, 2019
Lifetime Consumption Utility "Frontier" with both Trend-following (fake) and Partial Annuitization (also fake)
The Point
In my previous several posts I have been toying around with
- Simple abstracted 2-asset portfolio choice, along with a jointly made
- Spend choice (using constant spend for now), and then
- Adding a highly stylized third asset that might look like trend-following
to see how it plays out using a simulator that evaluates the expected discounted utility of lifetime consumption (EDULC) across the different combinations.
The point of this post is to now add some partial annuitization to the mix to see how it affects EDULC, especially when it is stacked on top of the other things we are working with before.
In my previous several posts I have been toying around with
- Simple abstracted 2-asset portfolio choice, along with a jointly made
- Spend choice (using constant spend for now), and then
- Adding a highly stylized third asset that might look like trend-following
to see how it plays out using a simulator that evaluates the expected discounted utility of lifetime consumption (EDULC) across the different combinations.
The point of this post is to now add some partial annuitization to the mix to see how it affects EDULC, especially when it is stacked on top of the other things we are working with before.
Jun 18, 2019
An attempt at a stylized lifetime consumption utility "frontier"
In the last several posts
- Self-Evaluation of My Own Lifetime Consumption Utility
- Self-Evaluation of My Own Lifetime Consumption Utility, Part 2
- Having Some Fun with Portfolio Choice vs. Lifetime Consumption Utility
- Lifetime Consumption Utility with addition of trend following-like behavior
- Self-Evaluation of My Own Lifetime Consumption Utility
- Self-Evaluation of My Own Lifetime Consumption Utility, Part 2
- Having Some Fun with Portfolio Choice vs. Lifetime Consumption Utility
- Lifetime Consumption Utility with addition of trend following-like behavior
I was playing around with portfolio choice along with a stylized version of an efficient frontier -- both with and without a third asset class that might resemble a trend following allocation of some amount unknown -- in order to see how an economic consumption utility game might play out. I now want to go back and add some more detail.
Honors (repost)
Repost...this time with picture. Blogger hates iPhones...
My Father’s Day present from my daughter: Stanford’s John G Sobieski Award for Creative Thinking In Economics for Honors Thesis “Market Timing: Individual Investor and Mutual Fund Performance in the Stock Market.” B.A. with honors with special recognition. Her honors honor me.
My Father’s Day present from my daughter: Stanford’s John G Sobieski Award for Creative Thinking In Economics for Honors Thesis “Market Timing: Individual Investor and Mutual Fund Performance in the Stock Market.” B.A. with honors with special recognition. Her honors honor me.
Jun 13, 2019
Lifetime Consumption Utility with addition of trend following-like behavior
This post is going to get very abbreviated treatment since I am headed out to a Daughter's graduation. In the last post Having Some Fun with Portfolio Choice vs. Lifetime Consumption Utility I was playing around with portfolio choice, spending, and consumption utility. At the end of that post I wondered what would happen if we added a trend-following-like behavior. Well, I took a shot at that question, though keep in mind none of this is real; it is highly highly FAKE.
If we were to hypothesize adding a third asset to our two asset portfolio -- and don't ask what or how much, this is just a hypothetical and I am interested in the behavior or movement more than I am the execution or plausibility -- we could re-envision the (old fake) efficient frontier in the last post like this (new fake) one where for the same level of return the vol shifts left but less on the safe end and more on the risk end. If I haven't mentioned it, the exact shift comes from only my imagination:
If we were to hypothesize adding a third asset to our two asset portfolio -- and don't ask what or how much, this is just a hypothetical and I am interested in the behavior or movement more than I am the execution or plausibility -- we could re-envision the (old fake) efficient frontier in the last post like this (new fake) one where for the same level of return the vol shifts left but less on the safe end and more on the risk end. If I haven't mentioned it, the exact shift comes from only my imagination:
 |
| Figure 1. What adding a trend following allocation might do to an eff frontier??? |
Jun 12, 2019
Having Some Fun with Portfolio Choice vs. Lifetime Consumption Utility
Point of the Post
The question is:
I know I've done something like this before (e.g., here) but
- I didn't do it specifically for me, and
- The 3D surfaces were cool and all, but were also distracting and washed out some of the nuance
So the point here is to now personalize it (with some redactions) and limit it to some finite, reasonable set of parameters just for illustration (and don't do 3D). This will not be too exhaustive or necessarily rigorous or "scientific." I just wanted to see what impact different choices along efficient frontier have on (my) consumption utility for different spend rates over (my) remaining lifetime and then compare it to where I am today. It'll go like this:
1. Create an efficient frontier in 11 allocation increments from 0% risk asset to 100%
2. Go up the frontier one allocation increment at a time
3. At each increment, seek out the spend rate that maxes a lifetime-consumption value function
4. Then: chart it and step back to behold the results...and maybe make some observations
The question is:
- What combination of portfolio choice and spend rate works the best given a particular set of limiting and probably naive and unstable-in-real-life assumptions
- for me at age 61
- using a lifetime consumption utility model?
I know I've done something like this before (e.g., here) but
- I didn't do it specifically for me, and
- The 3D surfaces were cool and all, but were also distracting and washed out some of the nuance
So the point here is to now personalize it (with some redactions) and limit it to some finite, reasonable set of parameters just for illustration (and don't do 3D). This will not be too exhaustive or necessarily rigorous or "scientific." I just wanted to see what impact different choices along efficient frontier have on (my) consumption utility for different spend rates over (my) remaining lifetime and then compare it to where I am today. It'll go like this:
1. Create an efficient frontier in 11 allocation increments from 0% risk asset to 100%
2. Go up the frontier one allocation increment at a time
3. At each increment, seek out the spend rate that maxes a lifetime-consumption value function
4. Then: chart it and step back to behold the results...and maybe make some observations
Jun 8, 2019
An amateur map of the psychology of irrational spending choice
Point of the Post
Since I was on a roll with this spending-choice thread (here and here, both of which were using my own assumptions rather than generic), and since risk-aversion has such a big impact in risk aversion math (surprise, that, eh?) I thought that I'd take the work I was doing recently with trying to optimize spend rates for a given set of assumptions (those are in the original post) using a consumption utility simulator...and now push it further. After the last run I was wondering:
Since I was on a roll with this spending-choice thread (here and here, both of which were using my own assumptions rather than generic), and since risk-aversion has such a big impact in risk aversion math (surprise, that, eh?) I thought that I'd take the work I was doing recently with trying to optimize spend rates for a given set of assumptions (those are in the original post) using a consumption utility simulator...and now push it further. After the last run I was wondering:
"what would all of the spending optima would look like if they were strung, like pearls, along an axis of risk aversion (RA, or alternatively "gamma") from low RA to high (abbreviated interval, in this case)?"
Self-Evaluation of My Own Lifetime Consumption Utility, Part 2
This inherits everything from Part 1, except here I am focusing on gamma = 2 and changing volatility (standard dev of returns) from .11 to .10. This might be similar to an incremental move into adding a trend following overlay. I know what will happen but wanted to chart it out, a chart that looks like this:
The outcome is
- ever so slightly higher optimal spend rate (3.4 vs 3.3) though the "flat ranges" on top are wide-ish
- ever so slightly higher lifetime utility of consumption
We already know that the model is very sensitive to risk aversion* which will push the optimal spend sharply to the left or right depending on the coefficient. Untested are any changes in other portfolio choice parameters, annuity purchase, spending volatility, fat tailed distributions, age, inflation vol and mean reversion, the subjective discount, different longevity structures, SS start age, etc...
*this is why I suggested last time, 95% tongue-in-cheek, that counselling and mental health services might be a powerful tool in a retirement finance tool belt. Skip the portfolio engineering and trend following overlays and just go get some therapy to get less risk averse: optimal spend rates magically go up.
- ever so slightly higher optimal spend rate (3.4 vs 3.3) though the "flat ranges" on top are wide-ish
- ever so slightly higher lifetime utility of consumption
We already know that the model is very sensitive to risk aversion* which will push the optimal spend sharply to the left or right depending on the coefficient. Untested are any changes in other portfolio choice parameters, annuity purchase, spending volatility, fat tailed distributions, age, inflation vol and mean reversion, the subjective discount, different longevity structures, SS start age, etc...
*this is why I suggested last time, 95% tongue-in-cheek, that counselling and mental health services might be a powerful tool in a retirement finance tool belt. Skip the portfolio engineering and trend following overlays and just go get some therapy to get less risk averse: optimal spend rates magically go up.
Jun 7, 2019
Self-Evaluation of My Own Lifetime Consumption Utility
I don't recall that I've ever run my lifetime consumption utility simulator on my own personal data. That seems odd given why I do the blog. So, this post is a stub-run for me and my data. This will not be entirely good practice since I am just winging it but I wanted to see.
The Model
The model has been discussed before but I am using an animated value function based on a survival weighted, subjectively discounted, CRRA utility of consumption over a lifetime where consumption snaps to income when wealth runs out before end of life. The model was discussed here so I won't belabor it in this post.
The Model
The model has been discussed before but I am using an animated value function based on a survival weighted, subjectively discounted, CRRA utility of consumption over a lifetime where consumption snaps to income when wealth runs out before end of life. The model was discussed here so I won't belabor it in this post.
Jun 4, 2019
100: Holy Crap That Hurt
I decided to take up a twitter challenge from someone today and do 100 push-ups. Not sure if I'm supposed to keep doing it every day but let's talk about today first before we get to tomorrow.
I've been working out every day now for 2 years. I used to be a competitive swimmer. I once challenged myself, and succeeded, to do 1000 pushups a day for three months. The mirror, to my squinting jaundiced eye, still says "fit." ahem...
So, 100 push-ups, no problem, right? Well, to ask the question is to answer answer it. First, the issue is not so much muscle strength as such. I mean I started with 10 reps but finished with a strong fast "30" from 71-100 and probably could still have done 50 sequentially if real money were on the line. The whole thing from 0 to 100 took like 20 minutes at the most. The problem, however, was with the first 10. And here I know that everyone over 60 is going to absolutely get this and everyone who is 25 or 30 is going to say "pfffft, old men suck."
The problem with the first 10 was the not so much the pec or tricep strength, which I would have expected. It was the other stuff. It was the shoulders, front (front delt and clavicular head) and rotator cuff (both current semi-injuries or at least inflamed or something); it was my elbow tendons; it was some weird injured-bicep pain, though that really shouldn't have come into play here; and it was also my back (sorta broke it 15 years ago). Even my left wrist was bitching: so, "shut up wrist, this is not your fight."
That really f'n hurt. It also felt like the distance between young-me and me, and the distance between idealized-mirror-me-now and real-old-man-me-now, seemed to be far. So: hurt. Pride and body.
But I think I might do it again tomorrow. Maybe even 200. After some Advil.
I've been working out every day now for 2 years. I used to be a competitive swimmer. I once challenged myself, and succeeded, to do 1000 pushups a day for three months. The mirror, to my squinting jaundiced eye, still says "fit." ahem...
So, 100 push-ups, no problem, right? Well, to ask the question is to answer answer it. First, the issue is not so much muscle strength as such. I mean I started with 10 reps but finished with a strong fast "30" from 71-100 and probably could still have done 50 sequentially if real money were on the line. The whole thing from 0 to 100 took like 20 minutes at the most. The problem, however, was with the first 10. And here I know that everyone over 60 is going to absolutely get this and everyone who is 25 or 30 is going to say "pfffft, old men suck."
The problem with the first 10 was the not so much the pec or tricep strength, which I would have expected. It was the other stuff. It was the shoulders, front (front delt and clavicular head) and rotator cuff (both current semi-injuries or at least inflamed or something); it was my elbow tendons; it was some weird injured-bicep pain, though that really shouldn't have come into play here; and it was also my back (sorta broke it 15 years ago). Even my left wrist was bitching: so, "shut up wrist, this is not your fight."
That really f'n hurt. It also felt like the distance between young-me and me, and the distance between idealized-mirror-me-now and real-old-man-me-now, seemed to be far. So: hurt. Pride and body.
But I think I might do it again tomorrow. Maybe even 200. After some Advil.
Jun 1, 2019
Volatility effects on a hypothetical real-wealth-option paid for by spending reductions
This post requires some knowledge of its precursor "Quick and Dirty Experiment with Real Options on Future Wealth vs Spending Choice" and it inherits all the assumptions and analytical models in that post. The basic concept is to propose the idea of a hypothetical real-wealth-option with a tenure of 30 periods and a strike of initial wealth in real terms -- with all the question marks about those stakes-in-the-ground that were mentioned in the last post. The underlying is the consumption portfolio with the current "price" being initial wealth at time zero and where the price trajectory is based on a net wealth process that is GBM-like but can go to and through zero. That means that for that underlying we have volatile, randomized returns from which we consume at a constant spend rate. The input arithmetic return assumption is 4% real and spend rates are the thing being varied to see what happens and for which the interval of interest will be 2 to 10%. Volatility, 12% in the last post, is varied here between 6% 12% and 25%. That's an odd assembly of vol but so be it. Also, note that the sim iterations were upped to 30k between the 3.5 and 4% spend in order to make sure that I had a good bead on the gap between the output lines in figure 1.
Using the framework from the last post and the new assumptions above, this is what we get:
Using the framework from the last post and the new assumptions above, this is what we get:
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