Why Roth conversions always pay off—if you can hold on long enough

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McQ
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Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

This thread draws on experience gained from participating in the thread started by indexlover on my SSRN working paper (https://papers.ssrn.com/sol3/papers.cfm ... id=3860359), plus two threads started by DSBH, and a thread started by Woodspinner. In addition to indexlover, DSBH and Woodspinner, I’d like to thank participants in those forums for insightful criticism, in particular, FiveK, cas, chip and JoinToday—and others too many to list here.

Roth conversion outcomes as an n-period game

Many discussions of Roth conversions get hung up on what I will call “2 period” analyses. Any time you read that “Roth conversions should work out as long as future marginal tax rates are higher than current rates,” a 2-period game will most likely underlie the analysis.

By extension, in that same 2-period game, if future tax rates are unchanged, then a Roth conversion can only breakeven. This breakeven result—zero gain, zero loss from the conversion—follows directly from the commutative property of multiplication. It holds regardless of how many years of returns separate period 1 from period 2 (invariance of outcomes over time), and regardless of fluctuations in the annual returns over those years (invariance across volatility).

But the 2-period analysis turns out to be a special case within the larger class of n-period games, and one that is not very helpful for the retiree who will evaluate conversion outcomes after RMDs begin. If the goal of the conversion was to accumulate greater after-tax wealth at some unspecified future date, by reducing tax exposure consequent to RMDs, then an n-period game must be set up and analyzed.

I will assume throughout that indeed, that was the goal of the conversion: to accumulate greater after-tax wealth at some unknown but distant future date, by reducing tax exposure that would otherwise be incurred by having to take RMDs not needed for living expenses. The claim made in the title of the thread presumes this is the goal of the conversion; if your goal in converting is to achieve something else, this thread may not be relevant to you.

In an n-period game, outcomes are not invariant over time (it matters in which period after-tax wealth is evaluated). As a result, it becomes possible for Roth conversions to accumulate greater after-tax wealth even when future tax rates are unchanged--or move lower. But it will take time; and the more unfavorable the future movement in tax rates, the longer the time it will take for the conversion to produce a pay off.

Put another way, RMDs change the game, and cannot be analyzed within a 2-period framework, since RMDs will continue for n periods, where n = [age at death + 10 – 71]. That means that in most cases n will be a two-digit number >20 and <50. Each time an RMD is taken that would not had to have been taken and taxed, had the conversion occurred, the prospective payoff from the Roth conversion will change.

Once the structure of the “n-period RMD game” is understood, it will become apparent why Roth conversions always pay off, if the time frame is long enough, but almost never produce a substantial pay off prior to age 90, and rarely produce a big pay off at any age < 100 when evaluated in real terms.

Caveats and Constraints

1st Caveat: as the tax rate paid on the conversion declines toward zero, the real payoff will expand more and more rapidly, and will begin to explode upward as the tax rate on the conversion drops below 1.0%. Translation: backdoor Roths are great! But this thread focuses on Roth conversions where the tax rate is going to be rather more than one percent. The assertion of only modest outcomes, therefore, mostly applies when the conversion is made at tax rates above 12%, and more especially at marginal rates of 22% and above.

2nd Caveat: The assertion of modest outcomes also mostly applies when future marginal rates are similar to conversion rates. If instead you can convert today at 12%, and your future rate turns out to be 32%--or 39.6%, then a Roth conversion can be quite lucrative indeed. It is when you convert at 22% to save post-TCJA tax at 25%, or any similar increment, that you should expect only modest outcomes.

3rd caveat: these maxims concern only the intrinsic outcome of a Roth conversion that holds both asset allocation and asset location constant. You may be able to turbocharge conversion outcomes by means of clever asset location, i.e., by putting high growth assets in the Roth and leaving low growth assets in the TDA. And if opening the Roth causes you to increase your allocation to high return assets, that too can turbocharge the outcome actually received. Best wishes!

But please don’t attribute your good fortune to the necessary and intrinsic operation of paying a lump sum in tax now to reduce a future stream of tax payments. This thread will be concerned only with the pure effect of reducing future tax exposure by means of a one-time tax debit paid today.

Analogy

The most familiar analogue to the n-period RMD game is the homeowner fixed mortgage prepayment game. Here a one-time paydown of the principal can be made at the homeowner’s option at any point. If the amount paid is to any degree substantial, and made in year 2 or at a similarly early point, that paydown will shorten the life of the mortgage, and save a multiple of itself in interest not paid. But it takes a long time for the payoff to be received (typically > year 25), and the dollar amount of the payoff will be far lower if, say, the homeowner refinances in year 10.

Most Roth conversions undertaken to reduce RMDs provide a similar level of payoff as mortgage prepays if evaluated over a mere 15 to 20 years; and with a similar degree of certainty. Conversely, if your planning horizon extends out past age 100, and stocks are part of your asset allocation, a Roth conversion can be rather more lucrative than a mortgage prepayment.

All these points were made in my SSRN paper; but for not a few Bogleheads, the spreadsheet constructed for that paper failed to close the sale. In fact, I started this thread because BH criticism has helped me to devise a better spreadsheet (looking at you cas—your insightful criticism of the old spreadsheet proved extremely helpful). The narrative developed for this thread will in turn provide a foundation for revising the SSRN paper.
Next post introduces the spreadsheet.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

New Spreadsheet

[9/24/2021:RMD divisors corrected with the assistance of FiveK]

The spreadsheet discussed here will eventually be made available on my website. For the moment I will only be presenting images, but if impatient, you should be able to reconstruct it at the cost of a few minutes of typing. Only images are presented for the moment because I hold out the hope the spreadsheet might be further improved by feedback received on this thread. Already, in the course of drafting these posts, I’ve caught and corrected several flubs and further improved my understanding; which for me, is the point of the exercise.

The spreadsheet is constructed to allow for limited sensitivity testing, in particular, it allows the user to vary the current and future tax rate. The image accompanying this post is based on a conversion tax rate of 24% and a constant future tax rate of 24%, as this base case will help to reveal how the n-period RMD game plays out.

This spreadsheet has two limitations worth noting that constrain its usefulness for personal planning, as opposed to theoretical demonstration, which is the goal here. First, all capital gains and dividends in the taxable account are taxed in the year received. In real life, one would seek not to incur capital gains annually in a taxable account, but to let them build up unrealized, in hopes of a step up at death. Conversion returns would be weaker, especially at death, if that strategy was used. Second, no attempt is made to exploit asset location: every account is invested in the same asset, taken to be stocks returning 10% nominal, 7% real after inflation at 3%. Again, the goal is a crystal-clear demonstration of the dynamics of n-period conversion outcomes, hence the simplifications.

Spreadsheet structure

1. Top row contains tax rates and other rates in blue shading. Formulae in the main body reference these cells, so changing one cell, say, future tax rate, updates all the calculations
2. Second row contains column headings, most of which should be self-explanatory
3. Third row cells use column labels to call out the formula used to generate entries in the column beneath.
4. Ultimately a notes tab will explain how to use secondary tabs, which will be clones of the main tab with additions to allow for specific types of sensitivity tests (e.g., widowed survivor paying single tax rates).
--Rightmost blue heading is cut off; future versions will allow for a different return for TDA assets versus Roth or taxable assets
5. But these secondary tabs haven’t been finalized as of this post, which is another reason why I only post an image for now


Image

Period by period analysis, constant tax rate of 24%

Here’s where we get down in the weeds. Constructed with the aid of caffeine and best perused with same.

Period 1

The conversion is made, presumed to be in late December in the year the retiree turns 71. The light green bloc can be treated as a counterfactual: pre-tax wealth in this portion of the TDA if that $100,000 had not been converted, but left in the TDA. The light gray bloc represents the result from reinvesting each year the after-tax remainder from each RMD.

Why are RMDs reinvested? Because of the underlying assumption about goals: that a conversion was contemplated precisely because these RMDs were expected to be surplus, i.e., not necessary to meet spending needs or living expenses. The conversion serves to reduce these surplus RMDs, thus preventing unwanted ongoing tax exposure, at the cost of a one-time tax payment up front. But if the conversion had not been done, the RMDs would still have been surplus, hence, the after-tax remainder of each RMD could have been immediately re-invested.

In this base case, tax is paid from converted funds. I’ll consider alternatives later.

Later I’ll also consider the outcome if plans change and the retiree begins to tap Roth funds for a sudden unexpected expense. I’ll also consider scenarios where Roth funds begin to be tapped annually to provide an ongoing boost to annual expenditure, i.e., to harvest the tax savings sooner, and live better thereby, as opposed to amassing more financial wealth for later, presumably for heirs.

Period 2

The first RMD is taken, again presumed to be at the very end of the year. Tax of $875.91 must be paid from the RMD of $3650, leaving $2774 to invest in the taxable account. Arriving late in the year, that $2774 is taken to be the end-of-year amount in the taxable account. Meanwhile, the Roth account has appreciated 10%.

Column N evaluates the outcome. This is the after-tax value of column G plus the end-of-year taxable account balance in column L (it always has a 100% cost basis). As can be seen in Column O, after 2 periods the commutative and distributive properties of multiplication apply: because tax rates have stayed constant, the Roth conversion exactly breaks even. Taxing the column G balance and adding the after-tax value of the RMD (column L) gives exactly the same outcome as taxing the pre-RMD’d column E value.

In other words, it’s only a 2-period game thus far.

Period 3

Another RMD is cranked out and its after-tax value added to the taxable account. But in this period new entries appear in columns J and K. Specifically, last year’s taxable balance has incremented by the indicated rate of return, and then been decremented by the capital gains & dividend tax levied on the increment.

But now, when the Roth outcomes are evaluated in columns M, N and O, the result is not the same as after two periods: here in period 3 the Roth account has pulled ahead. Ever so slightly.

Tax rates have not changed; why does the outcome appear to violate the commutative property of multiplication? Answer: tax drag. The $41.61 in tax paid on appreciation in the taxable account is a dead loss. In other words: the totally tax-free character of the Roth account has here begun to assert itself.

But I should note that we don’t yet have a 3-period game in the taxable account, since its creation lags the conversion by one period. Period “4” will be required before we can fully grasp the nature of an n-period RMD game.

Period 4

Another RMD, another taxed return on the taxable account; but now the Roth account has jumped further into the lead. In fact, its advantage has more than tripled relative to the prior period. Most interestingly, the Roth advantage is no longer equal to the tax drag on the taxable account that year of $90.89—it is bigger.

For those readers with good mathematical intuition: why is the Roth advantage in period 4 exactly $136.66? (Hint: approach this as a sum and decompose this value into its components).
Alright, a few blank lines follow while interested readers work on this quiz.




Time is up, please turn in your answers.

The value of $136.66 can be decomposed as follows:
$90.89 lost to tax in the current period
$41.61 lost to tax in the prior period
$ 4.16, representing foregone appreciation, at 10%, on the dead loss from the $41.61 paid last year and no longer available for investment tax-deferred. Put another way, because the Roth suffers no tax loss ever, the Roth always earns the full 10%. Accordingly, when tax drag occurs, the subsequent “cost” on the no-conversion path is the appreciation that could have been earned on the with-conversion path, which is 10%, "tax-free forever."

Period 5

All periods subsequent to period 4 have the same entries and structure and won’t be discussed in detail. But period 5 does allow for a makeup quiz. The Roth surplus is now $299.45; the current period tax of $149.12 is one component; please calculate and list the other components.

Multiple blank lines as before, to give interested readers time to attempt it.




That’s right: the formula for total tax drag after n+1 periods is:
Current year tax +
Prior year’s tax +
Lost appreciation on prior year tax +
Each Nth prior period tax paid +
Lost appreciation over n periods for each of the corresponding nth period prior tax payments

In short, tax drag compounds. The Roth advantage after 10 years is in the thousands; after 20 years, tens of thousands, and as age 100 approaches, over one hundred thousand dollars. Even though tax rates have not changed, and even though initially only $76,000 was placed in the Roth after paying conversion tax.

So far, so good; the difference between an n-period and a 2-period game has been demonstrated. After n periods, a series of dead losses has been incurred, and these dead losses represent an ever-increasing negative future value as these losses compound. The payoff from the Roth conversion increases each year and the increase is exponential in character. And all of this is achieved despite future tax rates staying exactly the same as the tax rate on the conversion.

* * *

Next, I need to combat a naïve view of these results. Some might jump to the conclusion that it is only tax drag on the taxable account that matters. The $875.91 in tax paid on the RMD doesn’t seem to enter into the calculations; tax drag appears to be confined to the reinvested RMDs. The next post will disentangle the roots of that mistaken conclusion.

However, I hope this first post has gotten me 80% of the way to delivering on the promise of the thread title.
Next post follows after a lag to see if readers spot errors or require clarification.
Last edited by McQ on Fri Sep 24, 2021 11:46 am, edited 2 times in total.
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jarjarM
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by jarjarM »

Sorry Professor, the image seems to be broken. A quick cursory check shows that us mortals don't have access to it. :beer Otherwise, continue to read the long post right now. Thanks for all the info. :beer
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by Lee_WSP »

I agree that in theory RMD's can go on forever, but at a distribution period of 1.9 (an effective halving of the portfolio each year), you quickly get to effective zero by age 130 (0.002863154%).
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by FiveK »

A spreadsheet that is available now is provided as part of the How do RMDs affect Roth conversion choices? thread.

I've done some looking at it without finding errors, but that was hardly an exhaustive check. Would be nice if it and McQ's tool arrive at the same conclusion given the same inputs. ;)
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

jarjarM wrote: Thu Sep 23, 2021 1:04 pm Sorry Professor, the image seems to be broken. A quick cursory check shows that us mortals don't have access to it. :beer Otherwise, continue to read the long post right now. Thanks for all the info. :beer
Thanks for the quick alert. I can see the SS image in Chrome, I cannot see the image if I open it in Microsoft Edge. But then, I also can't see LadyGeek's calculator image in Edge in the demonstration post at viewtopic.php?p=3469466#p3469466

So there may be browser settings at work. In the meantime, if you click on the quote button for my post, you will see the image URL. If you paste that into a browser, does the image of the spreadsheet appear?
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FiveK
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by FiveK »

McQ wrote: Thu Sep 23, 2021 3:55 pm if you click on the quote button for my post, you will see the image URL. If you paste that into a browser, does the image of the spreadsheet appear?
No. Putting https://lh3.googleusercontent.com/d/1hw ... rS4P45FF76 into either Firefox or Chrome returns an "Error 403 ...does not have permission to get URL..."

Have you changed access in your Google Drive for this file to allow "anyone with the URL" to read it?
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

FiveK wrote: Thu Sep 23, 2021 4:02 pm
McQ wrote: Thu Sep 23, 2021 3:55 pm if you click on the quote button for my post, you will see the image URL. If you paste that into a browser, does the image of the spreadsheet appear?
No. Putting https://lh3.googleusercontent.com/d/1hw ... rS4P45FF76 into either Firefox or Chrome returns an "Error 403 ...does not have permission to get URL..."

Have you changed access in your Google Drive for this file to allow "anyone with the URL" to read it?
[switched to postimages and corrected the SS per FiveK on 9-24-2021, so deleted this image]
Last edited by McQ on Fri Sep 24, 2021 12:27 pm, edited 1 time in total.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by kryptonic »

I can see that image.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by kardan »

Visible in Edge.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

Thanks to you both for the quick confirmation. Apologies to all for newbie ignorance about posting images; my first attempt here at BH. Resorted to postimages site because my (university-related) Google drive didn't seem to offer an option to "share with anyone who has the link." Tomorrow's post will use postimages.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by FiveK »

Small point: the RMD table in https://www.govinfo.gov/content/pkg/FR- ... -24723.pdf has slightly different divisors than what is in the (now very visible, thanks) spreadsheet image.

I don't know for sure which set of numbers will apply - there may have been an update since that federal register publication, but a quick internet search didn't find a more recent....
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by Broken Man 1999 »

My heirs will reap the most benefit. That is enough incentive for me.

Nothing like receiving a plump Roth account as an inheritance.

Broken Man 1999
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

FiveK wrote: Thu Sep 23, 2021 5:46 pm Small point: the RMD table in https://www.govinfo.gov/content/pkg/FR- ... -24723.pdf has slightly different divisors than what is in the (now very visible, thanks) spreadsheet image.

I don't know for sure which set of numbers will apply - there may have been an update since that federal register publication, but a quick internet search didn't find a more recent....
My bad, I will fix tomorrow. Numbers will change by a few dollars. Thanks for catching.

I made the mistake of relying on a secondary source: https://keeblerandassociates.com/2019/1 ... -1st-2021/
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by milktoast »

Thanks for this. Very clear explanation.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by dodecahedron »

Broken Man 1999 wrote: Thu Sep 23, 2021 6:23 pm My heirs will reap the most benefit. That is enough incentive for me.

Nothing like receiving a plump Roth account as an inheritance.

Broken Man 1999
Indeed. Especially if one's heir is one's spouse. One could even envision an infinite chain of Roth tax-free growth if the surviving spouses remarry.

For convenience, we will assume spouses die in alphabetical order. To begin with, Spouse A and B are married. Spouse A converts his IRA to Roth prior to age 72, then dies. After A dies, Spouse B retitles Spouse A's Roth into her own name, and (after a suitable interval) marries Spouse C.

Rinse and repeat ad infinitum. An infinitely stretchable Roth and no RMDs ever.

I am not actually suggesting this, let alone contemplating it. Just a theoretical mathematical possibility.

For garden-variety non-spouse heirs, Roths also have a lot of appeal. No trying to guess what the optimal timing of taxable distributions over the ten year period is, no worrying about distributions having an unknown impact on IRMAA or ACA premium costs, eligibility for any number of AGI-related means-tested programs, etc.

But for heirs with charitable inclinations and/or large medical expenses (e.g., LTC), tIRA may make more sense.

I am splitting the difference, diversifying (some Roth, some trad) and hoping for the best.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by 2pedals »

^^ +2
I just don't know what's going to happen. It doesn't feel too good using discretionary lumpy expenses and at the same time jumping into higher tax brackets and IRMAA payments. With adequate Roth it enables one to balance things out better when lumpy expenses are desired. RMDs are not friendly to single tax brackets for surviving spouse and 10 year distribution limits for single heirs.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by SGM »

We will never have RMDs and our IRMAA payments as well as income taxes are lower than if we did not do Roth conversions. DW has excellent health and extreme longevity in her family. Most if not all of the Roth will be inherited by DW and possibly our children. Our plan is to allow the Roth to grow and live off of SS, annuities and farm rental income.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by cas »

I'm going to bump this comment by FiveK.
FiveK wrote: Thu Sep 23, 2021 1:28 pm A spreadsheet that is available now is provided as part of the How do RMDs affect Roth conversion choices? thread.

I've done some looking at it without finding errors, but that was hardly an exhaustive check. Would be nice if it and McQ's tool arrive at the same conclusion given the same inputs. ;)
I haven't had time to look at closely at either McQ's or MDM's spreadsheet, but, as FiveK points out, it would definitely be a good test to see if two independently developed spreadsheets, examining the same phenomenon, produce the same outputs, if they have the same inputs. (Especially since both developers are at the stage where they are asking for other eyes on the mechanics of the spreadsheet.)

Except I think there is already one assumption (input) where they are diverging. (Edit: I take that back. After looking a bit at the MDM spreadsheet, the spreadsheet lets you set what the tax rate is after Year 1. And, in the default case, MDM doesn't seem to have followed Kitces' assumption.) FiveK? Did you understand why Kitces decided to use the BETR (Break Even Tax Rate) after Year 1 instead of the original tax rate? Once MDM figured out that was what Kitces was doing, he/she made a comment along the lines of "I guess that is a valid assumption you could make, as long as you are clear what your assumption is." And I thought to myself "Hmm. I don't quite see why Kitces decided to use the BETR. I need to think harder about that sometime." But I haven't yet done that thinking.

Maybe because using BETR was the assumption that was least beneficial to the Roth conversion, so it stress-tested the Roth conversion the most? (But I really haven't put appropriate effort into thinking about it, so that thought may be way off.)

I'm usually a bit wary of trying to gain too much security from spreadsheets when it comes to Roth conversions, given all the unknowns over a long period, but I'm interested in this examination of the effect of tax drag from reinvested RMDs. The MDM spreadsheet/discussion came up with some results that were at least slightly different from what my intuition would have been (e.g. on the topic of Roth conversions when the beneficiary is going to be a charity or in a scenario when the (human, non-spouse) heir has a significantly lower tax rate than the original owner.)
Last edited by cas on Fri Sep 24, 2021 12:25 pm, edited 1 time in total.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by Chip »

Thanks so much for continuing the discussion and building the models.
McQ wrote: Thu Sep 23, 2021 12:52 pm This spreadsheet has two limitations worth noting that constrain its usefulness for personal planning, as opposed to theoretical demonstration, which is the goal here. First, all capital gains and dividends in the taxable account are taxed in the year received. In real life, one would seek not to incur capital gains annually in a taxable account, but to let them build up unrealized, in hopes of a step up at death. Conversion returns would be weaker, especially at death, if that strategy was used. Second, no attempt is made to exploit asset location: every account is invested in the same asset, taken to be stocks returning 10% nominal, 7% real after inflation at 3%. Again, the goal is a crystal-clear demonstration of the dynamics of n-period conversion outcomes, hence the simplifications.
While I fully understand the need for the second simplification, I question the need for the first one. If the underlying assumption is that the RMD will not be spent, why would capital gains be incurred after moving the RMD to the taxable account, where it would continue to be unspent? I realize open end mutual funds distribute capital gains (with the exception of Vanguard), but few broad market ETFs do.

I would also like to lobby for using real returns rather than assuming both nominal returns and inflation. I personally can't easily compare Year 0 with Year 20 when Year 20 dollars are worth 45% less than Year 0, assuming 3% inflation.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by Watty »

Why Roth conversions always pay off—if you can hold on long enough
I did not follow the details but you need to be careful about using the word "always" since one exception is enough to disprove your primis.

For example a single person might do a Roth conversion when they are in the higher single tax brackets, but they could then get married and then be in the lower joint tax brackets.

Another is that someone might have a year when they have exceptionally high income and are in a higher than normal tax bracket, like when they sell a business. Doing a Roth conversion that year would likely not pay off either.

For either person the Roth conversion would not pay off so your argument would be shown to not be correct.

You obviously put a lot of thought and work into this you might want to rephrase that "always" claim since it sounds too extreme and bit like clickbait.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by cas »

Chip wrote: Fri Sep 24, 2021 8:08 am While I fully understand the need for the second simplification, I question the need for the first one. If the underlying assumption is that the RMD will not be spent, why would capital gains be incurred after moving the RMD to the taxable account, where it would continue to be unspent? I realize open end mutual funds distribute capital gains (with the exception of Vanguard), but few broad market ETFs do.

I would also like to lobby for using real returns rather than assuming both nominal returns and inflation. I personally can't easily compare Year 0 with Year 20 when Year 20 dollars are worth 45% less than Year 0, assuming 3% inflation.
I had these same two thoughts.

On the first one (what to assume about taxes on cap gains), there was another thread recently where this topic came up, in the context of looking at the output of a Fidelity Investments Roth conversion calculator. The Fidelity calculator said in the fine print that it was assuming that the taxable account (holding the reinvested RMDs) would be liquidated/tax paid at the end of the study period. This one assumption was making a huge difference in the "Break Even Tax Rate" for Roth conversions that the Fidelity calculator was showing, overshadowing pretty much all other factors (in the specific scenario presented by the original poster of the thread.). The original poster in that thread was not realizing the assumption or acknowledging the effect, causing ... umm ... vigorous discussion with other posters.

On the second one (nominal vs real), it appears that both the MDM spreadsheet (that FiveK mentions) and the 2009 Kitces study that preceded it, did calculations in nominal terms as well. (Edit: After looking a bit more at the MDM spreadsheet, I take that back. The spreadsheet just lets you put in your cap gain return rate and decide for yourself whether you are dealing in real or nominal terms. It doesn't mention inflation.) However, they both then proceed on to a "Break even tax rate" (BETR) calculation. I haven't looked at the equation to make sure, but my guess is that the nominal vs real distinction is cancelled out during that calculation. Then they discuss the results using the BETR, so they avoid the problem with the human mind having difficulty grasping the value/purchasing power of future dollars.

On the other hand, BETR doesn't really show the magnitude of dollar advantage/disadvantage of a Roth conversion, which seems to be what McQ is interested in. But I would agree that real dollars would be easier for my mind to grasp if magnitude is what McQ wants to highlight.

Also, I seem to recall FiveK and McQ having an unresolved discussion on the validity of BETR in some past thread. .I don't know where McQ stands with respect to the BETR calculation at this point.
Last edited by cas on Fri Sep 24, 2021 12:47 pm, edited 2 times in total.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

dodecahedron wrote: Thu Sep 23, 2021 8:02 pm
Indeed. Especially if one's heir is one's spouse. One could even envision an infinite chain of Roth tax-free growth if the surviving spouses remarry.

For convenience, we will assume spouses die in alphabetical order. To begin with, Spouse A and B are married. Spouse A converts his IRA to Roth prior to age 72, then dies. After A dies, Spouse B retitles Spouse A's Roth into her own name, and (after a suitable interval) marries Spouse C.

Rinse and repeat ad infinitum. An infinitely stretchable Roth and no RMDs ever.

I had not thought of that possibility!
It reminds me of the tough problems considered in social security books, where the benefit for spouse D or spouse E in your nomenclature has somehow to be figured.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

2pedals wrote: Thu Sep 23, 2021 8:19 pm ^^ +2
I just don't know what's going to happen. It doesn't feel too good using discretionary lumpy expenses and at the same time jumping into higher tax brackets and IRMAA payments. With adequate Roth it enables one to balance things out better when lumpy expenses are desired. RMDs are not friendly to single tax brackets for surviving spouse and 10 year distribution limits for single heirs.
I will take up the lumpy expense case in a week or two. Although your point is a staple of Roth discussions ("if I have a Roth, then I can fix the roof / replace the car / help with a down payment, without tapping my TDA and bumping up a bracket"), I'm not sure that will pencil out as expected. To be continued.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

cas wrote: Fri Sep 24, 2021 7:22 am I'm going to bump this comment by FiveK.
FiveK wrote: Thu Sep 23, 2021 1:28 pm A spreadsheet that is available now is provided as part of the How do RMDs affect Roth conversion choices? thread.

I've done some looking at it without finding errors, but that was hardly an exhaustive check. Would be nice if it and McQ's tool arrive at the same conclusion given the same inputs. ;)
I haven't had time to look at closely at either McQ's or MDM's spreadsheet, but, as FiveK points out, it would definitely be a good test to see if two independently developed spreadsheets, examining the same phenomenon, produce the same outputs, if they have the same inputs. (Especially since both developers are at the stage where they are asking for other eyes on the mechanics of the spreadsheet.)

...

Maybe because using BETR was the assumption that was least beneficial to the Roth conversion, so it stress-tested the Roth conversion the most?
The claim I will attempt to support in this thread (per the title, and see my response to Watty below) will be that the BETR for a Roth conversion is always zero (0%). Only if "distant future" is arbitrarily constrained to some near-term date (i.e., not distant at all, no longevity, no heirs, yada yada) will the breakeven rate for the conversion be meaningfully greater than zero.

I haven't shown that yet; early next week is the schedule for that post. But I did want to put a target on the back of BETR right away, given the role it has played in the work of other authors.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

Chip wrote: Fri Sep 24, 2021 8:08 am Thanks so much for continuing the discussion and building the models.
McQ wrote: Thu Sep 23, 2021 12:52 pm This spreadsheet has two limitations worth noting that constrain its usefulness for personal planning, as opposed to theoretical demonstration, which is the goal here. First, all capital gains and dividends in the taxable account are taxed in the year received. In real life, one would seek not to incur capital gains annually in a taxable account, but to let them build up unrealized, in hopes of a step up at death. Conversion returns would be weaker, especially at death, if that strategy was used. Second, no attempt is made to exploit asset location: every account is invested in the same asset, taken to be stocks returning 10% nominal, 7% real after inflation at 3%. Again, the goal is a crystal-clear demonstration of the dynamics of n-period conversion outcomes, hence the simplifications.
While I fully understand the need for the second simplification, I question the need for the first one. If the underlying assumption is that the RMD will not be spent, why would capital gains be incurred after moving the RMD to the taxable account, where it would continue to be unspent? I realize open end mutual funds distribute capital gains (with the exception of Vanguard), but few broad market ETFs do.

I would also like to lobby for using real returns rather than assuming both nominal returns and inflation. I personally can't easily compare Year 0 with Year 20 when Year 20 dollars are worth 45% less than Year 0, assuming 3% inflation.
Fair points both. Here's what I plan to do as the thread develops:
1. I'll construct a different version of the spreadsheet where capital gains are embedded and accumulate rather than being realized each year. That's not been done here because it complicates the analysis (realizing twenty or thirty years of capital gains all at once makes the tax rate uncertain--could be 18.8%, 23.8%, or some other number as currently under ...) oops can't talk about tax legislation in process here on BH.
A higher rate will weaken / slow the outcome of conversions but not change the pattern. And if there is a step up at death, conversion outcomes will weaken further. All grist for the mill, but only after the initial demonstration has been secured.

2. I understand the discomfort with looking at nominal dollars decades out. In a week or two I'll raise the issue of metrics, and at that point, will translate conversion outcomes into real dollars. But again, first the initial demonstration has to be secured.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by Chip »

McQ wrote: Fri Sep 24, 2021 12:56 pm 1. I'll construct a different version of the spreadsheet where capital gains are embedded and accumulate rather than being realized each year. That's not been done here because it complicates the analysis (realizing twenty or thirty years of capital gains all at once makes the tax rate uncertain--could be 18.8%, 23.8%, or some other number as currently under ...) oops can't talk about tax legislation in process here on BH.
A higher rate will weaken / slow the outcome of conversions but not change the pattern. And if there is a step up at death, conversion outcomes will weaken further. All grist for the mill, but only after the initial demonstration has been secured.
Fair enough. But I do think that under current law a majority of decedents will get a step up at death. So maybe that should be the base case. Unless all those Silicon Valley people you hang around with are already worth more than 11.4M. :D
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by dodecahedron »

Watty wrote: Fri Sep 24, 2021 8:47 am
Why Roth conversions always pay off—if you can hold on long enough
I did not follow the details but you need to be careful about using the word "always" since one exception is enough to disprove your primis.

For example a single person might do a Roth conversion when they are in the higher single tax brackets, but they could then get married and then be in the lower joint tax brackets.

Another is that someone might have a year when they have exceptionally high income and are in a higher than normal tax bracket, like when they sell a business. Doing a Roth conversion that year would likely not pay off either.

For either person the Roth conversion would not pay off so your argument would be shown to not be correct.
Arguably, the "if" contingency, "if you can hold on long enough" makes the statement almost* tautologically true. To your hypotheticals above, the easy defense is "Well, they simply did not satisfy the hypothesis, they could not hold on long enough.

Roth conversions are generally a gamble. One never knows how long one will live, how long one's spouse will live, etc.

The mathematical possibility of an infinite chain of remarried spouses I described means that it is at least theoretically possible to hold on for an indefinite period of time, during which tax drag from dividends can be expected to eventually overcome all kinds of initial disadvantages of Roth conversions.

*Edited to add: I used the word almost because it is possible to construct examples with no dividend (or capital gains) drag. (E.g., if the investment portfolio throws off only dividends and LTCG and if taxpayer lives in a state with no state or local income tax and also manages to keep future taxable income sufficiently low so that qualified dividends and capital gains are taxed at zero, there is no tax drag.)

Note that I have a mathematical bent and like to consider edge cases! :D
Last edited by dodecahedron on Fri Sep 24, 2021 1:17 pm, edited 3 times in total.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

Watty wrote: Fri Sep 24, 2021 8:47 am
Why Roth conversions always pay off—if you can hold on long enough
I did not follow the details but you need to be careful about using the word "always" since one exception is enough to disprove your primis.

For example a single person might do a Roth conversion when they are in the higher single tax brackets, but they could then get married and then be in the lower joint tax brackets.

Another is that someone might have a year when they have exceptionally high income and are in a higher than normal tax bracket, like when they sell a business. Doing a Roth conversion that year would likely not pay off either.

For either person the Roth conversion would not pay off so your argument would be shown to not be correct.

You obviously put a lot of thought and work into this you might want to rephrase that "always" claim since it sounds too extreme and bit like clickbait.
Hmmm, you are the second BH, here in a second thread where I was the topic author, to gently suggest I avoid the appearance of clickbait. It's a tough issue for an author like me--I want to be read the way a Labrador puppy wants to be fed.

I believe that thread titles, paper titles, email subject lines and any headline can be more or less successful at drawing readership. That inclines me toward more provocative titles. In fact, in my former life I earned tenure and promotion for my work on the rhetoric of ad headlines. If the topic is of interest, this paper is mostly in English: https://d1wqtxts1xzle7.cloudfront.net/5 ... GGSLRBV4ZA

Speaking of my former life, I was indeed taught never to use the word always (or never). I learned it the hard way, from journal reviewers. But in this case, I mean the title literally: Roth conversions always pay off. But note the hedge in the subtitle, it is absolutely crucial.

Haven't supported the claim yet, but that is my intent and the purpose of launching a new thread (it's not like there is a dearth of Roth conversion threads on the site ...). You and the BH community will judge, later, whether I succeeded.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

Chip wrote: Fri Sep 24, 2021 1:05 pm
McQ wrote: Fri Sep 24, 2021 12:56 pm 1. I'll construct a different version of the spreadsheet where capital gains are embedded and accumulate rather than being realized each year. That's not been done here because it complicates the analysis (realizing twenty or thirty years of capital gains all at once makes the tax rate uncertain--could be 18.8%, 23.8%, or some other number as currently under ...) oops can't talk about tax legislation in process here on BH.
A higher rate will weaken / slow the outcome of conversions but not change the pattern. And if there is a step up at death, conversion outcomes will weaken further. All grist for the mill, but only after the initial demonstration has been secured.
Fair enough. But I do think that under current law a majority of decedents will get a step up at death. So maybe that should be the base case. Unless all those Silicon Valley people you hang around with are already worth more than 11.4M. :D
Nope, nobody I know. But another piece of future tax legislation we are not permitted to discuss uses a different number.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by JBTX »

Will somebody explain the OPs premise in childlike ADHD fashion for me? I'm just not getting it.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by LadyGeek »

McQ wrote: Fri Sep 24, 2021 1:19 pm Nope, nobody I know. But another piece of future tax legislation we are not permitted to discuss uses a different number.
Let's stick with the current numbers.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by FiveK »

JBTX wrote: Fri Sep 24, 2021 2:13 pm Will somebody explain the OPs premise in childlike ADHD fashion for me? I'm just not getting it.
Don't know if this will help, but here's a quote from the How do RMDs affect Roth conversion choices? thread:
There can be a benefit to the Roth side of the scales if paying taxes out of cash on hand when making Roth contributions or doing Roth conversions, as this gets money out of taxable and into a Roth account.

It stands to reason, then, that there is a detriment to moving money out of a tax-advantaged account and into a taxable account, which is what RMDs force. The question is, how much detriment? As with most traditional vs. Roth questions, the answer starts with "it depends...."
Another quote from the same post, with emphasis added:
Some observations:
- If the original owner had lived to age 94, it would have been slightly better to do the Roth conversion even if the heir had been a tax-exempt charity.
- With the default scenario, not converting is slightly better for the heir if the heir would use the inheritance within two years. If the heir would let the money grow for the full 10 years, an age 71 conversion by the original owner would give the heir more spendable after-tax income after the 10 years.
Seems "the answer starts with 'it depends...'" and "if you can hold on long enough" are two ways of saying the same thing.

It's not interesting (in a practical sense) if "long enough" turns out to be 1000 years or so. It would be highly interesting if "long enough" turns out to be 5 years or so. It's probably interesting enough for discussion if "long enough" turns out to be 20 years or so - I think that is cas's point in this post.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by JBTX »

FiveK wrote: Fri Sep 24, 2021 3:11 pm
JBTX wrote: Fri Sep 24, 2021 2:13 pm Will somebody explain the OPs premise in childlike ADHD fashion for me? I'm just not getting it.
Don't know if this will help, but here's a quote from the How do RMDs affect Roth conversion choices? thread:
There can be a benefit to the Roth side of the scales if paying taxes out of cash on hand when making Roth contributions or doing Roth conversions, as this gets money out of taxable and into a Roth account.

It stands to reason, then, that there is a detriment to moving money out of a tax-advantaged account and into a taxable account, which is what RMDs force. The question is, how much detriment? As with most traditional vs. Roth questions, the answer starts with "it depends...."
Another quote from the same post, with emphasis added:
Some observations:
- If the original owner had lived to age 94, it would have been slightly better to do the Roth conversion even if the heir had been a tax-exempt charity.
- With the default scenario, not converting is slightly better for the heir if the heir would use the inheritance within two years. If the heir would let the money grow for the full 10 years, an age 71 conversion by the original owner would give the heir more spendable after-tax income after the 10 years.
Seems "the answer starts with 'it depends...'" and "if you can hold on long enough" are two ways of saying the same thing.

It's not interesting (in a practical sense) if "long enough" turns out to be 1000 years or so. It would be highly interesting if "long enough" turns out to be 5 years or so. It's probably interesting enough for discussion if "long enough" turns out to be 20 years or so - I think that is cas's point in this post.
OK, so it addresses the tax drag of doing conventional and rinvesting tax savings in taxable. I'm not sure why time would change the result.

There is also the instance where you want to hold (not spend) after RMD where keeping in Roth is better than taxable residual account. Is that part of it?
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by FiveK »

JBTX wrote: Fri Sep 24, 2021 3:21 pm OK, so it addresses the tax drag of doing conventional and rinvesting tax savings in taxable. I'm not sure why time would change the result.
Don't understand "doing conventional and rinvesting tax savings in taxable".
There is also the instance where you want to hold (not spend) after RMD where keeping in Roth is better than taxable residual account. Is that part of it?
That is all of it. As stated in the OP of this thread,
I will assume throughout that indeed, that was the goal of the conversion: to accumulate greater after-tax wealth at some unknown but distant future date, by reducing tax exposure that would otherwise be incurred by having to take RMDs not needed for living expenses. The claim made in the title of the thread presumes this is the goal of the conversion; if your goal in converting is to achieve something else, this thread may not be relevant to you.
See also this post for similar thoughts using different words.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by JBTX »

FiveK wrote: Fri Sep 24, 2021 3:39 pm
JBTX wrote: Fri Sep 24, 2021 3:21 pm OK, so it addresses the tax drag of doing conventional and rinvesting tax savings in taxable. I'm not sure why time would change the result.
Don't understand "doing conventional and rinvesting tax savings in taxable".
I'm talking about the usual traditional vs Roth investment decision, to the maximum annual investable amount in an IRA or 401k, to the extent you decide traditional, to keep the comparison apples to apples you would invest the traditional option tax savings in a taxable account, which will give a slightly less optimal outcomes due to dividends and capital gains.
There is also the instance where you want to hold (not spend) after RMD where keeping in Roth is better than taxable residual account. Is that part of it?
That is all of it. As stated in the OP of this thread,
I will assume throughout that indeed, that was the goal of the conversion: to accumulate greater after-tax wealth at some unknown but distant future date, by reducing tax exposure that would otherwise be incurred by having to take RMDs not needed for living expenses. The claim made in the title of the thread presumes this is the goal of the conversion; if your goal in converting is to achieve something else, this thread may not be relevant to you.
See also this post for similar thoughts using different words.
Thanks. So as I understand it, the usual traditional vs Roth comparison assumption is you will deplete / spend the money at a rate equivalent to the RMDS, or faster. To the extent that isn't true, and you wish to keep invested longer, over time the Roth gets better, vs the RMDd traditional that would have been rolled into a taxable account.

Sound right?

I've always wondered about this but don't recall seeing it discussed here.

Thanks.

Edit: if my posts here are disruptive to the purpose of a more explicit critique of spreadsheets I will request they be deleted.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

Sources of tax drag

Why does the $875.19 tax on the initial RMD, and all the other tax values on subsequent RMDs, not show up as part of the Roth advantage? Why does tax drag appear to be confined to the reinvested RMDs? (See SS image from my post #2)

These questions mis-frame the issue. To expose the mis-framing requires two steps. The first takes the form of a Socratic dialogue.

Step 1

Q: Why is the Roth ahead by $41.61 at the end of period 3?
A: Because that was the tax imposed on the taxable account.
Q: Why is the tax drag exactly $41.61 and not some other value?
A: Because exactly $2774 was invested at the specified rate of return and subject to the stated rate of capital gains /dividend tax.
Q: Why was exactly $2774 available to invest?
A: because exactly $875.91 was deducted to pay tax on the statutorily determined age 72 RMD amount.

To sum up: tax drag on RMDs does influence the Roth advantage, but it works through the taxable account, whose exact value is determined by it.

So far, so good; but Step 1 won’t satisfy everyone.

Step 2

Here is a different tab on the SS. Please note cell H1.

Image

In this image I have made one change to the spreadsheet: the future tax rate is made to be 25%, one point higher than the conversion tax rate.

Now let’s reexamine column O, showing the Roth advantage each period. With the future tax rate having increased, the Roth now pays off from the very first evaluation at period 2. The Roth advantage evaluated at the end of period 2 is $1100. Why that amount? With future tax rates increased by 1%, the after-tax liquidation value of the TDA is reduced by 1% (pre-tax value of $110,000, before the RMD, yields 1% less in after-tax value, or $1100 less, to the advantage of the Roth).

Time for another quiz. Note the period 3 Roth advantage of $1251.06. Why that value and not, say, $2200 and change? What are the components?



Time is up. The period 3 Roth advantage can be decomposed as $1100 + $110 + $41.06. In words:
-the 1% tax loss from the higher future tax rate, should the TDA be liquidated that period
-the incremented value of that loss, after one year’s appreciation on the undebited Roth at 10%
-plus the tax drag on the taxable account (which has decreased slightly, since less is contributed to the taxable account when the tax on the RMD went up).

The amount is not $2200 or some such value because column O does not show a series of investment contributions or the growth of an investment: it is a repeated evaluation of outcomes, with the evaluation repeated anew each period.

Next, it may help to decompose the period 4 Roth surplus of $1465.86:
It is 1100 + 110 + 121 (effects of the 1% increase in tax rate relative to an account compounding at an untaxed 10%)
+ $41.06 (period 3 tax on taxable) + $4.11 (lost appreciation on that tax) + $89.70 (current period tax on taxable).

In this second example, there are two sources of tax drag: tax on the taxable account, as before, plus tax on the RMDs.
Put another way, the RMD contribution to tax drag is only visible when future tax rates change. Under constant rates, the tax on RMDs matches the tax debit initially incurred by the Roth, no matter the period, and the only source of tax drag is the taxable account. (This point was made by FiveK in prior threads, and I was slow to grasp it).

So far, so good: everybody knows that a Roth conversion will be more successful if future tax rates were to increase. However, I think it is interesting to calibrate “more” successful. In today’s image, take a look at Column O, for age 100. By this point, the 30th period of the n-period game, the Roth conversion is ahead by just under $204,000. Next, look upthread at the first SS image, showing results for a constant tax rate. The same age 100 cell shows a Roth conversion pay off of $190,638.

So now “more” has been calibrated: a one percent increase in future tax rates improved conversion outcomes by … ~7%. That is an improvement; an extra $13,000+ from a conversion of $100,000 is not chump change. But relative to the $190,600 gained when tax rates didn’t change at all, I think the $13,000+ has to be described as frosting; or maybe, no more than icing.

Next, everybody also knows, or think they know, that Roth conversions must be less successful if future tax rates move down instead of up. As a case in point, pity the poor taxpayer who converted at 2016 tax rates, only to pay tax now on RMDs at lower TCJA rates.

I used to pity that poor unfortunate too, until I ran the numbers. The key is to understand the distinction between a description of poorly timed Roth conversions as “less” successful (correct) and “unsuccessful” (not correct).

Next post shows that Roth conversions still pay off even when future tax rates move down. It just takes longer, and the payoff shrinks.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

In the SS image for this post I have cut the future tax rate by 1%, to 23% (note cell H1). In this scenario the Roth account starts out behind; and it is behind, of course, by exactly $1100, corresponding to the 1% in tax savings from the change in rates, see previous post describing the effect of a tax increase.

Image

But then the Roth starts to catch up; its value will surpass the counterfactual, of no conversion, by age 80—despite the fact that future tax rates have dropped. And by age 100, the conversion path will be far ahead, in fact, will generate a surplus not too far behind that seen in the constant rate scenario. This was a key insight of the SSRN paper: when evaluating Roth conversion outcomes, future tax rates are nowhere near as important as they have been made out to be.

Returning to the details, it will be helpful to decompose the period 4 Roth deficit of -$1192.54. This consists of:
-negative $1331 (the initial period 2 Roth disadvantage of -$1100, incremented two periods by 10%;
Ameliorated by:
-the period 3 tax drag on taxable, of $42.15;
-lost appreciation on that tax drag, at 10%, of $4.22;
-period 4 tax drag of $92.09

In short: once future tax rates change, there are two visible sources of tax drag, the increment / decrement from tax on RMDs, plus tax drag on the taxable account. If future rates are higher, the Roth surplus increases from a higher starting point. If future tax rates drop, the Roth catches up from its initial deficit as tax drag accumulates.

But again, let’s calibrate, looking once more at the age 100 cell in column O. With this slightly ill-timed Roth conversion, there is still a quite substantial advantage to converting—about $177,300. That’s less than the outcome at constant rates (my post #2 upthread), and noticeably less than the outcome when rates went up (previous post). In fact, the swing in tax rates, of +/- 1%, lowers outcomes by about $27,000, best to worst. But the conversion still produced an advantage that was a multiple of the swing.

Of course, we’ll need to look at tax rate changes of rather more than 1% to get a reasonable benchmark for how much better / worse you might fare, if the timing of your Roth conversion is fortunate / unfortunate.

So much for preliminaries.

Next post considers realistic misfortunes likely to be encountered by the affluent taxpayer contemplating a Roth conversion. Consider, for example, the couple who converted in 2016 at 28%, only to find themselves taking RMDs at 24%. How bad will their outcome be? Or conversely, as I would prefer to put it, how long will it take their Roth conversion to breakeven, and how costly will their poorly timed decision be, at some distant future age, such as 95 or 100?

After presenting a couple of unfortunate outcomes, I’ll switch to a case of realistic good fortune: the savvy Boglehead who converts today at 22%, which allows them to avoid post-TCJA tax rates that revert to 25%. How lucrative might that well-timed Roth conversion be?
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by FiveK »

JBTX wrote: Fri Sep 24, 2021 4:46 pm I'm talking about the usual traditional vs Roth investment decision, to the maximum annual investable amount in an IRA or 401k, to the extent you decide traditional, to keep the comparison apples to apples you would invest the traditional option tax savings in a taxable account, which will give a slightly less optimal outcomes due to dividends and capital gains.
Ah, yes. That's the situation covered in the first of the More complicated situations, and allows for an analytic solution - presumably the same one used by both tools referenced there.
Thanks. So as I understand it, the usual traditional vs Roth comparison assumption is you will deplete / spend the money at a rate equivalent to the RMDS, or faster. To the extent that isn't true, and you wish to keep invested longer, over time the Roth gets better, vs the RMDd traditional that would have been rolled into a taxable account.

Sound right?

I've always wondered about this but don't recall seeing it discussed here.
Yes to all. Interesting that Kitces (and perhaps others) had broached this years ago, but it had been more or less ignored (including in the BH wiki) until McQ's recent paper resurrected the issue.

Seems there isn't an analytical solution to the RMD effect, so one would have to use a multi-row spreadsheet for the analysis. Given the difficulty of error-checking complex spreadsheet logic for all input combinations, "it would be nice" if the ones being developed by MDM and McQ (and any others?) give the same results for the same inputs. Wouldn't be proof positive that both were correct, but it would be strong circumstantial evidence. :)
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WoodSpinner
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by WoodSpinner »

McQ,

I am looking forward to this discussion, many thanks for posting it here! I also appreciate the kind words!

What I would find interesting in a future iteration is to:
  1. Include a series of Roth Conversions before RMDs begin an a better illustration of their affects over time. For instance, convert $100,000/year from 60-71 and then RMDs.
  2. Be able to demonstrate a mechanism to help determine if you are converting too much or too little given your assumptions. I think this would require a more dynamic approach to Tax Rates than the current model provides.
  3. Affect of turbo-charging the Conversions and RMDs by moving Equities from the TDA to a more optimal asset location for future growth. In other wards while keeping the same overall Equity/Bond allocation try and fill Roth with only Equities, Taxable with Equities and Bonds (if necessary) and TDA with Bonds and Equities ( if necessary).
Thanks

WoodSpinner
MAI
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by MAI »

You forgot to add as a caveat "As long as the government doesn't change the tax rules". Roths didn't even exist until 23 years ago, as a way to get tax revenue quicker. When enough money is sitting in Roths and causing a large drop in current tax revenue, the rules will change again.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by VanGar+Goyle »

Why Roth conversions always pay off—if you can hold on long enough

This is especially true for people who live forever, or at least very long time with old money,
so a rich vampire ( the RMD table for vampires must be very hard to calculate :)
Of course if you are a poor vampire, or a poor old human with no more savings,
a Roth conversion may not pay off when you live poor a long time.

Do they still have poorhouses like Dickens, or do you just merge in with the other homeless people?
Well, you pay a little bit, we're a little bit tough. | You pay very much,very much tough. | You pay a too much, we're too much a tough. | How much you pay? ... Well, then we're plenty tough. - Marx
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Riprap
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by Riprap »

Just remember, what rules politicians give us, politicians can take away. Read the newspaper and ask if this is likely to last.

Retirement accounts weren't meant to be vehicles to pass wealth to future generations, I wouldn't count on that ability lasting.
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willthrill81
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by willthrill81 »

Watty wrote: Fri Sep 24, 2021 8:47 am
Why Roth conversions always pay off—if you can hold on long enough
I did not follow the details but you need to be careful about using the word "always" since one exception is enough to disprove your primis.

For example a single person might do a Roth conversion when they are in the higher single tax brackets, but they could then get married and then be in the lower joint tax brackets.

Another is that someone might have a year when they have exceptionally high income and are in a higher than normal tax bracket, like when they sell a business. Doing a Roth conversion that year would likely not pay off either.

For either person the Roth conversion would not pay off so your argument would be shown to not be correct.

You obviously put a lot of thought and work into this you might want to rephrase that "always" claim since it sounds too extreme and bit like clickbait.
:thumbsup

In my case, I'm planning to retire at about age 45 and should be able to do Roth conversions until my SS benefits begin at age 70. Doing so will allow me to do Roth conversions in the 0%, 10%, and 12% brackets rather than pay 22% in taxes on Roth conversions and contributions right now; that's a huge win in favor of delaying Roth conversions until the right time. If I wanted to, I could Roth convert 100% of our tax-deferred assets in the period between retirement and starting SS benefits, and depending on how the taxation of SS benefits is working by that time, I just might do that.
“Good and ill have not changed since yesteryear; nor are they one thing among Elves and Dwarves and another among Men.” J.R.R. Tolkien, The Lord of the Rings
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by cas »

FiveK wrote: Fri Sep 24, 2021 5:11 pm Seems there isn't an analytical solution to the RMD effect, so one would have to use a multi-row spreadsheet for the analysis. Given the difficulty of error-checking complex spreadsheet logic for all input combinations, "it would be nice" if the ones being developed by MDM and McQ (and any others?) give the same results for the same inputs. Wouldn't be proof positive that both were correct, but it would be strong circumstantial evidence. :)
For what it is worth, I modified*** the MDM spreadsheet (just a copy local to my computer) so that I could use it to exactly match the assumptions in the current McQ spreadsheet.

The good news is that - for the exact 3 scenarios that McQ has so far presented - the numbers match up between the 2 spreadsheets.

That is definitely far from a thorough system test, but it is a good sign.

***nitty, gritty details on what I needed to add to the MDM spreadsheet so I could match up assumptions exactly between the MDM and McQ spreadsheets:
- an option to use the "new" RMD table
- a toggle on whether to do the initial Roth conversion at the beginning or end of the year
- a toggle on whether to take RMDs at the beginning or end of the year
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

WoodSpinner wrote: Fri Sep 24, 2021 6:01 pm McQ,

I am looking forward to this discussion, many thanks for posting it here! I also appreciate the kind words!

What I would find interesting in a future iteration is to:
  1. Include a series of Roth Conversions before RMDs begin an a better illustration of their affects over time. For instance, convert $100,000/year from 60-71 and then RMDs.
  2. Be able to demonstrate a mechanism to help determine if you are converting too much or too little given your assumptions. I think this would require a more dynamic approach to Tax Rates than the current model provides.
  3. Affect of turbo-charging the Conversions and RMDs by moving Equities from the TDA to a more optimal asset location for future growth. In other wards while keeping the same overall Equity/Bond allocation try and fill Roth with only Equities, Taxable with Equities and Bonds (if necessary) and TDA with Bonds and Equities ( if necessary).
Thanks

WoodSpinner
Hello Woodspinner: thanks for those questions, I learn more when I learn what my audience really cares about. Brief replies, mostly placeholders:

1. This one doesn't actually make a difference (if tax is paid from the conversion). Imagine you converted $100,000 seven years earlier at age 64 all in the 24% bracket; you'd start with $100,000 in the counterfactual and $76,000 in the Roth, same as my age 71 example. Seven years later you'd have about $200,000 in the counterfactual and $152,000 in the Roth, because until RMDs begin, the two will always be in the ratio of 100/76, because both are in the same asset and tax is deferred on both.
So, there's no difference in pattern of outcomes if you convert $800,000 at age 71 or $100,000 a year for eight years; excepting the fact that you can't convert $800,000 at 24% in a single year.
If tax is paid from outside, the starting age does make a difference; I'll cover that in a later post.

2. Not sure I will be able to get beyond the rule of thumb I gave you earlier, but I'll keep this idea in the back of my mind. Once I release the SS, it will be easy enough to supply the tax rate year by year rather than leaving it constant; then one can run sensitivity tests, per DSBH, with tax rates going up by yay much, going down by yay much; or going up and down versus going down and up. Pegging out the extremes will give you a sense of the robustness of the conversion amount.

3. Will do. In a first pass, I let the Roth and taxable earn 10% while the TDA counterfactual earns 6% (i.e., so much stock sculpted out of it that it earned a return more like the Vanguard Retirement Income fund, which is 30/70). Huge increase in the Roth surplus, of course; but depressed values in the TDA and the taxable. Still thinking about the proper conceptualization.
They that read the footnotes, they shall be saved; but they that pass over the appendices, they shall wander forever.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

VanGar+Goyle wrote: Sat Sep 25, 2021 8:34 am Why Roth conversions always pay off—if you can hold on long enough

This is especially true for people who live forever, or at least very long time with old money,
so a rich vampire ( the RMD table for vampires must be very hard to calculate :)
Of course if you are a poor vampire, or a poor old human with no more savings,
a Roth conversion may not pay off when you live poor a long time.
Actually, the IRS has the vampire case covered. Divisor drops to 2 at age 120 and stays there. Per the post from Lee_WSJ upthread, once you start removing one half the TDA each year, after ten years, only 1/1000 of the balance remains; after 20 years, 1/1,000,000
They that read the footnotes, they shall be saved; but they that pass over the appendices, they shall wander forever.
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by McQ »

You guessed wrong about future tax rates--how bad will it be?

This post examines unfortunately timed Roth conversions, or perhaps, poorly analyzed conversions where future tax rates turned out not to be as expected (or feared). This post is limited to realistic pratfalls. Next post looks at terrible, horrible, no good, very bad Roth conversions that never, ever should have been done (spoiler alert: they still pay off—eventually).

Case 1

The innocent: conversion pre-TCJA with RMDs post-TCJA

How many times have you read something like “now would be a good time to consider a Roth conversion, since future tax rates can only go up.” I have been reading that line for over twenty years. Consider Matt and Martha: they heard that scary prediction a lot during 2016, and jumped at the chance to convert at 28%. Now they find their conversion has avoided RMDs that would have been taxed at only 24%. How bad off are they going to be?

Here is the modified spreadsheet, note the rates in cells F1 and H1:

Image

Assuming they made the conversion just before tax rates changed, they will be $4400 behind in period 2. From there, of course, the Roth conversion begins to catch up, same as we saw for the 1% drop in rates. It takes longer to dig out of this deeper hole dug by a 4% drop in rates; but by age 88, they are better off with the conversion than without it. By age 100 they (or their heirs) will be $127,000 ahead with the conversion, compared to no conversion. In addition to being a substantial sum in its own right, that $127,000 is almost 70% of what they would have had if tax rates had stayed constant at 28%.

A bit of an ouch, but not so bad, really. Time, or rather, tax drag playing out over time, heals all wounds.

Case 2

The miscalculation: spreadsheet jockey, not savvy about tax law

Bob and Barb are pretty good at constructing spreadsheet projections. Looking ahead two decades, they project that their RMDs will push their income above $120,000, well into the 22% bracket, even after the standard deduction and the extra deductions for being over age 65. A friend warns them that TCJA would have expired long before, possibly leading to a rate of 25%.

That’s all they needed to hear, and they proceed to make a conversion at their current tax rate of 22%. They just don’t like having to pay taxes at so high a rate as 25%.

I am sure you see the miscalculation, right? What did Bob and Barb not understand about tax law?

Answer: tax bracket boundaries adjust upwards with inflation each year. At the 3% inflation rate assumed in the spreadsheet, the lower boundary of the 22% bracket with standard deductions, twenty years hence, will be north of $220,000. Their projected income of $120,000 will place them far down in the 12% (or 15%) bracket.

Tch, tch, Bob and Barb: You converted at 22% to save tax on RMDs at 12%. How bad will your outcome be?

Image

Well, it is certainly not great; they (or their heirs) won’t breakeven on the conversion until an age of 96. But by age 100, the conversion will have produced an extra $62,000 of wealth, not so shabby, even though only about one-third of the extra wealth they would have accumulated, if their tax calculations had been correct and their tax rate had stayed constant at 22% (because TCJA never lapsed).

Let me repeat the title of the thread: Roth conversions always pay off—if you can hold on long enough.

But with this example, a note of irony begins to creep into the thread title. Many BH would find the Bob and Barb outcome to be disappointing. After all, they are still $22,000 in the red as late as age 90.

Postscript: I include this example because it reflects the single most common failing in popular accounts: failure to adjust future tax brackets for inflation, along with the corollary, which is to project a constant future tax rate based on today’s income measured against unadjusted future brackets.

Case 3

The misled: told that tax rates in retirement will be as high or higher as while working

Here are Rob and Sue, affluent professionals located on the left coast, currently in the 32% bracket. They have piled up several million in their TDA; they anticipate deferring social security until age 70; plus they expect to get almost the maximum payout. When they pencil out their income once RMDs begin it is not that far below what they were making while working.

Sentiment in their social group is that few expect their tax rate to drop in retirement, and some fear it might even go up. They’ve never done their own taxes and accept their relative ignorance of the topic. Accordingly, Rob and Sue have pressed knowledgeable friends as to whether it makes sense to convert under an expectation of high but constant tax brackets. Most have shrugged, but one pointed out sagely that at least, making a conversion would provide them with tax diversification, as they don’t at present have any Roth accounts. They proceed to convert at 32%.

What they didn’t understand, not being tax mavens, is that a few years from now, with 3% inflation, the AGI ceiling of the 24% bracket, with standard deductions, will be pushing $400,000. They are on track only to pile up $5 million in their TDA; even with maximum social security they are still going to be well down into the 24% bracket when RMDs commence, with retirement income projected to be still under $300,000. [*note at end of post]

How will their conversion turn out?

Image

Because the drop in rates is only 8%, they do a little better than poor Bob and Barb, breaking even on the conversion at age 94. By age 100, their conversion profit is over $63,000, almost three-eighths of what it would have been had their rate stayed constant at 32%.

Not all that bad, but certainly not great.

Summary: When tax guesses go awry

If future tax rates drop a few points (e.g., 28 to 24), breakeven should still occur before age 90, and outcomes at age 100 will still be pretty good. However, if rates drop eight to ten points, which I hope to have shown in this post is completely plausible, given just a minor miscalculation of the sort to which any ordinary taxpayer might be prone, then breakeven may not occur until well into the 90s. There will still be a substantial (nominal) dollar pay off by age 100, but many may find the amount of the pay off in conjunction with the long wait to be disappointing…

Case 4:

The careful and knowledgeable

Next, let’s look on the bright side: the savvy BH who converts today at 22% to avoid post-TCJA tax of 25%. After all, the future is unknowable; but the statute says that TCJA will expire after 2025. Taking the statute at its word is surely the appropriate path, eh?

Image

If rates are constant at 22%, the payoff from conversion at age 100 would have been $196,000 (**see second note at end of post). If rates go up to 25% and stay there, the conversion will be more lucrative, with a payoff of about $236,000, $40,000 more, the reward for good timing and savvy tax maneuvering.

Happy? Of course; +$40,000 is nothing to sneeze at. But it is just a fraction of the $196,000 that would have been achieved in any case if TCJA had not lapsed and the future rate had stayed constant at 22%.

I’ll say it again: future tax rates are the tail and tax drag is the dog.

Next post engages in a reductio ad absurdum, presenting truly awful miscalculations unlikely to be made in practice. It will complete the process of proving the claim made in the title of the thread.

*1st note: I believe it is important to use AGI when calculating tax bracket ceilings. If a couple earns an AGI of exactly $172,850 in 2021, they won’t be $100 into the 24% bracket; rather, after their standard deduction of $25,100, they will be $25,000 down into the 22% bracket. AGI and its various modifications are also the crucial input into IRMAA, social security taxation, yada yada. Hence, I always express tax bracket floors and ceilings in terms of the AGI required to get there.

**2nd note: the payoff under constant rates varies with the rate. Note how a constant 22% rate produced a payoff of $196,000 at age 100, while a constant rate of 24% produced just under $191,000. I’ll return to that pattern at a later point.
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cbeck
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by cbeck »

I miss the part about the source of funds to pay the taxes. Does this analysis assume that taxes are paid from the IRA or from other, after-tax funds? If from after-tax funds, then that amounts to a conversion of taxable funds to Roth, which is a guaranteed winner, no?
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FiveK
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Re: Why Roth conversions always pay off—if you can hold on long enough

Post by FiveK »

cbeck wrote: Sat Sep 25, 2021 6:12 pm I miss the part about the source of funds to pay the taxes. Does this analysis assume that taxes are paid from the IRA or from other, after-tax funds? If from after-tax funds, then that amounts to a conversion of taxable funds to Roth, which is a guaranteed winner, no?
No, not guaranteed, although it can make the conversion more favorable (or less unfavorable) than it would be if paying the tax from the conversion money.

The one in the How do RMDs affect Roth conversion choices? thread allows that option. Thanks to cas for confirming that both spreadsheets seem to be giving the same results when the inputs are the same, at least for a small number of test cases.
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