How does rate of return affect Roth conversion payoffs?
Short answer: the lower the return, the lower the dollar payoff.
Just upthread I compared various scenarios yielding higher and higher payoffs, relative to the base case of converting at 71 under a constant 22% tax rate. I’ve selected the following cases to run different rates of return against:
1. Base case
2. Convert at 71, tax outside
3. Convert 12 years early, tax outside.
These were all initially tested with a 10% return rate and a 3% inflation rate. That level of return with that level of inflation corresponds closely to the ninety-four-year results for the S&P index from 1926 through 2019, per the Stocks, Bonds, Bills and Inflation Yearbook (10.2%, 2.9%). For the historically inclined, “10%,” as the best estimate of nominal long-term returns on US stocks, first appears in 1955 according to the SBBI. Excepting a brief dip into the 8+% level in the early 1970s, and a brief rise above 11% in the later 1990s, that 10% estimate has held for over 60 years, as the SBBI dataset lengthened in span from three decades to nine.
So 10% seemed like a good place to start. No guarantees going forward, of course. You may experience freakishly bad outcomes instead, quite different from the three-decade returns received by those who retired from 1955 to 1989.
In the first run, I test lower returns of 9%, 8%, 7% and 6%, again assuming an all-stock portfolio with favorable rates on dividends but capital gains realized each year. I don’t go below 6% in the all-stock tests because 3% real is the worst 30-year return recorded in the post-Civil War era (see my market history paper:
https://papers.ssrn.com/sol3/papers.cfm ... id=3805927). I’ll look at lower rates in a bit; but these are best represented by an asset mix that is not 100% stock.
Here are the results in table form. Age 85 results come first, then age 95 results in a separate panel below.
Age 85:
Code: Select all
Case 10% 9% 8% 7% 6%
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Base case age 71 $ 7,629 $ 6,175 $ 4,932 $ 3,874 $ 2,978
[22% --> 22%]
Pay tax outside
age 71) $17,288 $13,957 $11,118 $ 8,710 $ 6,678
Convert 12 years early
& tax outside $53,226 $38,665 $27,689 $19,482 $13,402
Age 95:
Code: Select all
Case 10% 9% 8% 7% 6%
------------------------------------------------------------------
Base case age 71 $ 42,190 $31,244 $22,815 $16,371 $11,487
[22% --> 22%]
Pay tax outside
age 71) $ 72,116 $53,378 $38,957 $27,940 $19,597
Convert 12 years early
& tax outside $184,260 $122,608 $80,370 $51,724 $32,522
The results are straightforward if you keep in mind that returns are geometric roots and years are the exponent. In the nature of exponents, when lower returns are assumed the decrease in payoff is more dramatic at age 95 and also more dramatic when the conversion takes place 12 years early, in both cases, because the exponent is greater.
Comparing the 10% and 6% columns, the biggest drop in payoff occurs at age 95 for the case where tax is paid outside and the conversion occurs 12 years early. The smallest percentage drop occurs in the base case at age 85.
What to make of these results? Drum roll: lower asset returns produce lower Roth conversion payoffs. Or, in the vernacular: Doh!
But the Roth payoffs are still positive here in the constant tax rate case. The question for the individual Boglehead: keeping in mind that these are real dollars, earned on a tax debit of $22,000, well then—is the payoff enough for you, with your particular risk profile, the intensity of your distaste for paying taxes, the time horizon you have chosen, etc. etc.? Keep in mind that the tax treatment of Roth accounts is a promise made by one Congress and upheld by those since; but is always hostage to the next Congress. Hence, all these estimates have an overlay of uncertainty.
Each investor must answer that question for themselves. Clearly, an individual whose return assumptions are pessimistic and whose planning horizon stops at age 85 is more likely to say No, not enough of a payoff to convert.
On the other hand, it is worth calling out that the 6% return case (3% real) is just this side of unrealistic for US investors; post-1860 US stock returns were depressed that low only for thirty-year periods ending about 1933. In the US, stock returns below 8% (or more exactly, below 5% real) have been the exception not the rule. International investors have not been so fortunate; but even here, the 120-year average, per Dimson et al., would fall between the 7% and 8% columns in these tables. And at age 95, at that level of return, results still look pretty strong to my eyes.
Balanced and fixed income cases
A reminder: the $100,000 conversion on-camera sits at the top of the stack of TDA funds. Per my reply to marcopolo and MattB upthread, unless you have a sweet government pension, there is likely another $1 million or $2 million of TDA funds, or more, that weren’t able to be converted. It’s hard (for me) to imagine an asset allocation that doesn’t have at least 5% or 10% in stocks, in which case, for a single $100,000 conversion, all the Roth funds can be in stocks and the tables above govern.
But if this is the nth conversion, or if for some reason all the stock allocation has been assigned elsewhere, then of course it might be necessary for this conversion to involve some asset other than stocks. And assets other than stocks can certainly provide returns less than 6% nominal, 3% real.
But to explore these low return cases, the tax assumptions have to change. Balanced funds, fixed income investments, and stable value funds throw off ordinary income. Although a 60/40 stock bond mix would have some qualified dividends and not be taxed at exactly the ordinary rate, here 22%, for best comparability of return rates, all entries in the next table are taxed at the ordinary income tax rate of 22%. That’s going to help Roth conversion outcomes for the 6% return case; but the question is, how much does that extra tax drag help when the return moves even lower?
Here are the tables, age 85 then age 95.
Age 85:
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Case 6% 5% 4% 3% 2%
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Base case age 71 $ 4,299 $ 3,217 $2,309 $1,553 $ 927
[22% --> 22%]
Pay tax outside
age 71) $ 9,591 $ 7,165 $5,135 $3,446 $2,054
Convert 12 years early
& tax outside $18,944 $12,718 $8,182 $4,924 $2,628
Age 95:
Code: Select all
Case 6% 5% 4% 3% 2%
------------------------------------------------------------------
Base case age 71 $ 16,376 $11,200 $ 7,342 $4,505 $2,452
[22% --> 22%]
Pay tax outside
age 71) $ 27,757 $18,996 $12,460 $7,650 $4,168
Convert 12 years early
& tax outside $ 45,530 $27,954 $16,435 $9,035 $4,403
First comparison: the rightmost column of the tables earlier, against the leftmost columns of the new tables, 6% return assumed in both cases, but different tax treatment reflecting the different character of the underlying investment.
How to portray? If a balanced portfolio might be converted instead of an all-stock portfolio; and if you have a balanced portfolio precisely because you think stocks are going to yield a historically low return over the precise multi-decade span of your retirement; then Roth conversions may pay off satisfactorily. A balanced fund or other asset returning 6%, 3% real, is certainly a candidate for Roth conversion.
Returning to the second set of tables, and looking at the right side, the implication seems pretty clear: if you are expecting nominal returns as low as 4% or 2% (+/- 1% real, respectively, in this spreadsheet treatment), well, why bother with a Roth conversion? Your assets are going nowhere fast; which means the tax burden on their return if unconverted is correspondingly small. Assets with expected returns this low are best left in the TDA. Low performance there means low future taxes paid in absolute dollar amounts.
In sum: although Roth conversions always pay off if you can hold on long enough, if you desire an early and substantial payoff, then you should convert only assets with the highest expected return. If you have already converted your highest return assets; and / or, you had substantial Roth accounts already, from Roth contributions, adequate to hold all your highest return assets, then you should focus on assets with relatively high expected returns, with a 60/40 allocation anchoring the top of this space and a 30/70 allocation the bottom.
If the only assets left to convert are low return assets, then look at these tables and decide whether the payoff for converting, say, a 2.4% stable value fund is a game worth the candle (looking at you, iceport).
I personally would not; but all such decisions are irredeemably personal.
Addendum
Marcopolo reminds that under favorable circumstances, a taxable account holding all stocks and recording no capital gains, and held until a step up at death, is a pretty tough bogie for a Roth conversion to overcome. The dollar payoff from a Roth conversion shrinks accordingly. In this addendum I want to re-figure the dollar payoffs for the higher return cases. A graphic representation will help. And because conversions are all about compounding, I am only going to look at age 95 results.
Here is a representation of the age 95 tables above, pre-marcopolo.
The exponential pattern across outcomes becomes more clear. The increase in payoff for a one percentage increase in return is much greater for moving from 9% to 10% than for moving from 6% to 7%; and converting early shows the effect in spades.
But now let’s apply a marcopolo lens. For the stock assets, with no capital gains realized, the annual tax burden is only 30 basis points (15% rate X 2 percentage points of return coming from qualified dividends). At 6% in the Roth the taxable account holding reinvested RMDs earns 5.70%, and so forth. Here is the chart. Note the change in vertical scale; dashed lines use the same values as in the previous chart.
Before interpreting this second chart, a reminder: the solid lines only hold true if you never touch the funds while alive & no future Congress alters the step up rule & the rate on qualified dividends doesn’t change. If you tap the funds, the previous chart applies.
If all those assumptions hold, then a conversion that moves a balanced fund under the Roth umbrella can actually payoff more than an all-stock conversion, given a balanced fund expected to return 4%+ to 6%+. The chart reflects the power of the very favorable tax treatment potentially attainable from holding a low dividend stock index fund in a taxable account.
If you die with it untouched.
You can take the academic out of the classroom by retirement, but you can't ever take the classroom out of his tone, style, and manner of approach.