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The Roth 401(k) for retirement

The Roth 401(k) has been slowly growing in popularity since its creation in 2006. According to this WSJ article, over 80% of employer retirement plans now offer these. In this article, we will discuss this relatively new way to accumulate retirement savings and the trade-offs made when using one.

Roth 401(k) plans continue to grow.

Pay taxes now or later

Employers that offer both traditional 401(k) and Roth 401(k) plans give employees greater control over when taxes are due on their retirement savings. An employee can defer taxes on retirement contributions with a traditional 401(k) plan. These contributions will likely reduce their current taxable income and consequently the amount of taxes owed during each working year. Additionally, gains in a traditional 401(k) plan grow tax-deferred. However, ordinary income taxes are generally due on future withdrawals or on Roth conversions of these tax-deferred plan assets rolled into an IRA.

Conversely, when an employee contributes to a Roth 401(k), there is no tax-deferred benefit. Instead, the contributions are part of their current year’s income. However, once the funds are in the Roth 401(k), like in a Roth IRA, the funds grow tax-free. Additionally, qualified withdrawals during retirement are generally tax-free.

Pros and Cons of a Roth 401(k)

Retirees gain the most obvious benefit from a Roth 401(k) when future taxes are higher. For example, if the Tax Cuts and Jobs Act (TCJA) from 2017 expires at the end of 2025 without the U.S. Congress intervening, tax rates will revert to pre-2017 levels, which are higher than current rates. Additionally, younger workers who expect significant wage growth may also benefit from the Roth 401(k). And, if there are unexpected large expenses in retirement, having some after-tax funds can help retirees avoid spikes in taxable income.

If you are not sure how much to contribute to a Roth 401(k), you can follow research by David Brown, an associate professor of finance at the University of Arizona. His research suggests a rule of thumb where you add 20 to your age and put that percentage into a traditional 401(k), with the rest in a Roth 401(k). For example, a worker who is 45 should put 65% of their 401(k) savings in pre-tax contributions, and the remaining 35% as after-tax Roth 401(k) contributions.

Our software may help

We offer two online software tools to help in this planning decision. The first can predict future retirement savings balances across tax-deferred, tax-exempt, and taxable accounts based on future contribution amounts. The second can predict the longevity of your portfolio, or what your non-spouse heirs may expect for an inheritance, based on the U.S. progressive tax system. We encourage you to use tools like these to better understand savings decisions made today to meet your future retirement goals.

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in tax-efficient investing with ETFs

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Bond ETFs amid rising interest rates

Interest rates continue to rise, with the Federal Reserve recently raising its benchmark rate to a range of 5.25% to 5.5%. While borrowers may face higher costs, new investors in short-term Treasurys now realize these higher annual rates. However, investors in certain bond ETFs could also realize this rate with added liquidity, and convenience, while potentially avoiding state and local taxes.

US Treasury Bills are backed by the full faith and credit of the U.S. Government

Short-term investment options

There are several common approaches for investing in the short term, which we characterize as less than one year. Thankfully, these investments have zero default risk because the full faith and credit of the US Government backs them.

These investments include bank CDs, direct purchases of US short-term Treasury bills, money market funds, and certain Bond ETFs. Firstly, bank CDs and money market funds may be the most convenient for individual investors. Short-term bank CDs are currently yielding over 5%, and money market funds provide similar returns within most brokerage accounts. Unfortunately, both of these short-term investments are often subject to both state and federal income taxes. For residents of California, Hawaii, and New Jersey, the top state income tax rate exceeds 10%.

Bond ETFs for Tax-efficient investing in the short term

Alternatively, similar returns are possible if an investor chooses to purchase short-term Treasury bills from the U.S. Department of the Treasury. Or, an investor may purchase US Government Bonds ETFs. Both of these options are exempt from state taxes. However, treasury bills have maturity dates of 4, 8, 13, 26, or 52 weeks. So, at maturity, the investor receives back their investment plus interest. That means that an investor would need to regularly re-invest in treasuries at TreasuryDirect.gov.

To avoid the need to continually re-invest, and likely avoid state taxes, there are several short-term Bond ETFs to choose from. Here are just a few, that with reinvested dividends have returned 2.5-2.8% so far this year (e.g. from December 30, 2022, to July 28, 2023).

  • SPDR Bloomberg 1-3 Month T-Bill ETF (ticker: BIL)
  • iShares Short Treasury Bond ETF (ticker: SHV)
  • Goldman Sachs Access Treasury 0-1 Year ETF (ticker: GBIL)
  • iShares 0-3 Month Treasury Bond ETF (ticker: SGOV)
ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in tax-efficient investing with ETFs
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The Arithmetic of Roth Conversions

In our recent posts from March, April, and May 2023, we highlighted some important considerations when making a Roth conversion. In this post, we continue this conversation with a recent article published in the May 2023 edition of the Journal of Financial Planning, entitled “The Arithmetic of Roth Conversions”. I was very fortunate to co-author this article with my colleague Dr. Edward McQuarrie, Emeritus Professor at Santa Clara University.


McQuarrie, Edward F., and James A. DiLellio. 2023. “The Arithmetic of Roth Conversions.” Journal of Financial Planning 36 (05): 72–89.

Executive Summary

• Roth conversions continue to vex planners. To clarify matters, this paper submits conventional rules of thumb to a strictly arithmetic analysis.

• The treatment shows that it must be optimal to pay tax outside the conversion with cash, confirming one common rule. But if tax must be paid to raise the cash used to pay the conversion tax, there will be an initial loss on the conversion and a subsequent breakeven point. This paper shows how to determine time to break even.

• By the same arithmetic, the paper refutes the common rule that future tax rates must be higher for a conversion to pay off. Given enough time, conversions can overcome moderately lower future tax rates and still produce a substantial payoff due to the power of compounding.

• Most Roth conversions will show a substantial payoff if the client’s planning horizon stretches over decades; however, shorter time frames may produce only a minimal payoff or even a loss.

• The paper gives practical advice regarding the optimum time to convert, points in the tax structure that favor or disfavor conversion, and the clients most and least likely to receive a substantial payoff from conversion.

Key points to consider when reviewing “The Arithmetic of Roth Conversions”

This article highlights the importance of the following key items:

  1. Current and future tax rates
  2. How time can help a conversion generate a positive payoff
  3. The type of retirees well suited and not suited for Roth conversions

We also encourage you to try our retirement income calculator. It was recently updated to include both optimal account drawdowns and Roth conversion analysis.

We hope you find this latest research article helpful in your own retirement planning or your financial planning practice!

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in tax-efficient investing with ETFs
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Roth Conversions with Optimal Withdrawals

In our posts from March and April, we discussed several aspects of Roth conversions. We showed that, if tax rates are higher in the future, Roth conversions can have a positive payoff. For tax-deferred assets, like pre-tax assets in a 401(k) or IRA, a retiree may pass some of these assets to an heir. The heir’s income tax rate determines the after-tax value of inheriting tax-deferred assets. This week’s post highlights the most recent software update made to our Optimal Retirement Income Calculator, which now includes Roth conversions and optimal withdrawals simultaneously!

How to model Roth conversions with Optimal Withdrawals

Roth conversions reduce tax-deferred assets by “converting” those assets in any year to a Roth account. Individuals performing a Roth conversion owe income taxes on the amount converted. But, the converted amount increases the individual’s Roth account assets, which a retiree can often access tax-free in retirement. One goal of generating tax-efficient retirement income is for optimal withdrawals to avoid large “spikes” in ordinary income. Our Optimal Retirement Income Calculator does this automatically and considers the tax rate of the heir under three distinct scenarios.

  1. A retiree has insufficient funds to satisfy retirement income
  2. A retiree has sufficient, but not excessive funds
  3. A retiree has excess retirement funds
Roth conversions and optimal withdrawals from Seeking Tax Alpha in Retirement Income
Source: “Seeking Tax Alpha in Retirement Income“, to appear in Financial Service Review (2023)

Excess retirement funds and the importance of your heir(s) tax rate

In scenarios 1 and 2, the top and middle portion of the image above, our calculator already finds the lowest marginal tax rate to efficiently distribute tax-deferred assets.  Consequently, our Optimal Retirement Income Calculator already provides a withdrawal strategy to utilize your tax-deferred assets efficiently. So, no additional tax-alpha is possible with a Roth conversion.  However, this is not the case in scenario 3 or the lower right portion of the image above.

When a retiree’s assets are far beyond what is needed to support their retirement income needs, many of their assets will eventually be passed to an heir. In this case, our Optimal Retirement Income Calculator previously left a significant amount of tax-deferred assets to an heir. With our latest software update, a new Roth Conversion Analysis includes converting tax-deferred assets to a Roth account “using up” the retiree’s tax brackets that are less or equal to those of the heir. For example, if your heir has an expected income tax rate of 25%, scenario 3 would perform a Roth conversion up to the 24% tax bracket. Doing so typically adds about 0.10% tax alpha. We encourage you to use our Optimal Retirement Income Calculator to evaluate possible situations for you or your clients. You can easily see if a Roth conversion with optimal withdrawals provides an additional benefit.

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in tax-efficient investing with ETFs
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Funding Roth Conversions

In our post from last week, we highlighted the potential benefit of converting tax-deferred assets to a Roth IRA. We showed that the amount of tax alpha, or the amount of additional return realized from converting, depended on current versus future tax rates. However, we simplified how a retiree may fund the tax liability by using retirement assets. In this post, we show the additional tax alpha when funding Roth conversions without using tax-deferred assets.

Funding Roth Conversions Using Assets in a Taxable Account

The additional tax-alpha from using taxable account assets arises due to these assets no longer generating taxable interest and dividends owed each year. Instead, a retiree could use these assets to pay for funding Roth conversions. Consequently, the benefit of funding Roth conversions with taxable account assets grows over time. But, two additional complexities arise. The return on the underlying asset is the first. The ultimate intended use of the taxable account assets is the second complexity. Markets dictate the first complexity, but not the second.

So, we may not know how the stock and bond market will perform in the future. But, a retiree may know whether they will use taxable assets to supplement their retirement income needs. If taxable assets are used to supplement retirement income and/or for funding Roth conversions, then there will likely be a long-term capital gain that would reduce the tax alpha. Otherwise, taxable assets may pass to an heir with a step-up in cost basis, thereby eliminating the capital gain tax owed by the retiree.

Case Study Results from Over 20 Years

To help quantify the additional tax alpha, we revisited the analysis in the Roth (2020) article for a 20-year period. We added the two complexities mentioned above, that the tax alpha will depend on market returns and if the taxable account assets received the step-up in cost basis. The left panel below shows the tax alpha without the step-up included. The right panel shows tax alpha when the step-up occurs.

Funding a Roth conversion with taxable assets with unrealized capital gains.
No step-up in cost basis
Funding a Roth conversion with taxable assets with no capital gains.
Step-up in cost basis

Key Insights from funding Roth conversions

The results above indicate the importance of the step-up in cost basis on the tax efficiency of funding Roth conversions. The horizontal axis represents the fraction of the cost basis of the taxable account assets used. So, using current interest, dividends or available cash from a taxable account implies a cost basis equal to 1, and highly appreciated assets would have a value approaching 0.

  • From the left pane, the tax alpha ranges from 0.10% to 0.30% per year over twenty years. Lower (higher) tax alpha occurs when markets underperform (overperform) their historical average returns.
  • When the heir realizes the tax-efficient step-up in cost basis, the tax alpha is up to 0.10% per year over twenty years. Also, the breakeven for this additional tax alpha occurs at approximately 0.70, implying that a highly appreciated asset intended for an heir should not be used for funding Roth conversions.
ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in tax-efficient investing with ETFs
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Roth Conversions that Payoff

Roth conversions for retirees and individuals nearing retirement often confuse financial planners and individual investors. In this post, we discuss the pros and cons of converting a portion of tax-deferred assets to a Roth IRA. The insights I share here reflect early results from a recently conducted research initiative.

Why Convert to a Roth IRA?

Converting funds from a tax-deferred account, like a 401(k), 403(b), traditional IRA, or rollover IRA, may seem counterintuitive to many. Indeed, in my recent award-winning article on Seeking Tax Alpha in Retirement Income, which will soon appear in the Financial Services Review, I highlighted how many tax professionals, like CPAs, generally advocate deferring taxes for as long as possible. Converting funds to a Roth IRA imposes a current tax liability, contradicting this conventional wisdom. However, the communicative law of multiplication suggests otherwise for funds converted at the end of the year. A positive payoff occurs when the current marginal tax rate is less than the future marginal tax rate. Stated more simply:

Always seek the lowest marginal tax rate, either now, or in the future, when converting, or distributing tax-deferred assets.

Adapted from DiLellio and Ostrov (2017) “Optimal Strategies for Traditional versus Roth IRA/Roth 401(k) Consumption During Retirement”, Decision Sciences Journal. 48(2).

Tax Alpha from Converting to a Roth IRA

In my recent unpublished research results with Ed McQuerrie, we propose to show the benefit of Roth conversions in terms of tax alpha or the additional annual return realized by converting. If a distribution from the Roth IRA then pays the taxes, the figure below shows the tax alpha over a number of holding periods, from five to 40 years. We see that when future tax rates are higher, there is a significant benefit, but that tax alpha diminishes over time. Similarly, if an investor converts their tax-deferred assets and the future tax rates are lower, the negative payoff can be significant initially, but the loss will also diminish over time.

Tax Alpha from Roth Conversions if future marginal tax rates are 50%, 95%, or 150% of the current marginal tax rates
Tax alpha if future marginal tax rates are 50%, 95%, or 150% of the current marginal tax rates

The Challenge to Roth Conversions

The U.S. Congress sets tax rates. So, we can’t know future tax rates with certainty. But, a retiree is able to control the amount of ordinary income generated by distributions from tax-deferred accounts. Also, the results above assume the investor is at least 59 1/2 so they can avoid the tax penalty on early withdrawals to fund the tax liability. In our next post, we will highlight some beneficial results if an investor pays conversion taxes with a non-retirement account.

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in tax-efficient investing with ETFs
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Inflation and Income Taxes in 2023

Happy 2023! Now is an excellent time to review changes to individual income tax brackets due to inflation. Here, we highlight the relationship between inflation and income taxes. To see details of all the 60 tax provisions changed for 2023, the Internal Revenue Service (IRS) published this document.

How inflation and income taxes are related

As we discussed in our post from last month, the Consumer Price Index (CPI) continues its downward trend. Unfortunately, the CPI of 7.1% for November is still above the long-term norm of 2-3%. However, there is some good news for U.S. income taxpayers in 2023. The IRS adjusts income tax brackets for inflation, so income and capital gains tax brackets in 2023 have increased by about 7%. The images below show these new brackets for income, capital gains, and the standard deduction.

Inflation and 2023 Income Tax Brackets for Single
2023 Income Tax Brackets for Single Filer
Inflation and 2023 Income Tax Brackets for Married Filing Jointly
2023 Income Tax Brackets for Married Filing Jointly
Source: https://taxfoundation.org/2023-tax-brackets

2023 tax rates on retirement income

So, income tax brackets recently changed in a significant way. Our optimal retirement income calculator now provides an updated forecast for after-tax retirement income using the 2023 tax brackets. Forecasts based on the Common Rule withdrawal strategy remain free for 2023. In addition, you can expedite your calculations by registering a free profile. For individuals or financial planners wishing to use our award-winning tool to see the details that led to their individualized tax alpha, please consider subscribing before the price goes up.

Click here to see your individualized tax alpha

Live Software Demonstration

On Saturday, January 14th from 10-11 am Pacific Time (1-2 pm Eastern Time), we will be conducting a live demonstration of our retirement income and retirement savings calculators, fielding your questions, and discussing new features planned for 2023. Please use the link below to join us at this time. If you wish, please contact us prior to this demonstration with any questions you may have or use cases you wish to see.

top view photo of people near wooden table
Photo by fauxels on Pexels.com
Live Software Demo on January 14, 2023, from 10-11 am Pacific (1-2 pm Eastern)

If you are unable to make this live software demonstration, please contact us to arrange for an individual demonstration.

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in tax-efficient investing with ETFs
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Seeking Tax Alpha in Retirement Income

On October 24th, 2022, the CFP (Certified Financial Planners) board’s Academic Research Colloquium recognized my most recent research (with A. Simon) entitled “Seeking Tax Alpha in Retirement Income” with a best paper award. I wish to thank Charles Schwab for sponsoring my award. In this post, I will highlight some of the key findings from this paper.

CFP Board's Academic Research Colloquium Best Paper Award for "Seeking Tax Alpha in Retirement Income".
CFP Board’s Academic Research Colloquium Best Paper Award for “Seeking Tax Alpha in Retirement Income”.

Key Findings

In this paper, we found that the Common Rule provides an important heuristic to guide better decisions in generating tax-efficient retirement income. Using it, we divided retirees into the following three categories that appear in the figure below. Then, we define tax alpha as the additional annual investment return necessary for the Common Rule withdrawal strategy to meet the same portfolio longevity or bequest as an optimal strategy.

Using the Common Rule as a heuristic when seeking tax alpha. Source: DiLellio and Simon (2022)
Using the Common Rule as a heuristic when seeking tax efficiency. Source: DiLellio and Simon (2022)

This chart shows that three regions must be considered with separate algorithms to maximize tax efficiency in retirement income. The opportunity for tax efficiency is highest in the middle region, where the retiree and their spouse have sufficient, but not excessive, assets to support their retirement income needs.

Sensitivity Analysis

We also conducted a sensitivity analysis to determine how varying our input values, like asset allocation, may affect outcomes for tax alpha. The chart below shows how the baseline of 0.54% per year changes when inputs are varied.

Sensitivity of Tax Alpha to input variations. Source: DiLellio and Simon (2022)
Sensitivity of tax alpha to input variations. Source: DiLellio and Simon (2022)

The chart above confirms that higher future taxes and bond interest taxed as ordinary income leads to higher alphas. Also, and somewhat surprisingly, the rate of return of stocks and bonds didn’t change outcomes very much.

What’s your tax alpha?

We invite you to see your tax alpha using our online calculator. Just change the inputs to match your specific situation, hit the “Find Optimal Withdrawals” button at the bottom of the page, then scroll down when the calculations are complete to see your personalized result.

Click here to see your tax alpha

We hope you find this research helpful in planning for your future retirement income needs!

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in tax-efficient investing with ETFs
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Mitigating the effect of the Widow’s Penalty

During our webinar earlier this year, we highlighted one of the retirement income challenges called “The Widow’s Penalty”. This situation occurs when the surviving spouse is filing taxes as a single, instead of married filing jointly. In this post, we elaborate on the effect of this penalty on a fictitious couple we call John and Jane and show that tax-efficient retirement income can help mitigate its effect.

Case Study for John and Jane and the widow’s penalty

The bulleted list here summarizes John and Jane’s situation at the start of their retirement.

  • John and Jane retired this year in a community property state.   
  • John is 65 and has a life expectancy of 80.  Jane is 62 and has a life expectancy of 82. 
  • Their after-tax retirement income needs are $150,000 per year, reduced to $140,000 per year for the surviving spouse. (Today’s dollars)
  • Both have RMDs starting at age 72. 
  • Their heir’s marginal income tax rate is 25%.
  • John and Jane both have retirement assets tax-deferred ($800k, $100k) and tax-exempt accounts ($400k, $50k). John owns a taxable account valued at $1M with a cost basis of $300k in stocks and $272k in bonds.
  • Their asset allocation is 60%/40% stock/bonds in all accounts, and they increase bond allocation by 1% each year. 
  • John and Jane have annual pension income starting at age 65 of $18,500 each, and social security income starting at age 67 of $11,000 each.

As we showed in our previous post, if Jane is the surviving spouse, she can realize an additional 0.55% of investment return by drawing down from a mix of taxable, tax-deferred, and tax-exempt accounts. But, can this benefit still be realized if Jane lives longer?

Tax efficiency for a longer-living surviving spouse

In the example above, Jane lived for five years as a widow so needed to file her taxes as a single. Re-running our retirement income calculator and increasing Jane’s retirement horizon yields the following results.

Widow's penalty and opportunity for tax-efficient retirement income
Widow’s penalty and opportunity for tax-efficient retirement income

So, these results show that Jane can still increase the inheritance for her heirs if she lives up to 15 years as a widow. If she lives 25 years as a widow, she will exhaust all of her savings but will be able to increase her portfolio longevity by 3.5 years. Either of these situations is possible by not following the common rule for retirement account drawdowns but instead using optimal account drawdown decisions.

Want to see how the widow’s penalty may affect your retirement plan? We invite you to try out our calculator to see how your heir’s inheritance or your portfolio longevity may improve!

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in tax-efficient investing with ETFs
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Introducing Our New Pre-Retirement Savings Forecast Tool

We just finished the development of a new savings forecast tool to help you in planning your retirement future. In today’s post, we will highlight this tool.

Our pre-retirement savings forecast tool can help you predict your future savings.
Our pre-retirement savings forecast tool can help you predict your future savings.

Forecast your savings

To determine your savings forecast, our online tool asks for a number of different inputs across the following categories.

  • Information about yourself, such as your current age, retirement and taxable account values, and future planned contributions.
  • Information about your spouse or domestic partner, such as their age, their retirement account values, and their future planned contributions.
  • Your savings horizon, in years, your current and future asset allocation, and your marginal tax rates.
  • Future rates for stock returns, bond returns, inflation and dividends.
  • Simulation inputs, such as number of trials, asset volatility, correlation and type of simulation used.

Like in our retirement income calculator, simple menus walk you through each of these inputs, along with tips on what these inputs mean. When you are done, simply press the “Forecast Retirement Savings” button to see an automated report. The tool adjusts all values down for inflation so are in today’s “buying power”. Also, for those considering drawing down a taxable account assets prior to retirement, negative contributions may also be used to see what taxable account balance (if any) remains at the end of this planning horizon. Advocates of FIRE (Financial Independence, Retire Early) may find this feature especially useful.

Forecast results

Our savings forecast tool provides two perspectives on retirement savings. The first perspective is what to expect or a so-called “best guess” based on a deterministic forecast. An example of a 10 year forecasted account values appears in the picture below for a current 52-year old and their 50 year-old spouse. You can then enter these account values and cost basis information into our retirement income calculator.

Our pre-retirement savings forecast tool can help you predict your future expected savings.
Expected values for account values after saving for 10 years, Retiree and Spouse

The second perspective is a probability distribution of future outcomes due to market uncertainty. Using 1,000 trials in a bootstrapped simulation with data from 1989-2021 for stocks, bonds and inflation, you can determine median (or 50th percentile) account values at the end of the planning horizon, along with visualizing the account values each year. Our software also supports geometric Brownian motion simulation, which can allow you to manually modify market returns and volatility, rather than sampling from historical values.

Our pre-retirement savings forecast tool can help you predict your median future savings.
Account values after saving for 10 years using bootstrapped simulation, Retiree and Spouse

The final images produced by this tool are a distribution of outcomes for account values at the end of the savings horizon. To provide savers with specific results, we also include a table with pessimistic, median and optimistic account values.

Our pre-retirement savings forecast tool can help you predict your future savings distribution.
Distribution of account values after saving for 10 years, Retiree

We hope you find this new tool helpful in planning for your retirement. Please drop us a message to let us know what you think!

ETFMathGuy is a subscription-based education service for investors interested in using commission-free ETFs in efficient portfolios.
ETFMathGuy is a subscription-based education service for investors interested in tax-efficient investing with ETFs