Tag: income tax

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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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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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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.

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
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Tax-efficient retirement and upcoming webinar

Greetings ETFMathGuy subscribers! In this post, I will introduce you to our updated interactive calculator for tax-efficient retirement planning.

tax-efficient investing with the Optimal Retirement Income Calculator by ETFMathGuy
Optimal Retirement Income Calculator by ETFMathGuy
Note:  This post has been prepared for informational purposes only, and is not intended to provide, and should not be relied on for, tax, legal or accounting advice. You should consult your own tax, legal and accounting advisors before engaging in any transaction.

Tax-Efficient Retirement

We moved the retirement income calculator location on our site. Updated for 2022 tax law, it provides insights into the following questions:

  • How long will my portfolio support my annual after-tax retirement income needed to support discretionary and non-discretionary expenses?
  • How much will my heir or favorite charitable organization receive?
  • What will my future tax liabilities look like?

We still assume a mixture of tax-efficient investing in stock and bond ETFs, like IVV and AGG. Specifically, we assumed ETF stock investments generate qualified dividends and ETF bond investments generate dividends taxed as ordinary income. Of course, these assumption are only relevant to taxable account assets held by a retiree. Retiree’s may incur income taxes when they withdraw assets from tax-deferred accounts, like 401(k)s and rollover IRAs funded with pre-tax dollars. Tax-exempt accounts (like Roth IRAs) are generally not subject to any tax if withdrawn after age 59 1/2. The image below summarizes how we modeled different retirement income sources and how they contribute to after-tax income.

Modeling Retirement Taxes in Our Retirement Income Calculator

What’s new?

We now offer the ability to expedite calculations by storing profile data, such as month and day of birth to determine your first Required Minimum Distribution (RMD) age, and state of residence for community property tax calculations. You can also find a “subscribe” button below your profile data. So, if after running the retirement calculator and viewing results from the Common Rule, you must subscribe if you are interested in seeing the details on the Modified Common Rule or Optimal Rule. For example, if you run the retirement income calculator with its default values, you will see the following information about your plan. But, only paid subscribers will be able to view future optimal drawdown decisions and other supporting information.

Default Retirement Income Calculator Results and Improvements Based on a Optimal Rule

Please note: You will need to register with us here for free and then confirm your email address with our new system. We have not transferred any previously provided email addresses, instead using them solely for distribution of this periodic commentary. We also plan for many additional upgrades and new calculators this year, as we discussed in our last post, or as you can see on our new home page.

Upcoming Webinar for Individual Investors and Financial Advisors

I will be presenting an in-depth review of this new online software, including details on how it is based on my latest research on tax-efficient investing, on Tuesday, March 1st at 9 am Pacific Time, 12:00 noon Eastern Time. Individual investors can register here, and financial advisors can register here. If you are unable to make the presentation, you are welcome to download my presentation here.

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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Happy new year!

Happy new year from ETFMathGuy! In this post, we will provide some updates to our plans for 2022.

happy birthday to you wall decor
Photo by Anna Tarazevich on Pexels.com

New Priorities

As 2022 begins, we decided to reset our priorities for this website. Up until now, we provided the following services to our subscribers.

For 2022, we’ve decided that the cost to produce and maintain the free and premium portfolios was simply too high. We also recognized that, while these portfolios did exceed their objective in 2020, they did not in 2021. All premium subscribers will receive a pro-rated refund of their subscription payments shortly. In the meantime, free and premium subscribers can now access the final monthly portfolios, based on data through December 31, 2021.

Coming soon

So, after receiving very positive praise on our retirement calculator, we’ve decided to make improving it a priority. Also, thanks to significant feedback from individual investors and financial services professionals, below is a list of features we hope to provide in the near future:

  • Projection of retirement assets at beginning of retirement for pre-retiree planning
  • Optimized social security starting age for single or married couples
  • Medicare Income-Related Monthly Adjustment Amount  (IRMAA) tax
  • State taxes, as applicable
  • 3.8% medicare surtax
  • Roth conversions using either IRA or taxable account funds
  • Robustness checks with an automated sensitivity analysis for selectable uncertain variables
  • Risk assessment with simulation of uncertain stock market returns, life exptancy, after-tax income needs, and others
  • Real estate income and residual value
  • Support for Financial Independence, Retiree Early (FIRE)
  • Online storage of previous results for future reference

Of course, our retirement calculator already has many features discussed in the FAQ and listed at the top of the calculator. Also, if you are interested in greater details, you are welcome to download this whitepaper that we developed recently to describe the current model in greater depth.

We hope you have a wonderful 2022!

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 Tax Brackets

Inflation has been in the news quite a bit lately, as the CPI (Consumer Price Index) has shown a year-over-year increase of over 5% since June of 2021. Higher inflation means a loss of buying power. Fortunately, the U.S. tax system does take inflation into account when tax brackets are updated each year. In this post, we discuss the implications of updated tax brackets for 2022 due to inflation.

quote board on top of cash bills
Photo by Karolina Grabowska on Pexels.com
Note:  This post has been prepared for informational purposes only, and is not intended to provide, and should not be relied on for, tax, legal or accounting advice. You should consult your own tax, legal and accounting advisors before engaging in any transaction.

Income Tax

Income tax brackets determine what tax rates apply to each additional dollar of taxable income. These rates are especially important for retirees. Below are the 2021 and 2022 tax brackets. As you can see, the Internal Revenue Service has increased the income limits up for all rates and for all types of tax filers. Thus, if your taxable income did not change from 2021 to 2022, your after-tax income will likely increase.

2021 Income Tax Brackets
2022 Income Tax Brackets

Capital Gains Tax and Standard Deductions

Capital gains taxes, as well as the standard deduction, also have increased from 2021 to 2022 tax years. The increase in standard deductions is $400 for single filers and $800 for married individuals filing a joint tax return. These higher deductions mean that, all else being equal, a taxpayer will likely have lower taxable income, and higher after-tax income and gains. Also, higher income limits for capital gains mean that qualified dividends and long-term realized capital gains on most investments should produce fewer capital gains taxes.

Other Changes

While there are quite a few other changes to taxes in 2022, there is no change to the contribution to Individual Retirement Accounts. But, for those with access to workplace retirement plans, like 401(k)s, 403(b)s, and 457 plans, individuals can contribute $20,500 in 2022, an increase of $1,000 from 2021. While such a decision will defer taxes and should lead to higher account values in the future, anyone concerned about future tax increases may wish to consider contributing to Roth 401(k)s and Roth 403(b)s if their workplace makes them available. You may also wish to use our free online calculator to forecast your taxable and retirement assets in retirement.

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 using commission-free ETFs in efficient portfolios.

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Retirement tax alpha and optimal retirement drawdowns

Tax alpha refers to the additional rate of return generated by making tax-efficient investment decisions. For retirees, we provide an optimal retirement income calculator that models the U.S. tax code and determines an optimal drawdown strategy. Here, we discuss a recent upgrade to this calculator that quantifies your potential retirement tax alpha using an optimal drawdown strategy.

retirement tax alpha and your optimal retirement income strategy
Retirement tax alpha and your optimal retirement income strategy
Photo by Nataliya Vaitkevich on Pexels.com

What is alpha?

In the investment world, the return not captured by the movement in the broad market is alpha. Thus, for many investors, it means a risk-less return. In fact, we’ve even talked about it before in the context of CAPM and its counterpart, beta. Alpha and beta provide portfolio statistics important for consideration by any investor.

What is tax alpha?

Tax alpha is a relatively new term and may differ based on the source. We like the following definition.

If “alpha” is the return generated by an advisor’s skill in picking and managing investments, then “tax alpha” protects that return and generates a boost by making sure that taxes don’t eat away more of a client’s wealth than absolutely necessary.”

Source: https://www.atstax.com/p/what-is-tax-alpha

What about in retirement?

In retirement, tax alpha focuses on tax-efficient drawdowns. In addition, the industry standard for retirement income drawdowns from taxable, tax-deferred, and tax-exempt accounts is the Common Rule. The image below shows a summary of the default case used in our optimal calculator, which compares its results with those from the Common Rule.

Summary of Optimal Retirement Calculator. Source: https://app.etfmathguy.com/

This last line (line 4) indicates the value of tax-alpha of 0.57%. That is, a retiree would need to generate pre-tax returns 0.57% higher using the Common Rule to generate the same after-tax inheritance for their heirs. Therefore, by making optimal drawdown decisions in retirement, a retiree can expect to increase their investment returns using the Common Rule. Interested in seeing the details of this example or inputting your own assumptions for retirement? If so, please try our free online calculator.

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 using commission-free ETFs in efficient portfolios.