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Case Studies

The good news is that even if you didn't understand a single bit of the above considerations, we are going to work through the only three possibilities:

Your marginal tax rate

1. Stays the same,

2. Increases; or

3. Decrease

from the year you contribute/convert to when you withdraw, by choice or not, from the account.

For each example we are going to look at the beginning and ending value pre-tax and post-tax for Roth, Traditional, taxable, and non-qualified tax deferred registrations.

Since contribution limits are set by account registration (401(k), IRA, SIMPLE) we will use a consistent figure of $10,000

We assume an 8% annual rate of return and a holding period of 10 years.

#1 Marginal Tax Rate Stays the Same

In summary, assuming a consistent marginal tax rate, there is a significant benefit to investing money in a qualified account (Traditional or Roth) over a non-qualified account (taxable or tax-deferred). However, whether the funds are placed in Traditional or Roth has no greater impact than the other from this perspective.

Logical Fallacy #1

It is here that we must pause and point out a logical fallacy that trips up even experienced professionals. In the above example we show a contribution of $10,000 to the Traditional account and only $7,600 to all other accounts. This is because we assume that the Traditional contribution is made with pre-tax dollars and all others are made with post-tax dollars.

Pre-tax dollars minus taxes paid equals post-tax dollars.

$10,000 - $2,400 (24% x $10,000) = $7,600

Where the contribution dollars come from matters, even if only slightly, but it's impact may be de minimis on the overall decision making process. See below.

If you frame the question like this:

"I have $10,000 in my pocket/bank account and want to make a contribution, which is better?"

You may fall victim to thinking or be lead to think of the problem this way:

One could stop here and conclude that if you keep everything else consistent, the Roth is better than the Traditional by over 5%.

Note that we assume the $2,400 is reinvested promptly upon being returned and ignore the days-week(s) long gap between filing and receiving a return.

Logical Fallacy #2

By stopping here you would be following victim to the second logical fallacy, which ignores two things:

1. The tax-deductibility of the refunded $2,400 re-contributed to the Traditional account in the new tax year; and

2. The time-value of money: the future tax refunds are not invested for the same amount of time.

The tax-deductibility of the refunded money re-invested creates a feedback loop with diminishing positive impact to the investor. In other words, the first $10,000 is invested longer than the re-invested $2,400 refund (although maybe by only a few days), which is deductible and creates a $576 refund that is invested for less time, which is deductible and creates a $138.24 refund that is invested for less time... you get the point. Each refund is invested for a different period of time due to annual tax filing and since tax-refunds are issued in post-tax dollars, each reinvestment of the refund creates a refund due next year.

This scenario assumed that the $2,400 refund loop can be contributed in subsequent years for a deduction due to not maxing out all possible deductible Traditional contributions.

We will review later what happens if you are hitting the max each year and therefore the $2,400 cannot be reinvested in a Traditional account for a deduction.

First let's observe the impact of reinvesting the refund that you receive for contributing post-tax dollars to a Traditional (pre-tax) account.

By adding up these future values we can get a better comparison across the board at a single point in time.

Okay so Roth wins here, but barely. It's certainly not the 24% margin shown earlier, or even the 5.76% margin. The 0.55% difference is only attributable to the time value of money problem which arises by waiting a year for each refund before reinvesting.

That problem does NOT exist when pre-tax dollars are put directly into a Traditional account, which is why Employer Sponsored Plans like 401(k)s and 403(b)s do not have this issue.

Only account structures which permit post-tax dollars to be contributed to a pre-tax (Traditional) account (for deduction) have this issue. Eg. IRAs

In essence, it is the process of taxing-refunding-reinvesting that creates a performance lag for the Traditional IRA vs Roth IRA when making contributions with post-tax dollars due to the time value of money.

Note that reinvestment of the earlier years' refunds are much more important than later years.

Full Circle

Wait! What if you made a one time contribution equal to the sum of the initially invested AND future reinvested tax return dollars, $13,158 to a Traditional account with pre-tax money?

We have arrived back to square one. This chart is the same as the first we reviewed except it has a different starting contribution. The result is the same, no greater benefit to Roth or Traditional. See below reference.

Hitting the Maximum?

Before we move on to the second case study, I promised we would review the circumstance where your tax refund cannot be reinvested in a Traditional account. This may happen if you are contributing ongoing to your IRA and reach the max each year or if your income changes and the aforementioned tax return is non-deductible.

In this case, we simply assume that the first year's tax refund is reinvested in the next-best alternative. For our purposes, a tax-deferred account structure. Eg. Annuity contract

We observe that in cases where an individual is making deductible contributions with post tax dollars to a Traditional (pre-tax) account and are not able to reinvest the tax-refund in a Traditional IRA, for a deduction is marginally better served in a Roth registered account.

This is not because of the time-value of money or feedback look discussed earlier, but simply because a non-qualified tax-deferred account contribution is not deductible so the loop ends.

You can see how this quickly starts to vary from person to person since differences in lifestyle and future plans impact how much you earn, save, and are eligible to contribute to qualified accounts.

Quick Sidebar - "Next-best Alternative"

You may be thinking, what about HSAs, ABLEs, ESAs and 529s as a next-best alternative?

As with all tax-sheltered account registrations, qualified or not, there is a reason behind the tax break. Qualified and non-qualified retirement plans encourage individuals to plan and save for retirement which reduces stress on government programs like Social Security.

529s and ESAs encourage saving for education which reduces stress on the educational system and promotes higher education.

HSAs encourage saving for health care expense which reduces stress on the healthcare systems including Medicare and Medicaid.

Typically, the more specific the parameters to qualify for the tax break, the greater the tax benefits.

In our analysis, we are reviewing retirement accounts specifically, and while other account registrations accumulate funds that can be spent during retirement or in some cases rolled into retirement accounts, the limit of their scope of use without penalty is the reason for withholding.

This is not to say that these are not excellent account registrations for their intended purposes, in some cases their tax-benefits exceed that of qualified retirement accounts.

Behavior Matters

It would not be right to summarize the findings of the first case study without briefly discussing behavioral finance.

Creating hypotheticals on a spreadsheet for illustrative purposes is one thing, but living it is a whole different beast. Your propensity to follow through with your strategy is just as important as the strategy you choose. Knowing the information and implementing year over year are different.

Ex: Are you likely to immediately contribute and invest your refund or might it end up going to the pizza guy over the next year?

Ex. How important is it to consider your take-home pay when making contributions?

Summary - Study #1 Marginal Tax Rate Stays the Same

In summary, assuming a consistent tax rate, we observe a difference between qualified employer sponsored retirement plans and individual retirement accounts.

In employer sponsored plans, we see no difference between the benefit of using a Roth or Traditional contribution, but see a clear benefit of using qualified plans over non-qualified plans.

In IRAs we acknowledge that, on paper, there may be benefit as high as the tax rate in favor of the Roth over Traditional, which is diminished by any reinvestment strategy of the corresponding tax-return dollars.

Case Study #2 Marginal Tax Rate Increases

In this case study we assume a marginal tax bracket increase of six percent. As one might expect, paying a lower tax rate leads to a better outcome. Roth wins here.

We observe that the opportunity cost of choosing a Traditional over a Roth at present value is equal to the increase in tax rate. We also observe that the future value opportunity cost of such a decision, less the foregone tax-rate, equals the opportunity cost in present value.

I personally found this very intriguing.

Non-Qualified Accounts

We find that non-qualified tax-deferred account structures' opportunity cost increases. This is unavoidable due to the logistics of converting all gains beyond principal investment to fully taxable at the terminal income tax rate rather than taxable at a blend of income tax and long-term capital gains rates which is usually lower.

Review that when tax rates were consistent we saw that a non-qualified tax-deferred account structure had less opportunity cost than a fully taxable account. In other words, we find that the benefit of non-qualified tax deferral can be lost and it can even begin to harm investors in the event their marginal tax rate increases.

Taxable accounts may or may not be impacted negatively by an income tax rate change. Their opportunity cost can remain the same.

Why?

The specific investments that you hold within a non-qualified taxable account determine how you will be taxed.

Ex: 100% non-dividend paying stock portfolio would only be subject to capital gains taxes (If the investments are held for more than one year).

Ex: 100% dividend paying stock portfolio would be subject to both capital gains and income taxes

Ex: 100% interest bearing bond portfolio (bought at par value and held to maturity) would be subject to only income taxes

In reality, most people have a mix of asset classes (equity, fixed income, cash) and investment vehicles (stocks, bonds, funds, etc.)

Annual Tax Drag - Mutual Funds & ETFs

We use annual tax drag to describe the annual performance cost of holding fund investments which have taxable events that roll-up to the investor's tax returns just by holding shares of the fund.

The issue of paying taxes on either capital gains, or dividends/ interest income based on the specific investment type is separate and yet related.

How it works?

Consider a balanced fund of stocks and bonds. The tax drag will be directly related to the management of the underlying investments in the fund and your tax rates.

Management of the fund's investments likely produce short-term capital gains, interest income, and dividends each year within the fund. All of which are passed along to the investor and would be subject to income tax rates.

The fund's investments may also produce long-term capital gains, subject to capital gains tax. Also, if you bought the fund for $100 per share and sold it for $200 per share, that gain is also subject to capital gains taxes if you owned the shares for more than a year.

In essence, a one fund may have less dividend paying companies and expects it's return to come from appreciation in the share price of investments it holds but may have a high annual turnover leading to significant short-term capital gains and tax drag. Another fund may have a large portion of it's annual return derived from the interest income of fixed-income asset with little to no expectation of share price appreciation or long-term capital gains.

The result is the same, the majority of taxes owed from buying, owning, and selling the fund are paid at income tax rates rather than long term capital gains rates.

Real World Application

Let's examine two funds:

VOO Vanguard S&P 500 ETF

DAGVX BNY Mellon Dynamic Value Fund A.

The Vanguard fund has a low annual turnover, less than 3%.

The BNY fund has a turnover greater than 100%, it replaces all of the assets in it's portfolio annually or more frequently.

First we acknowledge a strong correlation between the two funds total return . The Vanguard fund outperforms the BNY fund, but that is not the point here.

The below chart shows the price per share, or Net Asset Value NAV per share of each of the funds.

Whoa! The BNY fund remains relatively flat while the Vanguard fund looks a lot like the prior chart.

This is tax drag and annual turnover at play.

Funds are required to distribute capital gains from the sale of assets to share holders/owners. Since the BNY fund has high turnover and realizes capital gains, those gains are distributed and the price remains more consistent. Since the Vanguard fund has a low turnover rate, it has unrealized long-term capital gains yet to be distributed (until the assets are sold by the fund) and it's price reflects this.

So What?

We asserted above that non-qualified taxable accounts may or may not be negatively impacted due to a change in income tax rates. The above explanation of tax-drag explores the drivers behind this logic.

Most investors will have some negative impact in a non-qualified taxable account from an increase in marginal income tax rate, but the negative impact will not exceed that of a tax-deferred account in this case.

A best practice is to consider keeping any high-turnover or income funds in a tax-sheltered account where this issue does not occur.

Summary - Case Study #2 Marginal Taxes Increase

In summary, assuming an increase in marginal tax rates we find that a Roth account structure outperforms Traditional, taxable, and tax-deferred structures. Specifically, it outperforms Traditional by the difference in income tax rate in today's dollars.

We find that non-qualified tax-deferred structures have the greatest opportunity cost of the account registrations considered.

Lastly, we acknowledge that taxable accounts may or may not be negatively impacted up to, but not exceeding that of non-qualified tax-deferred structures.

Case Study #3 Marginal Taxes Decrease

In this case study we assume a marginal tax bracket decrease of 2% percent. As one might expect, like above, paying a lower tax rate leads to a better outcome. Traditional wins here.

We again observe the relationship between the opportunity cost of choosing a Roth and the change in tax rate. Specifically, we choose a 2% change to highlight yet another consideration that must be made. Discussed below.

Non-qualified accounts

Here we highlight the impact tax-drag has on the opportunity cost. Importantly, we notice that though appropriate tax-managed investing, a taxable account can have a lower opportunity cost than a non-qualified tax-deferred account.

In the above scenario we show a decrease in taxes, but the same remains true assuming a consistent tax rate; controlling tax drag can lead a taxable account to outperform a nonqualified tax-deferred account.

Tax-deferred, where's the love?

Notice that if we assume perfect tax drag management (only long-term capital gains tax is paid) and a decrease in terminal tax rate to 15%, or the same as the capital gains tax rate, we find a breakeven point leading to the benefit of non-qualified tax deferred structures over taxable structures.

This is to highlight that it is a combination of annual tax drag and the change in tax rates that impact the opportunity cost between non-qualified account structures.

Tax-deferred structures benefit from a decrease in marginal tax rate, that benefit may or may not outweigh the opportunity cost of choosing a taxable account as a next best alternative to Traditional.

It is likely best to assume some level of tax drag on taxable accounts as we do in all other examples.

Conservative investors and active strategies benefit more from the power of tax-deferral than do moderate to aggressive passive investors due to the tax-drag concept discussed above.

The risk of being wrong and the reward of being right

In this case study we show a decrease of 2% between the current and terminal tax rate. This should not be overlooked. Tax brackets are not the same width and rates are not evenly spaced.

Therefore, some investors bear greater risk for some making a false assumption about the change their tax rate over time than others.

In other words, being wrong by 6% is worse than being wrong by 2%

Summary - Case Study #3 Marginal Taxes Decrease

In summary, assuming an decrease in marginal tax rates we find that a Traditional account structure outperforms Roth, taxable, and tax-deferred structures. Specifically, it outperforms Roth by the difference in income tax rate in today's dollars.

We find that non-qualified account structures underperform qualified structures, but whether taxable or tax-deferred is better is based on assumptions surrounding tax drag and the depth of any marginal income tax rate decrease.

Conclusion

At first glance the question seems simple, Roth or Traditional? It is one you have likely asked your financial advisor, tax-preparer, or friends. If you are a financial professional it is certainly one that you have fielded from clients.

Approach any blanket answer to it with a healthy dose of skepticism.

After a careful analysis of your financial situation and consideration for your future plans and expectations there may be one option that is better for you than another. However, as we saw above, in some cases there is no greater benefit to one than the other.

Key Takeaways

Frame the Question Fairly

Remember that when considering the question, consider the angle that you are approaching it from. A fallacy here can drastically skew your results.

Behavior Matters

Even the best laid plans go to waste. I had a coach tell me that 10% of your efforts should go into making a decision and 90% should go into making that decision the right one for you. In cases where you could choose either Traditional or Roth, consider whether the reduction of your current after-tax income due to Roth contributions is a behavioral strategy to actually save more pre-tax by preventing you from spending it.

Stay Out of the Weeds

I am all for pinching pennies but consider if the juice is worth the squeeze. Concepts like tax drag and lowering expense ratios are great, but if through paralysis-analysis your money never ends up invested, you may have hurt yourself in the end.

Hope for the Best, Prepare for the Worst

When making assumptions that impact your finances it is best to review all likely outcomes, consider the ramifications of being right or wrong. Some would not risk a 6% loss for 2% gain and others do it all the time. Clear expectations are key.

Thank you!

For convenience, I have developed a web calculator which allows you to run these scenarios on the fly.

Thanks for reading! Any and all feedback or questions are welcome and appreciated!

Cheers,

David DuCharme