Roth Accounts: Seeing the Forest for the Trees

by Matthew B. Kenigsberg, CFA

Executive Summary

• There are four distinct types of scenarios in which a decision can be required regarding the possible use of a Roth account: (1) Roth conversion tax cost funded through taxable assets, (2) equal contributions to Roth and traditional IRAs, (3) Roth conversion funded through qualified account proceeds, and (4) Roth contributions vs. grossed-up traditional contribution.
• This article provides an analysis framework for advisers to take several key factors into account and provide investors with a robust and consistent way of making decisions involving conversions and contributions to Roth accounts.
• Many think that Roth conversions and Roth contributions are a simple bet on one’s future marginal income tax rate—that those who expect a higher rate when they draw down their assets should convert (or contribute) to Roth accounts, while those who expect a lower rate should not. In fact, future marginal income tax rates are only part of the story.
• Most investors consider qualified accounts to be assets. But a qualified account balance includes both assets and liabilities. The balance includes a deferred liability attributable to the income tax the investor would owe if he withdrew the entire account balance. The net value of the account is the account balance minus this deferred liability. Even if the eventual size of the deferred liability isn’t known with certainty, it cannot be ignored.
• The deferred liability is essentially a debt, and Roth conversion (and by extension Roth contributions) may be seen as an opportunity to prepay it. As with any debt, it may make sense to prepay this deferred liability depending on the interest rate, the maturity, the principal, and other factors.

Matthew B. Kenigsberg, CFA, is a senior quantitative analyst at Fidelity’s Strategic Advisers subsidiary. He holds an MBA from Columbia Business School and is a CFA Charterholder.

Roth retirement accounts have recently attracted a great deal of attention among academics and practitioners of financial planning. This is because of the abolition of the income limits on the conversion of traditional (that is, pre-tax) IRAs and pre-tax workplace plans into Roth IRAs, making them available for the first time to a large group of wealthy investors, as well as the increasing availability and popularity of Roth 401(k) and other Roth employer retirement plans.
 
Some commentators have discussed the idea that while it was once typical for investors to experience lower marginal income tax rates after retirement, as a result of various changes in the tax code, more exceptions have been made to this rule, and as a result, Roth accounts are more useful today than they might once have been.1 There also has been discussion of the notion that higher federal income tax rates are likely in the future as a result of the United States’ deteriorating fiscal position.² In addition, there has been analysis published of the other benefits of Roth accounts, such as those particular to estate planning.
 
However, many investors and financial planning practitioners hold that for investors focused on retirement, the decision to convert a traditional account into a Roth account, or contribute to a Roth account instead of a traditional account, comes down to a single, simple question: will the investor’s marginal income tax rate be higher when he or she withdraws assets from the account than it is now? The conventional wisdom holds that if the marginal rate is higher at withdrawal, Roth contributions and/or conversions will be beneficial, while if the marginal rate is significantly lower at withdrawal, the use of Roth accounts would be disadvantageous. If the marginal rate is unchanged, then the use of Roth accounts is held to make no difference.
 
In fact, there are often factors other than the future marginal income tax rate to consider. To do so, each of the contexts in which a Roth account may be considered in lieu of a traditional account as a vehicle for retirement savings must be considered separately. These contexts may be grouped into four Roth Decision Categories.

The Four Roth Decision Categories

Category 1: Roth conversion tax cost funded with taxable assets. The investor is trying to decide whether to convert the balance of an existing qualified account, such as a traditional IRA or 401(k), into a Roth IRA. The investor would use taxable assets to pay taxes on the conversion if he or she opts to convert.
 
Category 2: Roth contributions vs. traditional contributions of the same size. The investor is trying to decide between traditional contributions (to a traditional IRA or workplace plan) and Roth contributions (to a Roth IRA or workplace plan with a Roth option). The size of the investor’s contribution is fixed and would not be affected by the traditional vs. Roth decision. For many investors, a fixed contribution size is dictated by contribution maximums. For others, it is effectively set by an employer’s matching contributions in a workplace plan; many participants always opt to contribute just enough to capture all of their employer match, but no more. It is assumed that the traditional IRA option also includes a corresponding investment in a taxable account, which equals the estimated current-year tax savings resulting from the use of the pre-tax contributions. Category 2 is fundamentally similar to Category 1.
 
Category 3: Roth conversion funded with qualified account proceeds. The investor is trying to decide whether or not to convert an existing qualified account, such as a traditional IRA or a 401(k), into a Roth IRA. The investor would use part of the distributed assets from the converted account (or from another qualified account) to fund the conversion if he or she opts to convert.
 
Category 4: Roth contributions vs. grossed-up traditional contributions. As in Category 2, the investor is trying to decide between traditional contributions and Roth contributions. However, instead of making fixed contributions, as in Category 2, if a traditional contribution is chosen, the investor will gross up his or her contributions so as to make them equal in post-tax value to the Roth contribution. For example, if the investor’s current marginal income tax rate is 25 percent, he or she might compare a traditional contribution of $1,000 with a Roth contribution of $750, because the after-tax value of the traditional contribution is effectively $750. This decision is fundamentally similar to Category 3.
 
This paper will propose a quantitative analysis framework and then apply it to case studies and sensitivity analysis in each of the four decision categories listed above. I hope this analysis framework will prove a useful tool for advisers to assist their clients faced with Roth vs. traditional decisions.

The Analysis Framework

For decisions in Categories 1 and 2, the analysis framework is based on a projection of the net future value after all taxes (or NFV) of an investor’s assets at a given future point in time under two assumptions: (1) a conversion assumption, under which the investor converts his or her traditional IRA into a Roth IRA and uses taxable assets to pay the associated cost; and (2) a non-conversion assumption, under which the investor does not convert his or her traditional IRA and the assets that would have been needed for conversion remain invested in a taxable account. Roth conversion will be deemed beneficial in this framework if the NFV is higher under the conversion scenario than under the non-conversion scenario. (See Analysis Framework: Categories 1 & 2 sidebar.)
 
The computation of the outputs, including ConversionGain—the key measurement of the benefit of Roth conversion—is straightforward. These formulas can be entered into a financial calculator or spreadsheet program for computation, allowing readers to reproduce the results shown in the Outputs sidebar.

Application of the Analysis Framework to Category 1: Roth Conversion Funded with Taxable Assets

Investor A:

• Has $100,000 in a traditional IRA that he is considering for conversion 
• Has no basis in this (or any other) traditional IRA
• Invests in a portfolio of mutual funds (60 percent stocks and 40 percent bonds) that is expected to earn a compound pre-tax total return of about 7 percent 
• Has easily liquidated assets in taxable accounts to pay for the conversion 
• Has a net worth of about $1 million and expects a gross household income³ of about $250,000 and taxable household income of about $200,000 this year
• Lives in a domicile without state or local income tax 
• Is 45 years old and files his taxes jointly with his spouse
• Considers his investment horizon to be about 30 years

For 2010, the federal 28 percent tax bracket ends and the 33 percent bracket begins at a taxable income of $209,250, so depending on how and when Investor A chooses to convert his IRA, he might be able to convert some or even all of his balance at the 28 percent rate. But let us assume instead that effectively all of the $100,000 balance would be taxed at 33 percent. There are two further assumptions needed:
 
 1. The effective tax rate to be applied to withdrawals from the traditional IRA, if it is not converted
 2. The tax efficiency ratio, and by exten- sion, the compound after-tax total return that Investor A
     will earn on his taxable assets
 
There is no way to project with certainty what tax rate will apply to withdrawals in future tax years. Therefore, consider a range of rates from 15 percent to 60 percent. Currently, the 15 percent rate would apply to taxable incomes over $16,750 and below $68,000, so 15 percent is a reasonable lower bound. Also, while Investor A assumes a 30-year investment horizon, he does not anticipate withdrawing his assets in a lump sum. Rather, he expects to make withdrawals over a retirement starting about 20 and ending about 40 years from now. But as an estimate for Horizon, the mid-point of 30 seems a reasonable choice.
 
For the tax efficiency ratio, empirical data serve well as a starting point. The Morningstar Moderate Allocation Category⁴ represents the weighted average of 1,177 funds (as of 2009) that are broadly similar to Investor A’s portfolio. As of January 2010, the Morningstar database listed a 15-year total return, annualized (month-end) of 6.89 percent and a 15-year post-tax return, annualized (post-liquidation) of 5.08 percent. This implies a tax efficiency ratio of approximately 75 percent, with the other values for Investor A shown in the Inputs/Intermediate Values sidebar.

 
The resulting ConvertedNFV and UnconvertedNFV values are shown in Figure 1.

 
Many investors are surprised by these results. It is often assumed (given a ConvertTax value of 33 percent) that a WithdrawalTax value of 30 percent or less would always result in a ConvertedNFV that is lower than the UnconvertedNFV. However, as shown in Figure 1, the ConvertedNFV is in fact higher than the UnconvertedNFV with a WithdrawalTax value of 30 percent or 25 percent, and even at 20 percent the two NFVs are nearly equal. Only when WithdrawalTax reaches 15 percent is UnconvertedNFV significantly higher than ConvertedNFV. This counterintuitive result is because of the ReturnSpread of 1.75 percent.
 
Regardless of whether Investor A decides to convert, his combined portfolio is worth $100,000 on an after-tax basis. If he chooses not to convert, he begins the scenario with a traditional IRA that has an effective net balance of $67,000 ($100,000 gross of tax) along with $33,000 in a taxable account. So while $67,000 of his combined portfolio will grow at the PreTax rate of 7 percent, the remaining $33,000 will grow at the PostTax rate of 5.25 percent. The overall growth rate of his portfolio therefore will be between the PreTax and the PostTax rates.⁵ If, however, Investor A does convert, he begins the scenario with all $100,000 invested in a Roth IRA, all of which will grow at the PreTax rate of 7 percent. Therefore, conversion increases the return on a portion of the portfolio by the ReturnSpread.
 
Investor A could think of the tax liability inside his traditional IRA as a $33,000 debt that he is carrying with an interest rate equal to the PreTax return of 7 percent. Instead of requiring regular interest payments like most debts, this debt adds the interest cost to the principal balance, which will therefore grow by 7 percent annually. Because Investor A also has a $33,000 taxable asset that will grow at the PostTax rate of only 5.25 percent, it is often advantageous to use the slow-growing taxable asset to pay off the fast-growing deferred liability. Table 1, which details the case of WithdrawalTax at 33 percent, illustrates this concept.

 
In his book on taxable investing,⁶ William Reichenstein develops another analytical analogy that applies to the situation of Investor A: the traditional IRA is, for all intents and purposes, a trust in which the government is a limited partner. The investor has control over contributions to and investments in the trust, but whenever a distribution is taken from it, the government is entitled to a share equal to the value of the WithdrawalTax. The investor has, in effect, the option of buying out the government’s interest in the trust at any time through a Roth conversion. Just as general partners in investment trusts sometimes use outside assets to buy out their limited partners, traditional IRA owners may wish to buy out the government’s interest in their accounts using taxable assets.
 
Now consider the case in which WithdrawalTax is lower than ConvertTax. In Figure 1, a WithdrawalTax value of 30 percent resulted in a ConvertedNFV of $761,226 and an UnconvertedNFV is $686,029. (The bars representing these values are enclosed by a box on the figure.) All of the intermediate values leading to these results are shown in Table 2. Bear in mind that Table 2 is identical to Table 1, except that the WithdrawalTax value is set to 30 percent instead of 33 percent. This results in different values for UnconvertedNFV but does not affect ConvertedNFV values.

 
Notice that the traditional IRA tax liability actually drops between year zero and year 1, but then begins climbing. This is because the liability is computed at year zero using the ConvertTax value of 33 percent, but in year 1 and thereafter it is computed using the WithdrawalTax value of 30 percent. As a result, the UnconvertedNFV is actually higher than the ConvertedNFV until year 6. This is typical when the WithdrawalTax rate is assumed to be lower than the ConvertTax rate: the UnconvertedNFV starts out higher, and remains so for a while, but eventually the ConvertedNFV overtakes it. Of course, in the long run we’re all dead⁷—those who expect a WithdrawalTax that’s lower than the ConvertTax may not have enough time to realize the benefits of the ReturnSpread. This is always an important consideration, and often the most important consideration, when evaluating a Roth conversion: if ConvertTax is expected to be higher than WithdrawalTax, will there be enough time and is the ReturnSpread large enough to make up the difference?
 
The above analysis assumed that the traditional IRA contained a Basis of zero—that Investor A had made exclusively qualified contributions. If he had made non-qualified contributions—assume there were $25,000 in non-qualified contributions and no other IRAs—the advantage of conversion would be significantly enhanced. Table 3 is identical to Table 2 except that $25,000 of the initial traditional IRA balance is assumed to consist of Basis.

 
Notice that traditional IRA tax liability starts out at a much lower level, as does the corresponding value of the taxable account. This is because 25 percent of the traditional IRA is not subject to tax on conversion, so the initial value of the traditional IRA tax liability is also 25 percent lower ($24,750 is 75 percent of $33,000). As a result, the TaxableStart value is also 25 percent smaller, while the starting value of the Roth IRA is unaffected. This makes the benefit of conversion significantly larger, as shown by the fact that UnconvertedNFV in year 30 is now only $655,236, compared with $686,029 shown in Table 2. For those investors who have a non-zero Basis in their qualified accounts, Roth conversion is more attractive than it would otherwise be.
 
It may be useful to consider ConversionGain as well as the NFV figures shown in Figure 1. This is shown in Figure 2, which was created by starting with the same pairs of dollar values shown in Figure 1, converting them into compound annual growth rates (CAGRs), and then computing the differences between each pair.

 
For a WithdrawalTax value of 30 percent, the ConvertedNFV is $761,226 and the UnconvertedNFV is $686,029 (as shown in Figure 1). Given the StartVal of $100,000, the ConvertedNFV of $761,226 corresponds to a CAGR of 7 percent and the UnconvertedNFV of $686,029 to a CAGR of 6.63 percent. The difference between 7 percent and 6.63 percent is 0.37 percent, which is the value shown in Figure 2 for a WithdrawalTax of 30 percent. All of the other values on Figure 2 are computed similarly.
 
While Investor A isn’t sure what effective income tax rate will apply to his traditional IRA withdrawals, the rate would have to drop to 15 percent (or less) from the current level of 33 percent for the non-conversion scenario to be advantageous. Currently, that would happen only if Investor A saw his taxable income fall by about two-thirds, from $200,000 to below $68,000, during retirement. If Investor A were confident that his taxable income would fall at least that far, and that the applicable tax rates wouldn’t change, then conversion should probably be avoided. But if Investor A felt his taxable income would probably not fall that far, that tax rates could rise, or both, he should consider at least a partial conversion.
 
If Investor A were also interested in the way ConversionGain can be affected by other factors, he might use the analysis framework to conduct sensitivity analysis with respect to any of the inputs. For example, Investor A might feel that TaxEff would be higher or lower than 75 percent. Even though Investor A invests in a mix of stocks and bonds, he might wonder how high TaxEff could be if he held only stock funds, and only index funds at that. Using the same calculation described earlier⁸ to approximate a value for TaxEff, the highest value achieved by any equity index fund listed in Morningstar for the last 15 years is about 90 percent.⁹ So for purposes of Investor A, who invests through mutual funds, assume that 90 percent is an effective upper bound¹⁰ on TaxEff. As for the lower bound, the Morningstar High Yield Bond Category shows a TaxEff value of about 50 percent, which is the lowest value for any category with more than a handful of funds. Therefore, 50 percent will be set as the lower bound for TaxEff. Note that TaxEff values higher than 90 percent or lower than 50 percent are not impossible, and the possibility of such extremes will be discussed below. But the 50 percent–90 percent range is more than enough to demonstrate the sensitivity of Roth conversion to TaxEff. Given a TaxEff that varies from 50 percent to 90 percent, the resulting ConversionGain values are as shown in Figure 3.

 
Think of Figure 3 as a set of nine figures, each one of which is similar to Figure 2. The first row, shown as a set of dark blue bars, shows ConversionGain values similar to those in Figure 2, except that they reflect a TaxEff value of 90 percent. The second row reflects a TaxEff value of 85 percent, and so forth. The fourth row of dark purple bars is based on a TaxEff of 75 percent, so it is identical to Figure 2.
 
As Figure 3 makes clear, for Investor A there are many more combinations of WithdrawalTax and TaxEff values that yield a positive value for ConversionGain than a negative one. In fact, it is only when WithdrawalTax reaches a relatively low value (20 percent or less) that ConvertGain has any possibility of becoming significantly negative, given the other assumptions for Investor A. But if the WithdrawalTax value is in the middle or upper end of its range, ConversionGain is often greater than 1.00 percent.
 
The analysis shown in Figure 3, including the TaxEff range of 50 percent–90 percent, makes a number of assumptions. For example, it is assumed that the only difference between the returns to investments in different accounts is in the tax treatments of those accounts. It is possible, however, that an investor would have different           investment strategies in different accounts. In a recent Journal of Financial Planning article,¹¹ Edward K. McQuarrie examines, among other things, the effect of active asset location on the use of Roth accounts. The active asset location strategy described in the article was one in which an investor holds equities exclusively in taxable accounts and fixed income exclusively in tax-advantaged accounts, and McQuarrie’s analysis demonstrates that such a strategy can reduce or even eliminate the benefits of a Roth account. In terms of the analysis framework presented here, that assumption could be expressed as a very low or even negative ReturnSpread, that is, a TaxEff that’s close to, or even higher than, 100 percent. If applied to the analysis shown in Figure 3, this would have the effect of weighing the results against Roth conversion instead of in favor of it.
 
However, the assumption of differing investment strategies can cut both ways. Just as an active asset location strategy might cause the returns to an investor’s taxable account to outpace those of his tax-advantaged accounts, an investor might hold more aggressive strategies in his tax deferred accounts. He might, for example, prefer to hold aggressive investment strategies in tax-advantaged accounts because he associates them with distant goals, while taxable accounts, earmarked for the near-term, take more conservative strategies. An investor prone to procrastination might have his taxable holdings all in cash because he puts off making investment decisions, while his employer plan investments are made automatically into the same mutual fund that was the default investment for his account at the outset. So, while differences in the investment strategies may indeed affect the Roth conversion decision, as McQuarrie illustrates,¹² it is possible for such differences to influence the decision in either direction.
 
Recall that Investor A was assuming a ConvertTax value of 33 percent even though he might be able to convert at least some of his traditional IRA at 28 percent. He might keep the effective rate at 28 percent by: (1) converting over several years instead of in one lump sum; (2) taking advantage of the special rule in effect for 2010 that allows the income associated with a conversion enacted during 2010 to be recognized during 2011 and 2012; and/or (3) suppressing other sources of taxable income during the year of conversion in order to stay below the 33 percent threshold. In addition, consider that if Investor A were subject to AMT, he might be subject to a 28 percent effective rate on his conversion without taking any of these steps. Given a ConvertTax value of 28 percent instead of 33 percent, ConversionGain would increase as shown in Figure 4.

 
The green bars in Figure 4 are the same as those shown in Figure 2 and in the middle of Figure 3. The blue bars represent the same calculation except with ConvertTax set to 28 percent. Notice that now ConversionGain assumes a positive value when WithdrawalTax is as low as 20 percent, and even when it reaches 15 percent ConversionGain is barely negative, so for Investor A, keeping the ConvertTax value as low as possible can make an advantageous conversion even more so, or make a marginal conversion worthwhile. In addition to the three techniques mentioned above, the tax rules allow Investor A to partially recharacterize his conversion any time until October of the following tax year.¹³ By doing so judiciously, he can make sure that the amount converted takes him right up to, but not over the top of, a given tax bracket.

Application of the Analysis Framework to Category 2: Roth Contributions vs. Traditional Contributions of the Same Size

Now consider Investor B, who is identical to Investor A except that Investor B is trying to decide whether to make Roth contributions instead of traditional (that is, pre-tax) contributions to her 401(k) plan. For Investor B, assume that the size of the contribution is determined independently of the Roth vs. traditional decision. Investor B may be like many investors who contribute just enough to capture all of an employer match. Or she may be like others, particularly those with high incomes, who always elect to make the maximum contribution. McQuarrie argues instead¹⁴ that a traditional contribution should be assumed to be larger than a Roth contribution, so that they have the same after-tax value. This assumption, which corresponds to Roth Decision Category 4, is indeed possible for some investors, and will be discussed separately below.
 
Because Investor B would make Roth and traditional contributions of equal size, the tax savings that would result from a traditional contribution must be taken into account. In other words, if Investor B chooses to make a traditional contribution instead of a Roth contribution of the same size, other things equal Investor B will face a lower income tax liability in the year of the contribution. This would result in higher take-home pay or it might take the form of a tax refund. Either way, assume that this value is recaptured and invested in a taxable account.
 
Therefore, Investor B’s contributions will consist of either: (1) a Roth contribution, or (2) a traditional contribution plus an investment in a taxable account just large enough to cover the cost of converting that traditional contribution into a Roth. For example, Investor B might weigh a $10,000 Roth contribution against a $10,000 traditional contribution plus an additional $2,800 invested in a taxable account (assuming a 28 percent value for ConvertTax). Investor B is thus very much like Investor A, who has assets in a traditional account and a taxable account and could make a Roth conversion funded with taxable assets or do nothing. In fact, for a Category 2 case, a Roth contribution may be thought of as a contribution to a traditional account followed immediately by a Roth conversion. The same analysis framework used for Investor A will therefore be applied to Investor B.
 
There is, however, one important difference: unlike the Category 1 Roth conversion that Investor A is considering, retirement contributions typically take place over a very long period. In the case of Investor B, these Roth contributions would likely continue over the entire 20-year period remaining until retirement. This means that sensitivity to changes in Horizon becomes an important factor to consider in the case of Roth contributions. If Investor B assumes a ConvertTax value of 28 percent and a WithdrawalTax value of 25 percent (the latter implying taxable income between $68,000 and $137,300 for 2010), the ConversionGain values are as shown in Figure 5.

 
Notice that past a Horizon value of about 15 years, the ConversionGain values are relatively insensitive to Horizon. With a shorter Horizon, however, the ConversionGain values can be significantly negative, particularly for a high TaxEff value. This reflects the fact that over a very short Horizon, the benefit generated by the ReturnSpread isn’t able to overcome the disadvantage of a WithdrawalTax value that’s lower than the ConvertTax value. The practical implications of this for Investor B, as she considers Roth contributions, are obvious: because Investor B thinks her Horizon is about 30 years, Roth contributions are likely to be advantageous. As long as her WithdrawalTax is 25 percent (or higher), Roth contributions will lead to a positive ConversionGain, even if TaxEff is as high as 90 percent. However, as she approaches retirement and the Horizon falls 15 years or so, Investor B might want to discontinue her Roth contributions unless she thinks that WithdrawalTax is likely to be as high, or higher, than ConvertTax.
 
Suppose Investor B feels that her income tax rates are soon likely to increase sharply and remain high for the foreseeable future—specifically, assume she expects WithdrawalTax to be about 10 percentage points higher than ConvertTax. Investor B might, for example, be planning to move from one of seven states—including Texas and Florida—that have no state income tax, to California, which has a top rate of nearly 10 percent.
 
In cases like this, over the shorter Horizon values, the one-time benefit from having one’s income taxed at the ConvertTax rate instead of the WithdrawalTax rate can dominate the benefit from the ReturnSpread, which accrues over time. As a result, ConversionGain values are much higher over shorter Horizon values, as shown in Figure 6.

 
Similarly, if Investor B felt that her taxable income and/or tax rates were going to fall so sharply that WithdrawalTax would be 10 percentage points lower than ConvertTax (perhaps she’s planning to move from California to Texas, instead of the other way around), the one-time  disadvantage of having income taxed at the ConvertTax rate rather than the WithdrawalTax rate tends to dominate the calculation for short Horizon values. Generally speaking, with WithdrawalTax so much lower than ConvertTax, scenarios in which traditional contributions are advantageous are more common than scenarios in which Roth contributions are preferable, as shown in Figure 7. However, notice that when TaxEff is below about 80 percent and Horizon longer than about 20 years, positive ConversionGain values do appear. Thus, even when an investor expects a lower tax rate in the future than today, there are cases in which Roth contributions should at least be considered.

Application of the Analysis Framework to Category 3: Roth Conversion Funded with Qualified Account Proceeds

Now consider the question of using proceeds from a traditional IRA (or other pre-tax account) rather than taxable assets to pay for a Roth conversion. The key difference between this and the analysis of scenarios in Categories 1 and 2 is the absence of a ReturnSpread; because the assets used to pay for the conversion are themselves being withdrawn from a tax-advantaged account, there is no PostTax value, no TaxEff value, and hence no ReturnSpread. There’s also no TaxableStart value, because taxable assets aren’t involved. However, while the StartVal represented the starting value of both the traditional IRA (or other qualified account) and the Roth IRA in the original analysis framework, this is no longer the case. In Categories 3 and 4, the starting value of the Roth IRA is always lower than StartVal (assuming Basis is less than StartVal and ConvertTax is not zero), because some of StartVal must be used to pay for the conversion itself. Therefore a new variable—StartValRoth—is introduced to the analysis framework.
 
Under this new analysis framework, for all cases in which Basis is zero and there is no penalty associated with the withdrawal of assets from the traditional IRA, Roth conversion is beneficial when WithdrawalTax is higher than ConvertTax, detrimental when ConvertTax is higher than WithdrawalTax, and neither when the two values are equal. Those who are unable or unwilling to use taxable assets to pay for conversion may benefit if they feel confident that WithdrawalTax will be higher than ConvertTax, but because there is no ReturnSpread, there is no margin for error—if they are right, and WithdrawalTax is higher than ConversionTax, the conversion will have been beneficial, otherwise, it will not have.
 
Investor C is like Investor A except that: (1) Investor C plans to use proceeds from his traditional IRA to cover the taxes on a conversion, (2) Investor C is 60, so he is able to make withdrawals from his traditional IRA without incurring a penalty, and (3) Investor C has a Horizon of 15 years instead of 30, because he’s 15 years older than Investor A. The results are shown in Table 4. Notice that unlike Investor A, whose account details were shown in Table 1, the UnconvertedNFV and ConvertedNFV for Investor C are always the same.

 
Figure 8 starts with the same assumptions shown in Table 4, but varies the value for WithdrawalTax. The original ConvertTax value for Investor A was 33 percent, and that also applies to Investor C. Because there’s no ReturnSpread, UnconvertedNFV and ConvertedNFV are equal for a WithdrawalTax of 33 percent, and UnconvertedNFV trends further and further below ConvertedNFV the higher WithdrawalTax rises, and vice versa. Bear in mind that this analysis assumes an investor can withdraw assets from a traditional IRA without penalty.

 
The analysis in Table 4 and in Figure 8 assumes that there is a zero Basis. If, however, Investor C were instead assumed to have made non-qualified contributions to his traditional IRA, the conversion decision could be significantly affected. In Figure 9, Basis is assumed to be $25,000, or 25 percent of StartVal.

 
Now a WithdrawalTax value of 33 percent or even 28 percent results in higher value for ConvertedNFV. So if Investor C has a non-zero Basis, the conversion decision is no longer a symmetrical bet about the difference between WithdrawalTax and ConvertTax—the higher the Basis, the more the decision is skewed in favor of conversion. This is depicted on Figure 10.

Application of the Analysis Framework to Category 4: Roth Contributions vs. Grossed-Up Traditional Contributions

Finally, let us consider the case of Investor D. She is mostly similar to Investor B—she is trying to decide whether to make Roth or traditional (that is, pre-tax) contributions to a 401(k) plan or to an IRA. But unlike Investor B, if Investor D opts for traditional contributions, she can and will gross up their value so that they have the same post-tax value as the Roth contributions that she is considering as an alternative. That means unlike Investor B, there will not be any taxable assets considered in the analysis.
 
One must make several other assumptions. First, Investor D must understand the distinction between pre-tax and post-tax values and must be able to make the appropriate changes in her workplace plan contribution rate. Second, in order to avoid creating Basis, Investor D must make a contribution small enough that it is possible to appropriately gross up the traditional contribution to have the same post-tax value as the Roth contribution it will be compared with.
 
Given that taxable assets are not part of the analysis, even though Investor D is making contributions rather than considering a Roth conversion, she is actually more similar to Investor C—considering a conversion funded with proceeds from a qualified account—than she is to Investor B. Like Investor C, Investor D is faced with a decision that is essentially a bet on the value of WithdrawalTax—if it is higher than ConvertTax, Roth contributions are preferable; if lower, traditional contributions are preferable; and if the same, the choice of contribution type makes no difference. This is shown in Figure 11, which shows the value to Investor D at age 75 of a $1,000 contribution made now (at age 45). The ConvertTax value, however, has been set to 28 percent, because that was the marginal tax rate for Investor A before a conversion was made in the original case.

 
Just as was the case for Investor C, the introduction of a non-zero Basis can cause the results for Investor D to skew in favor of Roth contribution. In the case of Investor D, the Basis would be created as a result of contributions that were partially or entirely non-qualified. For example, if Investor D were considering a Roth contribution of more than about $12,000, to make an equivalent traditional contribution, she might be forced to make some of that contribution in the form of a non-qualified contribution to an IRA. The effects of a Basis equal to 25 percent of the traditional contribution are shown in Figure 12.

 
Once again, the addition of Basis skews the results in favor of Roth accounts, just as was the case for Investor C.

Conclusion

There are four distinct types of scenarios in which a decision can be required regarding the possible use of a Roth account. In all four, WithdrawalTax, the future marginal income tax rate may not be the only factor to be considered—ReturnSpread, Horizon, and Basis may all play a role as well. The analysis framework provides a way for advisers to take several key factors into account and provide investors with a robust and consistent way of making decisions involving conversions and contributions to Roth accounts. In most instances, one or more of the input values required for the analysis framework cannot be known with certainty in advance, so it may be beneficial to analyze results over a range of possible input values, as shown in the figures provided in this paper. In some cases, it may be useful to perform this type of sensitivity analysis on more than one input value at a time, so that their interaction may be observed. Figures 3, 5, 6, 7, and 10 provide examples of sensitivity analysis on two inputs simultaneously, but similar analysis across three or even four inputs is also possible.
 
This paper has touched only briefly on one area that may be important to the analysis of the Roth vs. traditional decision: the behavioral aspects. In the analysis of Investor B—who is trying to decide between Roth and traditional contributions of fixed size to a workplace plan—there was the implicit assumption that the current-year tax savings associated with the use of traditional accounts, which might take the form of higher take-home pay or a tax refund, would always be recaptured and invested in a taxable account. But what if this is not the case? What if certain types of investors tend to respond—for behavioral reasons—to tax refunds or higher take-home pay by increasing their consumption? In such a case, assuming maximizing the value of retirement savings is the most important goal, Roth accounts could be greatly more advantageous than the strictly financial analysis presented here would indicate. This behavioral effect could mean that, in essence, the use of Roth in place of traditional contributions would lead to a higher savings rate in addition to higher after-tax returns for certain investors. There are many other behavior effects to consider, and some of these might argue in favor of the use of traditional accounts instead.
 
Given that the widespread use of Roth accounts (particularly by those with high incomes) is a relatively new phenomenon, there may not yet be enough empirical evidence to determine how Roth accounts and behavioral finance interact. But as these data become available, an investigation into the behavioral aspects of Roth accounts will likely become an interesting and potentially useful project.

Endnotes

1. This shift and some of the factors behind it are explored in Vanguard Center for Retirement Research. 2005. “Tax Diversification and the 401(k).” 18 (Oct.): 11–18.
2. See “The Federal Government’s Long-Term Fiscal Outlook, Fall 2009 Update,” GAO-10-137SP, United States Government Accountability Office.
3. Gross income here represents all the income to a household, before all deductions, exemptions, and exclusions.  Taxable income refers to the value used on tax returns to determine income tax liability.
4. ©2010 Morningstar Inc. Morningstar’s definition of the Moderate Allocation category is as follows: “Moderate-  allocation portfolios seek to provide both capital appreciation and income by investing in three major areas: stocks, bonds, and cash. These portfolios tend to hold larger positions in stocks than conservative-allocation portfolios. These portfolios typically have 50 percent to 70 percent of assets in equities and the remainder in fixed income and cash.”
5. This overall growth rate is a function of the proportion of the portfolio invested in the taxable account. Because that proportion falls over time, the overall growth rate rises, but it will never reach the PreTax level.
6. Reichenstein, William R. 2008. In the Presence of Taxes: Applications of After-Tax Asset Valuations. Denver: FPA Press. 8.
7. This aphorism is attributed to John Maynard Keynes.
8. That is, dividing the 15-year post-tax return, annualized (post-liquidation) value by the 15-year total return, annualized (month-end) value from the January 2010 Morningstar database.
9. The only exceptions are Japanese equity funds that have TaxEff values greater than 100 percent because they have produced negative returns over 15 years.
10. Note that it is theoretically possible for an equity index fund with no turnover (or stocks held directly) to achieve a TaxEff value higher than 90 percent if the investment horizon were very long. However, there is no clear empirical evidence in the Morningstar database that it has happened with mutual funds in practice—outside of extreme situations such as the Japanese equity market. If the tax rates on long-term cap gains and qualified dividends increase from their current levels, the possibility will become even more remote.
11. McQuarrie, Edward F. 2008. “Thinking About a Roth 401(k)? Think Again.” Journal of Financial Planning (July): 38–41.
12. Ibid., 43.
13. For details see IRS Pub. 590, pg. 29.
14. McQuarrie, 41–42.

Analysis Framework: Categories 1 & 2
Inputs
StartVal is the starting value of the traditional IRA (or other qualified account) under the non-conversion scenario and the starting balance of the Roth IRA under the conversion scenario.
 Basis is the part (if any) of StartVal that represents non-qualified contributions.¹ It is assumed that Basis cannot be higher than StartVal.
 ConvertTax is the effective tax rate applied to the Roth conversion (the rate used is effective, not marginal, because the conversion itself may change the marginal rate).
 WithdrawalTax is the effective tax rate applied to withdrawals from the traditional IRA under the non-conversion scenario (the rate used should be considered effective, not marginal, because the withdrawals themselves may change the marginal rate).
 Horizon is the investment horizon in years.
 PreTax is the assumed total pre-tax compound return to investments held in an IRA (whether traditional or Roth).
 TaxEff is the Tax Efficiency Ratio, or the fraction of PreTax that remains after all taxes (including taxes in liquidation) are taken into account.

Intermediate Values
TaxableStart = (StartVal – Basis) ¥ ConvertTax
TaxableStart is the value of the taxable assets used to pay taxes on conversion in the conversion scenario; in the non-conversion scenario, the same value instead remains in the taxable account and is liquidated with the traditional IRA at the end of the Horizon.

PostTax = PreTax ¥ TaxEff
PostTax is the assumed total post-tax compound return to investments held in a taxable account (taxes on liquidation are reflected in this value).

ReturnSpread = PreTax – PostTax
ReturnSpread, or the Pre-Tax/Post-Tax Return Spread, is a key driver of the benefit to Roth conversion, as discussed in this paper.
 
1When an investor has made non-qualified contributions, the procedure for computing the Basis can be complex, and the process for IRAs is different from the process for 401(k) and other employer plans. See IRS Pub. 590, pg. 39–43 for details.

Outputs
ConvertedNFV = StartVal ¥ (1 + PreTax) ^ Horizon
ConvertedNFV is the value of the Roth IRA at the end of the Horizon under the conversion scenario (note that liquidation has no impact on its value).

ConvertedCAGR = (ConvertedNFV / StartVal) ^ (1 / Horizon) – 1
ConvertedCAGR is the compound annual growth rate that equates StartVal with ConvertedNFV. It is always the same as PreTax.

UnconvertedNFV = (1 ­–­ WithdrawalTax) ¥ (StartVal ¥ (1 + PreTax) ^ Horizon) + (WithdrawalTax ¥ Basis) + (TaxableStart ¥ (1 + PostTax) ^ Horizon)
UnconvertedNFV is the sum of the after-tax liquidation values of the traditional IRA and the taxable assets that would have paid the taxes for conversion in the conversion scenario.

UnconvertedCAGR = (UnconvertedNFV / StartVal) ^ (1 / Horizon) – 1
UnconvertedCAGR is the compound annual growth rate that equates StartVal with UnconvertedNFV. UnconvertedCAGR is usually in between the values for PreTax and PostTax.

ConversionGain = ConvertedCAGR – UnconvertedCAGR
ConversionGain is the benefit, in terms of annualized return, of conversion.

Inputs/Intermediate Values for Investor A
Inputs 
StartVal  $100,000
Basis  $0
ConvertTax  33%
WithdrawalTax  15%–60%
Horizon  30 yrs
PreTax  7.00%
TaxEff  75%

Intermediate Values 
TaxableStart $33,000
PostTax 5.25%
ReturnSpread 1.75%

Analysis Framework: Categories 3 & 4
Inputs
StartVal is the starting value of the traditional IRA under the non-conversion scenario and the starting balance of the Roth IRA under the conversion scenario.
 Basis is the part (if any) of StartVal that represents non-qualified contributions.¹
It is assumed that Basis cannot be higher than StartVal.
 ConvertTax is the effective tax rate applied to the Roth conversion (the rate
used is effective, not marginal, because the conversion itself may change the marginal rate).
 WithdrawalTax is the effective tax rate applied to withdrawals from the traditional IRA under the non-conversion scenario (the rate used is effective, not marginal, because the withdrawals themselves may change the marginal rate).
 Horizon is the investment horizon in years.
 PreTax is the assumed total pre-tax compound return to investments held in
an IRA (whether traditional or Roth).

Intermediate Value
StartValRoth = StartVal – (StartVal – Basis) × ConvertTax
StartValRoth is the starting balance of the Roth IRA at the beginning of the conversion scenario.

Outputs
ConvertedNFV = StartValRoth × (1 + PreTax) ^ Horizon
ConvertedNFV is the value of the Roth IRA at the end of the Horizon under the
conversion scenario (note that liquidation has no impact on its value).

ConvertedCAGR = (ConvertedNFV / StartValRoth) ^ (1 / Horizon) – 1 = PreTax
ConvertedCAGR is the compound annual growth rate that equates StartValRoth
with ConvertedNFV.

UnconvertedNFV = (1 – WithdrawalTax) × (StartVal × (1 + PreTax) ^ Horizon) +
(WithdrawalTax × Basis)

UnconvertedNFV is the sum of the after-tax liquidation values of the traditional
IRA and the taxable assets that would have been but were not used for conversion in the non-conversion scenario.

UnconvertedCAGR = (UnconvertedNFV / StartVal) ^ (1 / Horizon) – 1
UnconvertedCAGR is the compound annual growth rate that equates StartVal with
UnconvertedNFV.

ConversionGain = ConvertedCAGR – UnconvertedCAGR
ConversionGain is the benefit, in terms of annualized return, of conversion.

1 The procedure for computing the basis for IRAs is different from the process for 401(k) and other employer plans. Also, the process for determining how much of a rollover distribution is taxable earnings and how much is tax-free basis for an IRA can be complex if the owner has more than one. See IRS Pub. 590, pg. 39–43 for details.