Executive Summary

• An individual's retirement portfolio often contains funds (sub-portfolios) subject to different tax treatment (for example, a 401(k) plan and a Roth IRA) and different asset classes (stocks, bonds, and real estate.) This paper investigates the sequence in which different retirement sub-portfolios should be depleted when the goal is to provide the largest number of equal (after-tax) withdrawals from a given retirement portfolio.
• Using simple analytical tools, longevity of withdrawals is examined under three different scenarios on a pair-wise basis: stocks versus bonds, tax-deferred versus tax-exempt accounts, and tax-deferred and taxable accounts. Results indicate that order of withdrawal can significantly affect the withdrawal period.
• The stocks-versus-bonds comparison shows that it is clearly better to take distributions from the asset that has the lower expected return.
• In the presence of a single tax rate, it does not matter in which order withdrawals are taken from a tax-deferred or tax-exempt account, all else being equal.
• In a progressive tax system, owners can extend longevity by simultaneously withdrawing from both types of accounts.
• In the case of a tax-deferred versus taxable account, the conventional rule of "leave the tax-deferred account for last" is not automatic. Rather, the order of withdrawal depends on expected return.

John J. Spitzer, Ph.D., is professor of economics at the State University of New York in Brockport, New York, where he teaches courses in economics and statistics. His research interests include econometric modeling, asset allocation, and performance evaluation. He can be reached at jspitzer@brockport.edu or (585) 395-5528.

Sandeep Singh, Ph.D., CFA, is professor of finance at the State University of New York in Brockport, New York, where he teaches courses in finance and investment analysis. His research interests include asset allocation, performance evaluation, and financial education. He can be reached at ssingh@brockport.edu or (585) 395-5519.

When approaching investment objectives and policy for individual investors, financial advisors typically take a life-cycle approach. Depending on the human-capital phase of life and the current level of financial wealth, investors are broadly classified in one of the four stages of the life cycle: accumulation, consolidation, spending, or gifting. Advisors provide guidance on risk tolerance and suitable investments based on this classification. (For a succinct discussion on the investment implications of the four phases, see Reilly and Brown (2003).)
 
The spending phase of the life-cycle approach is the focus of this paper. At the time of retirement, an individual investor faces a number of strategic investment decisions, one of which is the focus of this study: "Does the order in which retirement sub-portfolio funds are withdrawn make a difference in how long the total portfolio lasts?" This question will be referred to as the "harvesting" question.
 
First, suppose that a retiree has two types of retirement portfolios. (For ease of exposition, we call them "pots.") These portfolios may differ in tax treatment or they may differ in risk (hence, expected return). If the retiree wishes to take a fixed amount (after taxes, if any) each year, what sequence of withdrawals will provide for the greatest number of years of withdrawals? This question will be examined by comparing the longevity of three pairs of portfolios that differ in significant ways.

1. The longevity of the drawdown for stocks and for bonds will be evaluated, contrasting different expected rates of return.
2. The longevity of the drawdown of a tax-deferred account (401(k)) versus a tax-exempt account (Roth IRA) will be compared, contrasting different tax treatments, but assuming equivalent rates of return.
3. The longevity between a tax-deferred account and a fully taxable one will be analyzed, where both the rate of return and the tax treatment differ.

The pair-wise comparisons assume constant rates of return to facilitate calculation and understanding. While it is certainly true that rates of return will change over time, it is also true that the tax-deferred status of the retiree's 401(k) and the tax-exempt status of the Roth will not likely change. The underlying principles the paper reveals are not dependent on the constancy of rates of return, but on the general tax practices of the federal government and the presumption that (generally) stocks have higher real returns than bonds.

Literature Review

Most of the research has focused on the accumulation phase of the life cycle. See for example, Dammon, Spatt, and Zhang (2004), Malkiel (1999), Jagannathan and Kocherlakota (1996), Jones and Wilson (1999), and Arshanapalli et al. (2001). During retirement, attention shifts to the withdrawal phase when money is removed from a portfolio rather than added to it. Recently, Kwok, Milevsky, and Robinson (1994) and Milevsky, Kwok, and Robinson (1997) use Canadian mortality tables and asset class returns to show that an optimal asset allocation during retirement is 75 to 100 percent in equities. Bengen (1994, 1996, 1997, and 2001) has provided perhaps the most extensive illustrations on the topic of withdrawals during the retirement phase of the life cycle. Generally, he has shown that a withdrawal rate from the initial portfolio of slightly over 4 percent is "safe."
 
Guyton (2004) has used mutual funds, a sophisticated withdrawal scheme, and a selected time frame of 1973–2003 to show that a portfolio subject to certain complex decision rules can produce a withdrawal rate that "ranges from 5.8 percent to 6.2 percent depending on the percentage of the portfolio that is allocated to equity classes." In the absence of an extensive description of the methodology, it is extremely difficult to subject Guyton's results to "out of sample" tests, though one can deduce that in the presence of stochastic returns, the outcomes can be different. Updegrave (2005), commenting on Guyton's methodology, urges his readers to wait for more empirical evidence before implementing it in their individual portfolios. Drawing from research in the area of dollar-cost averaging, Vora and McGinnis (2000) show that a 100 percent stock portfolio resulted in a higher withdrawal rate during retirement compared with a 100 percent bond portfolio.
 
The emphasis of this paper is on the effect of withdrawing from retirement accounts in different sequences. The goal is not to make the portfolio safely last for a specified number of years (à la Bengen and Guyton) but rather to determine whether withdrawing, say, from a Roth portfolio first and a tax-deferred portfolio second affects how long the combined portfolio lasts. The paper presents three asset pairs that differ in either expected rate of return or tax treatment and investigates the sequence that provides the largest number of fixed (after-tax) withdrawals. The paper also looks at the effect of different tax rates on withdrawals.

Does the Order of Withdrawal Matter?

If the amount withdrawn each year is less than or equal to the after-tax earnings, the portfolio will last in perpetuity. Suppose however, that a client cannot live on the "safe" withdrawal amount of 4 percent of the initial portfolio and is forced to withdraw an amount significantly in excess of 4 percent. (We have arbitrarily chosen a withdrawal rate of 7.5 percent of the initial portfolio). How long can the client stretch out the withdrawal process if more than the "safe" amount must be withdrawn? This section considers the question, "How should money be withdrawn from two different types of portfolios in a manner that allows it to last the longest?"
 
The term "withdrawal efficient" will be defined as follows: One portfolio is more "withdrawal efficient" than another portfolio if it provides a longer withdrawal period for equivalent after-tax withdrawal amounts. This section will compare the withdrawal efficiencies of three pairs of portfolios. While the outcomes to these questions may be unexpected, the results can easily be confirmed by using a financial calculator or a spreadsheet...no complex math is required!
 
The harvesting questions. Three questions are to be addressed. Each question attempts to isolate a single variable (or a simple combination of variables) that will affect the outcome. By examining the effect of a single variable, a better understanding of the underlying process is revealed.
 
Question 1. If the retirement portfolio is allocated between two asset classes, say stocks and bonds, what is the optimal order of withdrawal? In this scenario the expected return on stocks is assumed to be greater than that on bonds. For ease of exposition, it will be assumed that stock and bond returns are taxed identically. (In the "real world," the favorable tax treatment of dividends and capital gains makes the post-tax differences even greater.) Should bonds be depleted first or last?
 
Question 2. Suppose a retiree's nest egg has two components, one of which grows tax-deferred and the other tax-exempt. In the first component, withdrawals are tax-exempt (for example, a Roth IRA) and in the second component only withdrawals are subject to taxation (for example, a tax-deferred account such as a 401(k)). In this scenario, equal rates of return are assumed, but tax treatment differs. If one depletes these assets sequentially (say, the Roth first, then the 401(k)), which of the two possible sequences will allow the money to last the longest?
 
Question 3. Suppose a retiree's nest egg has two components: the first a tax-deferred account (401(k)) and the second a taxable account (a regular taxable brokerage account). The taxable account has taxes due on returns each year, while the tax-deferred account is taxable only on distribution. What is the most efficient sequence of withdrawals? That is, should the tax-deferred or the taxable account be depleted first? One account may have a rate of return that is different from the other; do the different rates of return affect the optimal order of withdrawal?
 
Assumptions. To answer the three questions, calculations are based on the following assumptions and conditions:

1. Identical (after-tax) per-period withdrawals are assumed.
2. No leverage is employed in the portfolio.
3. A uniform capital gain and dividend tax rate is assumed and estate-planning issues are ignored.
4. The marginal income tax rate is (arbitrarily) set at 31 percent. (This rate might mimic a 28 percent federal tax and a 3 percent state tax.)
5. IRS rules for minimum withdrawals are ignored.
6. The goal is to attain the longest period of equal post-tax withdrawals.
7. The real annual rate of return is 7.2 percent for stocks and 3.5 percent for bonds. (The returns are average annual inflation-adjusted returns over the 40-year period 1964–2003. The return on stocks is assumed to be the historic return on the S&P 500, and the return on bonds is on long-term U.S. Treasuries.) The data were obtained from Stocks, Bonds, Bills and Inflation, EnCorr Database, 2004 Edition, Ibbotson Associates.

The Harvesting Answers

Question 1: Stocks or bonds. No rebalancing. The portfolio at the beginning of the withdrawal period is assumed to be composed of $50 in stocks and $50 in bonds (see Table 1). Tax treatment is assumed to be identical for these sub-portfolios; both sub-portfolios have returns that are taxed in the same manner at a rate of 31 percent. Since bond coupons are taxed as ordinary income, the "real world" preferential tax treatment of dividends and capital gains will make the differences in post-tax rates of return between stocks and bonds even larger than this example demonstrates. Thus, the post-tax rate of return on stocks is r(1 – t) = 7.2*(1 – .31) = 4.968 percent, while the post-tax rate of return on the bonds is similarly calculated to be 2.415 percent. At the end of each year, $7.50 is withdrawn from either asset, until the money is depleted.
 
The last line of the column labeled "Question 1" in Table 1 shows how long the money will last, depending on the order of withdrawal. If the taxable bonds are harvested first, they will last 7.36 years. This will allow the stocks to grow for an additional 7.36 years, during which time they will grow to $71.43; this amount will run out of money in 13.22 years. Thus, depleting the bonds first allows this $100 portfolio to pay out $7.50 (after tax) for 20.57 years (7.36 + 13.22 ≈ 20.57 with rounding.) Alternately, if the stocks are harvested first, the money will run out after 17.45 years. It is clearly better to first take distributions from assets that have a lower expected return rather than a higher one. The decision to withdraw first from the lower-rate-of-return asset is correct for any distribution of stock and bonds, not only for the 50/50 distribution shown. Likewise, the decision holds for any marginal tax rate.
 
Question 2: Tax-exempt versus tax-deferred withdrawals. The column labeled "Question 2" in Table 1 corresponds to the following discussion. Both portfolios are assumed to be composed of 50 percent stocks and 50 percent bonds; thus the before-tax rate of return for both is 5.35 percent. (The composite return is 50 percent of 7.2 percent plus 50 percent of 3.5 percent). The initial $100 portfolio is evenly split between the two sub-portfolios (Roth and 401(k)) and $7.50 of after-tax money is to be withdrawn each year. In this example, the asset allocations and rates of return are identical between the two portfolios. Tax treatment, however, is different since the Roth will never be taxed. Which order of harvesting will make the money last the longest?
 
If the tax-exempt account is harvested first, it will last for 8.46 years. The tax-deferred account will have an additional 8.46 years to grow at an annual pre-tax rate of 5.35 percent and will attain a size of $77.72. To obtain $7.50 of after-tax money from the 401(k) account, $10.87 of pre-tax money must be withdrawn each year. The tax-deferred pot will last for an additional 9.25 years. Thus, the $100 will last for a total of 17.71 years when the Roth is harvested first. Surprisingly, if the 401(k) is harvested first, the money will also last 17.71 years! When taking money from a tax-deferred and a tax-exempt portfolio (both growing at the same pre-tax rate), the number of withdrawals is not affected by the order of the withdrawal. This result does not depend on the tax rate chosen, the initial amounts, or the fact that the amounts in both pots of money are the same. Lower tax rates will result in longer, but still equal, withdrawal periods regardless of withdrawal order. Similarly, different starting amounts in the two pots will affect how long the money lasts, but the withdrawal periods will be the same regardless of withdrawal order. This result seems counter-intuitive, but it remains true. (For the algebraically inclined reader, see the appendix for a mathematical proof of this contention.)
 
Figure 1 provides a visual assist. In the top graph, the tax-exempt Roth asset, in dark shading, is withdrawn first and lasts a little more than eight years. The tax-deferred 401(k) account, in light shading, which has continued to grow the first eight years, is then withdrawn and lasts for an additional 9.25 years, for a total of 17.71 years. The bottom graph shows the balance remaining in each of the two portfolios when the tax-deferred asset is withdrawn first. As can be seen, the tax-deferred asset lasts a little more than 5 years (5.42 years), but the tax-exempt continues to provide the withdrawal amount for another 12.29 years, for a total of 17.71 years. The sequence of withdrawals does not change how long the money lasts!

 
Question 3: Tax-deferred versus taxable withdrawals. This combination of assets is more complex. During the accumulation phase, financial advisors often urge savers to take advantage of tax-deferred growth. This logic would seem to suggest that leaving money in a tax-deferred account during the withdrawal phase for as long as possible would also be the best strategy. It turns out that which assets should be harvested first will depend on their respective rates of return.
 
First, for exposition purposes, assume that the 401(k) is a 25/75 allocation of stocks and bonds earning the historical average rate of return of 4.425 percent, and the regular all-stock brokerage account earns the historical average equity return of 7.2 percent, before taxes. Replicating the same algebra as in the previous examples, we can see in the column labeled "Question 3" in Table 1 that if the taxable brokerage account is depleted first, the combined assets will last a total of 16.26 years. If the tax-deferred account is depleted first, the money will last 16.75 years. In this example, depleting the tax-deferred asset first makes the money last the longest—though the next paragraph shows a different result. These results suggest that it is not always correct to postpone depleting tax-deferred assets in deference to taxable assets. Some might find this result surprising.

 
Second, assume that the stock/bond proportions in the tax-deferred account are such that the average after-tax rate of return increases to 4.968 percent (consistent with about a 40/60 stock/bond allocation) as in the column labeled "Question 3b" in Table 1. With this rate of return for the 401(k), either sequence of withdrawals last 16.92 years. Clearly, if the after-tax rate of return on the 401(k) exceeds 4.968 percent (say at a 50/50 stocks/bond allocation), the optimal sequence will be to withdraw from the taxable account first.
 
Note that 4.968 percent is the after-tax rate of return on the regular brokerage account. With this particular asset pair, if the rate of return on the tax-deferred account is less than the after-tax rate of return on the regular brokerage account, the 401(k) should be depleted first. Conversely, if the 401(k) has a higher rate of return than the fully taxable account, the tax-deferred account should be saved for last.
 
A simple rule such as "leave the tax-deferred account for last" should not be automatically followed. In fact, the optimal order will depend on the expected return from each component. The principle exhibited in this question is identical to that exhibited in Question 1: Take distributions first from the pot with the lower rate of return.
We have assumed that the entire return of the taxable asset was taxed as dividend income. If it is assumed that the majority of the return in equities is from capital gains, the retiree does not have to pay the tax on that portion of returns until the portfolio (or a portion thereof) is liquidated. Capital gains taxes are, of course, payable only upon realization and are often subject to a favorable tax treatment. To the extent that the capital-gains component increases the after-tax return on equities in the taxable sub-portfolio relative to the tax-deferred portfolio, it also makes holding taxable assets and withdrawing from the tax-deferred account more attractive.
 
Two variables are at work here: (1) the rates of return in the two pots and (2) the timing of tax payments. Noting again that the tax rates never change in these examples, the three questions posed in this paper suggest the following answers:

1. All else being equal, if deciding to withdraw money from two accounts that have different expected returns but are taxed equivalently, withdraw money from the account with the lower expected rate of return to increase the "withdrawal efficiency."
2. If the rate of return is the same between a tax-deferred and a tax-exempt account, the order in which money is withdrawn will not affect the longevity of withdrawals when the money grows tax-deferred. Since both grow tax-deferred at the same rate, the "withdrawal efficiency" is the same. Postponing the payment of taxes on withdrawals is of no value.
3. If deciding to withdraw money from an account that grows tax-deferred, but whose withdrawals are fully taxable, versus a regular fully taxable brokerage account where returns are taxed, withdraw money first from the account with the lower expected (post-tax) rate of return. The timing of the tax payment has a pronounced effect in this example; the 401(k) is taxed at the end of the accumulation process but the brokerage account is taxed during the process. If the post-tax brokerage rate of return exceeds the rate of return on the 401(k), then the 401(k) should be harvested first.

A Tax Savings Lesson

Our paper assumes a single, constant rate of taxation; if, however, the more realistic assumption of a progressive tax system is implemented, additional useful strategies are revealed. The parameters used earlier are still assumed to be in effect—namely the tax-deferred 401(k) and tax-exempt Roth portfolios have identical investments yielding 5.35 percent.
 
Case 1: two tax brackets. Suppose that the tax rate is 15 percent on the first $5 of taxable income and 25 percent on the excess over $5. This tax structure roughly mimics the federal Married Filing Jointly tax structure, with dollar amounts 10,000 times greater, of course. (Multiplying by 10,000 makes the portfolio $1 million and the withdrawal amount is $75,000. This will not change the results. Changing the withdrawal amounts from other than 7.5 percent of the initial portfolio will change the results.) It seems reasonable to assume that if the higher tax rate can be avoided, the number of withdrawals will be extended. Two scenarios presented below will illustrate this proposition.

1. Sequential withdrawals. Initially, assume that the entire withdrawal amount is taken from the 401(k) until it is exhausted, and then money is taken from the Roth. This is the same sequential withdrawal described in the previous section of the paper. The taxpayer will need to withdraw $9.33 from the 401(k) in order to obtain $7.50 post-tax. This follows from $7.50 = $5 (1 – t₁) + x(1 – t₂) where t₁ is the tax rate on the first $5.00 and t₂ is the tax rate on income over $5. The x amount must be $4.33 when t₁ = 15% and t₂ = 25%.
   Table 2 in the columns marked "Sequential" illustrates that if $7.50 of post-tax money is withdrawn sequentially, the portfolio will last 19.78 years. It will make no difference whether the 401(k) is depleted first or last; earlier results showed that the order of withdrawal from a 401(k) and from a Roth account has no effect on the number of withdrawals.
2. Simultaneous withdrawals. Now suppose that the portfolio is harvested in a manner that shields money from the higher marginal tax. Suppose that $5.00 before tax is withdrawn from the 401(k) and $3.25 is simultaneously withdrawn from the Roth. (Note that $5*(1 – t₁) + $3.25 = $7.50.) As the columns labeled "Simultaneous" clearly show, the 401(k) will run out of money after 14.69 years. After 14.69 years, the Roth will have $37.63 remaining. (Remember that $3.25 has been withdrawn from this account for almost 15 years!) The Roth will be able to furnish $7.50 annually for six more years. Adding the two periods together obtains 14.69 + 6.00 = 20.69 years. Clearly this is an important and significant extension of the withdrawal process. Harvesting the money simultaneously has extended the withdrawal process by about 11 months (20.69 – 19.78 = 0.91 years ≈ 11 months).

Case 2: three tax brackets. Let's repeat the exercise above, this time assuming that there are three relevant tax brackets. The tax brackets are 15 percent on the first $3, 25 percent on the next $3, and 28 percent on income above $6. This tax structure is approximately the same as for the federal Married Filing Separately category (with income 10,000 times greater, of course.)
 
Results are shown in Table 3.

1. Sequential withdrawals. The taxpayer will need to withdraw $9.75 each year in pre-tax money from the 401(k) in order to obtain $7.50 in post-tax money. The money in the 401(k) will run out in 6.15 years. The tax-exempt Roth will have grown in value over the 6.15 years, attaining a balance of $68.90. The Roth will last an additional 12.98 years before being depleted. The total tenure of the withdrawal will be 19.13 years. If the Roth is depleted first, it will still take 19.13 years.
2. Simultaneous withdrawals I: maximum from bracket one. The taxpayer will now attempt to reduce the yearly tax burden by withdrawing less than the $7.50 post-tax amount from the 401(k) and the remainder from the Roth. Let's assume that the taxpayer withdraws $3 pre-tax (the maximum without bumping into the second tax bracket) from the 401(k), which provides $3(1 – t₁) = $2.55 of after-tax income. The Roth account will simultaneously withdraw $4.95 each period. Note that some income is shielded from both second-bracket and third-bracket taxes. The Roth will run out of money first, lasting 14.92 years before being exhausted. At the end of the life of the Roth, the 401(k) will have a value of $42.86 remaining and it will last an additional 5.14 years, withdrawing $9.75 (pre-tax) each year. This strategy will allow the portfolio to last for 20.06 years.
3. Simultaneous withdrawals II: maximum from bracket two. Finally, the maximum amount is taken from the 401(k) without bumping into the third bracket. Thus, $6 of pre-tax income will be withdrawn. The post-tax value is $4.80 and the difference of $2.70 will be withdrawn from the Roth. The sequential withdrawal results in the portfolio lasting 19.71 years.

The results of this exercise are illuminating. Given identical rates of return (and disregarding estate planning issues), it is clear that withdrawing from the tax-deferred account in a strategic manner that minimizes taxes will prolong the withdrawal process.

Conclusions

1. When harvesting money from two assets with the same tax treatment but whose annual rates of return are different, the annual withdrawal should be taken from the lower-performing asset first.
2. When withdrawals are to be taken from a tax-exempt and a tax-deferred account, the sequence of withdrawals is immaterial. That is, the shortfall risk remains unaffected by the order of withdrawals as long as both accounts grow tax-deferred at the same rate of return.
3. When withdrawals are to be taken from a tax-deferred account and a taxable account, the optimal withdrawal strategy depends on the expected rates of return of the individual assets in these accounts. Withdrawals should be made first from the account with the lower expected (post-tax) rate of return. When making withdrawals, it is not true that the tax-deferred account should always be left for last.
4. Owners of Roth portfolios can potentially extend the withdrawal process by simultaneously withdrawing from the Roth and from a tax-deferred account.

Perhaps the lesson to be learned is that the "obvious" answer is often not the correct one. The advantages that are presumed of tax-deferred and tax-exempt accounts during the accumulation phase do not necessarily carry over into the withdrawal phase.

References

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———. 2001. "Conserving Client Portfolios During Retirement, Part IV,: Journal of Financial Planning 14, 5 (May) 110–119.

Dammon, Robert M., Chester S. Spatt, and Harold H. Zhang. 2004 "Optimal Asset Location and Allocation with Taxable and Tax-Deferred Investing." Journal of Finance. 59, 3 (June): 999–1038.

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Malkiel, Burton G. 1999. A Random Walk Down Wall Street, 6th ed. New York: W. W. Norton & Company: 368–371.

Milevsky, Moshe M., Kwok, Ho and Chris Robinson. 1997. "Asset Allocation Via the Conditional First Exit Time or How to Avoid Outliving Your Money." Review of Quantitative Finance and Accounting 9, 1: 53–70.

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Vora, Premal P., and John D. McGinnis. 2000. "The Asset Allocation Decision in Retirement: Lessons from Dollar Cost Averaging," Financial Services Review 9, 1: 47–63.

Acknowledgment

We would like to thank our colleague, Dr. Jeffrey C. Strieter, for calling attention to the fact that multiple tax brackets may allow for longer drawdown periods if withdrawals are made simultaneously rather than sequentially.