Taxadjusted asset allocation
If you have accounts with different tax treatment (taxable, traditional IRA or 401(k), Roth IRA or 401(k)), equal dollar amounts in those accounts have different aftertax values. Therefore, if you want to optimize the aftertax value of your portfolio, you should base your asset allocation on the aftertax value of the accounts.
Contents
Why to adjust
The purpose of asset allocation is to design a portfolio with the desired level of expected return and risk. Returns and mathematical definitions of risk should be based on aftertax values, since the aftertax value is what you will be able to spend. Emotional definitions of risk should be based on how you perceive the risk.
Returns
The goal of returns is to get the money you will spend to achieve your goal. If you have $100K in stock in a Roth and the stock market doubles in value, you have $100K more to spend in retirement. If you have $100K in stock in a traditional IRA, you have $100K more pretax but will lose some of the value to taxes upon withdrawal. If you have $100K in stock in a taxable account, the account will be worth less than $200K after the stock market doubles in value, because of taxes on dividends, and you will have even less to spend because you will pay tax on your capital gains.
Mathematical risk
Mathematical risk is based on your need and ability to take risk. Your need to take risk is determined by the returns you require; if you need your portfolio to double in order to provide an adequate standard of living, you actually need it to double in aftertax value. Your ability to take risk is determined by the consequences of losses; losing $100K in your Roth IRA will reduce your standard of living (or require more additional savings to keep the same standard) by more than losing $100K in your traditional IRA or taxable account does.
Emotional risk
Emotional risk is determined by how you will react to losses. If you pull out of the stock market after it falls, or you cannot sleep during a bear market, then your portfolio is too risky. In theory, the best way to handle emotional risk is the same as any other risk; if your portfolio software is set up to only present the aftertax value of your portfolio, then a $100K loss in an account taxed at 25% is only a $75K decrease in your bottom line. In practice, most investors will not be able to make these adjustments, particularly because the investment statements show dollar values.
How much to adjust
There are two reasonable formulas for adjustment, based on the marginal and overall tax rates. The marginal rate is the correct rate to use for considering changes in the asset allocation (and thus for most taxadjusted asset allocation), while the overall rate is correct for estimating the portfolio value or expected returns.
Adjusting by the marginal rate
You should value your Roth at its full value, and reduce the value of your traditional IRA or 401(k) by your expected tax bracket at retirement (including state taxes if your state taxes these withdrawals, which varies by state). You should also reduce the value of your taxable account by about 25% if you are early in your career, and 15% if you are near or in retirement, plus state taxes; estimated values are necessary because the tax cost depends on how much you will have in capital gains.
If all of your IRA or 401(k) withdrawals will be in a 25% tax bracket when you retire, then 25% of your withdrawals from a traditional IRA or 401(k) will be lost to taxes. Therefore, it makes sense to assume that the IRS owns 25% of the account; whatever the gain or loss in nominal dollars, 75% will go to you and 25% to the IRS. In contrast, the IRS owns none of your Roth, which is taxfree.
If your IRA or 401(k) is large enough that the withdrawals will span multiple tax brackets each year, the marginal tax rate is the rate which affects the risk and return of any marginal decisions you might make, such as a change in your asset allocation. For example, if you expect that half your withdrawals will be taxed at 15% and half at 25%, you will lose only 20% of the total to taxes. However, if you increase the risk of your IRA investments and earn an extra $1,000, you will pay an extra $250 in taxes, not $200; if the risk works out badly and you lose $1,000, you will pay $250 less in taxes. Thus, in this situation, the IRS owns 25% of the part of the IRA in which your decision will make a difference.
The IRS also owns part of your taxable account, representing the difference between what you earn on it and what you could have earned in a taxfree account. If your taxable account is invested in stocks, you will lose some money every year you hold it to the tax on the dividends, and more to the capital gains tax when you sell. If it is invested in municipal bonds, you effectively lose the difference between yields on municipal bonds and corporate bonds of comparable risk every year. The calculation is more complicated (and depends on assumptions about future returns and tax rates), but the adjustment usually comes out about the same for a taxable account and an IRA; this spreadsheet can make an estimated calculation. The spreadsheet calculates the marginal tax rate, for the same reason as above.
Adjusting for the overall tax rate
The overall tax rate, averaged over all your withdrawals, determines the actual aftertax value of your accounts, and thus affects the aftertax returns. A 401(k) or traditional IRA loses less to tax adjustment from the overall tax rate; a taxable account loses about the same amount because its taxes are at a mostlyflat rate on capital gains and qualified dividends.
A natural assumption for the overall tax rate is that you will have some taxable income independent of your retirement accounts (such as 85% of Social Security, which is taxable for higherincome retirees), and your IRA or 401(k) will be taxed on top of that. Estimate your other income and deductions, and then compute the tax on the difference between that income and the retirement accounts. This will be somewhat less than your marginal tax rate if your IRA or 401(k) spans multiple brackets.
If you have a taxable account, you will probably still need to adjust based on your marginal tax rate, because the tax on qualified dividends and longterm gains is effectively a flat 15% (plus state tax) in most tax brackets. If you expect to retire in a 15% tax bracket, you can neglect any federal tax on qualified dividends and capital gains in retirement. If you hold munis, the tax cost is unaffected by your retirement tax bracket, since it is an effective cost equal to the difference between taxable and taxexempt bonds of comparable risk.
Why to make these adjustments
It is easiest to see why the adjustment is necessary by comparing traditional and Roth accounts. For example, suppose you have $4,000 in a 401(k) and $3,000 in a Roth IRA, and you will be in a 25% tax bracket when you retire. You might choose to invest the entire 401(k) in stock and the entire Roth in bonds. If you do this, and the stock market gains 10% while the bond market gains 5%, your 401(k) would be worth $4,400, and your Roth would be worth $3,150. The IRS will take 25% of your 401(k) when you withdraw it, so you could now withdraw your investments for $6,450. Similarly, if you invested the 401(k) in bonds and the Roth in stock, your 401(k) would be worth $4,200, and your Roth would be worth $3,300. After taxes, you would have the same $6,450. Since both portfolios give you the same 7.5% return that you would expect from a portfolio which was 50% stock and 50% bonds, it is reasonable to treat both portfolios as having a 50/50 asset allocation, rather than the 57/43 and 43/57 which would result from the nominal values.
The tax adjustment also adjusts for the effective difference in risk between the two accounts. In the example above, suppose that the stock market loses half its value. If your 401(k) was entirely in stock, it would drop from $4,000 to $2,000, which would cost you $1,500 in aftertax value; if your Roth was entirely in stock, it would drop from $3,000 to $1,500. Either way, you lose 25% of the value of your portfolio, so your portfolio has the risk of a portfolio which is 50% stock.
Consequences
Asset location
Once you adjust for the aftertax value, it does not matter which assets you put in a traditional IRA or 401(k) and which you put in a Roth. If you are in a 25% tax bracket, investing $4,000 in the 401(k) or $3,000 in the Roth in the same investment will give you the same aftertax value.
If all else is equal (and it often isn't because of limited 401(k) options), it is slightly better to put assets with higher expected returns in the Roth. If your traditional account has lower than expected returns and you fall into a lower tax bracket, the IRS will not give back the same share of the losses; if your traditional account has higher than expected returns, the IRS will take a larger share of the gains. In the Roth, you get the same percentage (100%) of all gains and losses. In addition, the Roth is protected against potential changes in tax rates, has more flexible rules for required minimum distributions, and is not counted as income for making Social Security taxable.
It still does matter which assets you put in your taxable accounts; see Principles of taxefficient fund placement for details.
Roth conversions
You can evaluate a conversion of a traditional IRA to a Roth by its effect on your aftertax asset allocation. If you are in the same tax bracket now that you expect to be in at retirement, and you pay taxes on the conversion with IRA money (or with money you would have otherwise contributed to a 401(k) or IRA), the conversion is breakeven. For example, if you are in a 25% tax bracket and convert a $40,000 IRA, you will have $30,000 in the Roth after paying taxes. Previously, you owned $30,000 of the IRA and the IRS owned the other $10,000; after conversion, you own the entire $30,000 in the Roth.
In contrast, if you pay the taxes with taxable money, you have a net gain, and it may even be worth making the conversion if you are going to be in a slightly lower tax bracket at retirement. If you are in a 28% tax bracket but expect to retire in a 25% tax bracket, and have $11,200 in a taxable account and $40,000 in an IRA, you own 75% of the IRA and probably about 75% of the taxable account, a total of $38,400. If you convert to a Roth, paying the taxes with the taxable $11,200, you will have a Roth worth $40,000.
The advantage of a Roth
If you can max out either a traditional or a Roth IRA or 401(k), you are likely to be better off with the Roth, because you effectively taxdefer more money. You can contribute the same number of dollars either way, but you own all of the Roth and not all of the traditional account.
Investing in the Roth in this situation is equivalent to investing in a traditional IRA and immediately converting it to a Roth, paying the tax with aftertax dollars. Therefore, if you are in a much higher tax bracket now than you will be in at retirement, the traditional account may still be better, but if the brackets will be equal or close, you should prefer the Roth.
See also
External links
 Asset allocation spreadsheet which adjusts for aftertax asset allocation
 Do Your Asset Classes Care Where They Are?, William Bernstein, Efficient Frontier
 TaxAdjusted Asset Allocation from the Oblivious Investor blog.
 Exploring the Bogleheads(TM) Wiki  TaxAdjusted Asset Allocation by Mel Lindauer on Forbes.
 Principles of after tax asset allocation by Stephen M. Horan, CFA Institute, January 2007.
 Roth vs Traditional asset location  advanced discussion  thread in Bogleheads.org forum, Jan 18, 2011.
 Grok Tip 15 You're doing it wrong: Figuring stock/bond split, forum discussion
 Problems with Reichenstein's "Asset Location Decis Revisted", forum discussion
Bibliography

