Tax-adjusted 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 after-tax values. Therefore, if you want to optimize the after-tax value of your portfolio, you should base your asset allocation on the after-tax value of the accounts.

How Much to Adjust
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 30%; the exact value is variable and cannot be estimated precisely.

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 tax-free.

If your IRA or 401(k) is large enough that the withdrawals will span multiple tax brackets each year, it is still correct to use your marginal tax bracket for adjustment, because this 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 $1000, you will pay an extra $250 in taxes, not $200; if the risk works out badly and you lose $1000, 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 tax-free 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.

Why to Adjust
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 $4000 to $2000, which would cost you $1500 in after-tax value; if your Roth was entirely in stock, it would drop from $3000 to $1500. Either way, you lose 25% of the value of your portfolio, so your portfolio has the risk of a portfolio which is 50% stock.

Asset Location
Once you adjust for the after-tax 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 after-tax 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. 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 Tax-Efficient Fund Placement for details.

Roth Conversions
You can evaluate a conversion of a traditional IRA to a Roth by its effect on your after-tax 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, the conversion is break-even. 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 tax-defer 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 after-tax 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.

Links

 * Asset allocation spreadsheet which adjusts for after-tax asset allocation
 * Do Your Asset Classes Care Where They Are?, William Bernstein, Efficient Frontier

Academic Papers

 * Reichenstein, William E. "Calculating the Asset Allocation," Journal of Wealth Management Vol. 3, No. 2 (Fall 2000), 20–25. Available at http://finance.baylor.edu/reichenstein/fin4365/CalcultaingAssetAllocation.PDF
 * Reichenstein, William E., "Tax-Efficient Saving And Investing," TIAA-CREF Institute, Trends and Issues (Feb. 2006). Available at http://www.tiaa-crefinstitute.org/research/trends/docs/tr020106b.pdf
 * Reichenstein, William E., "Non-qualified Annuities in After-tax Optimizations," (May 11, 2005). Available at http://www.ifid.ca/Conference_Material/Reichenstein_paper.pdf
 * Reichenstein, William E.,"Asset Allocation and Asset Location Decisions Revisited," "Journal of Porfolio Management" (Summer 2001). Available at http://www.efficientfrontier.com/ef/704/REICHENSTEINJWMMarkOpt.pdf
 * Reichenstein, William E. "Savings Vehicles and the Taxation of Individual Investors," Journal of Private Portfolio Management Vol. 2, No. 3 (Winter 1999), 1–12.