I’m not talking about the game show.

And I’m not referencing the delightful thriller staring Ashley Judd.

Today, I’m talking about a very odd quirk that should make you think long and hard about how you fund your Roth 401(k) if the annual expense is anywhere north of .5%.

And I’m going to do this with as little number-crunching as possible. I’ve already written about retirement account expenses in my whimsically titled Are you 401(k)o’ed? I disclosed in that article that the average annual expense within the average 401(k) for plans with 1000 or more participants is 1.08%. The difference between the retirement account and a regular brokerage account is the tax status. In a 401(k) you hope to deposit money at say, 25-28% (this covers couples with a taxable $72,500 to $223,050 in 2013) and then withdraw it in retirement at a lower 10-15%.

There’s no complicated math – after 10 years, that extra 1% fee will wipe out all the benefit of a 25% to 15% tax difference.

Now, here’s where the Roth 401(k) Double Jeopardy comes in – In normal times, the market will double over a ten year period. This would be a return of 7.2% per year compounded. So, you’ve deposited $10,000 to your Roth 401(k), ten years go by, see the market grow 8%/yr and with that average fee of 1.08% you have $19,525 in the account. You then check to see that if the fee were 1% less, you’d have $21,430 or $1,905 more money. Drumroll, please. It just cost you $1905 to make that $9525 grow tax free, an effective 20% cost over the 10 years. Looking at it a different way, if $10,000 grew to $21,430 and you sold the stock or fund, you’d have a 15% capital gain to pay. You’d net $19,715.

I use the term Double Jeopardy because the effect of the fee over the 10 year period is doubled. While the standard 401(k) is deferring tax on the full deposit, the Roth flavor is eliminating tax solely on the growth. So over that 10 year period, your cost of $1905 to save you the tax on the $9525 growth was an effective 20% expense. If this doesn’t make sense, please read up to this point one more time.

The logical next step is to look at this effect for just one year, the very first year. In one year, the 1.08% retirement account will cost you $100 in fees. In the pretax 401(k) you’ve deferred tax on an account worth $10,692 so if you retire and withdraw the funds in a lower bracket, the result is favorable. In the Roth 401(k) however, you just spent $100 to avoid tax on the $692 growth. This is a 14% hit. The impact is exactly the opposite of the traditional account where the fee for a very short period of time makes sense for someone soon to retire or change jobs.

I hope this article prompts you to look at your retirement account expenses a bit more closely. If the 401(k) gets matched deposits, especially dollar for dollar, deposit to the matching limit, even if the ongoing fees are high. It takes a long time along with some very high fees to negate the benefit of that match.

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The math here doesn’t actually depend on the Roth situation. While one dollar of expenses costs more in a Roth, the tax situation means that you can contribute more to a traditional 401(k) for the same out of cost. If you are in a 25% tax bracket and have $10,000 to invest, you can contribute $10,000 to a Roth 401(k), but you could contribute $13,333 to a traditional 401(k) instead because your tax would be $3333 less. Thus the traditional 401(k) would grow to $26,033 with the high fees, or $28,573 with lower fees; the fees have now cost you $2540 of pre-tax dollars instead of $1925 of after-tax dollars. And if you withdraw the money in a 25% tax bracket, that’s a wash, as the $2540 becomes $1925 after tax and you have $19,525 to spend in retirement.

If you withdraw the money in a 15% tax bracket, the fees actually cost you more in the traditional 401(k), but the traditional 401(k) is still better because you wind up with $22,028 rather than $19,525.

I think we agree. There’s a great benefit in the traditional 401(k) when one can deposit at one bracket and withdraw at a lower one.

My focus today was how the Roth choice actually creates a multiplier effect, so that over the time it takes to double your money, the annual expense rate is doubled, e.g. a .5% fee over 10 years isn’t 5%, but 10%. And that’s nearly enough to kill the potential tax savings of the Roth 401(k).

And my point is that the multiplier effect is an illusion. You wrote, “While the standard 401(k) is deferring tax on the full deposit, the Roth flavor is eliminating tax solely on the growth.” Avoiding tax completely on a smaller amount is just as good as deferring tax on a larger amount, and it turns out to be a wash. One way to see the equivalence is to view a $13,333 traditional 401(k) as being 75% owned by you tax-free, and 25% owned by the IRS; if you invest it the same as a $10,000 Roth 401(k), you will always have the same emount after tax. That is what happens in our examples, in which ten years of expenses reduce the value of both accounts by 9% compared to a lower-cost option.

Thus, if the Roth and traditional options would be equally good with low expenses, they are also equally good with high expenses. If you expect to retire in a lower tax bracket, then you shouldn’t be using a Roth 401(k) in any case, so you don’t care whether high expenses make the Roth better or worse than a taxable investment.

You write, “The impact is exactly the opposite of the traditional account where the fee for a very short period of time makes sense for someone soon to retire or change jobs.” Actually, if you are going to retire or change jobs soon, you should invest in the 401(k) (whichever type is better in your situation), even if it has high expenses.

The reason is that you do not need to cash in your 401(k) when you leave your job. You pay the high expenses only as long as you stay in your job. When you leave, you can roll a traditional 401(k) into a traditional IRA, or a Roth 401(k) into a Roth IRA, continuing to gain the benefits of tax-deferred or tax-free growth until you withdraw the money years later, and with free choice of all low-expense investments.

All your points are true, Dave, this article is discussing a different fact. One last try to explain it.

Say we have 2 years of zero return. And then you change companies so you can bail on the high fee account. The 401(k) just cost you 2%, but you have the potential tax savings still there, the difference from say 28% to 15%, or 13% (less the 2%, now) that you’ll save at withdrawal.

The Roth cost the same 2%, but with no market gain, you’ve paid for something that never materialized. The Traditional 401(k) has its benefit frontloaded, but the Roth 401(k) only shows the benefit based on years of growth. This is the distinction.

But in that case, you roll the Roth 401(k) into a Roth IRA and leave it there for 28 years. Those 28 years of growth are tax free as well.

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