This past week has been somewhat exciting. I spend some of my downtime reading other personal finance blogs. I recently came across a series of posts discussing the virtues and vices of the traditional 401(k) and the Roth IRA (or Roth 401(k)). I've discussed this topic before in posts like "Roth vs 401k: Who Wins? …(no one will ever tell you this)" but I haven't always delved into some of the more interesting details.

Just in case you're not familiar with either type of retirement account by now, I'll give you the short version: traditional 401(k) accounts allow you to contribute money to the account on a pretax basis (you pay no income tax on contribution amounts). When you retire (sometime after age 59 1/2), you pay income tax on all distributions (withdrawals) from the account. Roth accounts work in reverse. You don't get any deductions on your contributions. All contributions are after-tax. Withdrawals are tax-free.

One of the posts that really caught my eye was a post by The Finance Buff:

This question of whether one is better off with contributing to the Traditional 401k or contributing to the Roth 401k has been the subject of a lot of debate. Although there is no one-size-fits-all answer, I think for most people the majority, if not 100%, of the contribution should go to a Traditional 401(k).

This struck me as a curious statement, since most personal finance writers seem to hold the opposite view of the argument. That is to say that a lot of personal finance writers argue for the Roth over the traditional.

To be fair, he does make several good arguments. One of the most important is this:

Fill in lower tax brackets in retirement. ...The tax system in the United States is progressive and it will probably stay that way. That means that income is taxed at increasing rates as it goes higher. Even if you think the marginal tax rate in the future will be higher, there will still be lower brackets and these lower brackets should be filled with money from a Traditional 401(k).

This is a good point. Many finance writers, even ones that work for major publications, often get this wrong. When you adjust anything for taxes, you have to operate on the average tax rate, not the marginal tax rate. When your tax adviser tells you that you are in a 25 percent tax bracket, that's not how much of your pay actually goes towards taxes. That's just how much your last dollar is taxed. The Finance Buff (TFB) makes a good point by explaining--in simple terms--our progressive tax structure. I don't know that our system will remain a progressive system. But, if it does, then TFB nails it on the head with this argument.

There are several other reasons a person might want to stick with a traditional 401(k) if they are convinced that these retirement accounts carry any significant benefits at all.

But, there are a few issues that work against TFB. First, the argument relies only on tax rates. What about investment returns? I have previously discussed average investment returns and when 8% may not be a true 8% return. Depending on the market, and how and when those returns occur, it could dramatically affect whether one would use a traditional 401(k) or a Roth.

I emailed TFB about this, and he didn't get the connection. The connection is that future investment returns may not be something you know in advance. If you don't know what those returns will be (and you won't unless you have a crystal ball), you won't know which account will perform better in the future and at what exact age your retirement savings will experience its peak performance (thus indicating the perfect year to retire). You might be able to guess long-term performance of a stock market, but nailing down performance in any given year is impossible at best.

If your traditional 401(k) does extremely well when you are ready to retire, then you could realistically be pushed up into a higher marginal tax bracket, thus increasing your average tax rate over the rate you were paying when you were working. This would mean that you should have invested in a Roth instead of a traditional 401(k). If you didn't do as well in your 401(k), or you ended up paying the same average tax rate as when you were working, a traditional 401(k) would have worked out just as well or better than the Roth.

This problem is something I call the "Monte Carlo Problem." Monte Carlo software is financial software that is designed to predict the probability of you running out of retirement savings prior to your death. The software randomizes investment returns based on an average rate of return that is chosen by the person running the software calculation. Combined with an assumed inflation factor, the software basically does what I've explained in my post about average rates of return. The actual amount of money varies wildly after 30 or 40 years of investing (remember, you'll likely keep investing money well into your retirement).

This means that the investment software takes an average rate of return of, say, 12 percent and comes up with 100s of different retirement account balances after 30+ years of investing. The point of the software isn't to try to guess at how much you'll have after those 30 years. It's assumed in advance that this is an impractical-impossible feat. The point of the software is to try to calculate probabilities of success. If the variance in returns is analyzed sufficiently, it is assumed that you could get a rough idea, in terms of a percent, your chances of successfully living out your retirement without spending all of your money.

What TFB doesn't seem to understand is the significance of this variance.

Let me show you what this means in concrete terms.

Assume an average single tax rate of 17.25 percent. Assume that a person has an income of $50,000 per year, which is fairly average for Americans. Well, in most major cities anyway. Invest $10,000 (this would represent an investment in a traditional 401(k)) and then invest $7,750 ( this would represent an investment in a Roth account, with after-tax dollars--I assumed NY State's tax rate for tax rates at the state level on top of federal because this is the state I am most familiar with at the time of this writing).

With the pretax $10,000 investment, you end up with $109,357 after 30 years and an average rate of return of 8 percent (if you throw in variance in returns, the results could be better or worse). With after tax investment in a Roth of $7,750, you end up with $84,282 assuming the same average rate of return and same number of years invested.

There's certainly less money in the Roth account. Now convert the traditional 401(k) to a Roth. What just happened? Remember you can't convert the $109,000 at the same tax rate that you made the contributions at because your tax rate now reflects a higher marginal rate (at current tax rates--which are the only ones we can know right now), which now pushes up your average tax rate to 22.16%, and that's assuming you don't have ANY other income in the year you make the conversion (how likely is that?). Now subtract state taxes of 7 percent (technically, 6.25% to 6.75% on the low end). You might live in a tax-free state, but then again you might not, for any number of reasons. What do you end up with? Even with a 6.25 percent state tax rate, you end up with $79, 803 after tax. Whoops. The traditional 401(k) didn't work this time.

If you had moved to a tax-free state, you would have a little more money with the traditional 401(k) account. Then, the traditional 401(k) would work out for you. It could happen. But, will everyone, or even a majority of people, who retire move to an income tax-free state? I doubt it. There are a lot of people who don't live in Alaska, Florida, Nevada, South Dakota, Texas, and Washington (all of the states that don't have an income tax right now). And, out of the seven states with no state income tax, I can imagine most people wanting to move to Texas, Florida or maybe Nevada. Something about South Dakota doesn't scream "retirement heaven." This is also assuming tax rates do not increase at the federal level in the next 20, 30 or 40 years. A traditional 401(k) could also work if you just withdraw enough for income instead of converting the whole amount at retirement. But, this again depends on your average tax rate at retirement (i.e. how much your savings amounts to and how much income you want to take).

In other words, where the variance in returns becomes a problem is when your investment returns start pushing you into a higher marginal tax rate. Then, you won't be able to rely on the idea that your tax rate will be the same in retirement as it was when you were working, even if tax rates don't change in the future. The Monte Carlo Problem is really a question being restated as a problem. The question is: "how do I predict the future?" The answer is: you can't. At least not in this context and with the degree of specificity that you'd need to successfully do "tax planning."

So much for the argument that most people should always invest in a traditional 401(k). The issue should really be thought of more simplistically: the more you make, the more the government takes. If you expect to do very well in your traditional 401(k), then expect to have less net income at retirement than with a tax-free retirement strategy.