“Arbitrage” is what we call it when one takes advantage of a difference in prices between two markets. Traditionally, it means buying a security in one market at a low price while simultaneously selling that same security in another market at a higher price — and pocketing the difference, taking advantage of that mismatch in prices.

So what does that have to do with Roth IRAs and Roth 401ks?

Roth conversions (and the decision whether to use a Roth IRA vs a traditional IRA or Roth 401k vs traditional 401k) — comes down to that one thing [**] — a “time-based tax rate arbitrage” — taking advantage of a mismatch in tax rates.

Taxes are *going* to be paid (unless you are leaving your IRA to charity).

It’s then purely a matter of when they will be paid. Pay them when your rates are low, not high.

The arbitrage in question is this: since taxes are going to be paid, if you pay them at a low tax rate, but avoid them at a high rate — you are engaging in a tax rate arbitrage and you get to pocket the difference.

Consider, for example, someone currently paying taxes (at the margin!) of, say, 32%. So someone earns, $1000, and chooses to put it into his traditional (deductible) 401k. Thus, $1000 goes into that account and no taxes are paid today. Suppose the investment doubles to $2000 over some period of time. And meanwhile, the investor has retired from a high paying job and now has a much lower income and is in the 12% tax bracket. If the (now) $2000 in the 401k is removed, taxes will be paid now at 12%, leaving our investor with $1760 to spend.

Was it the right move for this investor to use a traditional, deductible 401k instead of a Roth 401k? Let’s run the numbers the other way.

Our investor earns $1000 but, since the Roth 401k is non-deductible, taxes at our investor’s current 32% rate must be paid. (Yes, one could still put the full $1000 into the 401k, but then the $320 in taxes have to come from somewhere else — which would be better — but that still assumes other money comes from somewhere which is beyond the scope of this comparison). So only $680 ends up in the Roth 401k. Over the same period of time, the same investment will have doubled — to $1360. Distributions from the Roth are tax-free, so all $1360 can be removed and spent.

Note the difference in spending at the end: ($1760 – $1360 == $400) — that difference is precisely 20% of the ending value. That 20% is not a coincidence. It’s also precisely the difference in the tax rates which applied since the investor got to choose whether to pay taxes at 32% or at 12%. The choice of tax rates to be paid is controlled by the choice in timing as to when to pay the taxes. Hence — a “time-based tax arbitrage”.

The same math applies to Roth conversions. When you convert from a traditional IRA (or 401k) to a Roth IRA — the moment of the conversion is the moment you’ve chosen to cause it to be taxable.

Choose your moment carefully. You do have control over this. Choose to pay taxes when your rates are lower, not higher.

[** note that the “one thing” is sometimes quite complex. It’s not just the nominal marginal tax rate in the tax table based on your income, but it may also affect phase-ins or phase-outs of other taxes such as use of capital gains brackets, or whether or how much of your SS is taxable, and whether or not you trip over an IRMAA threshold. If only it were as simple as looking up your income in a single table. It’s not. But the overall issue is still the same — it’s all about your effective marginal rate (potentially taking all those other things into consideration to understand your actual effective rate).]