Real vs Nominal Return: Why Subtracting Inflation Is the Wrong Answer

Why it is a division and not a subtraction

Follow one unit of money. Put $100 to work at 7 percent and a year later you hold $107. Over the same year prices rose 3 percent, so what cost $100 now costs $103. The question real return answers is how much more you can buy, and that is $107 ÷ $103 = 1.038835 baskets, a gain of 3.8835 percent. Nothing was subtracted anywhere; two quantities measured in shrinking units were compared by dividing one by the other. Subtraction would only be exact if the inflation adjustment applied to the original capital and not to the gain, which is not how prices work.

The size of the discrepancy has a closed form: subtracting overstates the real return by (nominal − inflation) × inflation ÷ (1 + inflation). Both factors in the numerator matter, which is why the error grows in two directions. Hold inflation at 3 percent and widen the gap, and the error widens with it. Hold the gap at four points and lift both rates — 10 against 6 instead of 7 against 3 — and the error nearly doubles, from 0.117 to 0.226 points, even though the shortcut returns the same 4 percent both times. That is the tell: whenever the subtraction gives you the identical answer for two obviously different situations, it is discarding information.

What a tenth of a point does over thirty years

Compounding is what turns a rounding error into a planning error. Grow $10,000 at the shortcut's 4 percent and after ten years you project $14,802; the true 3.883 percent delivers $14,637, a gap of $165. Run it to twenty years and the gap is $486. Run it to thirty and it is $1,072, or 3.4 percent of the whole pot. Nothing in the input changed — the same 7 percent nominal, the same 3 percent inflation — only the decision to divide rather than subtract.

The sign of the error flips when the real return is negative, and it flips in the direction that flatters nobody. Hold cash paying 3 percent while inflation runs at 4 percent and the subtraction says you lost 1.000 percent of your purchasing power, while the exact figure is a loss of 0.962 percent. Here the shortcut is slightly pessimistic rather than optimistic, which is the one case in which it does no harm. Everywhere the real return is positive — that is, everywhere it matters for a plan — subtracting flatters the result.

Using the real return without fooling yourself

Keep the whole projection in one unit. Either work in nominal terms and inflate your future spending target alongside the pot, or work in real terms and leave the target at today's prices — but never mix, because a nominal growth rate applied to a target expressed in today's money is the most common way a retirement plan quietly doubles its own optimism. The real-terms version is usually easier to read: everything is already in money you understand the value of.

Two caveats sit on top of the arithmetic. The inflation figure you divide by is a national average built from a basket that may not resemble yours; if your spending is dominated by rent or energy, your personal inflation can differ from the published index by several points, and the real return you experience differs with it. And tax lands on the nominal gain, not the real one, so in a taxable account the sequence matters: subtract the tax from the nominal return first, then apply the Fisher division to what is left. Doing it the other way round understates the damage.

Frequently asked questions

When is subtracting inflation good enough?

For a single year at low rates, and for a figure you are speaking aloud rather than putting in a spreadsheet. Below about 3 percent inflation the shortcut is wrong by under a tenth of a point, which no plan is sensitive to. Use the exact division whenever you compound over more than a few years, whenever either rate exceeds roughly 10 percent, or whenever you are comparing two options that are close together — those are the three places the approximation changes the conclusion rather than the decimals.

Which inflation number should I divide by?

The one that covers the same period and the same economy as the return. For a year of investment returns, use that year's published consumer price index change for the country whose currency you hold; for a multi-year horizon, use a long-run average rather than the latest reading, which is noisy. Do not mix a headline index from one country with returns earned in another currency, because the exchange-rate movement is already inside the nominal return and you would be adjusting for the wrong price level.

Does the same formula work for interest rates on debt?

Yes, and it works in the borrower's favour rather than against them. A fixed-rate loan at 5 percent while inflation runs at 3 percent has a real cost of 1.942 percent, not 2, because the money you repay is worth less than the money you borrowed. That is why unexpected inflation transfers value from lenders to fixed-rate borrowers. It does not apply to a variable rate, which typically rises with inflation and removes the effect.