What is a real (inflation-adjusted) return?

A real return is the return on an investment after accounting for inflation. It measures the change in purchasing power: how much more, or less, the money can buy at the end of the period than at the start. The return as it is usually quoted, before inflation, is the nominal return.

A savings account paying 2% in a year with 3% inflation holds more euros at the end of the year and buys less with them. Its nominal return is +2%; its real return is about −1%.

The formula

The exact relationship between the nominal return $r$ , the inflation rate $\pi$ and the real return $r_{\text{real}}$ is:

1 + r_{\text{real}} = \frac{1 + r}{1 + \pi}

so that

r_{\text{real}} = \frac{1 + r}{1 + \pi} - 1

For small numbers the shortcut $r_{\text{real}} \approx r - \pi$ is close enough. For larger ones it overstates the real return, and the error grows with inflation.

A simple illustration

An investment returns 7% in a year in which consumer prices rise 3%:

r_{\text{real}} = \frac{1.07}{1.03} - 1 \approx 3.88\%

The shortcut gives 4%. With a 10% nominal return and 8% inflation, the shortcut says 2%, but the real return is only 1.85%.

Over many years

Inflation compounds just as returns do. Over 30 years, 2% inflation a year reduces the purchasing power of a euro by about 45%:

\frac{1}{1.02^{30}} \approx 0.55

That is why long-term plans are best made in real terms. A target of €500,000 in 30 years is worth roughly €276,000 in today's money at 2% inflation.

Why it matters

Cash and bonds can have negative real returns for years while their nominal returns are positive, as happened across much of Europe when inflation rose in 2022.
Comparing periods with different inflation rates is only fair in real terms: a 10% return in a year of 8% inflation is weaker than a 5% return in a year of 1% inflation.
Return assumptions for planning should always say whether they are nominal or real. Long-run real returns of global equities have been around 5% a year; nominal returns are higher by the rate of inflation. Mixing the two is one of the most common planning mistakes.

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