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What your investment really earned

Eight percent return, three percent inflation. The answer is not five.

An investment shows one number: what it gained. That number does not tell you what you can buy with it, and that is the only question worth asking when money sits still for years.

Real return is a ratio, not a subtraction

The habit is to subtract. Eight percent return, three percent inflation, five percent real. It is wrong, and always in the same direction: it flatters.

The correct calculation divides instead of subtracting, because you are comparing two multiplications. A hundred becomes 108. What that hundred used to buy now costs 103.

• 1.08 / 1.03 - 1 = 4.85%, not 5%.

A sixth of a point. Over one year nobody will notice. Over ten years, the error inflates the capital by 1.4%. Over twenty, by 2.8%. And the gap widens as inflation rises: at 12% return against 9% inflation, subtraction says 3% where the real figure is 2.75%.

Inflation in which country?

The second trap, and the costlier one: which index you measure against.

An asset is measured against the prices of its own country. A flat in Lisbon held from Berlin is measured against Portuguese inflation — the Portuguese market set its price, not the German one. Using the inflation of the country you live in would mix two unrelated stories.

Your total net worth, on the other hand, is measured against the prices of where you spend. That is the only place where "can I buy more than before" means anything.

Two different indices for two different questions, and that is as it should be.

What it changes in practice

A savings account at 2% while prices rise 3%: the real return is -0.97% a year. After ten years the amount is untouched on the statement and has lost 9.3% of what it could buy. Nothing on the screen says so.

A flat bought eight years ago, now worth 40% more, in a country where prices rose 35%: the gap is not five points. It is +3.7% in total, or 0.46% a year. The deal is not a bad one — it is simply not the one that 40% suggested.

What real return does not tell you

Three things no calculation settles on its own:

• Contributions. An account funded every month has not had all its capital working for the same length of time. Comparing today's value to the total paid in mixes money that worked for eight years with money that worked for eight days.
• Fees and tax. Real return is computed on what is left after them, not before.
• Currency. An asset held in a currency other than yours has two returns: its own, in its own currency, and what it is worth once converted. They are not the same, and the second depends on an exchange rate nobody controls.

What to take away

A nominal return answers "how much more money". A real return answers "how much more of everything else". For savings left alone for ten years, only the second question has a useful answer.

And if there is a loan against the asset, the reading changes again: a loan in your budget and in your net worth.