Radar Perene / Archive / science

Real vs. nominal interest rates: inflation decides who wins

◦ Index methodology v2.2 (working papers with DOI). See the methodology.

Science

Between August 2020 and March 2021, anyone earning Brazil's base rate on their savings watched the balance grow every month. The statement did not lie: there were more reais in the account. Neither did the supermarket: each of those reais bought less than before. The two documents told opposite stories about the same person — and only one of them answered the question that matters.

The nominal interest rate is the number written in the contract: how much the money grows in currency. The real interest rate is what remains after subtracting the period's inflation: how much the money grows in purchasing power. The distance between the two is not a technicality — it is what decides, in any credit contract or investment, who ends the period richer and who merely appears to.

The distinction carries a century of literature. Irving Fisher formalized it in The Theory of Interest, in 1930: the nominal rate tends to embed expected inflation, so that what is truly negotiated, behind the contract's number, is always the real rate. The hypothesis became known as the Fisher effect — and Brazil, with its inflation history, is one of the harshest laboratories it has ever been offered.

The arithmetic, spelled out

The math is short, but it has a catch. The real rate is not the simple subtraction "rate minus inflation"; it is the division of factors: one plus the nominal rate, divided by one plus inflation, minus one. At low rates the two calculations nearly coincide; at Brazilian rates, the difference shows.

Two methodological choices must be declared before any conclusion — and it is by failing to declare them that so many return comparisons mislead. The first is the deflator: the result changes depending on whether one discounts the IPCA, the INPC or the IGP-M, and each index measures the inflation of a different basket. The second is the timing of the gaze: the ex-post real rate uses the inflation that actually occurred and only exists afterwards; the ex-ante real rate uses expected inflation — in Brazil, typically the median of the Focus survey — and is what guides decisions in the present. Both are legitimate; confusing them is not.

The Brazilian series, rebuilt from open data

None of this requires a paid terminal. The Selic target is series 432 in the SGS, the Central Bank's time-series system; the monthly IPCA variation is series 433, compiled by the IBGE and mirrored there. With those two columns and the division of factors declared above, any reader can rebuild the trajectory of Brazil's real interest rate — the path the house described in open data from the Central Bank.

The rebuilt series tells a story the folklore summarizes poorly. Brazil spent long stretches of recent decades among the highest real rates in the world — and still visited the opposite territory. In numbers: the Selic spent the period from August 2020 to March 2021 at 2% per year, while the IPCA accumulated 10.06% over 2021 — a deeply negative base rate in real terms, verifiable by anyone in series 432 and 433. Whoever "earned" that period's nominal rate lost purchasing power every month; whoever owed at fixed rates watched the debt melt in real terms. Inflation decided who won, and it did not consult the contract.

The Fisher effect, in the Brazilian case, is less a law and more a tendency with delays: nominal rates chase expected inflation, but the fit is never immediate or exact — and it is in those mismatches that the real rate swings between generous and negative.

Where the archive recorded this frontier

The distinction is not decorative for the house: the real interest rate is one of the archive's permanent rulers. At the end of 2024, the monitoring registered in market real rates one of the rarest premiums of the entire historical series — the episode is documented in real interest rates in anomaly. The nominal Selic closed that year at 12.25% and kept rising to 15.0% by July 2025; but it was the real rate in anomalous state, not the nominal headline, that separated the outcomes inside the stock market — on one side the sector that lives off high rates, on the other the assets most sensitive to the real discount. The nominal was the headline; the real was the variable doing the work.

It is the applied version of the definition at the top: two agents looking at the same Selic lived opposite realities, because each one's reality was the real rate of their own position.

What changes for the reader of return figures

The reading discipline fits in one question: deflated by what, and over which window? A return announced without a deflator and a period is half a number. The ruler works in every direction — investments, debts, rents, wages. And it holds three years from now as well as it holds today, because it depends on no current rate level: it depends on a subtraction inflation always collects, wherever it stands.

Frequently asked questions

Can the real rate be negative?

It can, and recent Brazil offers the example: between 2020 and 2021, the nominal base rate stayed below realized inflation. In purchasing-power terms, whoever received the base rate was paying to lend.

Which index should deflate the calculation?

It depends on the question. The IPCA measures the household consumption basket and anchors the inflation target; the IGP-M carries heavy wholesale and exchange-rate weight; the INPC focuses on lower-income households. Honest research declares the chosen index and the reason — and tests whether the conclusion survives another deflator.

Can ex-ante and ex-post real rates disagree by much?

They can, and they do whenever inflation surprises. The ex-ante embeds the expectation of the moment; the ex-post records what happened. The difference between the two is, itself, a measure of how much the economy surprised.

Why is Brazil's real interest rate historically high?

The literature has accumulated hypotheses — fiscal history, low domestic savings, inflationary memory, risk premiums — without a single verdict. The honest record is this: the phenomenon is documented; the full explanation remains in dispute.

If inflation decides who wins, the next question is how contracts try to defend themselves against it — and what that defense costs: inflation and indexation →

House readings: each day's real rate is in today's note, in the Daily; the episodes when it left the ordinary, in the precedents, in the Atlas.

Rebuilding the real-rate series for a specific period or deflator is an exercise the house conducts on request.

Characters: Rates (Selic)