Radar Perene / Archive / science

The Ibovespa and the dollar: what correlation doesn't tell

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

Science

No pair of Brazilian numbers gets explained as frequently — and with as little ceremony — as the stock index and the dollar. One day, the dollar "knocked down" the Ibovespa; the next, the index fell "despite" the dollar; on a third, both rose together and the headline swapped verbs without apologizing for the previous one. The arrow connecting the two changes direction according to the needs of the evening edition. What is almost never asked is whether the arrow exists.

In the Ibovespa × dollar pair, the correlation — the tendency of the two to move in opposite directions over many windows — is measurable in any spreadsheet. Causation — one of them pushing the other — would require a study design the headline never runs: prior hypothesis, control of the common factor, and testing outside the window that displayed the pattern. The reading most compatible with the data is not that of a lever between the two prices, but of two mirrors of the same thing: the appetite for Brazil risk.

The general ruler for this problem — the three classic traps, the role of study design — the house has already written in correlation is not causation. This page descends to the specific case, because the index×dollar pair has an anatomy of its own: real channels that exist, channels that oppose each other, and a pattern that changes sign over time.

The mirror and the lever

What makes the pair treacherous is that it is not spurious like the escalators of spurious regression — there are real mechanisms linking the two prices. The problem is that there is more than one, and they pull in opposite directions.

The flow channel suggests negative correlation: when foreign capital withdraws from Brazilian assets, it tends to sell stocks and buy dollars in the same movement — the two prices record, simultaneously, the same exit. The revenue channel suggests the opposite: a relevant share of the Ibovespa consists of exporters and commodity producers, companies whose revenue in reais fattens when the dollar rises — for that slice of the index, a weak currency is accounting profit. Two true mechanisms, opposite signs. Which one dominates depends on the index's composition at the time, the origin of the shock and the global environment — which is why the pair's correlation, measured in rolling windows, swings from strongly negative to weak without asking the folklore's permission.

Whoever observes "stocks fell, dollar rose" observes, most of the time, the double mirror: a third factor — global risk appetite, external flow, domestic fiscal perception — reflected in two prices at once. Synchronized mirrors seem to talk to each other. They do not; they face the same scene.

What a study design would demand of the pair

Turning the headline into a testable hypothesis forces three commitments the routine never makes. First, declare the direction and the mechanism before looking at the result: "the dollar knocks down stocks" and "stocks knock down the dollar" are different hypotheses, and the headline uses both according to the day. Second, control the common factor: subtract the global environment — the behavior of other emerging currencies, the mood of international equity markets — before attributing any exclusive relation to the pair; when the control enters, the "Brazil versus Brazil" relation usually thins in a revealing way. Third, test outside the window: an arrow that only works between two dates is not a law, it is an episode — and the index×dollar pair is a repeat offender at changing behavior between regimes, as the archive compared in 2013 × 2024, when the currency dictates.

None of this is exotic; it is the same protocol of any serious causal question. The difference is that, applied to this pair, the protocol usually returns a modest verdict: the coincidence is robust, the arrow is not.

When the archive watched the pair up close

Two dates in the archive test the mirror reading. In March 2020, the dollar closed in statistical anomaly while the stock market collapsed — and that fortnight's headlines distributed daily arrows between the two. The house record, documented in the ruler of March 2020, confined itself to what the data contained: each price's distance from its own history, the environment of aversion, and the explicit refusal to promise direction. In numbers: the R$ 4.8839 close stood more than three deviations from the mean of its own history — a sentence that records rarity, not cause.

December 2024 offered the counterexample the folklore did not foresee: the market's internal panel turned to appetite — the intermarket score jumped to the top of the scale — and, by the script, that mood should have "dragged" the currency back. It did not: the dollar remained in anomaly, indifferent to the neighboring mirror, as documented in the dollar in anomaly, December 2024. When two prices that "always move together" spend weeks ignoring each other, the headline's arrow loses its job — and what remains is what was always there: two mirrors, not always facing the same scene.

Frequently asked questions

So the dollar never moves the stock market?

It does move it — through the exporters' accounting channel, which is real and measurable company by company. What the data does not sustain is the newsroom's single, stable arrow, because the flow channel pushes the other way and the balance shifts with the regime.

Why does the pair's correlation change sign?

Because the outcome is the sum of opposing mechanisms with varying weights: the index's sector composition, the origin of the shock (domestic or global), the risk environment. Conditional correlation is not a defect of statistics; it is statistics describing a pair with more than one true engine.

Does measuring correlation in rolling windows solve it?

It helps reveal the instability — which is already information. But a rolling window describes; it does not identify cause. The leap from description to arrow still requires the full study design.

What is the house's day-to-day reading?

The thermometer's: the two prices are read as simultaneous gauges of the environment, each against its own history, with no arrow manufactured between them. The doctrine is in the entry the dollar as thermometer.

Coinciding on the day is one thing; walking together for decades is a question of another nature — with a test of its own: cointegration →

House readings: the pair, read without an arrow, is in today's note, in the Daily; the regimes in which it changed behavior, in the precedents, in the Atlas.

Running the pair — or any other — through the full design, with declared controls, is an exercise the house conducts on request.

Characters: Dollar