The Perene Risk Index: A Composite Regime Indicator for the Brazilian Equity Market

Radar Perene Working Paper Series, No. RPWP-001 · Version 2.3 · July 2026 Market observers in Brazil, as elsewhere, habitually reason from isolated indicators — an index level, a volatility print, a single valuation multiple — even though episodes of systemic stress and systemic exuberance are joint phenomena that no single series captures. The result is a persistent interpretive gap: participants can state where the Ibovespa is, but not where the market stands within its own behavioural history. This paper introduces the Perene Risk Index, a daily composite regime indicator for the Brazilian equity market and the founding instrument of the Radar Perene research program. The index measures the market's prevailing appetite for risk — the degree to which the domestic equity environment is behaving in a risk-embracing or defensive manner — by aggregating observable, market-priced behaviour rather than opinion or survey data. Its components are drawn from three categories: market breadth and internals (the participation of a broad, liquidity-filtered universe of Brazilian listed equities in prevailing trends), which is the dominant spine; size/liquidity preference (the standing of small-capitalization equities relative to the large-capitalization benchmark, measured as a relative level); and credit conditions (the price of credit to the private sector), a light macro-financial reinforcement that adds the financing channel equity internals do not observe. Sentiment-type inputs are deliberately excluded; within the Radar Perene program these are held by a sibling indicator, so that no sentiment-type input enters both instruments — the two may share behavioural inputs such as breadth, but the sentiment family is exclusive to the sibling. Construction proceeds in three conceptual stages, described here without proprietary parameters: each component is bounded through a rolling-percentile transformation against its own recent history; bounded components are aggregated with renormalization over the components present on each date; and the aggregate is expressed through a final range-ranking within a rolling window, producing a 0–100 scale in which 0 and 100 denote the extremes of the market's own recent range. Daily history extends to 2000, with coverage gating where underlying data begin later. The index locates the present within the distribution of the market's own past — capitulation extremes (readings near 0 in January 2016, May 2018, and March 2020), euphoric extremes (cyclical tops historically near 93 on the pre-saturation composite), and the transitions between them. It does not forecast returns or time securities. A sequential-signal study on the index's public bands shows favourable but imperfect asymmetries — roughly two signals in three were followed by positive nominal windows, against an unconditional base near three in five, an asymmetry that a per-era decomposition (Section 7.2) locates in the mature 2009-onward record while the pre-2009 events of the breadth-only construction fall below the unconditional base in frequency — and the paper documents saturation at the extremes, coverage limits before the size (2009) and credit (2011) components begin, and the post-2000-only scope. A documented 2026 recalibration, in which a component-sourcing defect was found and corrected with essentially unchanged results, evidences the construction's robustness and audit discipline. Version 2.0 refines the construct — the size dimension becomes a relative level and a light credit channel is added — with construct-validity evidence that these reinforcements sharpen the description of contemporaneous stress in recent, credit-active regimes while the breadth-dominated composite stays, over the full sample, essentially tied with its spine: a conditional improvement, never a forecast. Version 2.1 added the tests this discipline demands and reported them regardless of outcome: a race against trivial single-series benchmarks, whose result is unfavourable — the composite does not track contemporaneous stress more closely than the trivial alternatives (Section 8.6) — and a placebo-and-permutation study establishing the composite as a serially dependent state variable, with mean band-regime duration 2.86 times a permutation null (p < 0.001), a property the final percentile/range-rank transformation does not manufacture (Section 7.6). Version 2.2 completes that discipline by racing the persistence property itself against the same trivial benchmarks, and the result is again unfavourable: under an identical permutation protocol with quantile-matched thresholds, all four trivial alternatives are more persistent than the composite (duration ratios of 3.13 to 7.53 against 2.88) and more autocorrelated at every horizon examined, so persistence — real against chance — is not a differentiator and is withdrawn from the statement of the index's value (Section 7.6). What remains, stated with the same frankness as the negative results themselves, is this: the index's value rests on its bounded scale with exact endpoint semantics, on its deliberately separated dimensions — the one differential property this paper's evidence supports, with the credit axis carrying the composite's only macro-financial content — and on its infrastructure and governance: a twenty-six-year daily Brazilian series with public bands, a dated changelog, and a companion verification package against which every inferential number in this paper can be recomputed. Keywords: market regimes; risk appetite; composite indicators; market breadth; credit conditions; financial conditions; Brazilian equity market; Ibovespa; risk-on/risk-off; indicator methodology; investor behaviour; index construction ---