A Descriptive Atlas of Conditional Exceedance Structure Across a Multi-Asset Universe

We present a large-scale descriptive study of conditional tail co-movement across a universe of 161 financial instruments spanning equities, cryptocurrencies, commodities, fixed income, volatility, and foreign exchange, using daily data spanning 1993–2026 for the core equity universe, with some rates series extending to 1960 and crypto series beginning as late as 2024. Our central object is the Conditional Probability of Exceedance (CPE): the empirical frequency with which a target asset's forward log-increment over a horizon breaches a chosen quantile threshold, conditional on a predictor asset's trailing log-increment having breached its own threshold. We compute this quantity exhaustively over a grid of trailing and forward horizons spanning one to three hundred trading days and over a grid of quantile thresholds from the median to the 99th percentile, in both bullish (upper-tail) and bearish (lower-tail) directions, retaining roughly 169,000 pairwise configurations that exceed pre-set support and lift filters. We then extend the analysis to joint conditioning sets of up to ten predictors via a greedy intersection procedure. The study is explicitly descriptive rather than predictive: every threshold is an in-sample quantile and no out-of-sample or forecasting claim is made or implied. Read at the level of asset-class structure rather than individual ranked pairs, the atlas reveals coherent and interpretable regions of strong conditional co-exceedance — within-complex metal linkages, a pronounced volatility-to-equity lower-tail channel, dense intra-crypto coupling, and a recurring crypto-to-commodity association mediated by the post-2024 spot Bitcoin ETFs. We document these structures, characterise their dependence on horizon and threshold, and discuss the important interpretive limits imposed by overlapping observation windows and heterogeneous sample start dates. Alongside CPE, a lift statistic—the ratio of CPE to the unconditional exceedance probability—is computed for each configuration; only signals with lift ≥ 1.5 and a minimum of 100 conditioning observations are retained. An interactive companion dashboard exploring the full CPE atlas is available at https://quantarram.github.io/quant-regime-research/notebooks/cpe_dashboard.html.