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before this target is evaluated in this task; original 2000–2024 one-month benchmark has already been inspected. RETROSPECTIVE benchmark, not a fresh or prospective holdout.","target":"Y_t=1 iff min(P_{t+1},...,P_{t+12}) <= 0.8*P_t. All twelve consecutive future monthly observations must be present to score a row, including positive outcomes. Every feature-ready forecast month is eligible, including already-drawn-down months. Price is reset to current P_t for every forecast; this is additional loss, not crossing a prior peak threshold.","horizon_months":12,"threshold_fraction":0.8,"feature_set":["ret1","ret12","vol12","drawdown"],"features":"Log(P_t/P_t-1), log(P_t/P_t-12), sample std ddof=1 of 12 consecutive log returns, P_t/max(P_t-11...P_t)-1. No future inputs. Missing months are not filled.","candidates":{"constant":[],"distance_volatility":["drawdown","vol12"],"full":["ret1","ret12","vol12","drawdown"]},"distance_definition":"Distance is past drawdown from trailing peak, not distance to the target barrier: prospective loss barrier is always20% below current price, making current barrier distance constant. The simple model uses only past drawdown and volatility.","train_outcome_months":["1926-07","1984-12"],"development_outcome_months":["1987-01","1997-12"],"test_outcome_months":["2000-01","2024-12"],"partition_rule":"Both first future month and twelfth future month must fall within the partition; latest forecast dates train1983-12, development1996-12,test2023-12. Earliest development forecast1986-12, test1999-12. Embargo outcome years1985–1986 and1998–1999; no labels cross boundaries.","fit":"Train-only mean/population-std scaling; pooled unweighted logistic mean log loss with unpenalized intercept and lambda/2 squared standardized slopes. No class weights. Constant=train event prevalence. No refit on development or test.","lambda_candidates":[0.0001,0.001,0.01,0.1],"selection":"Each logistic candidate selects lambda by development Brier; choose final candidate, including constant, by smallest development Brier. Ties favor constant then simpler model then full; lambda ties favor first grid entry. No later model choice based on test, Nasdaq or case performance.","operating_thresholds":[0.1,0.2],"calibration_edges":[0,0.05,0.1,0.2,0.3,0.4,0.6,0.8,1.0000001],"primary_metrics":["Brier vs constant train prevalence","calibration bins","FP/FN/TP/TN at10% and20%"],"secondary_metrics":["log loss","AUROC","average precision","mean estimate vs event rate"],"uncertainty":"2000 circular moving-block bootstrap resamples of24consecutive forecast calendar months. Within-month all industries retained jointly; extend blocks with wraparound, truncate to original month count. Paired Brier differences vsconstant and full-vs-simple. Approximate intervals address overlapping labels and shared shocks but not longer dependence, model-selection uncertainty, or prospective generalization.","seed":20260907,"nasdaq":"Fixed selected industry candidate applied without retuning to Nasdaq month-end closes, retrospective outcome windows2000–2024. Current asofAugust2026 forecasts Sep2026–Aug2027 and has no observed outcome. It is a broad-tech price-index transfer, not an AI probability.","cases":"Main10 replacesUS1987 withUSrailroadsApr1872pricepeak/name1873panic; other original9unchanged. Display asof24months before through24months after peak. Nasdaq andNikkei use true month-end daily closes; BTC daily reference-rate last observation each month; others retain monthly published/mean indices and explicit target-frequency mismatch. Coefficients/future-period leakage and feature range are labeled; selected cases are not performance denominator.","out_of_domain":"Always flag cross-asset/country/price-vs-total-return population transfer. For each row also report features outside train min/max (univariate support only; withinrange does not establish joint-domain validity). No clipping/recalibration.","sources":[{"url":"https://academic.oup.com/qje/article/132/1/367/2724543","scope":"IanMartin2017QJE, What is the Expected Return on the Market? Studies20%crash probabilities at1/6/12month terminal horizons using option information. Supports horizon/threshold relevance, not this monthly-min target or fitted model."},{"url":"https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5954394","scope":"Haghani/White2026, How Likely is a Stock Market Crash? Explicit12month path loss from current level, but30%threshold and different methods. Our20%monthly-close minimum is a declared adaptation, not replication."},{"url":"https://www.nber.org/papers/w23191","scope":"Industry return-runup/volatility/path evidence motivates limited predictors; original longer crash horizon differs."},{"url":"https://stat.uw.edu/research/tech-reports/strictly-proper-scoring-rules-prediction-and-estimation","scope":"Proper scoring rules support probabilistic Brier evaluation."}]}}