A Conditional Exceedance Framework for Interpretable Trading Decisions

This paper makes two distinct contributions and keeps them clearly separated. First, a descriptive finding, verified independently of any trading outcome (Section 8.10): conditioning SPY’s forward price moves on comparable past moves systematically raises the probability of a future exceedance, with positive lift in all 54 tested horizon-threshold combinations (mean 2.56×). Second, a predictive test (Sections 7–8) of whether thresholding that probability into a mechanical entry rule, fully specified as numbered equations with every parameter frozen before 2025, produces a trading edge. It does not. The strategy underperforms SPY buy-and-hold on capital-weighted return in all three active configurations (Section 8.5), and its portfolio-level Sharpe (0.62–1.15, Section 8.4) is statistically indistinguishable from a randomly-timed exposure of the same size — confirmed by a within-strategy randomisation test and an independent random-entry benchmark using no parameters from the conditioning analysis (Section 8.8). We report both the per-trade-normalised statistics implied directly by the equations (Eq. 11, 13) and the capital-constrained, account-realisable analogues (Eq. 11c, 13d), since the two differ by 108–147× and must not be conflated (Section 8.3). A 23-year walk-forward extension (2003–2025, same train-on-prior-data discipline; Section 8.12) shows the gap widens, not narrows, with more history: 2.3 percent annualised against SPY’s 11.0 percent, because an entry rule requiring a prior sustained rise is structurally excluded from the sharp post-crash recoveries that drive much of the index’s long-run return. Underperforming buy-and-hold is not unusual — 79 percent of active large-cap managers did the same in 2025 (SPIVA; Section 8.7) — and this paper’s contribution is the verified descriptive structure and auditable methodology, not a demonstrated edge. The companion Conditional Exceedance Atlas (Ramanathan, 2026b; Section 3) extends the same construct descriptively across 161 instruments and two applied multi-predictor dashboards, whose performance under this same discipline remains an open question (Section 8.15).