The Deflated Sharpe Ratio: A Unified Framework for Search-Adjusted Performance Inference

Investment research is a search process: Researchers compare factors, model specifications, machine learning designs, parameter choices, trading rules, and managers, and then they focus on the strongest result. The winner of that search cannot be evaluated as though it had been specified in advance. The Deflated Sharpe Ratio (DSR) addresses this fundamental selection problem by judging reported performance against what the research process itself could have produced without skill. We unify the principal DSR implementations and explain their complementary roles. DSR-L provides the original parsimonious location benchmark for search-adjusted significance and minimum track-record analysis. DSR-LS adds the dispersion of the selected maximum, preserving a tractable location-and-scale form compatible with PSR and MinTRL while supporting power and related operating characteristics. DSR-EO uses the complete search distribution when exact tail inference is available. We also derive general calibration results linking distributional approximation error to false-positive and p-value distortion. Gaussian and Student-t benchmarks show that tail shape can alter both the magnitude and direction of approximation error, while a general GEV-domain result establishes asymptotic calibration of DSR-LS when its reference shape is matched to the extreme-value limit, with a plug-in extension under the stated scale-relative consistency conditions.