deflated-sharpe

You tested 1,000 parameter combinations and found a Sharpe 2.0 strategy. Is it real — or did you just test enough times to get lucky?

deflated-sharpe implements the Deflated Sharpe Ratio (Bailey & Lopez de Prado, 2014) and related statistical gates. Pure Python, zero required dependencies, designed to be the last check before you deploy a strategy.

Install

pip install deflated-sharpe

Quick Start

Deflated Sharpe Ratio

from deflated_sharpe import deflated_sharpe_ratio

dsr, p_value = deflated_sharpe_ratio(observed_sr=2.0, num_trials=1000, num_obs=252)
print(f"DSR={dsr:.2f}, p={p_value:.4f}")

A positive DSR with p < 0.05 means your strategy likely has real alpha after accounting for the number of trials you ran. A negative DSR means the expected maximum Sharpe from random chance alone exceeds your observed Sharpe.

Minimum Backtest Length

from deflated_sharpe import min_backtest_length

min_obs = min_backtest_length(target_sr=1.5, num_trials=500)
print(f"Need at least {min_obs} observations")

Before running a large search, compute how many observations you need. If your backtest window is shorter than min_obs, no strategy can pass the DSR gate regardless of performance.

Regime Decay Detection

from deflated_sharpe import RegimeDecayDetector, StrategyBaseline, TradeResult

baseline = StrategyBaseline(win_rate=0.55, trade_count=200, max_drawdown_pct=12.0)
detector = RegimeDecayDetector(baseline=baseline)
detector.fit_market_baseline(training_features)  # list of (atr_ratio, trend_pct, atr_percentile)

for trade in live_trades:
    detector.add_trade(trade)
assessment = detector.assess()
print(f"Decay confirmed: {assessment.decay_confirmed} ({assessment.signals_fired}/3 signals)")

Triple-confirmation system: Bayesian win rate decay, drawdown exceedance (1.5x backtest MDD), and Mahalanobis out-of-distribution detection. Two of three signals must fire simultaneously to confirm decay.

How DSR Saved Us

In March 2026, we ran a grid search over 19,200 parameter combinations on BTCUSDT 1H walk-forward data (23 periods, 3-month IS + 3-month OOS). Multiple strategies showed Sharpe ratios above 1.5 in-sample. The DSR gate rejected every single one — correctly preventing deployment of overfitted strategies.

The math was simple: with M=19,200 trials and only 30-50 trades per window, the expected maximum Sharpe from pure chance exceeded every observed value. We then tested LLM-guided search (M~30 per period, 640x fewer trials) and found the same result: trade count was the binding constraint, not search method. DSR saved us from deploying strategies that looked profitable but had zero statistical significance.

Full analysis: Phase 15 Case Study

Tools

deflated_sharpe_ratio(observed_sr, num_trials, num_obs, skewness, kurtosis)

Computes the Deflated Sharpe Ratio per Bailey & Lopez de Prado (2014). Adjusts the observed Sharpe for selection bias from multiple testing, accounting for return non-normality via skewness and kurtosis corrections.

The key insight: when you test M strategies, the maximum Sharpe you expect from pure luck grows as O(sqrt(ln(M))). DSR subtracts this expected maximum from your observed Sharpe and normalizes by the standard error.

Returns (dsr, p_value). DSR > 0 with p < 0.05 indicates statistical significance.

Reference: Bailey, D.H. & Lopez de Prado, M. (2014), Eq. 2-4.

min_backtest_length(target_sr, num_trials, alpha, skewness, kurtosis)

Binary search for the minimum number of observations T such that DSR > 0 at the given significance level. Use this to determine if your backtest window is long enough before running a parameter search.

from deflated_sharpe import min_backtest_length

# "I want Sharpe 1.5 after testing 200 strategies. How much data do I need?"
min_obs = min_backtest_length(target_sr=1.5, num_trials=200, alpha=0.05)

benjamini_hochberg(p_values, alpha)

Benjamini-Hochberg FDR correction for evaluating multiple strategies simultaneously. When you have N candidate strategies each with a DSR p-value, BH controls the false discovery rate at level alpha.

from deflated_sharpe import deflated_sharpe_ratio, benjamini_hochberg

p_values = [
    deflated_sharpe_ratio(sr, num_trials=50, num_obs=500)[1]
    for sr in [1.2, 0.8, 1.5, 0.3]
]
results = benjamini_hochberg(p_values, alpha=0.05)
for idx, p, sig in results:
    print(f"Strategy {idx}: p={p:.4f}, significant={sig}")

RegimeDecayDetector

Live monitoring for strategy regime decay. Three independent signals with 2/3 majority vote:

• S1 Win Rate Decay: Bayesian Beta updating with backtest prior. Fires when P(win_rate < breakeven) exceeds threshold.
• S2 Drawdown Exceedance: Fires when current drawdown exceeds dd_multiplier (default 1.5x) times backtest maximum drawdown.
• S3 Market OOD: Mahalanobis distance on market features (ATR ratio, trend, ATR percentile). Fires when recent trades are beyond the training distribution's 95th percentile.

Anti-false-positive measures: minimum 20 trades before assessment, cooling period of 5 trades after trigger, Bonferroni correction for multiple strategies.

Paper Verification

The DSR implementation is verified against the original paper's mathematics: Gumbel approximation for E[Z_max], standard error with non-normality correction, and the full DSR test statistic. See tests/test_paper_verification.py for numerical checks against known values from Bailey & Lopez de Prado (2014).

Zero Dependencies

The core library uses only Python standard library (math, dataclasses). The _math.py module implements norm_cdf, matrix inversion, and Mahalanobis distance from scratch to avoid pulling in NumPy/SciPy for basic usage.

For the regime detector's Bayesian win rate signal (S1), scipy.stats.beta is used if available; otherwise a point-estimate fallback is used. Install the optional dependency:

pip install "deflated-sharpe[scipy]"

References

Bailey, D. H., & Lopez de Prado, M. (2014). "The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting, and Non-Normality." Journal of Portfolio Management, 40(5), 94-107. DOI: 10.3905/jpm.2014.40.5.094

License

Apache-2.0