feat(metrics): Deflated Sharpe Ratio (Bailey & Lopez de Prado)

Aggiunge expected_max_sharpe e deflated_sharpe_ratio per correggere
multiple testing nella valutazione di strategie. Considera skewness,
kurtosis e numero di trial.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

src/multi_swarm/metrics/dsr.py

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+from __future__ import annotations
+
+import numpy as np
+import pandas as pd  # type: ignore[import-untyped]
+from scipy import stats  # type: ignore[import-untyped]
+
+from .basic import sharpe_ratio
+
+EULER_MASCHERONI = 0.5772156649015329
+
+
+def expected_max_sharpe(n_trials: int, sharpe_var: float) -> float:
+    """E[max SR] su n_trials con varianza sharpe_var (Bailey & Lopez de Prado).
+
+    Formula: sqrt(sharpe_var) * ((1-gamma) * Phi^-1(1 - 1/N)
+             + gamma * Phi^-1(1 - 1/(N*e)))
+    dove gamma e' la costante di Eulero-Mascheroni.
+    """
+    if n_trials < 2:
+        return 0.0
+    e = np.e
+    z1 = stats.norm.ppf(1 - 1.0 / n_trials)
+    z2 = stats.norm.ppf(1 - 1.0 / (n_trials * e))
+    return float(
+        np.sqrt(sharpe_var) * ((1 - EULER_MASCHERONI) * z1 + EULER_MASCHERONI * z2)
+    )
+
+
+def deflated_sharpe_ratio(
+    returns: pd.Series,
+    n_trials: int,
+    periods_per_year: int = 8760,
+    sharpe_var: float = 1.0,
+    skewness: float | None = None,
+    kurtosis: float | None = None,
+) -> tuple[float, float]:
+    """Deflated Sharpe Ratio (DSR) e p-value associato.
+
+    Restituisce (DSR, p_value). p_value e' la prob. che lo SR osservato sia
+    superiore al massimo atteso sotto null. p_value bassi (es. < 0.05)
+    indicano significativita' dopo correzione per multiple testing.
+    """
+    n = len(returns)
+    if n < 30:
+        return 0.0, 1.0
+
+    sr = sharpe_ratio(returns, periods_per_year=periods_per_year)
+    sr_period = sr / np.sqrt(periods_per_year)
+
+    if skewness is None:
+        skewness = float(stats.skew(returns, bias=False))
+    if kurtosis is None:
+        kurtosis = float(stats.kurtosis(returns, fisher=True, bias=False))
+
+    sr_expected_max = expected_max_sharpe(n_trials, sharpe_var) / np.sqrt(periods_per_year)
+
+    denom = np.sqrt(
+        max(
+            (1 - skewness * sr_period + ((kurtosis - 1) / 4.0) * sr_period**2) / (n - 1),
+            1e-12,
+        )
+    )
+    z = (sr_period - sr_expected_max) / denom
+    p_value = float(1.0 - stats.norm.cdf(z))
+    dsr = float(stats.norm.cdf(z))
+    return dsr, p_value

tests/unit/test_metrics_dsr.py

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+import numpy as np
+import pandas as pd
+
+from multi_swarm.metrics.dsr import deflated_sharpe_ratio, expected_max_sharpe
+
+
+def test_expected_max_sharpe_grows_with_n_trials():
+    e1 = expected_max_sharpe(n_trials=1, sharpe_var=1.0)
+    e10 = expected_max_sharpe(n_trials=10, sharpe_var=1.0)
+    e100 = expected_max_sharpe(n_trials=100, sharpe_var=1.0)
+    assert e1 < e10 < e100
+
+
+def test_dsr_zero_when_sharpe_equals_expected_max():
+    np.random.seed(0)
+    returns = pd.Series(np.random.normal(0, 0.01, 500))
+    _dsr, p = deflated_sharpe_ratio(
+        returns, n_trials=10, periods_per_year=8760, sharpe_var=0.0
+    )
+    # Con sharpe_var=0 e Sharpe stimato vicino a 0, p-value deve essere alto.
+    assert 0.0 <= p <= 1.0
+
+
+def test_dsr_significant_for_strong_sharpe():
+    np.random.seed(42)
+    returns = pd.Series(np.random.normal(0.005, 0.005, 1000))
+    dsr, p = deflated_sharpe_ratio(
+        returns, n_trials=5, periods_per_year=8760, sharpe_var=1.0
+    )
+    # Sharpe atteso > 0 e p-value basso
+    assert dsr > 0
+    assert p < 0.5