sharpe-ratio-non-iid-corrections

Sharpe Ratio Non-IID Corrections

Sharpe ratio inference for a single strategy whose returns are non-Normal and serially correlated. Reference implementation of the generalized sampling variance in López de Prado, Lipton & Zoonekynd (2026), and of the single-test statistics that use it.

Self-Evolving Skill: This skill improves through use. If instructions are wrong, parameters drifted, or a workaround was needed — fix this file immediately, don't defer. Only update for real, reproducible issues.

Out of scope — do not re-add (operator rule, 2026-10-15)

Never compute, report, rank by or cite the Deflated Sharpe Ratio or any other trial-count correction: FWER and FDR procedures (Holm, Bonferroni/Šidák, Benjamini-Yekutieli, the paper's pFDR/oFDR/SFDR), e-LOND and other online multiple testing, expected-maximum-Sharpe deflation, effective-number-of-trials estimates, and the minimum backtest length (MinBTL), which is a function of the number of trials. MinTRL is a different quantity (one rule's own track record) and stays. They were removed from this skill on purpose. Instead:

• Judge parsimony on the model itself (how many free parameters, how much was tuned), not by deflating a Sharpe for the number of trials.
• Guard selection with registration before runs and with unused data: fix the hypothesis, rule and evaluation window before running, and confirm on data no run has touched.
• Report each rule's own statistics: its Sharpe, ρ-corrected σ[SR̂], PSR, MinTRL and power.

PSR, MinTRL, the ρ-corrected variance and power are single-test statistics and stay. PBO/CSCV describes a selection procedure and is not covered by the rule.

Quick Start

# Run the 9 validation tests (paper Exhibit 1 numerical examples)
uv run --no-project --with numpy --with numba \
  python plugins/quant-research/skills/sharpe-ratio-non-iid-corrections/references/sharpe_numba.py

Paper Metadata

Field	Value
Title	How to Use the Sharpe Ratio
Authors	Marcos López de Prado, Alexander Lipton, Vincent Zoonekynd
Series	ADIA Lab Research Paper Series, No. 19
Date	March 7, 2026
SSRN	5520741
Replication	https://github.com/zoonek/2025-sharpe-ratio
Source PDF	lopez-de-prado-sharpe-2026.pdf

The PDF is kept because the variance derivation (Section 2, Appendix A.1–A.2) and the PSR/MinTRL/power equations this skill implements are cited by equation number from it. Only those sections are used; the transcription omits the rest.

References

Topic	Reference File
Paper transcription (implemented excerpt)	how-to-use-the-sharpe-ratio-2026.md
Equation → Implementation Tracker	sharpe-paper-tracker.md
Numba JIT Implementation	sharpe_numba.py
Source PDF	lopez-de-prado-sharpe-2026.pdf
Paper Figures	media/ (Exhibit 2, variance vs autocorrelation, pp. 12-13)

Preflight: what to compute

Inputs are all objective, computed from the return series under evaluation:

Parameter	Meaning	Source
SR̂	Observed (non-annualized) Sharpe ratio	Return series
T	Number of return observations	Return series
γ₃, γ₄	Skewness, Pearson kurtosis (γ₄=3 is Gaussian)	Return series
ρ	Lag-1 autocorrelation	Return series
SR₀	Benchmark Sharpe under the null (often 0)	Fixed before the run
SR₁, α	Alternative Sharpe and test size, for power	Fixed before the run

Fix SR₀, SR₁ and α in the registration, before looking at results. Report SR̂, σ[SR̂], PSR, MinTRL against T, and power together.

Key Formulas

All equations use the paper's non-IID variance (Eq 2-3) with Pearson kurtosis convention (γ₄=3 for Gaussian).

Eq	Name	Formula	Function
2-3	SR Variance	V[SR̂] = (1/T)·(a − b·γ₃·SR + c·(γ₄−1)/4·SR²)	sr_variance()
9	PSR	Φ((SR̂ − SR₀) / σ[SR₀])	psr()
11	MinTRL	(a − b·γ₃·SR₀ + c·(γ₄−1)/4·SR₀²) · (z_{1−α}/(SR̂−SR₀))²	min_trl()
8, 14	Critical SR	SR₀ + σ[SR₀]·z_{1−α}	critical_sr()
13-15	Power	1 − Φ((SR_c − SR₁) / σ[SR₁])	power()
17	β (Type II)	Φ((z_{1−α}·√(a(ρ)) − SR₁·√T) / √(a − b·γ₃·SR₁ + c·(γ₄−1)/4·SR₁²))	power() → 1 - power

Where a = (1+ρ)/(1−ρ), b = (1+ρ+ρ²)/(1−ρ²), c = (1+ρ²)/(1−ρ²) are AR(1) variance coefficients (ar1_variance_coeffs()).

Numerical Example (Paper Exhibit 1)

Hedge fund: T=24 months, γ₃=−2.448, γ₄=10.164 (Pearson), SR=0.036/0.079≈0.456, ρ=0.2.

Quantity	Equation	Value	Notes
σ[SR̂] (non-Gaussian)	Eq 3	0.379	vs 0.214 Gaussian — 77% wider
PSR (SR₀=0)	Eq 9	0.966	Still significant despite wider CI
PSR (SR₀=0.1)	Eq 9+5	0.900	Harder benchmark reduces confidence
MinTRL (SR₀=0)	Eq 11	19.543 months	T=24 > 19.5 → sufficient
MinTRL (SR₀=0.1)	Eq 11	39.369 months	More than doubles for SR₀ closer to SR̂
β (power, SR₁=0.5)	Eq 17	0.411	vs 0.224 IID Normal — 84% higher
Power (1−β)	Eq 15	0.589	Low for 24-month track record

Implementation Architecture

4-tier dependency hierarchy (Numba JIT, Rust-ready):

Tier 0: erfinv, norm_cdf, norm_ppf
Tier 1: sr_variance (Eqs 3/58), ar1_variance_coeffs
Tier 2: psr (Eq 9), min_trl (Eq 11), critical_sr (Eq 8)
Tier 3: power (Eqs 12-17)

Related Skills

Skill	Relationship
opendeviation-eval-metrics	Consumes PSR and MinTRL for range bar evaluation (ρ=0 quick-ref)
adaptive-wfo-epoch	Reports PSR per walk-forward fold

Post-Execution Reflection

After this skill completes, check before closing:

1. Did the command succeed? — If not, fix the instruction or error table that caused the failure.
2. Did parameters or output change? — If the underlying tool's interface drifted, update Usage examples and Parameters table to match.
3. Was a workaround needed? — If you had to improvise (different flags, extra steps), update this SKILL.md so the next invocation doesn't need the same workaround.

Only update if the issue is real and reproducible — not speculative.