Statistics Fundamentals

This gives Claude the statistical toolkit for quantitative finance work: descriptive stats, covariance matrices, OLS regression, hypothesis testing, and bootstrap resampling. You'll reach for it when analyzing return distributions, estimating correlations between assets, running CAPM regressions to get alpha and beta, or figuring out why your optimizer is producing unstable weights. It includes Ledoit-Wolf shrinkage for fixing ill-conditioned covariance matrices, which is the usual culprit when you have more assets than observations. The formulas cover the basics like volatility and skewness, plus practical diagnostics like R-squared and t-statistics. Also handles fat tails and non-normality, which matters because financial returns almost never pass a Jarque-Bera test.

skills.sh installs: 856
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last updated: Aug 21, 2026

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Install

$ npx -y skills add joellewis/finance_skills --skill statistics-fundamentals --agent claude-code

Installs into .claude/skills of the current project.

Files

Statistics Fundamentals

Core Concepts

Conventions and Decision Rules

Sample variance: use n-1

When estimating variance or standard deviation from a sample of returns, divide by n - 1 (Bessel's correction), not n. Dividing by n systematically underestimates dispersion. Standard deviation of returns is "volatility"; annualize with sigma_annual = sigma_period * sqrt(periods_per_year) (e.g., * sqrt(12) for monthly, * sqrt(252) for daily).

Normality testing: Jarque-Bera and its limits

JB = (n/6) * (skew^2 + excess_kurtosis^2 / 4), distributed chi-squared with 2 df under the null of normality (5% critical value: 5.99).

Low-power caveat: with small samples (n below roughly 50), JB rarely rejects even for clearly non-normal data — failing to reject is weak evidence of normality, not confirmation. With large samples, financial return series almost always reject due to fat tails and (for equities) negative skewness. Treat the test as a screen, and pair it with a look at the actual skew/kurtosis magnitudes and extreme observations.

SKILL.md on GitHub