{"enrichment":{"faq":[{"a":"statistics-fundamentals computes volatility as the standard deviation of your return series, applying Bessel correction (n\u22121 divisor) for unbiased sample estimates. For monthly returns, multiply the result by \u221a12 to annualize; for daily data, use \u221a252. The skill handles both raw and log returns, letting you test whether your data exhibits fat tails or skewness that violate normality assumptions.","q":"How do I calculate volatility from returns using statistics-fundamentals?"},{"a":"statistics-fundamentals includes the Jarque-Bera test to assess whether financial returns are normally distributed by examining skewness and kurtosis. The test flags fat tails and asymmetry common in stock data. You can also inspect raw descriptive statistics\u2014mean, variance, skewness, kurtosis\u2014to diagnose departures from normality before running parametric models like CAPM.","q":"What normality tests does statistics-fundamentals provide?"},{"a":"Unstable weights typically arise when you have more assets than observations, causing the sample covariance matrix to be ill-conditioned. statistics-fundamentals addresses this via Ledoit-Wolf shrinkage estimation, which blends your sample covariance toward a structured target (often the identity or single-factor model). This stabilizes weights and improves out-of-sample performance without discarding data.","q":"Why does my portfolio optimizer produce unstable weights with statistics-fundamentals?"},{"a":"statistics-fundamentals computes sample covariance and correlation matrices from your return data, then optionally applies Ledoit-Wolf shrinkage when assets exceed observations. It also supports rolling-window estimation to capture time-varying correlations. These stabilized estimates feed directly into mean-variance optimization and risk decomposition for portfolio construction.","q":"How does statistics-fundamentals estimate covariance matrices for portfolio construction?"},{"a":"Yes. statistics-fundamentals performs CAPM regression of asset returns against a market benchmark, reporting beta (market sensitivity), alpha (intercept), and R-squared. It computes t-statistics and p-values to test whether alpha is significantly different from zero, helping you assess whether a fund or strategy has genuine outperformance or just noise.","q":"Can statistics-fundamentals run CAPM regression to measure alpha and beta?"},{"a":"statistics-fundamentals uses non-parametric bootstrap resampling to generate confidence intervals for statistics like Sharpe ratio, volatility, and correlation when analytical formulas are intractable or assumptions are violated. It resamples your return observations with replacement, recalculates the statistic thousands of times, and constructs percentile-based intervals\u2014ideal for fat-tailed financial data.","q":"How do bootstrap confidence intervals work in statistics-fundamentals?"}],"shadow_tags":["portfolio-optimization","risk-measurement","hypothesis-testing","tail-risk","factor-models","sampling-methods","matrix-conditioning","performance-attribution"],"summary_rewrite":"Analyze financial return series with descriptive statistics, normality tests, and covariance estimation. Run CAPM regressions with significance testing, apply Ledoit-Wolf shrinkage for stable portfolio optimization, and bootstrap confidence intervals for statistics without clean analytical solutions."},"files":[{"bytes":8994,"path":"plugins/core/skills/statistics-fundamentals/SKILL.md","sha256":"f9c40377bf1a1e400b57746dba396e466f47c8221c09e8ea56f19c32f56e9802","url":"https://skillfed.io/files/JoelLewis/finance_skills/statistics-fundamentals/bcf3b04f/SKILL.md"}],"id":"JoelLewis/finance_skills/statistics-fundamentals","links":{"html":"https://skillfed.io/JoelLewis/finance_skills/statistics-fundamentals","md":"https://skillfed.io/JoelLewis/finance_skills/statistics-fundamentals.md","repo":"https://github.com/JoelLewis/finance_skills"},"meta":{"agents_supported":[],"first_seen":"2026-07-28","forks":32,"language":"Python","last_updated":"2026-07-18","license":"MIT","name":"statistics-fundamentals","publisher":"JoelLewis","stars":159},"relations":{"similar":[{"id":"JoelLewis/finance_skills/factor-investing"},{"id":"wangyendt/wayne-skills/statistics"},{"id":"tondevrel/scientific-agent-skills/statsmodels"},{"id":"liangdabiao/claude-data-analysis-ultra-main/data-explorer"},{"id":"OpenSenseNova/SenseNova-Skills/outlier-detection"},{"id":"JoelLewis/finance_skills/forward-risk"},{"id":"foryourhealth111-pixel/Vibe-Skills/statsmodels"},{"id":"drshailesh88/integrated_content_OS/statsmodels"},{"id":"zLanqing/codex-claude-academic-skills/statsmodels"},{"id":"LeonChaoX/qinyan-academic-skills/statsmodels"}]},"slug":{"owner":"JoelLewis","repo":"finance_skills","skill":"statistics-fundamentals"},"version":"bcf3b04f"}