quants.wiki

A machine-readable reference for quantitative finance estimators: the exact formula, the conditions under which it is valid, and a worked number. Performance statistics with the Lo autocorrelation correction, Sharpe standard errors and small-sample bias; drawdown statistics against the expected maximum drawdown of a random walk; covariance conditioning, Ledoit-Wolf shrinkage, EWMA and GARCH, and the Parkinson, Garman-Klass, Rogers-Satchell and Yang-Zhang volatility estimators; mean-variance, risk parity, hierarchical risk parity, Black-Litterman and Kelly in closed form; deflated Sharpe, probability of backtest overfitting, minimum backtest length and purged cross-validation; implementation shortfall, square-root impact, Almgren-Chriss and Kyle's lambda.

Quantitative finance is well served by libraries and badly served by references. Implementations are readable but do not state their assumptions; papers state their assumptions but not the arithmetic; glossaries state neither. This corpus is the third thing: the estimator, the exact conditions under which it is valid, and a worked number computed from data published here so the reader can check it. It is written for someone implementing, not someone learning vocabulary, and an entry that a practitioner would find obvious has been left out. Notation is uniform across the whole site. Returns and moments: r_t is a periodic return, mu the arithmetic mean return per period, g the geometric mean, sigma the standard deviation of returns and sigma^2 the variance, gamma3 the skewness and gamma4 the kurtosis (not excess kurtosis - 3 for a normal distribution). Samples and frequency: T is the number of observations, P the number of periods per year (12 throughout the worked examples, 252 for the daily volatility estimators), n a window length in periods, and q an aggregation horizon in periods. Rates and ratios: rf is the risk-free rate per period, MAR a minimum acceptable return, SR the Sharpe ratio, and IR the information ratio. Portfolios: w is a vector of weights, Sigma an N by N covariance matrix, 1 a vector of ones, m the vector of expected excess returns, N the number of assets or of independent trials depending on context and stated at each use, and beta a regression coefficient against a benchmark. Correlations and autocorrelations are both written rho, subscripted by asset pair or by lag as the context requires. Distributions: Z() is the standard normal cumulative distribution function and Z^-1() its inverse. Lambda appears as a risk-aversion coefficient, an EWMA decay factor and Kyle's price-impact coefficient, and which one is meant is stated at every use. Every performance, risk and drawdown statistic on this site is computed from one return series, published in full in the first table of the performance section: 24 monthly percentage returns for a strategy, a matching benchmark series, and a constant risk-free rate of 0.20 percent per month. The volatility estimators are all computed from one set of ten daily OHLC bars, also published in full. The portfolio construction rules are all applied to one three-asset covariance matrix, also published in full. A reader can therefore reproduce every figure on the site from three tables, and any figure labelled Worked that cannot be reproduced is an error worth reporting. Where a worked example needs inputs outside those three datasets - an order size, a GARCH parameter set, a trial count - the inputs are stated explicitly in the entry. Where a statistic has more than one estimator in general use, every variant is given with its own worked value rather than one being chosen silently. That is the main editorial decision on this site: the disagreement between two conventions is usually larger than the difference the statistic is being used to measure, and hiding it is the failure mode this reference exists to avoid.

Sections

• Performance statistics Sharpe, Sortino, Calmar, Sterling, Omega, information ratio, Treynor, Jensen's alpha, M-squared and capture, each with its exact estimator, annualisation rule and standard error. - 16 entries, 4 tables
• Drawdown and path statistics Maximum drawdown, Ulcer index, duration and recovery, time under water, and the expected maximum drawdown of a random walk that tells skill from path luck. - 8 entries, 3 tables
• Covariance and volatility estimation Why the sample covariance matrix fails when N approaches T, Ledoit-Wolf shrinkage, EWMA and GARCH recursions, and five realised-volatility estimators on the same ten bars. - 14 entries, 4 tables
• Portfolio construction Mean-variance, tangency and minimum-variance in closed form, risk parity and the Euler risk-contribution identity, hierarchical risk parity, Black-Litterman, Kelly, and the turnover penalty. - 14 entries, 3 tables
• Backtest validity Multiple-testing corrections, the deflated Sharpe ratio, probability of backtest overfitting, minimum backtest length, and purged cross-validation for overlapping labels. - 14 entries, 6 tables
• Execution and microstructure arithmetic Implementation shortfall decomposition, effective against quoted spread, the square-root impact law, Almgren-Chriss trajectories, VWAP tracking, and Kyle's lambda. - 10 entries, 5 tables

For machine readers

Every section has a parallel JSON endpoint at /{section}.json containing the same facts without markup. A manifest of the full corpus is at /llms.txt. Structured data is emitted as schema.org DefinedTermSet on every page.

Related references

This site is one of 9 topical references built from the same open generator, indexed at wallstreet.wiki. Each one owns a single subject. Where two subjects touch, the arithmetic lives on one site and the other links to it rather than restating it. The whole network is machine-readable at /network.json.