Knowledge library

This tutorial introduces maximum likelihood estimation through normal and exponential distributions. For a normal sample, it derives estimates for the mean and standard deviation and compares them with library estimates. For an exponential sample, it…

This tutorial explains how a model can fit historical observations closely by learning noise rather than the underlying process. It identifies small samples and excessive model complexity as common causes, and uses polynomial curve fitting to contrast an…

This tutorial explains how conditional volatility in an ARCH or GARCH process can produce return series with heavier tails than a normal distribution. It simulates a GARCH(1,1) series, compares its tail behavior with Gaussian samples, and outlines a…

This introductory tutorial shows how to use Jupyter notebooks for quantitative analysis. It explains the distinction between code and text cells, cell execution and output, importing common analysis and plotting libraries, and using tab completion and inline…

The lecture describes how transaction costs affect strategy performance and how institutional trading teams assess execution. It distinguishes explicit commissions and fees from indirect costs such as spread and market impact. Slippage is linked to…

The document explains multiple linear regression as a way to model an outcome using several predictors. Ordinary least squares chooses coefficients by minimizing squared prediction errors; each coefficient represents the predictor’s association with the…

This tutorial introduces NumPy arrays and linear algebra operations used in quantitative finance. It explains array dimensions, shapes, indexing, slicing, and element-wise functions, then applies them to simulated asset returns. Randomly generated assets…

This lesson uses a factor model to separate portfolio risk into common factor risk and asset-specific risk. It constructs market, size, and value factor returns, estimates each stock’s exposure through regression, and explains how those exposures and factor…

This lesson introduces pairs trading as a way to trade a hypothesized economic relationship between two securities. It distinguishes cointegration from correlation, illustrates both concepts with simulated series, and describes testing a candidate pair with…

This introductory lesson explains core Python concepts that help readers follow quantitative finance code. It covers comments, variables and common data types, basic arithmetic, lists and tuples, indexing and slicing, and the difference between mutable lists…

The lecture explains how regression residuals—the differences between observed and predicted values—can reveal whether a linear model's assumptions are plausible. A residual plot should look like an unstructured cloud around zero. Curvature or other patterns…

The lecture presents a workflow for assessing whether an equity factor ranks stocks by future relative performance. Its momentum example measures price change over a long lookback while excluding the most recent period, then uses a filtered stock universe…

The lecture introduces principal component analysis as a way to summarize a large matrix with a smaller set of orthogonal components that capture much of its variation. A synthetic image illustrates covariance decomposition, ranking components by eigenvalue,…

This lecture presents parameter estimates as uncertain quantities that can change with new observations or with the sample window. It suggests measuring that instability by estimating a statistic on multiple subsets of data and examining how the resulting…

This lecture explains how violations of regression assumptions affect parameter estimates and statistical inference, and why residual analysis is useful even for complex models. It discusses non-normal residuals and the Jarque-Bera test, then contrasts…

This lecture surveys ways a regression can be misspecified and how those choices affect estimates and predictions. Omitting a variable correlated with included predictors can bias coefficients, while adding weak or irrelevant predictors can make an in-sample…

This lecture explains why mean and variance alone do not describe a return distribution. Skewness captures asymmetry and the direction of a longer tail; kurtosis describes tail heaviness and peakedness relative to a normal distribution. It gives sample…

This lecture explains how a sample mean can estimate a population mean and how a confidence interval expresses its uncertainty. It derives the standard error from sample variability and sample size, then describes constructing intervals with normal or…

This lecture presents linear regression as a way to estimate how an outcome variable changes with one or more explanatory variables. Its market example regresses one stock's daily returns on another's and interprets the slope as estimated sensitivity.…

This tutorial introduces pandas Series and DataFrames as structures for organizing, filtering, transforming, and analyzing financial data. Series hold labeled one-dimensional data, while DataFrames organize multiple columns against a shared index. The…

This lecture explains how random variables represent uncertain outcomes and how probability distributions describe their behavior. It distinguishes discrete outcomes, summarized by a probability mass function, from continuous values, described by a density…

This lecture examines why regression coefficients may change substantially across samples, limiting a model’s reliability on new data. It uses simple linear regression examples to show how a small sample and influential observations can produce misleading…

This lecture introduces factor models as regressions that explain an asset’s returns using other return series. It estimates an asset’s beta to a benchmark from historical returns, then uses a short benchmark position sized to offset the estimated market…

This lecture explains leverage as borrowing to increase the capital deployed in a trading strategy. It defines the leverage ratio and uses single-period examples to show how borrowed funds can amplify gains while interest reduces the benefit. Borrowing costs…