Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
23 documents
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…
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…
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…
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 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 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 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…
This lecture explains how the Capital Asset Pricing Model relates expected asset returns to a risk-free rate and exposure to broad market risk. It distinguishes diversifiable, firm-specific risk from systematic risk, and uses regression beta to estimate an…
This lecture introduces portfolio Value at Risk (VaR) as a loss threshold associated with a chosen coverage level, then demonstrates historical VaR by calculating a low percentile of weighted portfolio returns over a lookback window. It contrasts this…
The document surveys measures of how widely observations vary around a central value. It defines the range, mean absolute deviation, variance, and standard deviation, noting that standard deviation is expressed in the same units as the observations and that…
The document introduces autoregressive models, which predict a time series from its own lagged values, and explains that meaningful estimation requires covariance stationarity: a stable finite mean, variance, and lagged covariance over time. Financial series…
The document explains how covariance describes the way asset returns vary together and how a covariance matrix collects these relationships alongside each asset’s variance. Portfolio construction uses this matrix to estimate combined risk, assess…
The document presents a workflow for reviewing a trading portfolio with performance statistics and diagnostic plots. It describes common measures such as Sharpe ratio, market beta, and maximum drawdown, along with return distributions, cumulative and…
The document explains how market beta and sector exposure can make a portfolio’s individual forecasts move together, reducing the number of independent bets and, in turn, its risk-adjusted potential. It frames this through the Fundamental Law of Active…
This lecture uses factor models to explain portfolio returns and quantify exposure to systematic sources of risk. It describes regressing active returns, measured relative to a benchmark, on factor returns, then using estimated sensitivities and factor…
This lecture explains how universe selection defines the securities available to a trading algorithm and can shape both strategy behavior and risk. It presents a daily screen for common stocks ranked by average dollar volume as a basic liquidity filter,…
The document explains how spreading exposure across independent or weakly correlated bets can reduce portfolio volatility, while adding highly correlated assets may leave risk largely unchanged. It illustrates the principle first with simulated bets that…
The document defines correlation as covariance scaled by the standard deviations of two series, yielding a measure between -1 and 1 that is easier to compare across data. It explains covariance and correlation matrices, with examples showing positive,…