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.
5,922 documents
The document asks how to generate many asset return histories that match summary statistics from capital market assumptions, including expected returns, quartiles, volatilities, and incomplete correlation information. One response suggests initially setting…
This note distinguishes a local trading hedge from protection against large portfolio losses. For a position in one asset hedged with another, a correlation-based hedge weight can help manage small, day-to-day changes in portfolio value. A tail-focused hedge…
The document describes a user’s attempt to create a risk-return scatter plot from quarterly portfolio returns that include missing values. Replacing missing entries with zero does not resolve the problem: the assignment expression passed to the plotting…
The document considers how to balance minimum-variance portfolio construction with maximum diversification. It presents several responses: the minimum-variance and maximum-diversification portfolios are each unique and generally differ; treating both…
The document explains why factor returns should be evaluated against a benchmark suited to the portfolio’s construction. For a passive long-only asset allocation, the return above the risk-free rate measures compensation over cash. For a tradable factor, the…
The document discusses how to normalize stock data when comparing series, such as through correlation analysis. Its responses recommend working with returns rather than raw prices because price levels are generally nonstationary, and favor subtracting a…
The document shows how to replicate a payoff that is zero below a lower strike, rises linearly between two strikes, and is capped above the higher strike. The call construction is a bull call spread: buy a call at the lower strike and sell a call at the…
The document examines how to estimate a stock correlation matrix when securities have different history lengths and those histories may cover different market regimes. It outlines several approaches: truncate all series to a common period, use…
The document explains how to calculate covariance between two portfolios from their asset weights and a covariance matrix. The key is the order and orientation of the vectors: use the first portfolio's weights as a row vector, multiply by the asset…
The document asks whether portfolios built from simple rules should be called efficient. In Markowitz portfolio theory, efficiency has a specific meaning: for a given expected return, a portfolio has the lowest possible risk, placing it on the efficient…
The document examines why a two-stock tangency portfolio calculation produces negative variance while deriving a capital market line. The proposed procedure computes expected returns and variances, forms a covariance matrix, applies its inverse to excess…
The document clarifies that VWAP serves both as a benchmark and as an execution tactic. As a benchmark, it is the day’s volume-weighted average traded price, with certain special trades excluded. As a tactic, a broker’s algorithm aims to match its share of…
The document clarifies that mean-variance portfolio optimization does not require every asset’s return history to have the same length. It requires a covariance matrix, which may be estimated from data, proxies, or judgment. The practical problem is how to…
The document concerns maximizing a portfolio's Sharpe ratio when expected excess payoffs and the covariance matrix of asset payoffs are given. It writes the objective as expected excess payoff divided by portfolio volatility, then differentiates it with…
The document derives the exponential correction needed when expectations of products and powers of jointly log-normal variables are rewritten using their individual means. The motivating expression involves a numerator with a variable multiplied by a powered…
The document outlines a workflow for evaluating a portfolio under non-parallel interest rate shocks. Start with specified scenarios, apply the tenor-specific shifts to the relevant curves, reprice affected instruments, and measure the resulting price…
The note considers cross-sectional estimation of factor returns when asset-loading columns are linearly dependent. Ordinary least squares then has no unique solution because the loading matrix’s cross-product is singular. A market factor combined with…
The document examines why adding risky assets can move the mean–variance frontier toward lower volatility without making it approach zero in every case. For equal-variance, uncorrelated assets, it considers an equally weighted portfolio and shows that…
The document asks how to estimate a company’s pre-tax cost of debt when its borrowings include bonds with different coupon rates, maturities, and repayment schedules. The proposed method is to calculate the yield on each bond for the relevant fiscal year,…
The document discusses converting a quoted three-month Treasury bill rate into a weekly risk-free return and subtracting it from an asset’s weekly log return. It endorses scaling the log of one plus the quoted annual rate by the weekly fraction of a 360-day…
The document explains how to attribute a portfolio’s volatility to a subset of its assets, such as an equity sector, while accounting for the portfolio covariance structure. It defines an asset’s marginal risk contribution as the change in portfolio…
The document considers a three-day, 99% value-at-risk estimate for a portfolio split equally between two stocks, given an annualized covariance matrix and joint Student t returns with five degrees of freedom. It asks whether portfolio returns can be combined…
The document raises a mathematical question about expressing the self-financing condition for a continuously traded portfolio when gains are defined through Lebesgue–Stieltjes integration. It contrasts this setting with discrete trading, where portfolio…
In the classical mean-variance setup, expected returns and covariances are treated as known inputs, so optimization produces deterministic portfolio weights. The weights become random when the inputs are estimated from return data: changing samples can…