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 addresses how to obtain value at risk and expected shortfall measures for exchange-traded funds when the figures are not readily available from common financial data websites. It recommends calculating the measures from the ETF’s return data,…
The question asks whether the same portfolio or index can have different Sharpe ratios when analyzed with CAPM or Arbitrage Pricing Theory. The answers distinguish ex-post Sharpe ratios, calculated from realized excess returns and their variability, from…
The note asks how prices connect across periods when returns are defined from consecutive prices in a single-period CAPM setup. It distinguishes the price used to calculate a period’s return from the equilibrium price in a subsequent period, and asks how an…
The note explains how to define portfolio weights when a long position is fully funded by an equal-sized short position. For a $200 long in Apple and a $200 short in Google, it uses signed weights of +1 and −1, calculated relative to the portfolio’s net…
The document examines why a large simulation of randomly generated long-short equity weights may fail to find the theoretical global minimum-variance portfolio. The analytical portfolio is calculated from the inverse covariance matrix and normalized to sum…
The document addresses whether SMB and HML factor returns should have the risk-free rate subtracted when they are used as risk premia in a Fama–French expected-return model. Its explanation focuses on how the factors are constructed: HML is a long position…
The document explains how to express the Sharpe ratio of a portfolio containing two risky stocks as a function of one stock’s weight. With the other stock’s weight set to the remainder, expected return is a weighted average, while portfolio variance depends…
The document concerns calculating portfolio and backtest performance statistics through callable Python functions. It names Quantopian’s Empyrical package as a library for measures such as cumulative and annual returns, Sharpe ratio, and Omega ratio. The…
The document asks how portfolio choice changes when the objective is to win a winner-take-all competition rather than to balance expected return against risk. Its example contrasts maximizing expected return and variance with conventional mean-variance…
The discussion considers how to calculate simple and logarithmic returns for a portfolio, including what changes when holdings are added, removed, replaced, or rebalanced during a measurement period. It emphasizes comparing like with like across the start…
The document explains how to allocate portfolio variance across assets. It first questions a proposed allocation that adds covariance terms directly to each asset’s weighted variance, then presents a derivative-based approach associated with Euler…
The document examines a minimum-variance portfolio problem using a bank account, a stock, and call options on that stock. Monte Carlo paths under geometric Brownian motion supply estimated returns and covariance. Because the options and stock share a driver,…
The document explains why parametric portfolio risk is often calculated from asset returns and their covariance matrix. If portfolio positions are held constant, portfolio PnL is a weighted sum of the asset return vector, so its variance follows from the…
This document raises a conceptual question about how CAPM’s Security Market Line can classify a stock as overpriced or underpriced when CAPM is derived from mean-variance portfolio theory and is often discussed alongside the Efficient Market Hypothesis. The…
The document presents an exam-style portfolio risk problem. It supplies a current portfolio value, a sequence of ten daily log returns, an initial variance forecast, and an exponential moving volatility parameter. The requested outputs are one-day historical…
The document examines how to choose notionals for a three-bond, proceeds-weighted butterfly using bonds identified as the wings and belly. It lays out a duration-neutrality condition and a proceeds or notional neutrality condition, then tries to solve both…
The document outlines a monthly portfolio strategy that ranks stocks by their trailing three-year return volatility, divides them into five groups, and equally weights the stocks in each group. The answer demonstrates one implementation approach in R using a…
The document describes how to attribute a portfolio’s variance to principal components derived from the covariance matrix of asset returns. PCA expresses that covariance matrix using eigenvectors and eigenvalues. Projecting portfolio weights onto the…
The document derives the correlation between one asset and a portfolio formed from two other assets. It defines the portfolio as a weighted combination of the two holdings, then applies covariance linearity to express the portfolio’s covariance with the…
The document examines how commonly internal rate of return (IRR) is used in capital budgeting and why practitioners may continue to use it despite known limitations. It cites an earlier report on CFO practice, then contrasts IRR’s simplicity with net present…
The document reviews the internal rate of return (IRR) and net present value (NPV) as capital budgeting measures, drawing on reported survey results and practitioner accounts. IRR offers a compact rate that managers may find easy to compare with a financing…
This note describes a factor-based way to stress portfolio covariance. It starts with asset returns, asset factor exposures, and factor returns, and estimates an ex-post covariance matrix from observed asset returns. The analyst then chooses the direction…
The document explains how an ETF can be replicated using either its underlying holdings or derivative exposures. Physical replication holds all or a selected subset of the constituent instruments; an optimized subset may aim to reduce tracking error or…
The document surveys ways to estimate multivariate conditional volatility when a Python workflow is desired. It notes that common Python GARCH support may focus on univariate models, and suggests that a basic multivariate model could require custom…