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 discussion explains how to apply CAPM when a portfolio contains technology stocks traded on different US exchanges. Exchange membership alone does not determine the appropriate market benchmark: the index should reflect the systematic risk relevant to…
The note explains how to calculate portfolio volatility when asset weights, return standard deviations, and a correlation matrix are available. It first converts correlations into covariances by placing the asset standard deviations on a diagonal matrix and…
The document considers whether a small grid-computing setup is worthwhile for recurring research computations. It describes task-scheduling needs such as priorities, software dependencies, resource requirements, job dependencies, runtime limits, and…
The document explains a forecast transformation from portfolio research: center a vector of raw forecasts by subtracting its mean, then multiply by the inverse transpose of a matrix factorizing the forecasts' covariance. If the covariance matrix is written…
The document contrasts the conventional arithmetic-return Sharpe ratio with a geometric version for evaluating mutual fund performance. The geometric approach is described as using compounded excess returns and their dispersion; it is also related to the…
The document discusses how portfolio skewness and kurtosis relate to the higher-order co-moment tensors of asset returns. Its main practical point is that the tensor formulas can be understood as contracting each tensor with the portfolio weights until a…
The document asks how to encourage a portfolio optimizer to use only as much turnover as its return and risk objectives justify. It explains that an upper bound on absolute weight changes limits trading but does not discourage the optimizer from using the…
The document considers a resampled efficient frontier procedure that simulates multivariate normal monthly returns. An investment horizon of six years is described, while the lecturer’s program generates twelve years of data and uses a six-year slice to…
The document addresses how to calculate value-weighted or equal-weighted portfolio returns when a security’s return is missing for a period. It recommends using beginning-of-period market-capitalization weights and the period’s observed returns, filtering…
The document proves that a two-by-two determinant arising in the Markowitz portfolio allocation derivation is nonnegative when the covariance matrix is symmetric and positive definite. It rewrites the determinant using the inverse covariance matrix, then…
The document raises a benchmark currency problem for a European investor whose portfolio is measured in euros but holds mostly unhedged US securities. It asks whether converting a US equity benchmark using spot EUR/USD rates produces a fair comparison, and…
The question outlines a procedure for constructing the size and value portfolios used to form the Fama–French three-factor model from monthly stock data. At each period, stocks are split into small and big groups using market capitalization, then each size…
The document asks whether Markowitz portfolio weights can be updated efficiently when each new price observation changes the covariance estimate through a rank-one update. It also asks whether using the previous time step’s weights as the optimizer’s initial…
The document explains that a minimum-variance portfolio does not necessarily assign a nonzero weight to every risky asset. A weight can be zero, and unconstrained optimization can also produce negative weights when short selling is allowed. Its example uses…
The document considers what can be inferred about a risk-free return when one risky investment is said to be efficient under CAPM assumptions. The answer offers a geometric argument: compare the candidate investment and the other listed portfolios in…
The document asks how a squared information coefficient can equal a sum of squared correlations when deriving the Fundamental Law of Active Management. The question distinguishes an aggregate measure from correlations associated with individual signals and…
The document asks how to position for a change in the Treasury yield curve while a five-year corporate bond’s credit spread remains constant. It contrasts a duration-neutral trade using Treasuries at different maturities with a proposed trade that shorts the…
This document is aimed at a project supervisor seeking a broad map of machine learning methods relevant to an algorithmic momentum strategy. It names families such as neural networks, reinforcement learning, regression, clustering, Markov models,…
The discussion points to sources of analytical Value at Risk and Conditional Value at Risk formulas across continuous distributions. It explains that VaR is obtained from a distribution's cumulative distribution function by taking the relevant quantile, and…
The discussion explains why annualized return figures cannot be carried across different holding periods without specifying the compounding convention. It contrasts an investment growing by an annual rate compounded once with alternatives compounded monthly…
The document distinguishes stochastic programming from stochastic dynamic programming and recommends different references for each. It identifies Birge and Louveaux’s second edition as a useful introduction to stochastic programming, highlighting its…
The document considers whether a portfolio’s volatility can be estimated directly with GARCH instead of first estimating the covariance matrix of its component assets. The responses clarify that the model should be fitted to portfolio returns rather than…
The document questions whether modern portfolio theory and mean–variance optimization adequately address fat-tailed returns and the difficulty of estimating covariances. It asks whether ideas associated with Mandelbrot and Taleb, including fractal…
The document asks whether a one-million spread option should be treated as one million of notional or as separate pay and receive legs totaling two million for initial-margin purposes. One response frames the spread as changing the payoff on a single…