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 adjust existing weights when combining multiple strategies whose returns are correlated. Its answer begins by tying the adjustment to the portfolio objective: if the goal is return diversification, strategies with highly correlated…
The document addresses whether portfolio optimization constraints in CVXPY should be expressed using list-like constructions or matrix notation. The answer says both approaches are valid and recommends matrices because they can make the optimization problem…
The document investigates why expected shortfall from the PerformanceAnalytics R package can differ when calculated on a portfolio return series versus component returns and weights. The accepted explanation points to inconsistent volatility normalization in…
The document sets up a mean–variance portfolio problem with multiple risky assets and one risk-free asset. It defines the risky-asset mean vector and covariance matrix, assumes the covariance matrix is invertible, and introduces three scalar quantities…
The document shows an attempted Black–Litterman calculation in R using a covariance matrix, a view-link matrix, view uncertainty, and equilibrium excess returns. The author’s intermediate figures appear close to a tutorial, but the updated-return vector is…
The document asks whether the Herfindahl-Hirschman Index can measure concentration in an FX portfolio built from currency pairs that share USD as a leg. It focuses on the complication that Markowitz portfolio weights may be negative, using a short USDJPY…
The document considers an interview prompt asking for a Monte Carlo method to construct an efficient frontier, minimum-variance portfolio, and maximum-Sharpe portfolio under long-only, fully invested constraints. Expected returns, variances, and covariances…
The document gives a rank argument for why a sample covariance matrix cannot be positive definite when the number of observations is smaller than the number of variables. Each centered observation contributes an outer product of a vector with itself, a…
The document asks whether investors can find historical records of forecasts for future returns, broken down by asset class and issued at regular intervals. The desired data would preserve what an institution expected at each date for a coming year, quarter,…
The document explains how to calculate the standard deviation of project returns when outcomes depend on discrete market scenarios with given probabilities. For each project, first compute the probability-weighted expected return, then take the square root…
The document considers choosing a small subset from a ranked stock list while accounting for diversification. It presents several approaches: derive portfolio weights from the inverse covariance matrix under an equal normalized-return assumption; enumerate…
The document examines how to interpret the risk aversion coefficient in a Markowitz mean-variance objective. It introduces absolute and relative Arrow-Pratt measures, which require a specified utility function, and considers whether observed portfolio…
The document sets out a Bellman problem for a representative investor in an endowment economy. The investor chooses current consumption, money to carry into the next period, and portfolio shares to maximize discounted expected lifetime utility. The budget…
The document asks how a portfolio’s Value at Risk and Expected Shortfall limits should relate to its annual profit target, including a proposed calculation that turns a daily return target and assumed Sharpe ratio into a daily VaR figure. The response points…
The document considers forecasting an automotive company’s future cash flows from a short historical record, with proposed uncertain drivers including oil, plastic and steel prices, and consumer disposable income. It asks whether these drivers should be…
The document considers two equity portfolios with the same benchmark and investable universe, and asks how to estimate the correlation of their ex ante tracking errors. It describes forming each portfolio’s active weights by subtracting benchmark weights,…
The document explains the relationship between borrowing, risk-free investment, and a portfolio’s market beta. Scaling exposure to a risky portfolio scales its market sensitivity: borrowing to enlarge the position raises beta, while holding some wealth at…
The document explains a first-order effect in the context of asset pricing and portfolio consumption risk. If consumption is initially c and an asset pays x, adding a small position of size ξ changes consumption to c + ξx. Expanding the variance gives the…
The document clarifies how to calculate returns for portfolios formed by sorting S&P 500 companies on market-to-book ratios. For a value-weighted return within each bucket, each constituent’s monthly return is multiplied by its market capitalization divided…
The document considers whether 2-, 5-, 10-, and 30-year GBP swap tenors are suitable risk buckets. It outlines PCA of daily swap-rate changes and suggests examining how much variation the leading components explain, how chosen tenors relate to component…
The document describes how to formulate mean-variance portfolio selection when the portfolio may hold at most a specified number of assets from a larger universe. It introduces a binary inclusion variable for each asset, links that variable to the asset’s…
The document asks how to calculate variance and value at risk for a portfolio containing several stocks. It compares two approaches: estimate each asset’s risk and combine the results using portfolio weights and a correlation matrix, or first construct the…
The document asks whether dynamic portfolio rebalancing can be optimized without specifying a model for how asset prices evolve. It contrasts this goal with the static Markowitz approach, which estimates asset means and covariances to calculate portfolio…
The document explains the notation in a paper’s test for whether a simulated return sample is arbitrage-free. In the linear system, the symbol 1 denotes a vector of ones, and adding it to a return matrix converts simple returns into gross returns. Solving…