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 recommends Nelson-Siegel and related Diebold-Li models for parameterizing government yield curves. These models describe changing curve shapes, including rising, inverted, flat, and humped forms. Instead of assuming the curve is monotonic or…
The document asks how to derive the correlation between the global minimum-variance portfolio and another portfolio on the mean-variance efficient frontier, given their covariance. The answer applies the definition of correlation: divide covariance by the…
The document presents a Python workflow for exploring portfolio risk and return from a table of asset returns. It generates random long-only weights that sum to one, estimates annualized portfolio return and volatility from sample means and covariances, and…
The document explains why covariance matrices must be symmetric and positive semidefinite. It uses three assets with unit variances and pairwise covariances of minus one as an example: the matrix has a negative eigenvalue, so it cannot describe a valid joint…
This note asks how to interpret a banking risk-capital recommendation that distinguishes gross standalone risk from net enterprise-wide, diversified risk. The question is whether the distinction refers to diversification benefits when a bank aggregates risks…
This collection presents examples of incorrect AI answers to quantitative finance questions and briefly contrasts them with corrections. Topics include converting yield quotations between compounding frequencies, whether mean-variance portfolio theory…
The document raises a conceptual question about Roll’s critique of the CAPM: if a portfolio is mean-variance efficient, its returns satisfy a CAPM-style relation, and testing that relation for a market proxy is equivalent to testing the proxy’s efficiency.…
The document explains why a mean-variance equilibrium relation can express the market risk premium as proportional to market variance, even though the Capital Market Line is usually drawn against standard deviation. For an investor choosing between the…
The answer explains why differentiating portfolio variance with respect to a single asset weight removes the full summation from view: only terms involving that weight contribute to its derivative. It expands the result using covariance bilinearity, then…
The document raises questions about holding large and mid-cap equities alongside a small-cap tracker, with each fund initially allocated according to market capitalization. It asks whether an investor’s proportional ownership of publicly traded companies…
The document works through a minimum variance portfolio under a linear factor model. It defines portfolio risk from factor covariance and stock-specific residual risk, then imposes a budget constraint requiring weights to sum to one. The discussion corrects…
The document outlines a proposed factor analysis comparing sustainable equity indices with conventional benchmarks across several regions. The author has compared performance using Sharpe ratios and Jensen’s alpha, and wants to explain return differences…
The document asks how to choose portfolio weights for a Post Modern Portfolio Theory efficient frontier, where risk is measured by downside loss rather than variance. It contrasts calculating downside risk for an existing portfolio with the harder task of…
The document compares three standard mean-variance portfolio formulations: maximizing expected return subject to a risk limit, minimizing variance subject to a return target, and minimizing a risk-adjusted objective with a tradeoff parameter. It assumes…
The document asks how to obtain a covariance matrix when modeling asset returns with an AR(1)-GJR-GARCH(1,1) specification. A univariate GARCH model estimates conditional volatility for an individual return series, but that alone does not model the…
The document examines a formula for the weights of a conditionally optimal portfolio, called the unconstrained minimum-variance efficient portfolio, in a setting with multiple risky assets and no riskless asset. The weights depend on the conditional mean…
The document asks how to combine Barra factor exposures for individual assets into exposures for a long-short portfolio, with the eventual aim of attributing portfolio returns to factors. It raises a key weighting choice: divide each position’s dollar value…
The document poses an allocation question: how to split capital between an active fund and a passive ETF when the active fund’s risk relative to a benchmark exceeds the investor’s portfolio active-risk budget. It compares two proposed rules: divide the…
The document asks how a Monte Carlo approximation of conditional value at risk can be expressed as a linear optimization problem. The approximation uses a threshold variable and the positive part of each scenario's loss beyond that threshold. Introducing one…
The document discusses how to include cash currencies in the market-capitalization benchmark used to initialize a Black–Litterman portfolio. One response says weights depend on the investor’s risk-free reference currency: domestic cash may serve as…
The document explains how to limit the number of assets selected by a linear portfolio optimizer. The motivating case has a large monthly universe, limited trading capacity, and an objective that maximizes the sum of each asset’s score multiplied by its…
The document proposes a cash-flow accounting framework for the stock market. It lists investors and institutions as sources of investment capital, and dividends, acquisitions, and buybacks as flows back toward shareholders. It places IPO proceeds, share…
The document explains why portfolio variance depends quadratically on asset weights and why covariances enter the calculation. For one asset, scaling its return by a weight scales its variance by the square of that weight; extending this relationship to…
The document collects research leads on how index investing and ETFs may affect equilibrium prices, volatility, correlations, information production, liquidity, and corporate oversight. The motivating model has two risky assets with jointly Gaussian payoffs…