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 note considers a minimum-variance portfolio when weights need not sum to one and total variance must stay below a limit. It starts from the fully invested minimum-variance solution and asks whether scaling that portfolio can satisfy the volatility…
The document explains a two-asset mean-variance allocation in which the risky asset receives a weight greater than one and the risk-free asset receives a negative weight. For an investor with a fixed amount of capital, the interpretation is to invest the…
The document asks whether portfolio optimization can be understood as a form of feature selection. It compares assets’ return series, represented as columns in a data matrix, with features in statistical learning. Under that analogy, mean-variance…
The document explains how to turn a correlation matrix into a covariance matrix when asset standard deviations are available. For each asset pair, multiply their correlation by the standard deviation of each asset; the resulting entries form a covariance…
The document explains why quadratic portfolio objectives often write variance with a one-half multiplier. This factor does not change the portfolio that minimizes variance, since multiplying an objective by a positive constant preserves its minimizer. Its…
The document clarifies the distinction between independence across Monte Carlo trials and dependence among variables within a trial. In the example, each of 1,000 simulation draws contains 100 credit-related components. The draws can be independent of one…
The document outlines a tactical allocation process for a fully invested portfolio spanning domestic and international equities, domestic fixed income, and foreign currencies. Managers express relative views on a discrete scale, including an equity…
The document asks whether the internal rate of return (IRR) of combined investments can be recovered from the component IRRs and initial investments. It explains that an IRR is determined by the amounts and timing of all cash flows, so component IRRs alone…
The document responds to a student seeking practical guidance for building portfolios with real assets and data. It recommends an applied portfolio-optimization course using R as a starting point, covering time-series work and several portfolio methods:…
The document works through a portfolio choice problem for a CARA investor holding multiple risky assets with jointly normal returns. It frames expected utility in terms of a certainty equivalent, then uses a Lagrangian to impose the constraint that the asset…
The document discusses how to make a sample covariance matrix positive definite when small negative eigenvalues appear, especially before inverting it for portfolio calculations. It compares replacing negative eigenvalues with zero or a small positive value,…
The document examines how an R implementation computes the Ledoit–Wolf shrinkage estimator’s variance term from a time-by-asset return matrix. It focuses on why the product of the transpose of elementwise-squared demeaned returns with the squared matrix…
The document discusses whether to center asset returns before using PCA or singular value decomposition to estimate statistical risk factors. It says the choice depends on the goal: decomposing raw data may help identify outliers, while centering each…
The document compares ways to value the tax savings created by corporate interest deductions and asks whether they should be discounted at the cost of debt or at WACC. One explanation treats the shield as a consequence of a borrowing decision: when borrowing…
The document discusses selecting historical index data for testing portfolio optimization methods and benchmarking a 60/40 equity and fixed-income allocation. It emphasizes that the appropriate series depends on the portfolio the simulation is meant to…
The document considers how to include single-name emerging-market corporate bonds in a multi-asset portfolio when their histories are short, missing, or unreliable and trading is illiquid. Because these holdings make up a material share of the portfolio,…
The document asks whether smoothing each return series’ empirical cumulative distribution function (CDF), then mapping the CDF values through the inverse normal distribution, gives a better correlation estimate than calculating correlation from standardized…
The discussion explains why the Sharpe ratio is not a complete portfolio evaluation tool and surveys alternatives tied to different definitions of risk. The Sharpe ratio compares excess return with total return variability, so it is most informative when…
The document derives how changing one asset’s standalone volatility affects the variance of a portfolio when asset correlations and portfolio weights are held fixed. It writes the covariance matrix as the product of a diagonal volatility matrix, a…
The document raises a reconciliation problem when applying the Brinson performance attribution model to year-to-date portfolio returns. The author reports that weighting fixed income, equity, and cash returns by their portfolio weights does not reproduce the…
The document discusses covariance estimation through the lens of shrinkage and Bayesian methods. Its respondent argues that shrinkage estimators can be understood as Bayesian point estimates with different implicit prior distributions, and recommends…
The document explains the discrete-time identity for a self-financing investment strategy. It starts with portfolio value as holdings multiplied by asset prices, then compares value at consecutive times. The change separates into a price-movement component…
The document considers which global equity index to use as the market benchmark when estimating CAPM betas from monthly portfolio and benchmark returns. The portfolio is internationally diversified but has limited emerging-market exposure, raising the…
The note distinguishes the Capital Asset Pricing Model from the statistical single-index model. The single-index approach represents each asset’s return using a chosen index, a loading, and an idiosyncratic term. With assumptions that residuals are…