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 considers how to allocate capital among several assets when one trading strategy can generate signals for multiple assets on the same day. It proposes using historical daily returns to estimate each asset’s variance and cross-asset covariances,…
The document derives the covariance between two portfolios on the mean-variance efficient frontier. It expresses each frontier portfolio as a weighted combination of the global minimum variance portfolio and a second reference portfolio, then relates the…
The document examines the efficient frontier when a risk-free asset is available. It formulates minimum-variance portfolio selection for a target excess return and derives risky-asset weights using the inverse covariance matrix and expected excess returns.…
The document presents a continuous-time portfolio problem in which an investor divides wealth between a risky stock and cash. Wealth follows a diffusion with stock drift and volatility, and the objective is to maximize expected log wealth at a future…
The document asks how to combine several securities’ NAV time series into one series for comparing simulation results. It presents an example that takes the arithmetic mean of three NAV values on each date, with each series starting near the same baseline,…
The document reviews a strategy-selection pipeline that fits models on training data, tunes hyperparameters using validation-period simulated profit and loss, selects top-performing instruments or strategies, and evaluates the resulting portfolio on a…
The document asks how to express the terminal value of a stock portfolio over five years when annual price returns and dividends follow separate lognormal models. It proposes adding a price return and a dividend amount for one period, then asks whether that…
The document explains how to adjust a portfolio so its exposure to selected principal components is neutral. It frames portfolio positions and PCA eigenvectors as vectors, with component exposures calculated by projecting positions onto the eigenvectors. For…
The document considers the terminal value of periodic deposits when each contribution grows according to a lognormal return model. It asks whether the desired quantile of the total accumulated amount can be found by calculating each deposit’s quantile…
The document describes a portfolio construction approach that uses ordinal rankings instead of explicit expected return estimates. In a portfolio of sorts, the centroid of each ranked group supplies the inputs, while the optimization retains a…
The document compares two portfolio optimization formulations used to describe the efficient frontier. In the first, portfolio variance is minimized subject to a target expected return and a full-investment constraint. In the second, expected return is…
The document compares two approaches to estimating factor returns: cross-sectional regression using asset returns and factor exposures, and sorting assets by a characteristic to form a long-short portfolio. The answer says these approaches do not necessarily…
The document considers minimizing a ratio of two quadratic forms in portfolio weights, subject to a weights-sum equality constraint. It gives the Lagrangian derivatives with respect to the weights and multiplier, then explains why the denominator’s…
The document explains the role of risk tolerance in a portfolio optimization problem that maximizes expected return minus a variance penalty, subject to linear equality constraints. Its closed-form weight expression includes a term scaled by risk tolerance,…
The document demonstrates how to retrieve an iShares ETF holdings file directly from a data endpoint and load it into a dataframe, either by saving the file first or by reading it from the endpoint. The example skips introductory rows before displaying the…
The discussion compares regression-based alpha with the simpler return-minus-benchmark measure used in some fund reporting. In a market model, regression alpha estimates performance after accounting for benchmark exposure, while the simple difference also…
The document presents a proposed ex-post Sharpe calculation using daily portfolio returns and S&P benchmark returns. It subtracts the benchmark return from each portfolio return, computes the arithmetic mean and sample standard deviation of those daily…
The document outlines practical measures for assessing interest rate exposure beyond duration and convexity. It frames risk in terms of how prescribed rate shocks affect fair value, economic value of equity, or net interest income, and describes reverse…
The document surveys practical ways to measure interest rate risk beyond duration and convexity, emphasizing that the right measure depends on the portfolio and use case. It describes scenario impacts on fair value, economic value of equity, or net interest…
The document presents a portfolio attribution problem across four periods. It gives sector returns and weights for a portfolio and benchmark, then reports their compounded returns and active return. The author calculates Carino linking coefficients and…
The document poses a two-risky-asset equilibrium problem in which some investors are unaware that the second asset exists. It gives the benchmark equilibrium price vector for the case where all investors know both assets, then asks how equilibrium prices…
The document describes how to optimize portfolio allocations against objectives such as drawdown or the Sortino ratio. It recommends expressing the chosen risk or reward measure as a scalar function of portfolio weights, then using an optimizer suited to…
The document asks whether a portfolio’s vector of total risk contributions uniquely determines its asset weights. It defines each contribution as the asset weight multiplied by the derivative of portfolio volatility with respect to that weight, and frames…
The document distinguishes exposure measured as a currency amount from exposure expressed relative to assets under management. In common long–short fund reporting, gross or net market exposure generally counts the risky positions, such as stock longs and…