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 explains why a minimum-risk portfolio optimization with fully equal active weights can return the benchmark itself. It defines each active weight as the difference between a portfolio weight and its benchmark weight. If both the portfolio and…
The document surveys alternatives to Kelly sizing, focusing on how statistical arbitrage portfolios balance positions. Sector neutrality groups assets by industry, while risk neutrality uses a model of shared factor exposures to help an optimizer construct a…
The document frames a one-month portfolio problem involving cash, a stock, and a six-month European put. Returns are evaluated under the physical measure, but the option’s future market value depends on risk-neutral pricing. The author explains why valuing…
The document compares minimizing portfolio variance for a specified expected return with maximizing expected return at a specified variance, while also requiring weights to sum to one. It derives a candidate solution for the unconstrained version of the…
The document explains why a Bloomberg PortfolioDataRequest may fail when used to retrieve an ETF’s holdings. It distinguishes a portfolio identifier shown in PORT from the interface needed to request constituent data, and says the PORT look-through view…
The discussion considers how to estimate the market return input to CAPM when an index has flat or declining historical performance and its average return falls below the risk-free rate. One response says a negative market risk premium is mathematically…
The document addresses whether a positive-weight, minimum-variance portfolio optimization maps each expected-return vector to a distinct set of weights. Its answer is no: distinct return inputs can lead to the same portfolio, so the mapping from expected…
The document explains why the first principal component of a stock return covariance or correlation matrix is sometimes used as a proxy for a market factor. PCA finds the direction that accounts for the greatest cross-sectional variation. When the first…
The document presents a proposed mean-variance portfolio optimization using residual covariance from a diagonal model. Its constraints set a target expected return, require the portfolio weights to sum to one, impose a beta-related condition, and specify a…
The document considers how to express portfolio performance as a percentage when daily trading PnL and exposure are available but beginning and ending account asset values are not. It highlights that exposure may change because of accumulated PnL, yet cash…
The document asks how portfolio volatility reports might better match investors’ perception of risk. It starts from the sample standard deviation of monthly returns and notes that the estimate depends on the length of the lookback window. The questioner…
The document raises a replication question about Ledoit and Wolf’s covariance matrix shrinkage method. The author is trying to reproduce a plot relating Percentage Relative Improvement in Average Loss (PRIAL) to the ratio of the number of variables to the…
The document presents a market-neutral portfolio optimization objective that minimizes the absolute sample correlation between portfolio log returns and an index’s log returns. Long and short security weights determine portfolio value at each time, from…
The document explains how to determine the weights of two stocks when the portfolio must achieve a specified expected return. It uses scenario probabilities and stock returns to calculate each asset’s expected return, then combines the target-return equation…
The document explains two features of a rewritten global minimum variance portfolio objective: the negative sign and the factor of one-half. A variance-minimization problem can be written as a maximization by negating the objective, which accounts for the…
This document explains how to allocate a market-cap-weighted crypto index when no constituent may exceed a chosen maximum weight. It presents a sequential calculation: start with each asset’s share of total market value, scale that share by the weight and…
The document derives the familiar annualization rule for covariance of asset log returns: multiply the per-period covariance by the number of periods in a year. It uses the covariance-of-sums identity. When returns within each period may co-move but returns…
The document considers how to store and represent constraints in an asset-allocation program. It raises options such as classifying constraints into categories, defining a small domain-specific language and parser, or using a structured representation such…
The document asks how to attribute the total loss from a sequence of monthly returns to selected months. It points out that returns compound multiplicatively, so simply adding the monthly percentages and assigning a fraction of that sum to the ending loss…
The document discusses how to design a cross-asset pricing library that supports multiple models and numerical methods while keeping products and payoffs immutable for serialization. Its central design principle is to keep a payoff focused on contract terms…
The document asks how to approximate a portfolio’s loss distribution with a single-factor Vasicek model when individual loans have different default probabilities and correlations to the risk factor. The stated goal is to match the aggregate expected loss…
The document connects portfolio theory, CAPM, factor models, and the Sharpe ratio to the problem of analyzing short-term loan repayment data. It explains that loan portfolios are often assessed through loss distributions, since losses are a central driver of…
The document addresses a question about why portfolio weights from a mean variance optimization may not sum to one when short selling is allowed. It presents the Lagrange multiplier setup for minimizing portfolio variance subject to a budget constraint and a…
The document describes a study design for sorting S&P 600 stocks into three portfolios according to historical return volatility. The proposed process estimates each stock’s volatility over a formation year, assigns stocks to terciles at the year end, and…