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 answer treats a cointegration spread as a synthetic position: going long the spread means buying one leg and shorting a hedge-ratio-weighted amount of the other, with the reverse positions for a short spread. It then discusses practical sizing across…
The document discusses resampling as an alternative to traditional mean-variance optimization (MVO). Its main practical benefit is that the resulting portfolio allocations may vary less over time, which can reduce how often a portfolio needs to be…
The document considers how to form a self-financing portfolio of bonds and stocks to replicate a basket of options, with each option written on a different underlying stock. It suggests constructing a replicating portfolio for each option separately and then…
This document shows that minimizing portfolio standard deviation under a fully invested constraint produces the same weights as minimizing variance. Since standard deviation is the square root of variance, it preserves the ordering of feasible portfolios, so…
The document asks how to express a CAPM statement about a risky asset whose return has zero covariance with the market return. The cited passage characterizes such an asset as contributing nothing to the variance of the market portfolio, while describing a…
The document explains how to calculate portfolio returns when security weights may be negative or may sum to less than the full portfolio value. It assumes the positions are not rebalanced and starts with a total portfolio value of one. Returns are converted…
Covariance shrinkage can improve mean-variance optimization even when the sample contains more observations than assets. The discussion frames shrinkage as a way to limit estimation risk: combining the sample covariance with a more stable estimate can make…
The document explains that broad sector and industry labels may be too coarse for some investment or research tasks, and asks about more detailed classifications of stocks. The response describes several established taxonomies that divide companies from…
The document raises a portfolio statistics question about constructing a covariance matrix in two stages. The proposed approach estimates each asset's variance from its own data, estimates pairwise correlations separately, and combines the two sets of…
The discussion explains a central reason SPY and the S&P 500 index ticker can diverge: the index is a price index that excludes dividends, while SPY owns shares of the constituent companies and receives their dividends. SPY holds the resulting cash during…
The post describes a historical S&P 500 simulation that forms annual portfolios from companies ranked by return on equity: a top group, a bottom group, and a portfolio combining both. Holdings that leave the index are sold and their value redistributed among…
The document presents several proposed ways to set relative objective weights for alpha forecasts and transaction costs in a portfolio optimizer. The setting is monthly standardized factor-model forecasts combined with a nonlinear market-impact model…
The document considers funding a liability due in the future with a portfolio of four-year zero-coupon bonds and a perpetual annuity, using duration matching. It writes one duration equation at the initial date and another one year later, when the bond’s…
The document shows how to compute the composition of the efficient risky portfolio, also called the one-fund or tangency portfolio, from asset covariances and expected excess returns. It gives a three-asset example with specified volatilities, a correlation…
The document presents a decision problem in which Monte Carlo simulation has produced cost distributions for two alternatives. Their benefits are assumed equal but are not specified, and the decision maker is described as risk averse. Because the simulated…
The document outlines the main steps for constructing a factor model from firm characteristics and stock returns, using a Fama–French-style approach. It recommends cleaning the data, forming characteristic-sorted portfolios for factors such as SMB, HML, RMW,…
The document asks how practitioners choose the observation window, weighting scheme, and regularization method for estimating covariance among factor returns. It begins with the usual sample covariance estimator based on daily factor returns. The response…
The document explains why estimating a covariance matrix for many stocks can require at least as many observations as assets. It represents each stock’s return history as a column in a data matrix, with observations as rows. When there are fewer observations…
The document describes a portfolio construction problem in which an optimizer can process at most a fixed number of assets at once, while the full investment universe is larger. The proposed workflow is to divide the assets into groups no larger than the…
This explanation distinguishes portfolio returns, cumulative sums, and compounded performance. It first defines each asset’s simple return from adjusted prices, accounting for events such as dividends and stock splits. To calculate a value-weighted portfolio…
The document outlines ways to set long-term capital market assumptions for fixed-income assets, including government bonds and high-yield credit. One approach builds expected returns from a cash-return estimate plus relevant premia, such as government bond…
The document outlines a proposed portfolio framework that combines probabilities for four market states, historical asset data, simulated returns, and an investment committee’s views on distribution moments. It focuses on the difficulty of generating…
The document explains why Ledoit–Wolf covariance estimation blends a sample covariance matrix with the identity matrix. The blend shrinks estimated covariances toward zero and variances toward a common scale, limiting the influence of extreme sample…
The document explains how to derive state prices from asset payoffs by constructing portfolios that replicate Arrow–Debreu securities. For each state, solve a linear system in which the payoff matrix multiplied by portfolio weights equals a payoff of one in…