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 asks whether an individual can earn positive returns with a home algorithmic trading setup, focusing on strategies held for several days to a month. The questioner seeks quantitative approaches with an edge at capacities too small to interest…
The document asks why mean-variance optimization remains unevenly adopted despite its long history and commercial use. The responses describe practical obstacles: the method needs expected-return estimates and a covariance matrix, while return forecasts are…
The document explores how to value an annuity or perpetuity when its cash flows depend on a stochastic price process. The question formulates discounted operating cash flows with fixed costs, a liquidation value, and a stopping horizon, then asks whether a…
The document presents a portfolio score from an academic paper on selection in a value-at-risk framework and asks whether it has a recognized name comparable to the Sharpe ratio. The score uses expected portfolio return relative to the risk-free rate, scaled…
This document explains how to use the PMwR backtesting framework when trade sizing depends on portfolio state at each decision point. The example defines a signal function that reads current wealth, cash, and holdings, then uses that information while…
The document asks how to break a portfolio’s compounded return into contributions from sectors when each fund holds a mix of sectors. Its example allocates each fund’s return across technology, energy, and other holdings, then compounds those sector-level…
The document explains why investors may expect additional return for holding assets with systematic risk. It corrects the premise that investors cannot avoid this risk: they can choose a risk-free investment or, within the Capital Asset Pricing Model…
The document explains two ways to measure a portfolio’s return across periods when the amount invested changes. Compounding each period’s return produces a time-weighted return (TWR), which treats periods equally and is not directly affected by the timing or…
The discussion examines why portfolios that minimize variance, without forecasting expected returns, can produce attractive historical returns. Proposed explanations include the low volatility and low beta anomalies: high risk stocks may be bid up by…
Portfolio weights far above 1 or below 0 can represent leveraged long and short positions. In mean-variance optimization, extreme paired positions may arise when the model estimates that two similarly risky assets have sharply different expected returns. It…
The document frames a practical fund-selection problem: find one ETF or mutual fund for each of the market, size, value, and momentum factors, with the goal of tracking the Carhart four-factor returns cheaply. It proposes evaluating a candidate fund by…
The document concerns portfolio construction with monthly returns for several assets. It asks whether asset log returns should be averaged arithmetically and whether multiplying asset returns by portfolio weights gives the portfolio return when the…
The document addresses where a researcher might obtain ETF holdings histories, including records of when securities enter or leave a fund. It points to ETF providers’ own websites, which may publish holdings as part of their disclosure practices, and to the…
The discussion addresses how repeated runs of stochastic optimization can produce changing stock rankings, even after the model has converged. Suggested approaches include running multiple instances with different random seeds and aggregating their…
The document presents a cash-flow replication method for determining the price of a risk-free bond from two other bonds. Each bond is represented by its payments at the present, six-month, and one-year dates. The target bond pays nothing at the intermediate…
The document answers a practical question about displaying portfolio allocations across rebalancing dates. The example uses a matrix whose rows correspond to annual dates and whose columns represent stocks; the weights are equal in the sample. The desired…
The document compares two ways to weight multiple trading signals using historical data. Linear regression chooses weights to minimize prediction error for a target return series; its unconstrained solution relates signal-return covariance to the inverse…
The document compares two ways to estimate value at risk for a fixed-income portfolio. A simple method combines yield volatility, measured in basis points, with position sensitivity such as PV01. For multiple bonds, summing individual VaRs assumes their rate…
The document clarifies that the basic CAPM does not require investors to have identical degrees of risk aversion. Under mean-variance portfolio choice and homogeneous expectations, investors select the same optimal risky portfolio, identified in the model as…
The document explains a timing problem in estimating covariances from daily returns on international stocks: markets close at different times, so their recorded closing prices do not represent the same point in the global trading day. It proposes first…
The document concerns an implementation of the Betting Against Beta strategy that ranks stocks by estimated market beta, shorts higher-beta names, and takes long positions in lower-beta names. The author describes adjusting exposures toward a beta target and…
The note addresses how nonlinear dependence between asset returns can matter for portfolio analysis even though portfolio weights combine returns linearly. It recommends framing the question through the joint probability distribution and checking whether a…
The document asks how investment banks manage guarantees attached to retail funds, including pension-style products with a minimum return-of-contributions promise. The answer describes several possible arrangements rather than a single standard practice. For…
The note explains a relationship between the Sharpe ratio of an actively managed portfolio, the benchmark’s Sharpe ratio, and the manager’s information ratio. It derives the result by scaling active bets and expressing portfolio return as benchmark return…