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 compares two ways to estimate performance relative to factors. In a two-stage approach, asset exposures are first estimated from time-series regressions, then factor risk premiums are estimated from cross-sectional regressions at each date and…
The document asks how to turn a sequence of per-trade percentage returns into a cumulative return. It proposes multiplying the gross returns, then subtracting one, which is the standard way to compound sequential returns when each return applies to the…
The question challenges the use of return standard deviation as the sole basis for allocating capital across uncorrelated assets. It asks what principles might support equal weights, growth-based weights, or another allocation rule when conventional…
The document compares adding long- or short-duration Treasuries to an equity portfolio, including whether to use leverage. For an investor optimizing across stocks and both bond maturities, the first answer recommends evaluating expected returns, risks, and…
The note considers how to calculate monthly and cumulative returns for three stocks and an equally weighted hedge fund portfolio. Its answer emphasizes that portfolio weights matter: an equal-weight allocation at the start does not by itself establish that…
The document sets up a comparison between investing with one exponential-utility optimization over a full horizon and reoptimizing at an intermediate date before the final horizon. It presents the martingale-method terminal wealth expression for a complete…
The document examines two formulas for measuring average correlation among assets in a weighted portfolio. It presents an R example using simulated returns to build a covariance matrix, correlation matrix, and portfolio variance, then compares the two…
The document explains how to choose a self-financing hedge portfolio when an investor already holds positions in part of an asset universe. It partitions the full return covariance matrix into blocks for the existing holdings and the assets available for…
The document raises two practical questions about turning cointegration relationships into a pairs trading portfolio. It compares a regression of log prices with one using raw prices, each expressed as a fitted relationship between assets and a residual…
The discussion seeks a derivation for the portfolio weights often written as the inverse covariance matrix multiplied by expected returns. One answer applies Lagrange multipliers to a Sharpe-ratio objective with weights summing to one. Another uses the…
The discussion asks whether CAPM is suitable for valuing a stock when the analyst believes the market price is wrong. It outlines a common valuation use: estimate beta from historical returns, use CAPM to estimate the equity return investors require, and…
The document examines a proposed way to summarize the return of a single security position built through purchases at different prices. The method calculates each purchase’s return to the present, weights those returns by the purchase’s fraction of current…
The document asks how to define portfolio shares whose values sum to one at every time, and how their period-to-period growth factors must relate. It treats each share as a proportion of the total and defines its growth as the ratio of its next-period value…
The document asks whether negative interest rates require separate pricing models for electronic and physical cash flows. It proposes treating physical settlements as observed portfolio cash flows, discounting outgoing and incoming amounts using…
A financial benchmark provides a reference for judging a portfolio manager’s performance, such as a broad equity index or a risk-free asset. The document offers SAMURAI as a set of selection criteria: a benchmark should be specified in advance, appropriate,…
The note describes a factor-investing approach that begins with a diversified, market-cap-weighted index portfolio. Practitioners can adjust stock weights according to their estimated exposures to the Fama–French size and value factors, increasing weights in…
The note explains how a portfolio gain process can be written using undiscounted asset prices while still displaying excess returns over the risk-free rate. It starts from risky assets whose proportional returns contain drift and diffusion terms, then…
The document discusses how to evaluate stock-return factor models and whether information criteria should be applied to time-series regressions for individual assets or to cross-sectional models. It explains that the answer depends on the model’s purpose and…
The question concerns portfolio optimization over a large investment universe under long-only, equal-weight, and asset-count restrictions. It seeks both a maximum-Sharpe portfolio and a minimum-standard-deviation portfolio at a target return, and reports…
The document presents an approach to allocating partial fills across a sequence of stock trades when the final position must stay within a fixed share limit. The original formulation uses dynamic programming over possible positions and execution amounts, but…
The document frames a portfolio problem involving N assets, each modeled as a geometric Brownian motion with drift and volatility. It asks how to express the stochastic differential equation for a function of all asset prices, with clear drift and diffusion…
The document addresses how to test whether one factor can be removed from a multi-factor asset pricing model. A factor’s average return alone is not a sufficient criterion: omitting it changes the estimated exposures to the remaining factors. The proposed…
The document explains how to choose a risky-asset weight for a one-period portfolio when the investor has power utility, a risk-free return, and a probability distribution for the risky asset’s return. The return distribution is represented by possible…
The document poses a portfolio construction question about equally weighting short put positions by option price across different stocks with a shared maturity. The author describes Monte Carlo results in which portfolios involving more highly correlated…