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 compare two mutual funds when only a short sequence of annual returns is available, alongside market returns. A standard test of mean returns and a bootstrap estimate are mentioned, but the central issue is that a small sample…
The document considers selecting five stocks from a universe of fifteen by enumerating combinations and comparing the eigenvalues of each candidate portfolio's data. It notes that a large first eigenvalue can indicate substantial variance concentrated in a…
The document outlines a common design for quantitative fundamental equity research. Investors select company measures spanning value, momentum, quality, and growth, rank stocks on those measures, and group them into deciles. They then choose a portfolio…
The document explores how a market-cap-weighted ETF with two stock holdings might represent a two-times long position. It asks how to determine the fund’s initial share price and share count, then works through a one-day example in which the holdings rise by…
The document addresses why explanations of futures notional value may multiply contract size by either the futures price or the spot price. The response argues that futures contract size and notional conventions are not universal measures of comparable…
The document outlines how to construct a self-financing portfolio that replicates a bounded terminal claim when an equivalent martingale measure exists. It discounts the claim by the savings account and takes its conditional expectation under that measure,…
The document considers how to turn multi-day price forecasts and predictive intervals into trade selection and capital allocation. It cautions against maximizing forecast return alone, since that can lead to concentrated, all-in positions. Instead, it points…
The document surveys several ways discrete mathematics and graph theory appear in quantitative finance. Network analysis can model links among banks and trace how credit stress spreads, examine industry concentration and stock returns, and study how…
The discussion considers which standard finance models become problematic when nominal interest rates turn negative. It distinguishes models that impose a nonnegative rate floor, such as the basic CIR specification, from Gaussian models that can already…
The document surveys ways to judge whether a fund manager’s excess returns reflect repeatable skill or chance. One proposal compares portfolio and market returns using a market-adjusted standard deviation, then forms a t-statistic from average excess return…
The document considers a real estate portfolio whose historical return series may understate risk because it reflects market averages and contains gaps. It asks how an optimizer can incorporate concerns about particular property types or locations when…
The document explains how portfolio return variance relates to the covariance of constituent returns. For a portfolio holding fixed share counts, each period’s return is a weighted sum of the assets’ returns, with weights determined by each holding’s market…
The document considers a 16-week portfolio contest in which participants seek the highest return, can observe one another's weekly results and holdings, and do not affect market prices. It asks whether copying successful portfolios offers a game-theoretic…
The document clarifies that Markowitz mean-variance optimization does not mathematically require normally distributed asset returns. It requires the investor to make decisions using expected return and variance as the relevant criteria. Normality is one way…
The document explains how to separate an industry factor’s returns from broad market movements when estimating security exposures. It describes a Gram–Schmidt-style adjustment: regress industry returns on market returns, subtract the market component using…
The document considers moving a portfolio from current holdings to target weights when transaction fees are deducted from the traded assets and there is no separate cash balance. One proposed approach estimates post-fee portfolio value from initial…
The document frames return-based style analysis as finding nonnegative weights on index returns that sum to one and minimize the variance of the difference between a portfolio’s returns and the weighted index returns. This estimates how a portfolio’s return…
The document derives portfolio weights that minimize variance subject to achieving a specified expected return. It uses a Lagrangian for the quadratic variance objective and the linear target-return constraint, then solves the first-order condition to…
The document compares two ways to calculate returns and volatility for a 70/30 stock-and-bond risk benchmark. One method rebalances to the target weights monthly; the other lets weights drift for a chosen period before calculating returns. The question is…
The document explains why the characteristic portfolio for a chosen asset characteristic is not constrained to have weights summing to one. In the cited construction, the portfolio minimizes variance subject to achieving a unit exposure to the…
The document frames required return as a threshold expected return that makes an investor indifferent between holding a market portfolio alone and adding a risky asset. It starts with a probability model for the asset and market returns, derives the…
The document considers whether an investor comfortable with all-equity exposure could hold a diversified stock-bond portfolio and use leverage to bring its volatility up to the level of stocks. The proposed rationale is that the mix may offer better…
The question asks how an asset with zero standalone return, such as insurance, could improve the compound growth of a portfolio when combined with a risky holding. The intuition offered is that the hedge can offset severe losses, helping preserve capital…
This note derives marginal risk contribution for a two-asset portfolio by differentiating portfolio volatility with respect to an asset weight. Applying the chain rule to the square root of portfolio variance leaves portfolio volatility in the denominator;…