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 describes a two-period portfolio comparison using historical returns. It estimates an in-sample efficient frontier from the first period’s empirical covariance matrix, generating portfolios across target returns. It then keeps those portfolio…
The document explains the beta adjustment behind the betting-against-beta factor. It treats a risky asset's return above the risk-free rate as a zero-cost excess return, then scales that return by the inverse of its market beta. This changes the portfolio's…
The document weighs whether investors should include commodities in diversified portfolios. It presents arguments on both sides, noting that asset-allocation products and some institutional portfolios use commodity exposure, while the cited research is not…
The discussion considers default counts in a loan portfolio when each loan has a specified marginal default probability and defaults may share a common latent macro factor. One answer standardizes a shared-factor Gaussian construction to preserve the…
The discussion examines whether European stock portfolio returns should be converted to euros before regression against Fama-French factors reported in dollars. It first points out that a portfolio of ten high book-to-market stocks is not constructed like…
The document asks what the number of independent forecasts, N, means in the Fundamental Law of Active Management, commonly expressed as information ratio equal to information coefficient times the square root of N. It quotes a definition that describes N as…
This discussion surveys Python approaches to portfolio construction, focusing on mean-variance and minimum-variance optimization. It points to convex optimization packages that can solve quadratic portfolio problems, with higher-level interfaces for…
The document presents an attempt to calculate the tangency portfolio for five risky Dow stocks and a risk-free asset using weekly simple returns over ten years. It supplies estimated asset returns, a covariance matrix, and its inverse, then applies a…
The document resolves a portfolio valuation question by clarifying the option position’s direction. A portfolio holding shares plus a long call includes the call’s positive value; a portfolio that has sold the call must subtract the liability represented by…
The document describes a thesis analysis using randomly selected stocks grouped into portfolios and asks why estimated Fama–French three-factor betas, especially SMB and HML, have p-values above 0.05. The proposed workflow constructs SMB and HML portfolios…
The discussion explains why factor risk contributions may not add up to a portfolio regression’s R-squared when a portfolio contains multiple instruments. Aggregating each instrument’s factor betas by portfolio weight can produce exposures, but the resulting…
The document collects several answers to whether the central limit theorem justifies treating asset returns as normally distributed. A core distinction is that the standard theorem describes the distribution of standardized sample means under assumptions…
The document asks how to show that a portfolio’s percentage contribution to loss equals its percentage contribution to risk, in the setting of a quantitative equity portfolio management exercise. It defines percentage contribution to risk for asset i as that…
The document explains how to extend minimum-variance portfolio construction by adding a penalty on asset weights while keeping the weights summing to one. It notes that a convex penalty yields a convex optimization problem that can be solved numerically,…
The document explains why expected shortfall for the sum of two loss variables is no greater than the sum of their separate expected shortfalls. The key idea is that the worst observations for the combined portfolio generally differ from the worst…
The document answers a request for accessible textbook guidance on constructing factor-mimicking portfolios. It recommends CFA Level III study notes as a relatively plain-language source, specifically citing two volumes from an older edition. It also points…
The document considers how to allocate a fixed portfolio among four hedge funds when their returns are assumed independent and each fund has a purchase limit. It explains that zero correlations do not prevent mean-variance optimization: the covariance matrix…
The document considers how to build a weighted index from several equity index series when their market calendars do not match. It identifies two basic approaches: restrict calculations to dates common to all series, or carry forward the previous available…
The document asks whether bootstrap resampling should happen before strategy data mining or after a candidate strategy has been selected. It describes a monthly SPY and TLT rebalancing strategy tested over six years and 72 trades, reporting a backtest Sharpe…
The document explains why two derivatives for a two-asset portfolio's volatility differ when one asset's weight is constrained to equal one minus the other's. Roncalli's marginal risk contribution is a partial derivative: it varies one asset's weight while…
The document considers how to choose portfolio weights that are proportional to risk budgets divided by asset volatilities, while meeting a target portfolio volatility and other constraints. It contrasts this objective with a risk-budgeting formulation that…
The document explains why pension funds and endowments may invest directly alongside private equity or venture capital funds. Co-investment can let an institution increase its exposure to a deal it finds especially attractive beyond its proportional…
The document explains why a historical portfolio Value at Risk calculation can return an empty result at a high confidence level. The cited implementation converts the confidence level to a lower-tail probability, multiplies that probability by the number of…
The document presents ways to explain bond P&L in a format resembling swap curve attribution. One method maps each bond’s risk to maturity buckets, such as splitting a bond between adjacent swap tenors, then estimates bucket moves by minimizing the…