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 note describes an attempt to explain daily EUR swap yield-curve changes using three principal components, commonly interpreted as level, slope, and curvature moves. The author forms daily tenor changes, estimates a covariance matrix from a one-year…
This exchange explains how a set of 25 portfolios is formed by independently sorting stocks into five market-cap groups and five lagged-momentum groups, then taking the intersections. Size groups use regional capitalization breakpoints; momentum groups use…
The document defines eigenvector centrality for a node in a minimum spanning tree using the adjacency matrix and its largest eigenvalue. It then asks how to combine the centralities of multiple nodes with a portfolio weighting vector, framing centrality as a…
The document starts from the Markovian log-utility portfolio problem, where expected return and volatility depend on the current state. It summarizes the associated Hamilton–Jacobi–Bellman equation and gives the familiar feedback allocation proportional to…
The document explains ways to find a portfolio with the highest Sharpe ratio when asset weights have lower and upper bounds. One direct formulation uses covariance as the quadratic objective, constrains the portfolio’s excess return to a fixed value, and…
This discussion addresses mean–variance allocation when investors can combine risky assets with a risk-free asset. Under the standard assumptions behind the Capital Allocation Line, efficient portfolios are formed by mixing the risk-free asset with a risky…
The document derives the worst-case portfolio return when estimated asset returns are uncertain within a spherical region around their estimated vector. The uncertainty radius is proportional to the magnitude of the estimate, with a parameter controlling its…
The document explains how to combine constituent ESG ratings into a portfolio score when portfolio positions can be long or short. Its central proposal is a weighted sum of individual scores using signed position weights. Under this convention, a short…
This exchange describes cross-sectional regression as a way to relate securities’ returns in a given period to attributes thought to be priced, such as book-to-market ratios or market capitalization. The resulting coefficients can be interpreted as returns…
This exchange considers how to represent transaction costs when a futures calendar spread can be traded as a single exchange-listed contract. The question observes that the spread contract may have a lower execution cost than trading its outright legs…
The document asks why a Black–Litterman likelihood or return distribution might use the investor’s view means and observed market covariance as its parameters. The response frames the choice in Bayesian terms, describing it as a simple way to obtain a prior…
The document asks whether bootstrap estimates of returns, variances, and correlations should be used to construct an efficient frontier from two stocks’ historical returns. The response clarifies that bootstrapping is primarily a way to estimate the sampling…
The document considers why minimum-variance optimization over ETFs may concentrate holdings in bonds and government securities: assets with lower variance can dominate the objective. It presents several ways to pursue broader diversification. Risk parity…
The document raises a portfolio risk question: how to use principal component analysis when positions depend on more than one correlated time series, such as UK and euro yield curves or several commodities. PCA on a single curve can summarize its major…
The note explains the intuition behind the betting-against-beta strategy and its connection to the Capital Asset Pricing Model (CAPM). CAPM implies that higher-beta stocks should offer higher expected returns to compensate for their greater market risk,…
The document shows how to model a dollar cost averaging schedule in the Python bt backtesting framework. The proposed strategy runs monthly, selects the available asset, adds a fixed capital contribution, assigns equal weights, and rebalances. The…
The document explains how repeatedly renewing short-dated FX forwards can hedge a foreign-currency portfolio position even when the investment has no fixed exit date. The key mechanism is that a change in spot exchange rates creates gains or losses on the…
The document addresses a universe-construction problem: a strategy draws symbols from NYSE, Nasdaq, and AMEX, but its author wants to exclude ETFs and other funds. The accepted response points to an exchange-published downloadable symbol list identifying…
The document considers how investors might distinguish asset classes for strategic allocation and tactical decisions. It argues that classes should reflect different economic drivers and responses to short-term events, while liquidity may matter because…
The document asks what distribution and price process arise when a fixed-weight portfolio combines stocks modeled as lognormal processes. It writes the portfolio increment as the weighted sum of each stock’s drift and diffusion terms, then points out that…
The document asks how to assess a dynamic portfolio strategy when a backtest is divided into multiple periods and the strategy is tested with different rebalancing intervals. For each interval, the author has period-level mean return, standard deviation, and…
The document explains duplication invariance in the Most-Diversified Portfolio (MDP): adding a second asset with returns identical to an existing asset should not make the portfolio treat that exposure as a new diversification opportunity. The clarification…
The document explains that efficient portfolios do not all have the same beta. Under the framework described, beta is measured relative to the market portfolio, which is identified as the point where a line from the risk-free rate is tangent to the efficient…
The document discusses why exact future stock or bond price levels are difficult to predict while noting that some narrower patterns and investment decisions may still be useful. The answers distinguish price forecasting from portfolio management,…