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 explains why portfolio weights may sum to one, zero, or another value, depending on what the weights measure. Absolute weights describe positions relative to the investor’s capital or portfolio value. Relative weights compare a portfolio with a…
The document compares portfolio optimization using a full asset return covariance matrix with a factor model. In the factor formulation, each asset’s return is represented by exposures to a smaller set of factors plus an idiosyncratic component. The…
The document considers how to attribute the volatility of an equally weighted portfolio of three stocks to its components, given their individual volatilities and pairwise correlations. It distinguishes incremental risk, measured by comparing portfolio…
This short explanation connects the tangency portfolio in mean–variance theory with the market portfolio. The tangency portfolio is the risky portfolio with the highest Sharpe ratio relative to the risk-free asset. Under the stated framework, investors are…
The document sets up a way to infer discount factors from the prices and cash flows of coupon-paying bonds when zero-coupon bonds are unavailable. Each bond price is expressed as the sum of its coupon and principal payments multiplied by discount factors for…
The document shows how to calculate covariance matrices from successive blocks of asset returns in MATLAB and store the results in one stacked array. It gives two approaches: an overlapping window that advances one observation at a time, and a…
The document explains why a large investment manager’s reported assets under management may greatly exceed the value visible in its Form 13F filing. The filing covers certain reportable U.S. equity holdings, rather than providing a complete inventory of…
The document asks how to calculate a portfolio holding’s beta against a benchmark made from several assets with stated target weights. One proposed method is to build a benchmark return series and estimate the holding’s beta against it. That raises a…
The example compares equity valuations based on free cash flow to the firm (FCFF) and free cash flow to equity (FCFE). With the original assumptions, both approaches produce the same equity value. When the example raises return on invested capital while…
The document examines how to assess a causal portfolio controller that allocates capital among event-driven trades with different holding periods. Its root-only model optimizes expected log wealth over sampled scenarios, then follows a fixed base policy for…
The document introduces random matrix theory (RMT) through its study of eigenvalue distributions and collects suggested introductions and financial applications. The central application described is improving large covariance and correlation matrix…
The document addresses slow computation of modified expected shortfall, also called modified CVaR, for a weighted portfolio using the PerformanceAnalytics package. The question compares Gaussian and modified estimation in a component-risk workflow. The…
The document frames a portfolio-weight optimization problem for a variable number of assets. Its objective is portfolio return variance, computed from the asset covariance matrix and the candidate weights. The stated constraints require weights to sum to…
The document explains asset allocation contribution by comparing each sector’s return contribution under the fund’s weights with its contribution under benchmark weights. In the example, sector returns are held constant while the weights differ; the…
The document asks whether CovTools’ implementation of Ledoit–Wolf covariance shrinkage can be trusted. The method estimates a covariance matrix by shrinking the sample covariance toward a structured target, with the aim of improving estimation for portfolio…
The document addresses portfolio construction when holdings must stay close to a benchmark while the number of trades is constrained. It separates risk estimation from optimization: a factor risk model estimates tracking error from factor exposures, factor…
The document asks how to interpret covariance-based asset risk contributions when portfolio weights include both longs and shorts and sum to zero. It contrasts the usual calculation, based on portfolio weights multiplied by the return covariance matrix, with…
The document examines how holidays and mismatched exchange calendars complicate daily return correlations across securities. When one asset lacks a closing price on an intermediate date, assigning an invented price or return—through interpolation, carrying a…
The document presents a portfolio optimization problem with cumulative prospect theory (CPT) preferences over a multi-period horizon. The questioner highlights reference dependence and probability weighting as reasons the objective may be non-time-separable…
The document asks how to constrain a tangency portfolio so its weighted average ESG score exceeds a chosen threshold. It presents Python calculations for the unconstrained efficient frontier, global minimum-variance portfolio, and tangency portfolio from a…
This item presents a portfolio-allocation claim: the active-risk level that maximizes a portfolio's Sharpe ratio is proportional to benchmark volatility, with the scale set by the information ratio divided by the benchmark Sharpe ratio. It defines active…
The document proposes a risk indicator for evaluating portfolio returns against a benchmark. Its numerator is the expected portfolio return minus the expected benchmark return. Its denominator aggregates squared shortfalls in cases where the portfolio return…
The document frames basket replication as choosing a smaller subset of the original constituents while preserving return correlation. It sets constraints: the replicating portfolio must use only basket assets, have nonnegative weights, and match the original…
The document considers how a bank could hedge a seeded portfolio of global equities when its goal is to build a performance record without taking much market risk. It asks whether to hedge each market’s equity exposure with futures or adjust the hedge for…