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 corrects an attempt to reconstruct an equity index by multiplying constituent share prices by published weights and summing them. It explains that an index such as the FTSE 100 is based on company market values rather than a simple weighted…
The document asks whether a portfolio’s expected returns should use only statistically significant factors identified through Fama–MacBeth analysis or all factors in the model. The response distinguishes a statistical selection view, which would omit…
The document presents the Manipulation-Proof Performance Measure (MPPM), a risk-adjusted portfolio performance statistic based on the average of relative gross returns raised to a power determined by a risk-aversion parameter. It describes the measure as a…
The document explains how to account for long and short contracts for difference (CFDs) when calculating a portfolio’s profit and loss and return. It treats each position’s mark-to-market gain or loss as an asset or liability, even when an open position has…
The document asks how to optimize a portfolio across multiple periods when asset holdings, trades, returns, and transaction costs are linked over time. It presents a deterministic linear programming formulation in which holdings evolve as assets are bought…
The document considers how to build a hedge from quarterly short-term interest-rate futures using weights from a first principal component. It normalizes the component weights to one contract month to create a spread representation, then shows how equal tick…
The document clarifies the units behind a consumption constraint in a continuous-time asset-pricing problem. In discrete time, an investor’s consumption can be written as an endowment adjusted by the cost of an asset position, with later consumption…
The document derives the variance of a multi-period compounded return when single-period returns are independent and share the same mean and variance. It first expands the squared gross return, showing that its expectation equals the return variance plus the…
The document explains a practical use of Fama–French style factor models: assessing whether a stock or portfolio earns returns beyond those associated with established risk factors. It describes regressing the portfolio’s returns on the factors and…
The document clarifies the meaning of the vector often denoted by u in a matrix expression for minimum-variance portfolio weights. A student initially wonders whether it represents expected returns, but distinguishes it from the separately named return…
The document compares dedicated bond portfolios with immunized portfolios used to fund known future liabilities. A dedicated portfolio holds bonds whose cash flows match the amount and timing of the required payments, commonly using zero-coupon bonds. This…
The document asks why adding regression residuals to asset returns can leave their covariance unchanged. In a factor model, return covariance separates into covariance explained by the shared factors and covariance between residuals. If residuals are…
The document tests whether a stock contributes a stated amount to portfolio volatility when its weight, volatility, and correlation with the portfolio are specified. The questioner starts from the portfolio variance expansion but applies it incorrectly,…
The document discusses how to set strategic weights across broad asset classes while overlaying separate tactical signals. The questioner seeks long-horizon allocations informed by economic and country views, rather than risk parity or mean-variance…
This exercise studies pricing and hedging in a discrete-time market where the risky asset can move to one of three outcomes per period. Because a single risky asset cannot span all three outcomes, the market is incomplete. The exercise first relates…
The document asks why two estimates of portfolio beta can differ: one sums individual asset betas weighted by portfolio weights, while the other estimates beta from the portfolio return series. It explains that beta is covariance with the market return…
The document asks which discount rate is appropriate for market-consistent valuation of liabilities when an insurance arrangement uses return smoothing. The setup distinguishes general assets earning a risk-neutral rate from insurance capital whose return…
The document clarifies that the classic Fama-French factors are formed through characteristic sorts rather than portfolio optimization. It outlines a size and book-to-market procedure: classify stocks into small or big groups using market capitalization,…
The document introduces a problem in arithmetic performance attribution: component contributions may add up to the active return within individual periods but fail to match the total active return when aggregated across periods. It asks how a linking…
The document considers how to estimate expected returns for mean-variance portfolio optimization, noting that a simple historical average is a basic and potentially inadequate choice. It emphasizes that return estimates are difficult to make reliably because…
The document examines a weighted average correlation measure formed from portfolio variance, individual asset volatilities, and pairwise cross terms. It asks whether the measure must stay within the usual correlation bounds when weights may be negative, and…
The document explains how to calculate portfolio variance from position exposures and a covariance matrix. It distinguishes dollar exposures from normalized weights: dividing by net asset value can produce misleading signs when a portfolio is net short,…
The question describes annual sorting of stocks into portfolios by ESG score, holding each portfolio for seven years, rebalancing annually, and regressing monthly returns on the Fama-French five factors plus momentum. The reported pattern is negative alpha…
The question concerns generating a vector whose components have mixed marginal distributions, with some normal variables and some gamma variables, while also matching a specified correlation matrix. It notes that transforming components of a multivariate…