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 examines a second-order approximation for the certainty equivalent of a risky payoff. Expanding utility around the payoff’s mean approximates expected utility using the utility curvature and payoff variance; a first-order expansion of utility at…
The note addresses whether factors in an asset-pricing model must be returns on traded portfolios. It describes a macroeconomic factor model that includes measures such as industrial production growth and inflation surprises alongside bond return spreads.…
The document explains how to estimate an index-futures hedge for a portfolio of stocks under the Capital Asset Pricing Model. For each holding, multiply its market value by its beta to the chosen index, then add those amounts. The resulting exposure…
The discussion considers how to simulate returns for a portfolio containing many equities and bonds while retaining realistic dependence across assets. The initial proposal estimates historical means, standard deviations, and correlations, draws multivariate…
This document collects book recommendations for readers who want to understand the mathematics used in quantitative finance research. The suggestions span introductory mathematical tools, including calculus, optimization, numerical methods, and risk-neutral…
The document asks how a risky-asset portfolio weight enters wealth dynamics and then the Hamilton-Jacobi-Bellman equation for maximizing expected log wealth. It presents a risky asset whose excess return follows a mean-reverting signal, alongside correlated…
The document explains why option delta is generally tied to a particular underlying asset, so a portfolio containing options on different stocks does not have a single ordinary delta obtained by simply adding the component deltas. For a portfolio whose value…
The document concerns how to design a simulation study comparing hierarchical risk parity with the analytical global minimum variance portfolio formula for stocks. The question highlights that results may depend on assumptions about the covariance structure…
The document asks how to assign equal risk contributions across asset classes in a portfolio that includes nonlinear instruments such as options. One response recommends first converting each instrument into a return stream, estimating risk parameters from…
The note clarifies the ingredients in a Hansen–Jagannathan distance calculation and relates the measure to stochastic discount factor pricing. It derives a bound connecting the maximum Sharpe ratio attainable from a set of assets with the volatility-to-mean…
The note considers how an NPV function should handle cash flows when the valuation date falls during an instrument’s life. For basic instruments, the accepted answer recommends valuing only future cash flows. For products whose future payoff depends on past…
The discussion considers how to convert assets denominated in different currencies into an account currency during portfolio backtests. The central tradeoff is computational cost versus fidelity: applying an FX rate to every market tick may be expensive,…
The document asks how to normalize eigenportfolio weights when some components are negative, in a setting based on statistical arbitrage in U.S. equities. It contrasts dividing each weight by the signed sum with dividing by the sum of absolute weights. The…
The document derives an index’s single-period total return from security weights, price changes, and income. It rewrites each holding’s contribution as the sum of its price return and income return, then takes the weighted sum across holdings. This makes the…
The document discusses how to improve a bank’s estimate of the maturity of non-maturing chequing deposits for funds transfer pricing. The starting method assigns active accounts the historical average time until full withdrawal, split by customer…
The document addresses how to construct a zero-coupon Treasury curve when a cash-flow matrix has more coupon-date columns than bond-price rows. One proposed approach is to select a maturity-spaced set of securities, then create hypothetical bonds from nearby…
The document asks what “global” means in the term global minimum-variance portfolio and how it differs from a minimum-variance portfolio. The accepted answer distinguishes the unconstrained search across all possible return levels from the common…
The document describes a proposed research approach: define learning environments from market microstructure models with known solutions, then use reinforcement learning to see whether agents recover features of those equilibria. As an initial example, the…
Black–Litterman needs equilibrium weights for a market portfolio to infer implied returns. When the investment universe contains a mix of assets such as stocks and bonds, market capitalizations may be unavailable or hard to compare, so the document…
The document explains how to calculate variance for a portfolio that is long one stock, short another, and holds the remaining capital in cash. Its example uses weights of 1.0 in stock A and -0.5 in stock B, with cash completing the total portfolio weight.…
The document presents a long-short portfolio with a small long position, a much larger short position, and cash held alongside the positions. Its reported portfolio contribution is sharply negative even though the portfolio’s net market value is positive.…
The document surveys approaches to estimating time-varying dependence with copulas in R. It points to vine copulas with evolving parameters as one research direction and mentions the CDVine package and related materials for statistical inference. It also…
The document addresses an attempt to maximize expected portfolio return at a specified volatility using R's optim function. The proposed penalty based on an if statement gives the optimizer a discontinuous objective, and the answer instead describes…
The document derives an inverse covariance matrix for a single-factor CAPM model with a zero risk-free rate. It represents total asset covariance as the sum of a diagonal matrix of idiosyncratic variances and a rank-one market-factor contribution. The…