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 asks how to estimate portfolio volatility when each of two assets has an exponentially weighted variance estimate. The central guidance is to calculate correlation using the same weighting convention as the variances. Applying common weights to…
The document discusses how to judge the uncertainty in an estimated portfolio tracking error and how sample size affects confidence in that estimate. It recommends resampling observed tracking errors with replacement to build a nonparametric bootstrap…
The document considers how to stress a correlation matrix used in mean-variance portfolio allocation and risk calculations. Simply multiplying every entry can make diagonal self-correlations exceed one; scaling only off-diagonal entries can still create…
The document asks how to benchmark covariance forecasting methods used to build minimum-variance portfolios. The strategy described estimates covariance from historical daily returns, forms portfolio weights, and rebalances weekly. For a perfect-information…
The discussion considers portfolio construction without relying directly on asset return estimates. One approach is liability-driven investing: choose assets that hedge future spending or obligations, such as pension payments, education costs, or…
The document introduces duality in convex optimization and explains several ways a dual problem can help analyze a primal optimization problem. For a minimization problem, the dual can provide a lower bound on the primal objective. Dual-variable values also…
The document raises a portfolio-construction question: how should raw signals that produce instrument positions be combined into a final portfolio? It considers averaging or weighting signals within each instrument, then applying a portfolio method such as…
The document asks how to combine two return series when holding a long position in one asset and a short position in another, with capital weights of 0.7 and 0.3. The response describes converting each period’s return into a gross return factor, applying a…
The document derives a portfolio that has unit exposure to a chosen asset attribute while minimizing portfolio variance. Given an attribute vector and an invertible covariance matrix, the optimization minimizes the quadratic risk expression subject to a…
The document asks how to express risk in one set of securities in terms of another correlated set. It considers principal component analysis but identifies difficulty standardizing the inputs and concern about overfitting. The response recommends regressing…
The question asks how to divide assets into portfolios whose returns are mutually weakly correlated, either assigning each asset to only one portfolio or allowing assets to appear in multiple portfolios. It notes that direct optimization can become expensive…
The discussion considers how to assign benchmark weights to currencies when constructing a currency portfolio with Black–Litterman optimization. Currency weights require a chosen base currency and a defined date and rebalancing frequency. Possible weighting…
The question asks how to classify stocks beyond familiar categories such as sector, industry, exchange, currency, and market capitalization, in the context of analyzing portfolio margin. The answer proposes unsupervised hierarchical clustering, followed by a…
The discussion explains the return convention for a dollar-neutral long-short position: a long investment in one asset is paired with an equal-dollar short position in another. The question concerns whether the return should be the long asset’s return minus…
The document outlines data requirements for estimating an implied equity risk premium with a cash-flow valuation approach. The author is building a free-cash-flow stock valuation library and, following a Damodaran framework, has gathered historical S&P 500…
The document asks whether funds with returns negatively correlated with the S&P 500 are more likely to hold non-index assets or to own index stocks whose returns behave differently from the benchmark. It presents a linear regression of fund returns on index…
The question asks why eigenvectors from the Johansen cointegration procedure can serve as hedge ratios for a portfolio intended to be stationary. The answer offers a geometric account of eigenvectors and relates the weights to historical dependence among…
The document explains why mathematical optimization is useful in quantitative finance, focusing on derivative pricing, portfolio construction, and mean-reverting baskets. It connects the duality theorem in linear programming to the arbitrage theorem, which…
The document presents a way to hedge a long position in one security using a basket of peer securities. It chooses peer holdings to minimize the variance of the combined portfolio while keeping the target security’s holding fixed. The solution uses the…
The document explains how SMB is constructed differently across the Fama–French three-factor and five-factor models. In the five-factor framework, SMB combines size spreads from portfolios sorted on book-to-market, operating profitability, and investment.…
This discussion considers portfolio construction when expected returns come from a non-normal predictive distribution and its spread represents estimation uncertainty. It examines several candidate approaches: optimizing a portfolio for each Monte Carlo draw…
The document considers whether a bond index can stand in for the risk-free rate in the Capital Asset Pricing Model. One response argues that broad bond indexes can contain government, municipal, corporate, high-yield, mortgage-backed, and loan exposures, so…
The note decomposes the risk of a USD-denominated Mexican corporate bond into USD interest-rate exposure, the spread of USD-denominated Mexican sovereign debt over the USD risk-free curve, and the issuer’s additional idiosyncratic spread. It suggests hedging…
The document asks for a verbal explanation of how carried interest affects the purchase price consistent with an investor’s target net return multiple. It presents an example involving a stated payoff, a target return multiple, and a manager’s percentage…