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 why a single unusually large daily return can have a disproportionate effect on annualized variance when returns are aggregated to a lower frequency, such as monthly. Since the outlier remains one observation but represents a longer…
The document raises a portfolio optimization question about shrinkage estimation of a Newey–West covariance matrix. It describes combining the contemporaneous covariance matrix with a symmetrized lagged covariance term, and considers using an identity matrix…
The document explains a two-asset mean-variance optimization with a target portfolio return and a fully invested weight constraint. It interprets the solution weights as asset positions and the accompanying Lagrange multipliers as measures associated with…
The document distinguishes factor evaluation from factor modeling. It asks whether a factor’s long-short portfolio return and statistical significance correspond to the factor return in a model where asset returns depend on factor exposures. The answer…
The document considers allocating a portfolio across five asset categories while imposing lower or upper bounds on selected weights. It asks whether maximizing expected return under such constraints can be formulated as linear programming. The replies…
This question compares an extreme value theory approach to value-at-risk with simulation from empirical return distributions. The proposed EVT workflow models the center of returns with a Gaussian kernel and the tails with a generalized Pareto distribution,…
The document explains why portfolio construction may benefit from shrinking an estimated covariance matrix, even when computation is cheap. Shrinkage pulls extreme covariance estimates toward more central values, which can reduce the estimation errors that…
The document compares three ways of working with investment factors. One approach builds long-short portfolios by ranking stocks on a characteristic such as price-to-book and buying the highest-ranked group while shorting the lowest. The author notes that…
The document explains that a valuation discount rate must match the cash flow being valued. It distinguishes dividends and free cash flow to equity, typically discounted at the required equity return estimated with CAPM or another equity model, from free…
The document asks how to construct the tangent portfolio when short selling is prohibited. With short sales allowed, it gives the familiar solution proportional to the inverse covariance matrix times expected excess returns, then normalizes the risky-asset…
The discussion considers replacing discretionary Black-Litterman views with systematic signals. The proposed example estimates each stock’s residual return from a market model, standardizes residual averages by their volatility, and uses the difference…
The note asks why the maximum-Sharpe portfolio problem can be reformulated as minimizing portfolio variance subject to a fixed excess-return target. Its central idea is scale invariance: multiplying portfolio weights by a positive constant leaves the Sharpe…
The document explains why stock and government bond prices can have changing correlations. Both asset classes respond to changes in risk-free discount rates: when rates rise, the present value of their future cash flows can fall. Equity prices also depend on…
The document describes a Monte Carlo resampling approach to mean-variance portfolio optimization. It outlines fitting return distributions to assets, simulating returns while respecting assumptions about expected returns, volatility, and correlation,…
The discussion explains why daily component contributions that add to a portfolio’s return cannot each be compounded independently and expected to reproduce the portfolio’s compounded performance. Contributions allocate each period’s portfolio gain across…
The document asks whether a long-short portfolio formed from a cointegrated pair can be shown to have zero CAPM beta. It writes the portfolio’s market exposure as the beta of the long position minus the hedge ratio times the beta of the short position.…
The document compares monthly Fama-French factor returns with values obtained by geometrically compounding the published daily series. It focuses on the market excess return and the SMB and HML factors, which are built from portfolios formed by size and…
The document considers an equally weighted portfolio of three stocks with equal volatility and zero pairwise correlation. It asks what fraction of an individual stock’s risk is diversified by including it in that portfolio, and presents a variance-based…
The answer explains which portfolio risk report fields can be scaled by position size and netted across trades. Most sensitivities, including Greeks, typically scale with notional, but aggregation needs care: unlike-for-like positions should be combined, and…
The document discusses combining forecasts from different trading methods, including sentiment measures, signal processing, and neural networks. One recommendation is to express forecasts in comparable units, such as expected returns or event probabilities,…
The document explores how to set asset-level risk contribution budgets while also requiring a portfolio to meet a target volatility. It presents an optimization that minimizes squared differences between each asset’s share of portfolio variance and its…
The document presents an informal argument linking arbitrage to the existence of an investor’s optimal consumption and trading choice. It says that if an optimal strategy exists and utility is strictly increasing, adding an affordable arbitrage that delivers…
The document describes an olive plantation scenario-generation problem involving investment costs, delayed revenues, and temperature. The author proposes fitting a four-variable Gaussian copula to ranked observations of costs, revenues, temperature changes,…
The document asks whether portfolio variance computed from a fixed vector of weights equals the quadratic form using the return covariance matrix, and whether the same identity holds with sample estimates. The answer applies linearity of expectation: for…