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 addresses a question about Lagrange multipliers for non-negativity constraints in a mean-variance portfolio problem. The response describes the allocation problem as maximizing expected return less a risk penalty, subject to fully invested and…
The document considers a portfolio objective that combines expected return, covariance-based risk, and a cubic co-skewness term. It explains that the cubic objective cannot generally be rewritten exactly as a quadratic, but can be approximated locally with a…
The discussion considers whether cryptography and speech recognition methods inform financial forecasting, with the accepted answer reframing cryptography as information theory. It connects Kelly-style allocation to sizing capital across strategies and notes…
This brief question challenges the idea that retail investors can reliably secure a currently high yield by buying long-term bonds and holding them to maturity. It argues that investors without fixed, matching liabilities remain exposed to inflation and may…
The document discusses portfolio variance calculated as the weight vector multiplied by a historical variance–covariance matrix and by the transposed weight vector. With weights held fixed, this calculation represents the variance of portfolio returns over…
The document asks whether the coefficients in a regression with two predictors can be recovered without the underlying observations, given each predictor’s separate regression coefficient, the predictors’ variances and correlation, and the outcome variance.…
The document asks how to interpret an asset’s beta when the reference portfolio is a personal portfolio rather than the market. Its example considers a high-volatility stock with zero correlation to an existing portfolio, then discusses how the stock’s…
The document asks how to backtest a minimum-variance portfolio that is rebalanced at regular intervals while using all return observations available before each rebalance. It focuses on the training-period and rolling-window arguments in PortfolioAnalytics’…
The document explains why a tangency portfolio in mean-variance analysis can fall on the lower half of the risky-asset frontier when the risk-free rate is sufficiently high. In this case, the tangency portfolio is not on the efficient portion of the…
The document frames a dimensionality-reduction problem for an interest-rate par risk strip with many buckets. It seeks a smaller set of representative risk buckets and an aggregation function that best preserve the original strip’s delta P&L. Principal…
The document discusses the ANTICOR portfolio algorithm, introduced in a paper on learning to outperform the best stock. It characterizes the method as a windowed form of constant rebalanced portfolio allocation and notes that its appeal rests on strong…
The note explains how to estimate skewness and kurtosis for a two-asset portfolio from return observations. It first frames the inputs as aligned return time series combined using portfolio weights, with the resulting portfolio returns serving as the…
The document asks which utility function is appropriate for evaluating multi-asset funds using historical return distributions across different levels of risk aversion. It compares constant relative risk aversion (CRRA) utility with quadratic utility and…
The document compares several ways to quantify portfolio diversification. One approach allocates total portfolio volatility across assets and treats a portfolio as more diversified when those risk contributions are more evenly distributed. It also mentions…
The document distinguishes risk parity from simply assigning equal asset volatilities. A portfolio’s total volatility is derived from its covariance matrix, and each asset’s risk contribution is its weight multiplied by its marginal contribution to portfolio…
This explanation derives a first-order approximation of portfolio loss when value is modeled as a function of time and observable risk factors. Applying a Taylor expansion separates the change in portfolio value into a time derivative and exposures to…
This explanation distinguishes the Capital Market Line (CML) from the Security Market Line (SML). The CML relates expected return to standard deviation for efficient portfolios, while the SML relates expected return to beta for individual securities or…
The document considers how to choose a tradable universe for statistical arbitrage that models shared factors or indices and trades residuals. It contrasts liquidity cutoffs, selecting assets by their contribution to strategy performance, and using principal…
The note derives the Black–Litterman risk-aversion coefficient from the market portfolio’s equilibrium weights and implied excess returns. Starting from the unconstrained mean–variance objective, its first-order solution gives implied returns as risk…
The document discusses how to interpret negative cost of equity estimates produced from CAPM beta calculations. It argues that a negative expected return can be consistent with portfolio theory: an asset that offsets another asset’s risk may have a negative…
The document presents a long-only portfolio problem that seeks to maximize expected excess return divided by portfolio volatility, then asks how to recast it for a general quadratic programming solver. The proposed transformation introduces scaled portfolio…
The document explains how the Hamilton-Jacobi-Bellman equation arises in the Merton portfolio problem. An investor allocates a fraction of wealth to a risky asset and the remainder to a risk-free asset, giving a stochastic differential equation for wealth.…
The document explains how principal component analysis (PCA) can reduce the number of risk drivers used to model a commodity forward curve. At each historical observation date, the data matrix has one row per delivery bucket and one column per date; its…
The document asks how to apply Marchenko–Pastur random matrix filtering to an exponentially weighted moving average (EWMA) correlation matrix. For a conventional sample matrix, it describes using the ratio of observations to variables to set an eigenvalue…