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 explains how the scalar tau and the view error covariance matrix omega influence the combination of equilibrium returns with an investor’s views in the Black–Litterman model. Under Idzorek’s method for constructing omega, tau is incorporated…
The document proposes linking uncertain expected returns and covariance matrices in a portfolio objective that rewards expected return while penalizing variance. It contrasts uncertainty sets where higher means pair with higher covariance against sets where…
The document raises a portfolio-construction question about estimating the covariance matrix under the Capital Asset Pricing Model. The author is simulating a portfolio of five assets and comparing optimal weights from a single-index statistical model with…
The document frames portfolio selection as maximizing expected utility over asset weights subject to a fully invested constraint. It presents an expected-utility expression for quadratic utility in terms of initial wealth, portfolio mean, and portfolio…
This explanation analyzes a self-financing strategy that holds shares of each of two risky assets in quantities linked to the price of the other asset. It defines the combined asset value as twice the product of the prices and applies multivariate Itô…
The document collects examples and explanations of volatility pumping, also called the rebalancing premium or optimal growth portfolio. It describes the Kelly criterion as a way to choose growth-oriented exposure, and gives the example of a portfolio…
Incremental value at risk (iVaR) measures the change in a portfolio’s VaR after adding a position: calculate VaR for the expanded portfolio and subtract VaR for the original one. The document explains that this is a difference between two risk estimates, not…
The document explores a multivariate Kelly allocation workflow for two return streams. It estimates rolling mean returns and covariance matrices from historical daily log returns, then uses those estimates to calculate changing strategy fractions. The author…
The document explains how linear inequalities in a constrained portfolio optimization model represent investment rules. In a maximum expected return problem with a variance ceiling, the quadratic risk constraint sets the permitted portfolio variance, while a…
The document asks how performance attribution can separate an asset’s local-currency return from the foreign-exchange return when reporting in a base currency. It presents the continuous-compounding identity that expresses the base-currency return as the sum…
The document compares the Capital Market Line (CML) with the Capital Asset Pricing Model (CAPM), focusing on whether an asset’s beta can be equated with its volatility relative to market volatility. One response develops the connection between market risk…
The document explains how portfolio weights, asset returns, volatilities, and correlation determine expected return and standard deviation for a two-asset portfolio. Expected portfolio return is calculated as the weighted average of the assets’ expected…
The discussion compares ways to optimize portfolio return while limiting Value at Risk (VaR) or Conditional Value at Risk (CVaR). It recommends treating expected return as a constraint while minimizing CVaR, and explains that scenario based CVaR can be…
The document explains how combining assets can lower portfolio variance by spreading exposure across returns that are not perfectly correlated. It gives the two-asset variance relationship, in which portfolio risk depends on each asset’s variance, portfolio…
The document gives a practical way to choose the scale constant in a volatility-managed portfolio whose next-period factor return is multiplied by a constant divided by recent realized variance. The proposed procedure begins with a trial value for the…
The discussion considers using skewness, kurtosis, and other higher-order co-moments beyond the mean and covariance in portfolio allocation. It mentions Omega-style objectives and mean-CVaR optimization as alternatives or related approaches, and notes that…
The document clarifies the sign convention in a portfolio containing a riskless account and a stock. Portfolio value is defined as the number of units held in each asset multiplied by its price, then summed. A positive holding represents a long position,…
The document frames a thesis project applying equal weighting, minimum variance, the most diversified portfolio, and equal risk contribution to Brazilian equities represented by the IBOV index. It also raises a practical portfolio construction question: how…
The document addresses why eigenvalues of stock or ETF correlation matrices may not resemble the Marchenko–Pastur distribution when the data contain highly correlated groups. The answer explains that the distribution is a reference for eigenvalues expected…
The document presents a portfolio objective combining expected return, a covariance-based risk penalty, and a third-moment co-skewness term. It asks how to choose an optimizer when the objective’s convexity is uncertain and many weight constraints may shape…
This excerpt discusses deriving portfolio weights in a mean–variance framework, in the context of a paper on market portfolio weights. It sketches a way to solve a linear system involving the covariance matrix, expected returns, a constraint vector, and…
The document discusses moving from a single-factor credit risk model, in which one latent factor represents the economy, to models with multiple risk drivers. Suggested factors depend on the portfolio and available data. For corporate portfolios, sector,…
The document compares Direct Alpha (DA) and the GEM implied private premium (IPP) as ways to express private-equity performance relative to a public market equivalent. DA represents the spread geometrically, while IPP expresses it arithmetically. The author…
The note asks whether maximizing a portfolio’s Sharpe ratio is equivalent to evaluating portfolios along the mean-variance efficient frontier. The answer says that the maximum-Sharpe portfolio is the tangency portfolio, the single portfolio on the frontier…