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 whether normally distributed asset returns would let a Markowitz mean-variance portfolio recover strong out-of-sample performance. Its answer is no: normality and standardized moments do not remove the difficulty of estimating expected…
This discussion interprets a formula from a study of risk spreading across financial markets. The answer concludes that the formula yields a shrunk correlation matrix: each exponentially weighted pairwise correlation is blended with the average correlation…
The document explains two related private-equity partnership concepts. A limited partner makes a capital commitment when the partnership is formed, agreeing to contribute up to a specified amount under the partnership terms. This commitment sets the…
The discussion concerns adding an L1 norm penalty to a Markowitz mean-variance portfolio model and asks how to formulate the optimization in MATLAB. The response proposes splitting each portfolio weight into positive and negative components. With the…
The document raises a practical question about converting daily asset return data into monthly covariance estimates. Its example uses adjusted closing prices for three equities, groups observations by calendar month, computes percentage changes, converts…
The document addresses how to compare an investor’s money-weighted return with a benchmark while separating investment selection from the timing and size of deposits and withdrawals. Applying the same dollar cash flows to both portfolios, as in the…
The document formulates portfolio construction as minimizing variance, measured by the quadratic form of portfolio weights and the asset covariance matrix, subject to a fully invested constraint and a target portfolio beta. Using Lagrange multipliers, the…
The document considers the variance of a weighted linear combination of two random variables, expressed using their individual variances and covariance. Differentiating this quadratic with respect to the weight gives the unconstrained weight that minimizes…
The document proposes applying volatility management to the six Fama–French factors, including momentum, and using the scaled factor returns to estimate risk premia. It describes scaling excess returns by a volatility target relative to conditional variance,…
The document explores constructing a risk parity portfolio directly from simulated asset return scenarios. It defines an objective that seeks similar behavior in each asset’s marginal contribution to portfolio risk across scenarios, then considers adding…
The document clarifies how Fama-French factor portfolios use breakpoints when sorting stocks by size and book-to-market. The breakpoints are computed from NYSE stocks, then applied to stocks across NYSE, AMEX, and NASDAQ. Because stocks on the latter…
The document asks how the training_period and rolling_window arguments in PortfolioAnalytics’ rebalancing optimizer control out-of-sample testing. The author describes a monthly rebalancing strategy using daily returns and wants to optimize on an initial…
The discussion distinguishes PCA components from investment factors such as momentum, value, carry, and volatility. Economic factors are defined by an interpretation or investment characteristic, while PCA is a statistical technique that extracts orthogonal…
The document introduces Hamilton–Jacobi–Bellman equations as a framework for solving continuous-time financial control problems, including consumption choice, optimal stopping, and robust control. It points readers toward classic treatments of consumption…
The document examines whether delta, gamma, and vega can be meaningfully aggregated across a portfolio containing equities, convertible bonds, and options. The answer explains that standard option Greeks are partial derivatives with respect to an…
The document asks whether a covariance matrix alone is enough to identify portfolios on the minimum-variance line at a specified volatility. It describes the variance as a quadratic form in portfolio weights and imposes the usual constraint that weights sum…
The document examines whether the sum of two stocks following geometric Brownian motions is itself geometric Brownian motion, and whether correlation between the stocks changes the conclusion. Applying Ito’s formula to the linear portfolio shows that its…
The document considers two ways to organize a backtester: assign several strategies to one portfolio, or run separate portfolios with one strategy each. The question is whether this choice matters for portfolio optimization and for simulating a fund that…
This post walks through a portfolio risk calculation using two stocks and a broad market ETF. It lays out market exposure from dollar positions and betas, idiosyncratic variance from asset-specific volatilities, total volatility, and annualized tracking…
The document addresses how average variance and average covariance relate to the variance of an equally weighted portfolio. Its central formula expresses portfolio variance using the full asset variance-covariance matrix and a vector of portfolio weights.…
The document explains why maximizing mean-variance utility, expressed as expected return minus a risk-aversion-weighted variance term, selects an efficient portfolio. The efficient frontier consists of portfolios that offer the highest return at each fixed…
This response collects resources and outlines ways investors can think about climate-related financial risk across equities, fixed income, derivatives, and portfolios. It distinguishes physical risk from climate impacts, transition risk from policy and…
The document raises implementation questions about portfolio optimization based on Jacobs and Levy’s enhanced active equity strategy framework. It asks whether to optimize first for minimum variance and then evaluate the resulting portfolio with a quadratic…
The document asks why empirical studies may find Kelly portfolios concentrated in fewer stocks, with higher returns and variance, despite a reported theoretical result that Kelly and tangent portfolios have the same weights. The answer describes Kelly as…