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 explores how a strategy can have positive estimated alpha while its cumulative return trails the benchmark. It explains the distinction through a factor model: alpha measures performance unexplained by market exposure, while realized total…
The document derives the portfolio weights that maximize the Sharpe ratio for two risky assets with equal variances and a shared correlation, alongside a risk-free rate. It defines each asset’s excess return as its expected return minus the risk-free rate,…
The note compares the minimum-variance hedge or portfolio choice with minimizing risk capital defined from value at risk and expected return. Under a full-investment constraint and a fixed target return, the efficient frontier is found by minimizing…
The discussion examines whether randomly selecting a long-only portfolio of S&P 500 stocks should match the index on average, and whether a naïve investor should therefore be expected to underperform. It distinguishes the mean return from the median: with…
The note diagnoses a failure in an equal risk contribution portfolio optimizer that returns its starting weights after one iteration. The central bug is in the objective function: although the optimizer passes candidate weights into it, the calculations…
The document examines how to calculate daily performance for a long-short portfolio with equal capital allocated to each side. It defines each asset’s simple daily return from consecutive closing prices, then combines the long return and short return by…
The document concerns an error encountered when running a rebalancing optimization in R’s PortfolioAnalytics package. The example uses monthly return data, long-only, full-investment, and box constraints, with risk and return objectives. A non-rebalancing…
The document distinguishes two choices in mean-variance portfolio theory. The tangency point between the capital allocation line (CAL) and the efficient frontier identifies the optimal portfolio of risky assets, given the model’s assumptions. It is the…
The document questions whether historical means and covariance matrices are useful for portfolio allocation when an asset’s risk can change after new information. It frames the issue using a multivariate Gaussian model, where allocations are chosen to shape…
The document describes a random matrix theory approach to separating noise from structure in a correlation or covariance matrix. It explains that the matrix is decomposed into eigenvectors and eigenvalues, noisy eigenvalues are adjusted, and the matrix is…
The document compares risk parity with smart beta and shows why their relationship depends partly on how each term is defined. Risk parity is described as a portfolio construction and risk management approach that seeks diversification across risk…
The document presents a portfolio geometry question: given a fully invested portfolio on the efficient frontier other than the global minimum variance portfolio (GMVP), can another fully invested frontier portfolio have zero covariance with it? The accepted…
The document asks why a portfolio might impose dollar neutrality in addition to beta neutrality. Beta neutrality constrains estimated market exposure, while dollar neutrality balances total long and short weights. The answer illustrates that a beta-neutral…
The document considers how to estimate a portfolio’s return distribution for an expected shortfall constraint when only a limited history of asset returns is available. It questions whether a normal approximation based on the central limit theorem is…
The document considers why the same asset-allocation strategy can show different skewness and kurtosis when evaluated with weekly rather than monthly index returns. The responses say that the reported weekly values are plausible, since higher-frequency…
The document distinguishes a manager’s historical information ratio from a prediction that the manager will continue to outperform. It asks whether managers with high past information ratios tend to retain above-median ratios, but the response offers a…
This note explores how to display portfolio returns when allocations span more than two assets. For a two-asset portfolio with weights constrained to sum to one, the author describes a heatmap-like view in which color and circle size encode the return…
The document considers how to compare portfolios optimized using mean-variance (MV), mean-variance-skewness (MVS), and mean-variance-skewness-kurtosis (MVSK) approximations to a CARA utility function. It proposes evaluating performance out of sample using…
The document presents a minimum-variance portfolio problem with bounds on individual stock weights and a limit on turnover from current holdings. The questioner introduces separate buy and sell variables to represent changes in weights, but their equality…
The document asks how to combine many statistically significant in-sample signals and whether historical covariance with mean-variance optimization is the best approach. Its answer offers a portfolio-balance intuition: add an asset or alpha exposure while…
Portfolio beta is calculated as the weighted sum of the constituent assets’ betas. If the assets have positive betas, a portfolio made only of long positions generally has positive beta; combining long and short weights can offset those exposures and bring…
The document discusses ways to obtain a spreadsheet of large companies ranked by market capitalization, with company names, countries, and comparable market values or weights. The suggestions include using holdings from a global equity ETF to approximate a…
The document recommends research on how hedge fund tail risk relates to fund performance and where that risk originates. It points to a study of equity-oriented hedge funds that examines both the tail risk of stocks held by funds and the effects of funds’…
The document asks whether mean semivariance optimization and Post-Modern Portfolio Theory (PMPT) downside risk are equivalent when they use the same benchmark. It presents semivariance as the average squared shortfall of observed returns below a threshold,…