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 considers whether mean-variance (MV) portfolio theory remains useful when its assumptions do not match real investor behavior. It points out that investors may estimate expected returns and covariances differently, and may choose assets for…
The discussion asks why portfolio research focuses on reducing estimation error instead of finding a more realistic return distribution. The answers explain that mean-variance optimization needs estimates of expected returns and covariances, and that optimal…
The document explains why the mean and volatility pairs attainable from long-only portfolios in a finite asset universe form a closed set. It frames portfolio construction as a continuous map from asset weights in the simplex to the portfolio’s mean and…
The document asks where covariance shrinkage belongs in a Black–Litterman workflow: on the covariance input used to estimate posterior returns and risk, or on the posterior covariance after running the model. The accepted response recommends estimating the…
The document collects suggestions for backtesting equity strategies that use fundamental data. For Zipline, one answer explains that fundamental datasets are generally accessed through Pipeline, so a user may need to implement a custom loader for the chosen…
The document explains why two assets can offer portfolio benefits even when they have identical means and standard deviations. Their individual return statistics describe only the first two moments of each asset; they do not capture how the assets move…
The document proposes allocating a limited budget across long call options on three correlated assets: an equity fund, government bonds, and gold. Its workflow estimates a covariance matrix with a multivariate GARCH model, uses that matrix to simulate…
The document clarifies terminology for the wealth multiplier associated with a period’s return. If wealth begins at one and a period earns a return, adding one to the rate gives the gross return, also called the gross rate of return. Multiplying successive…
A regression of benchmark returns on fund returns can provide portfolio weights that minimize tracking error when the regression is fit without coefficient constraints. The coefficients need not sum to one, so their total has a direct funding implication: if…
The document considers how to estimate a portfolio’s ex-ante tracking error against the S&P 500 when holdings have return histories of different lengths. Most stocks have 180 weekly observations, but several large relative positions have fewer than 36. It…
The document examines why a standard Black-Litterman portfolio may change weights only for assets explicitly named in investor views. It explains that a view against one company can lead the model to reduce that holding while keeping correlated peers, since…
The document asks how to interpret constraints for changing the probabilities of a discrete distribution while retaining its possible outcomes. One condition makes each probability adjustment proportional to the reciprocal of the distance between that…
The document sets up a global curve calibration problem using a piecewise cubic spline to represent rates across maturities. It proposes choosing the spline coefficients so that prices or rates implied by the resulting discount curve match observed market…
The document compares two proposed MATLAB formulations for finding a maximum diversification portfolio. One minimizes portfolio variance measured with a correlation matrix, then rescales the solution using asset volatilities. The other is intended to…
The document asks whether Black-Litterman portfolio construction can incorporate several forecasts for the same asset, such as views from independent factor models or analysts. It frames the issue using the usual pick matrix and view vector, and asks whether…
The document considers how to compress a bond portfolio’s risk across an entire yield curve into exposures to a few liquid benchmark maturities. It outlines principal component analysis as one approach: project the bond risk vector onto a small set of…
The discussion asks how downside semivariance can be extended to measure co-movement between assets and form a covariance-like matrix. It presents two candidate constructions: multiply each return after truncating it below a chosen reference level, or…
The document raises practical questions about estimating portfolio betas with monthly CAPM returns, including whether monthly excess returns should be compounded for annual reporting, whether shorter months deserve different weights, and how to handle…
The question asks why differentiating a quadratic expression, one-half times a vector transposed, multiplied by a symmetric matrix and the vector, produces a linear gradient term. The answer explains the role of the one-half factor: differentiating a scalar…
The document frames the search for stock portfolio signals as an optimization problem. An expression combines market or fundamental variables with unary and binary operators and parameter choices; evaluating it across stocks produces weights, which are…
The document surveys ways to optimize ETF portfolios without assuming normally distributed returns. One proposal uses the empirical return distribution with mean-CVaR optimization, where expected shortfall measures downside risk. It also mentions resampling…
The document asks how to extend the Kelly criterion, which seeks to maximize long-run growth, to a portfolio of correlated stocks. It points to a multivariate treatment in an investment science text and summarizes a constrained quadratic optimization model…
The document asks how to turn simulated returns from an ARMA-GARCH-EVT-copula model into allocations for three portfolio objectives: maximum Sharpe ratio, global minimum variance, and minimum CVaR. Its central practical questions are whether the simulated…
The document explains why one stock can have higher return standard deviation yet lower beta than another. Standard deviation measures an asset’s total return variability, while beta measures how strongly its returns move with a benchmark. Since beta depends…