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 frames tactical portfolio tilts, such as overweighting or underweighting a stock-bond pair trade relative to a benchmark, as a constrained optimization problem. The decision vector represents trade sizes, the signal vector represents desired…
The document explains why multiplying a covariance matrix by a nonzero constant should leave global minimum variance portfolio weights unchanged. In the standard solution, the inverse covariance matrix is multiplied by a vector of ones, then the resulting…
The document describes a practitioner’s difficulty estimating a variance–covariance matrix that reduces portfolio volatility out of sample for a Russell 3000 universe. Approaches tried include direct covariance estimates from daily, weekly, or monthly…
The document compares two ways to estimate factor betas in equity risk models. A time-series method defines factor returns in advance and estimates each security’s exposure from its historical returns. A cross-sectional method uses current, normalized…
The document asks how to estimate the change in a diversified portfolio’s value after a specified upward shock to the S&P 500. It proposes fitting an ordinary least squares regression of portfolio value on the index and multiplying the estimated beta by the…
The document considers how to evaluate strategies whose trades begin and end at irregular event times. It distinguishes measuring the average return around an event from measuring the cumulative performance of a strategy. For event analysis, the question…
The discussion surveys approaches developed to address practical weaknesses in mean-variance optimization. It highlights Black-Litterman, equal risk contribution or risk parity, minimum-volatility portfolios, and resampled efficient frontiers as ways to…
The document explains why a discrete portfolio value change can contain a cross-term formed by a change in holdings multiplied by a change in an asset’s price. When holdings are adjusted during the same interval as prices move, the added units are not…
The document asks why the market portfolio is treated as the tangency portfolio in the CAPM framework when real investors hold different portfolios, including undiversified ones. The question recalls the theoretical result that investors choose the same…
The document asks how to choose portfolio weights when estimated mean returns are too uncertain to distinguish reliably. It frames the problem with three assets that share the same correlations and variances, where some pairwise tests fail to reject equal…
The document asks how to choose portfolio weights under Fernholz’s Stochastic Portfolio Theory when asset prices follow correlated geometric Brownian motions and the holdings are reset at event-triggered times. The proposed trigger occurs when an asset’s…
The document explains why adding another stock does not always reduce the variance of an unconstrained minimum-variance portfolio. In its example, an added stock is highly correlated with and less attractive than an existing holding; the unconstrained…
The document derives the covariance matrix for asset returns from a linear factor model. Each asset return is represented by its factor exposures applied to factor returns plus an asset-specific residual. Assuming factor returns have a covariance matrix and…
The document asks how to measure an individual investor’s utility over a year when only daily stock holdings are observed. It proposes calculating each asset’s share of the portfolio, applying a utility function to each asset’s dollar value, weighting those…
The document considers how to weight stocks after sorting an equity universe into portfolios by market-to-book ratio and then comparing excess-return regression alphas. Equal weighting gives each company the same portfolio influence, which can increase the…
The note examines how to choose portfolio weights that make a basket of assets track a target return series, subject to weights summing to one. It compares minimizing tracking error, defined as the standard deviation of portfolio returns minus target…
The document presents a question about forecasting asset returns and conditional volatility with an ARMA and sGARCH specification, then using forecasts to build a portfolio covariance matrix. It shows an R workflow based on historical prices, log returns, an…
The document introduces Cover’s Universal Portfolio as a way to combine many candidate portfolios. Each candidate holds fixed asset proportions and is repeatedly rebalanced; the overall portfolio weights these candidates according to their accumulated…
The document defines a statistic formed from a sample covariance estimate, the inverse of the true covariance matrix, and a vector of ones. It notes that the statistic arises as a maximum equilibrium Sharpe ratio under certain conditions, then asks how its…
The document formulates a portfolio selection problem: maximize the Sharpe ratio while requiring every included asset to receive the same weight and every excluded asset to receive zero. It represents the decision with a binary vector that marks selected…
The note explains how to calculate portfolio volatility when adding an independent stock position of the same size to an existing holding. Because the two returns are assumed independent, their variances add for the combined dollar positions. The example…
A common quick backtest multiplies each day’s asset returns by lagged signals, combines the resulting returns across assets, and compounds the daily portfolio series into net asset value. This construction implicitly resets exposures as portfolio value…
The document presents a factor decomposition for approximating corporate bond returns and deriving their variance. It starts with the duration approximation, which relates a bond’s return to the negative product of duration and yield change. Yield changes…
The document describes a low-sample event-driven allocator that chooses total invested capital and divides it among concurrent signals. Its current approach maximizes worst-case expected log growth over Bayesian-bootstrap return scenarios, subject to…