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 examines a portfolio holding fixed fractions of wealth in a risky asset and a riskless account. The risky asset follows geometric Brownian motion, while the account grows at a constant rate. The question is whether continuously restoring the…
The document asks whether portfolio volatility can be annualized by computing daily portfolio variance from asset weights and the return covariance matrix, then multiplying the resulting standard deviation by the square root of the number of trading days in…
The document explains how regularization can stabilize global minimum-variance portfolio weights. In the unconstrained case, the optimization objective can penalize large weights using an L2 norm, as in ridge regression, or an L1 norm, as in lasso. This…
The document explains an Excel adjustment intended to recover average correlation from a square correlation matrix. The desired statistic is the mean of the off-diagonal pairwise correlations, counting each unique pair once. The spreadsheet’s rectangular…
The document addresses how to distinguish total return and absolute return funds when applying a fund risk classification framework. It warns that the terms can suggest a distinction between price appreciation alone and returns including income such as…
The document compares introductory and advanced textbooks for learning asset pricing, grouping recommendations by their emphasis and mathematical level. Cochrane is presented as an accessible bridge between theory and empirical testing, organized around…
The document explains how portfolio returns can be reported when investors add or withdraw capital. It distinguishes investment performance from changes in account value caused by external cash flows, using an example in which an initial investment grows…
The document examines whether a realized efficient frontier from mean-variance optimization with monthly rebalancing should rise smoothly as target volatility increases. The responses explain that an out-of-sample frontier can be nonmonotonic: portfolios…
The document asks how to modify a portfolio covariance matrix so that the resulting mean-variance efficient frontier moves right by a fixed amount in volatility while retaining its original shape. The author uses an analytical frontier derived from Merton’s…
The document describes a government-bond curve fit that minimizes squared bond-price errors while imposing a monotonicity condition on discount factors. This price-focused fit can produce a pronounced hump. It then presents a regularized objective combining…
The document asks how to impose a diversification cap of the form that each portfolio position's absolute value cannot exceed a fixed fraction of the portfolio's total absolute exposure. It presents the constraint for a three-stock example and mentions a…
The document presents an attempted implementation of an information-theoretic method for selecting the number of clusters in asset data. It first computes correlations among asset returns, applies k-means for a range of cluster counts, and assigns each asset…
The document answers whether quantitative finance considers the risk–reward trade-off. It connects the idea to mean–variance portfolio optimization, where portfolio weights are chosen to minimize variance subject to a target expected return. It also…
The document frames a decision problem in which an asset owner compares possible actions using a profit-and-loss distribution for each. The distributions may be estimated from empirical distributions of uncertain inputs, and can differ in expected profit,…
The discussion concerns estimating a covariance matrix for many assets from a shorter return history, where the matrix is singular or nearly singular and standard Cholesky decomposition can be unstable. It explains that when the number of variables exceeds…
The document asks whether limiting portfolio weights to long-only bounds or allowing bounded short positions can cause a sudden change in the slope of an efficient frontier as risk aversion varies. It frames the effect as a consequence of restricting the…
The document asks how the maximum-Sharpe portfolio relates to linear homogeneity and its economic interpretation. It presents a portfolio formula based on the inverse covariance matrix and expected returns, along with a corresponding Sharpe ratio, then…
The discussion asks whether Black–Scholes models are weakened by representing only a few risky assets. It explains that pricing a portfolio of options on different underlyings together can require their correlations: a basket option generally has a different…
The document explains why portfolio optimizers may constrain or penalize the L1 or L2 norm of asset weights. It connects these constraints to regularization in regression: L1 and L2 penalties can limit estimation error and produce more stable weights, while…
The discussion explains how to aggregate profit and loss across long and short holdings to calculate a portfolio return relative to total starting capital. It also clarifies that a stock’s beta does not become negative merely because the position is short;…
The document clarifies how to use monthly returns for portfolios sorted by size and other characteristics in empirical asset-pricing regressions. The portfolio-return series from the Kenneth French data library are raw returns, so researchers testing the…
The note explains the Roll critique: for a portfolio on the mean-variance efficient frontier, asset excess returns satisfy a CAPM-style relation using that portfolio as the benchmark. It gives the efficient portfolio’s risky-asset weights in terms of the…
The document explains defeasance as a way to economically set aside funds against debt without immediately prepaying a loan that carries prepayment penalties. Dedicated cash or assets are placed in an escrow or similar account so their principal and interest…
The document considers whether the CAPM regression alpha and beta of an equally weighted portfolio can be found by averaging the corresponding estimates for its constituents. For assets measured over the same observations against a common benchmark and…