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 how to construct quantity values associated with an already ordered price series, while controlling their dependence, to study how correlation changes a total-revenue curve. The responses offer two approaches. For a short fixed vector, one…
The document explains how annualization differs across common performance ratios calculated from monthly returns. Under an independent and identically distributed monthly-return assumption, Sharpe and Information ratios scale by the square root of twelve:…
The document presents a portfolio optimization modeling problem. The decision variables represent net asset weights and separate gross long and short positions, with constraints linking net weights to those positions and bounding total gross exposure. The…
The document reviews risk-neutral valuation in a binomial model with constant or adapted, time-varying interest rates. It describes valuing a payoff by taking its conditional expectation under the risk-neutral measure and discounting by the relevant sequence…
The document explains that beta’s sign is determined by covariance, or equivalently correlation, with the chosen reference market. The market portfolio in the CAPM is an idealized aggregate; empirical analysis usually uses a narrower index, such as a stock…
The document explains the inputs and calculation used by MATLAB’s PORTVAR function. Asset data are arranged with one security’s historical observations in each column, and portfolio weights correspond to those columns. If weights are omitted, the function…
The document asks how to reduce a covariance matrix for 100 stocks to a five-by-five matrix after grouping the stocks into five clusters. The intended use is a two-stage asset allocation process: first allocate across clustered returns, then perform a…
The document presents questions about a continuous-time Kelly allocation derived for a risky asset modeled as a diffusion and a risk-free asset. Under the stated assumptions of self-financing trading, continuous rebalancing, and no market frictions, the…
Money-weighted return is an internal rate of return computed from an investment’s dated cash flows. When those flows change sign multiple times, the return equation can have more than one solution, so the reported rate may not uniquely describe performance.…
This discussion examines whether downside market capture should use compounded returns or sums of periodic returns. One answer explains that simple percentage returns do not add to produce cumulative wealth: compounding uses the product of one plus each…
The document discusses ways to reduce the runtime of repeated mean-variance portfolio optimizations, such as daily rebalancing for a universe of fewer than one hundred assets. It suggests first considering whether the work can be parallelized, then using the…
The document examines a convex optimization formulation for constructing a portfolio with a target risk budget. The stated objective combines portfolio variance with a logarithmic penalty weighted by each asset’s desired budget. The questioner imposes a…
The document considers how to assess performance when an investor adds money at uneven intervals and holds a mix of securities, including ETFs and options, potentially with leverage. Its response separates investor cash flows from the return series used for…
The document explains how to calculate each asset’s contribution to a portfolio’s volatility from the covariance matrix and portfolio weights. For covariance matrix Σ and weight vector w, portfolio variance is wᵀΣw. The covariance between asset i and the…
The document explains how to convert a correlation matrix and a set of standard deviations into a covariance matrix. For each pair of variables, multiply their correlation by both standard deviations. On the diagonal, each variable’s covariance with itself…
The note asks how to measure the relationship between a portfolio of assets and an external series, such as housing prices. Averaging each asset’s correlation with the external metric, weighted by portfolio holdings, may seem appropriate, but the response…
The document poses a quantitative finance problem: how portfolio values evolve when the underlying investment follows geometric Brownian motion and a fixed dollar amount is withdrawn at the beginning of each year. It asks whether an approximate analytical…
The document examines daily returns for a portfolio holding one stock long and another short, with cash proceeds from the short sale included in net asset value. It shows that the portfolio return for a later day should be calculated from the change in total…
The discussion examines why rational investors may dislike risk in the CAPM framework and challenges the claim that holding a risky investment for many years makes it effectively safer. It distinguishes the expected annual return from realized returns: a…
The document explains what serves as collateral in a collateralized loan obligation. A special purpose vehicle buys leveraged loans and issues debt tranches as well as a junior equity security. The loan pool is held by the vehicle; the manager is paid to…
The document considers whether the optimal risky-asset weight in the classical Merton portfolio problem must lie between zero and one. In the setup described, the investor allocates a fraction of wealth to a risky asset, with zero interest rates assumed for…
The document addresses the tedious process of downloading adjusted closing prices for several stocks individually and merging the resulting files. It presents two programmatic alternatives: using a Python data-reader library to request multiple symbols over…
The document proposes studying a quantity formed by multiplying the difference in expected returns of two return series by the square root of the variance of their return difference. This reverses the variance term’s placement in the conventional information…
The document clarifies how group constraints differ from general linear inequality constraints in portfolio optimization. Both can express limits on a weighted sum of asset positions. A group constraint is a specialized case in which every included asset has…