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.
21,023 documents
The discussion examines whether Brinson performance attribution can be adapted from sectors to style factors such as size, momentum, and volatility. It contrasts returns-based regression, where factor coefficients describe portfolio exposure, with a…
The document explains how to find the weights of a three-asset portfolio that minimize variance while requiring the weights to sum to one. It expresses portfolio variance using each asset’s variance and the pairwise covariances, then presents two solution…
The note classifies operating income divided by total assets as a profitability measure, commonly used in banking. It distinguishes profitability from leverage, asset composition, and liquidity by considering what the ratio’s inputs capture. Because the…
The document formulates a maximum expected return portfolio as minimizing negative expected return, subject to fully invested weights and nonnegative positions. It asks how to construct the Lagrangian and derive a closed-form solution for the portfolio…
The document asks whether correlations should be calculated from simple returns, log returns, or log prices, and whether the choice is merely conventional. The response ties the answer to the intended use: when correlations will drive a simulation, estimate…
The document questions whether a prominent spike in the autocorrelation of squared intraday price changes supports the usual account of volatility clustering. It compares a figure in a highly cited article with a later figure in a book by the same authors,…
The document proposes estimating portfolio profit distributions by simulating monthly generation for each energy asset and electricity forward prices, multiplying generation by price to estimate asset revenues, summing across assets, and taking lower-tail…
The document examines whether Lévy’s characterization implies that every discounted traded asset price is Brownian motion. It distinguishes the cited result—that a continuous martingale with continuous paths and finite quadratic variation can be represented…
The document poses a martingale condition problem for a process formed from the square of standard Brownian motion, a linear Brownian term, a deterministic time term, and a constant. Its hint evaluates the conditional expectation between two times by…
The document describes bootstrapping spot rates from US Treasury par yields. It explains that Treasury par yields are bond-equivalent yields based on securities with semiannual coupon payments, then presents a Python example that solves sequentially for spot…
The document explains how an exponential change of measure shifts a Brownian motion’s drift. It first uses the Radon–Nikodym derivative and moment-generating functions to show that the original Brownian value at a fixed time has a normal distribution with…
The document sets up a mean-reverting jump-diffusion with deterministic, time-varying mean-reversion, level, volatility, and jump-arrival parameters. It gives an integral representation of the process and derives expressions for its conditional mean and…
The document describes numerical instability when using the Carr–Madan Fourier transform to price deep in-the-money and out-of-the-money options under the Heston model. Direct numerical integration may produce implausible results, such as a call price above…
The document explains how to calculate a bond’s discrete-period return from its beginning and ending clean prices, accrued interest at both dates, and coupon payments received during the period. The calculation includes bond income as well as the change in…
The document asks what mathematical assumptions underlie a continuous asset price model introduced heuristically in an option valuation text. It proposes that log returns over an interval are normally distributed, with a mean adjusted by half the variance…
The document raises a practical question about using estimated stock beta to hedge a concentrated portfolio. With a short sample or a volatile stock, an estimated beta can be large by chance even when the true relationship to the index is zero. A…
The document explains how to generalize first-passage results for geometric Brownian motion when the starting value and threshold are not normalized to convenient constants. Taking logarithms turns the process into Brownian motion with drift, so the relevant…
The document addresses how to calculate pivot points and first support and resistance levels from a stream of trade data. The key preprocessing step is to aggregate trades into five-minute bars using calendar time. Each bar should contain its open, high,…
The document values a perpetual claim that pays one unit when a non-dividend-paying stock first falls to a lower barrier. It presents two equivalent routes: risk-neutral expectation of the discount factor at the hitting time, or an ordinary differential…
The document explains why a model-free measure built from option prices ideally requires a continuum of strikes, and how finite market listings change the problem. With observable prices across strikes and negligible bid-ask spreads, vanilla calls and puts…
The document addresses how to normalize real-time observations for a support vector machine trained with automatic scaling. Its central guidance is to apply the mean and standard deviation estimated from the training data to out-of-sample observations.…
The document considers the expectation of a time integral whose integrand is a bounded function of Brownian motion. It applies Itô’s lemma to the arctangent of the process, rewriting the ordinary time integral as a stochastic integral minus a terminal-value…
The document clarifies how to calculate a one-step-ahead density forecast from an estimated ARMA-GARCH model with Gaussian errors. At each forecast origin, estimate or update the model using information available so far, then obtain the forecast conditional…
The document explains how to model constant conditional skewness alongside an ARMA conditional mean. Its central point is that ARMA specifies the structure of the conditional mean, while the innovation distribution can be chosen to have skewness and…