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.
16,761 documents
The document asks about an asymptotic expansion used in a paper on convergence of European option prices under binomial trees. It presents an expression for the inverse function used in the Leisen–Reimer construction, followed by a claimed large-step…
The document asks how researchers recognized that standard t-based inference fails for an autoregressive process with a unit root, and how to simulate data to measure test-size distortion. Its answer gives a historical account: earlier work addressed…
The document compares two ways to estimate hedge positions for replicating a signed, equal-weighted portfolio of stocks with other instruments. One approach runs a separate rolling regression for each constituent and averages the resulting hedge…
The document addresses why a t-statistic can change when someone scales a monthly mean and standard deviation to annual figures but leaves the sample-size term unchanged. The response derives annual return and variance by adding monthly returns under an…
The document addresses whether portfolio weights should be optimized using asset returns or returns measured relative to a benchmark. Its answer favors raw portfolio returns when the goal is to evaluate a complete investment strategy without a specific…
The document describes a terminal-wealth portfolio allocation problem with a quadratic penalty for falling below a target wealth level. It approximates expected utility under normally distributed portfolio returns using Gauss–Hermite quadrature, then…
The discussion concerns joint maximum likelihood estimation of the drift and volatility of a geometric Brownian motion from simulated log prices. Although the likelihood can identify volatility clearly, it may appear nearly flat in the drift direction when…
The document considers how to report 95% VaR when a return sample contains no losses. Under a historical quantile calculation, the measured lower-tail return may still be positive; the accepted answer recommends flooring reported loss VaR at zero under a…
The document raises a pricing question about arithmetic-average Asian options with discrete sampling. The author describes simulating asset paths with the Euler method and estimating expected payoffs by Monte Carlo, then observes that at-the-money Asian…
The document explains the distinction between overlapping and non-overlapping return observations, in the context of preparing a variance-ratio test. Non-overlapping monthly returns use successive, separate periods, such as one return for each calendar…
The document discusses whether a trading strategy’s returns differ meaningfully from a benchmark. It outlines comparing mean returns and variances, and introduces the Sharpe ratio test: under independent, identically distributed returns, its relationship to…
The document challenges broad claims about diversification, rebalancing, and the relationship between arithmetic and geometric means. Its answer corrects a central mathematical misunderstanding: for nonnegative observations, the arithmetic mean is at least…
The document explains how to reproduce a plot illustrating the False Strategy theorem: as more independent strategies are backtested, the best observed Sharpe ratio can rise even when the strategies have no genuine edge. The example computes the 25th, 50th,…
The document considers whether Yahoo Finance adjusted closing prices can be used to calculate mutual fund total returns. It distinguishes returns based on unadjusted closing prices, which track changes in quoted prices, from total returns that account for…
The document asks whether a low-frequency US equity statistical arbitrage strategy can assume that liquid stocks are available to borrow. The strategy holds roughly equal-sized long and short stock baskets, trades at the open, and replaces much of its…
The document describes a simulation question for a SABR-LMM model under a selected numeraire. Forward LIBOR rates have shifted SABR dynamics, stochastic lognormal volatilities, and correlated Brownian drivers. The author already uses Euler discretization…
The document explains how to approach pricing a barrier option on a basket when the available QuantLib Monte Carlo engines do not support both features together. It uses a worst-of down-and-in put as an example of the unsupported combination. The suggested…
The document describes a numerical edge case in inverse-CDF sampling: mapping a uniform draw of zero or one through the normal quantile function yields an infinite value, which can break sample statistics. It presents several practical responses, including…
This note raises a modeling question about calculating a spread for mean-reversion pairs trading with a Kalman filter. It contrasts the measurement prediction error, formed from the observed value and the filter’s predicted measurement, with a residual…
A geometric Brownian motion process has a continuous-time solution that remains positive when its starting value is positive. The note addresses why a numerical simulation of the stochastic differential equation may nevertheless produce negative values. Its…
This note explains why researchers building cross-sectional stock portfolios need to account for delistings. Omitting delisted firms or mishandling their final returns can distort the return history used in analysis. It points to CRSP’s monthly delisting…
The document separates three questions: whether next-day variance is forecastable, whether the full return distribution can be forecast, and how to evaluate those forecasts. It describes ARCH/GARCH models and explains why early comparisons using squared…
The document explains how to detect missing daily or intraday market observations when trading days differ across countries, venues, and securities. A simple holiday list can help, but it may not capture cases where a security follows rules different from…
The document asks how to update confidence in a strategy’s true future Sharpe ratio as returns arrive, distinguishing that unknown quantity from the Sharpe ratio calculated on a backtest. Strong or weak realized performance can reflect either luck or a…