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.
765 documents
The document raises a diagnostic question about a pair-trading setup: after using linear regression to estimate a hedge ratio, the residuals appear stationary but visually resemble the price series of the dependent asset. It asks what this appearance means…
The document explains a simple way to generate two non-stationary time series that are cointegrated. Start with a series containing a unit root, such as a random walk, then form a second series by adding a stationary process. The shared stochastic trend…
The document explains a bootstrap comparison designed to test whether pairs trading returns reflect pair-specific reversion or simply the tendency of recent losers to rebound and recent winners to fall. On each historical date when a selected pair opens, the…
The document asks how to classify a strategy that goes long in the cheaper of two markets and short in the more expensive one after their prices diverge beyond a threshold. The assets are described as fungible, but the strategy does not move them between…
The document outlines a basic covariance hedge for two securities believed to move together. It first converts each price series into daily percentage returns, then estimates each return variance and their covariance. The hedge ratio is the covariance of the…
The document compares ways to estimate a hedge ratio for two cointegrated price series, including when their ordinary correlation is low. One answer recommends regressing one series on the other and using the estimated slope as the hedge ratio. Another…
This discussion explains the basic direction of a pair trade when two stocks diverge from a relationship assumed to persist. Under that assumption, the trader shorts the stock judged relatively overpriced and goes long the one judged relatively underpriced.…
The document asks how to size two stock positions in a long-short portfolio intended as a hedge, rather than as a cointegration-based pair trade. One response gives the basic beta hedge rule: set the hedge position opposite to the original position and scale…
The discussion explains how the sign of a cointegration coefficient affects the positions implied by a spread. With the stated spread defined as Stock A minus beta times Stock B, a negative beta makes the second term positive, so a long spread corresponds to…
The document asks how to compare company performance while reducing the influence of macroeconomic changes such as interest rates, crises, and inflation. It also raises the idea of expressing company financial metrics relative to other companies instead of…
The document outlines how to build an equity curve for a two-stock pair-trading backtest. It starts from entry and exit signals, assigns long and short portfolio weights, and estimates share quantities using initial capital and prices at entry. It then…
The discussion addresses a backtest in which a mean-reversion pairs strategy scales positions as the spread moves farther from its mean. Its central recommendation is to track daily profit and loss in currency terms, reflecting the strategy’s actual position…
The document formulates a fit between a target time series and a linear combination of two other series. It minimizes the sum of absolute residuals, the L1 norm, while constraining both coefficients to lie between minus one and one. This differs from…
The question considers three stocks where X is cointegrated with Y and Y with Z, but X and Z are not reported as cointegrated and no three-variable cointegrating relation is available. It asks whether the two pair relationships can support a dynamic…
The document explains why a rolling regression can make a pairs spread appear stationary even when the apparent mean reversion comes from repeatedly updating the hedge ratio. A short lookback window can adjust the ratio to recent price movements, pulling the…
The discussion distinguishes portfolio volatility from portfolio return measurement for a long position in one stock and an equal short position in another. A covariance-based volatility formula can produce a small value when the assets have similar…
The document describes estimating a hedge ratio for a pairs trading spread from two aligned price series. Ordinary least squares regresses one security’s prices on the other, and the fitted slope is used to scale one leg when calculating the spread. A Java…
The document compares two ways to estimate a current fair price for one instrument from the historical prices of a correlated instrument pair. One method multiplies the current price of the target instrument by the ratio of the two instruments’ average…
The document raises a practical sizing and spread-construction question for a pairs trade involving one Brent contract and one Gasoil contract. Although the two contract prices are of a similar scale, their minimum price fluctuations have different monetary…
The document outlines a two-step way to apply an error correction model to a candidate pair of nonstationary price series. It assumes the series are integrated to the same order, commonly first order. First, estimate a long-run relationship by regressing one…
The document discusses a pairs strategy that recalculates a hedge ratio from a rolling window of prices, forms a spread, and tests it for stationarity with the augmented Dickey–Fuller test. The central question is whether a failed test should force an exit…
The document compares the continuous-time Ornstein–Uhlenbeck (OU) process with the discrete-time AR(1) model for stationary, mean-reverting data such as a spread. It presents OU as a continuous-time model with an analytic solution and explains that a simple…
The document outlines an empirical sequence for assessing whether two price series are cointegrated. First, test each series for a unit root. If both are stationary, model them in levels; if only one is nonstationary, difference that series. If both are…
The document considers how to analyze price histories for a company with no trading record by using similar firms whose shares trade thinly across two exchanges. Stale prices and differing market conditions make direct time-series modeling difficult, and the…